EP2652044A1

EP2652044A1 - A system for evaluating the current evolutionary status of events or processes in a geographical region and for generating and visualizing predictions of the evolutionary dynamics in time and space

Info

Publication number: EP2652044A1
Application number: EP11810818.2A
Authority: EP
Inventors: Paolo Massimo Buscema; Roberto SCIBETTA
Original assignee: CSI Ricerca and Ambiente Srl
Current assignee: CSI Ricerca and Ambiente Srl
Priority date: 2010-12-16
Filing date: 2011-12-16
Publication date: 2013-10-23
Also published as: WO2012089539A1

Abstract

A system for evaluating the current evolutionary status of events or processes in a geographical region and for generating and visualizing predictions of the evolutionary dynamics in time and space. The said system operates by means of a virtual model which is directed to the simulation of a process or of an event which takes place in a geophysical territory, the territory being described by a two or three dimensional geometrical map, the said virtual model is in the form of a suite of executable programs which can be loaded in the working memory of a processing unit and executed by the said processing unit on demand; a representation of the status and of the evolution of the process at certain time being in the form of a graphical representation displayed on a screen; The event or process which the system evaluates and for which the said system generates and visualizes the evolutionary dynamics in time and space is the landslide in a certain geographical territory for monitoring and prediction giving a strong decision support system to the territorial authority and specialist teams; The computed current condition of the landslide dynamics in whole territory based on the data obtained for certain geographical points distributed on the territory and highlight the said status by means of one or more graphical outputs or the computed evolution of the process or event at a certain time instant is visualized as a grid which is deformed according to the geographical positions of the points in time and which is registered and superimposed to a two or three dimensional map or aerial or satellite image of the territory; the condition of the event or process, namely of the landslide, is determined by means of the displacements measures of certain number of sensors placed on the territory taken at different time.

Description

A system for evaluating the current evolutionary status of events or processes in a geographical region and for generating and visualizing predictions of the evolutionary dynamics in time and space.

The invention relates to a system for evaluating the current evolutionary status of events or processes in a geographical region and for generating and visualizing predictions of the evolutionary dynamics in time and space.

The object of the present invention is to provide a several useful tools for evaluating the current evolutionary status of events or processes in a geographical region and for generating and visualizing predictions of the said evolutionary dynamics in time and space..

The system according to the invention operates by means of a virtual model which is directed to the simulation of a process or of an event which takes place in a geophysical territory, the territory being described by a two or three dimensional geometrical map. The said virtual model is in the form of a suite of executable programs which can be loaded in the working memory of a processing unit and executed by the said processing unit on demand. The event or process which the system evaluates and for which the said system generates and visualizes the evolutionary dynamics in time and space is the evolution of landslides in a certain geographical territory for monitoring and prediction giving a strong decision support system to the territorial authority and specialist teams.

The output consists in providing information on the current condition of the landslide dynamics in whole territory based on the data obtained for certain geographical points distributed on the territory and highlight the said status by means of one or more graphical outputs. Furthermore the task is also to generate by means of a simulation model the evolution of the landslide condition in space and time at future times. The condition of the event or process, namely of the landslide, is determined by means of the displacements measures of certain sensors placed on the territory taken at different time.

The suit may comprise one or more routines or interoperative programs each one carrying out a specific processing task on the input data which consist in the measurement of the displacement in time of a certain number of points distributed on a certain geographical territory and thus on a two or three dimensional map of the said territory, as well as routines for graphically representing the outputs of the predicted evolutionary dynamics in relation to the map of the geographical territory or satellite or aerial images of the said territory.

In its basic configuration the system consist in a hardware device comprising a processing unit with means for loading and executing software programs, one or more user interfaces for inputting data and commands; one or more means for displaying the output data, i.e. the results of the processing tasks carried out on the input data by executing one or more software programs; means for inputting measured data in the form of data strings or a database; interface means for connecting to one or more measuring units and directly inputting data measured by the said measurement units; one or more communication ports for connecting and exchanging data with remote devices through a public or private network, such as remote servers;

The measuring units being a certain number of position sensors each of which is placed on a certain location of the geographical territory and each one of which measures at certain times of a predetermined sequence of time instants the changes in its position or the displacement relatively to the position determined at the preceding time instant in the predetermined sequence of time instants;

The measured data are position data of each sensor and time data at which the position data has been determined; The software programs are:

At least a program for generating a virtual mathematical model for simulating the dynamics in time of the landslide starting from position data at different times of differently located sensors distributed on the said territory and for generating a graphical output in the form of a map on which the locations of the sensors at different times are visualized and points having different dynamical behaviour are highlighted as single points or in form of a grid formed by lines connecting points on the map having identical dynamical behaviour or having a dynamical behaviour falling within a certain range;

At least a program for determining geographical points on the map and on the territory where non sensor has been placed but which have a specific relevance for the process or event, namely for the landslide such as the points and the corresponding location from which the landslide is originating, the points and the corresponding locations in which unexpected dynamical behaviour is predicted and for representing the said points on the map and at the geographical location;

A connection program with a website furnishing satellite or aerial photographs of the territory and for downloading said;

A program for registering by means of the geographical coordinate information of the points on the map corresponding to the sensors the map of the territory and the related representation of the points on the map and the said grid with the satellite or aerial image and for displaying the said map and/or points and/or grid overlaid on the said image.

As a further improvement the software programs may comprise a database of images of the site on the territory at which the sensors or measurement points are located in order to allow to monitor the appearance of the territory at this sites which images are retrieved and displayed by clicking on the representations of the corresponding point. Several variants are possible. In place of the database the zoomed satellite image of the site of location of the sensor or the measurement point can be downloaded and displayed.

Alternatively or in combination the images registered by remote cameras placed at the said sites, such as web cams pr similar devices which are connected by a private network.

A further variant may provide the display of a map or a satellite image of a certain territory and the selection of regions of the said territory as the territory which maps and the sensors or measurement points provided on the said map may be used.

Landslide is a particular kind of geological application, but the present invention is not limited to landslides and can be equally applied to modification in time of the path of rivers or lakes or of the dynamics of the glaciers and the dynamics of the polar caps.

In a preferred embodiment the hardware of the present system is in the form of a table computer or of a so called wall computer, which is a touch screen and a computer which are housed in the same case having the form of a flat case or frame for the touch screen such as for example the ASUS - EeeTop PC ET2400IGTS or similar devices of other brands.

The software programs are loaded or loadable in the memory of the said devices and are executable on demand by the said hardware while the outputs are displayed on the touch screen. The touch screen itself is the user interface.

Further features of the present invention are subject matter of the dependent claims.

The characteristics of the invention and the advantages derived therefrom will be more apparent from the following detailed description of an example of embodiment and from the annexed drawings, in which Fig. 1 is a schematic box diagram of the hardware of the system according to the present invention Fig. 2 is a schematic view of the selection interface of the processing software to be executed by means of the graphic user interface.

Fig. 3 to fig. 18 are the images displayed on the touch screen for representing the evaluated current evolutionary status of the landslides or the predictions of the evolutionary dynamics in time and space.

Figure 19 illustrates an example of a grid describing a space on which grid several points are positioned which points correspond to measured values of parameters at a certain instant. The propagation or evolution in time and space of the event or process is evaluated by means of the displacement of the said points according to the values acquired in at least a second measurement at a second time and in which the measured parameters of the present example are the positions of the point on the grid.

Figure 20 illustrates a schematic view of a trajectory of a point corresponding to a measured parameter at two times, i.e. the position of the point at a first time and at a later time.

Figure 21 illustrates a diagram of the distance equations («) , (») .

Fig. 22 illustrates a bird view picture of a region of the territory of

Corvara where an landslide is monitored and in which the points 1 to 12 represents the monitored points on the map by means of GPS sensors and in which the Harmonic points 1 and 2 are represented encircled.

Fig. 23 is the picture of the inclined trees found on the territory at the harmonic points which can be opened by clicking or touching the said point on the touch screen.

Figure 24 is a table illustrating the data of a database of a first example of problem to which the method of the present invention can be applied for reconstructing a causation process from the time varying data describing a unknown process dynamics and for predicting the evolution dynamics of the said event. Figure 25 illustrates a second example to which the present method is applied in a table containing the numerical data as in fig. 24.

Figure 26 illustrates the map in which the entities of the data of figure 25 are drown as points.

Figure 27 illustrates the tables relatively to the strength of g [n ,n + \]

connections ^{1 ,J} between the entities and the presence of

£f [w ,w +l]

connections ^{1 ,J} for the data of figure 2 calculated according to the present method and for the two time steps for which the quantities data are provided in table of figure 25.

Fig. 28 and 29 illustrates a possible way of representing the causation process as tables of numerical data and connections between entities respectively for the first and for the second time steps, i.e from instant zero to 1 and from instant 1 to 2.

Figure 30 and 31 illustrates respectively the table of the presence absence of connection for the first time step and the graphic representation of the connection in the map with entities as arrows connecting the entities between which a connection id present.

Figure 32 and 33 illustrates respectively the table of the presence absence of connection for the second time step and the graphic representation of the connection in the map with entities as arrows connecting the entities between which a connection id present.

Figure 34 illustrates the table of the starting data, the taw o table of connections for the time steps 1 and 2 and the graphic representation in which the graphic representations of the step 1 and step 2 according to figures 31 and 33 are overlapped.

Figure 35 illustrates the scalar field representation of the causation process for the time step 1 .

Figure 36 illustrates the scalar field representation of the causation process for the time step 2. Figure 37 illustrates the scalar field representation of the causation process for the time step 1 and 2 joined together.

Figure 38 shows the table of data for a further database of entities and time varying quantities of the said entities at five different time defining four time steps.

Figure 39 illustrates the tables relating to the strength of connection among the entities and the tables relating to the presence absence of connection among the entities at each one of the four time steps provided in the data represented by the table of figure 38.

Figure 40 illustrates for each time step, separately, the causation process table and the relative graphical representation.

Figure 41 is a table representing the new database obtained by the joining of the four table s of connection according to figure 39 and an example of distribution of the records of the said database for carrying out an experiment comprising training, tuning blind testing and predicting with a predictive algorithm, specifically an artificial neural network, which prediction should determine the unknown evolution of the process or event starting from the knowledge of the quantity data for the entities at a number of preceding time step.

Figure 42 is a table comparing the results of the estimation carried out by the predictive algorithm with the real data on presence/absence of connection for the places considered and the time step considered for prediction in the experiment according to figure 41 .

Figure 43 is a table of the sensitivity, specificity and accuracy value of the prediction.

Figure 44 and 45 show graphically respectively the real dynamics of the time step subjected to prediction in the experiment and the one obtained by the estimation by means of the artificial neural network.

Figure 46 illustrates on the left side the graphical representation of the minimum spanning tree obtained by means of the known method of a 5X5 array of points or grid. On the right side of the figure there is shown the minimum spanning tree obtained for the same 5x5 distribution of points which minimum spanning tree is calculated according to the present invention by adding to the initial 5x5 grid the new points.

Figure 47 is a table representing the algorithm expressed in a programming language.

Referring to figures 1 and 2, the system according to the present invention comprises a hardware unit which consists in a processing unit 1 which processes input data and prints the processing results on a screen, 2. Different kinds of user interfaces can be connected to the processing unit 1 such as a usual pointing device and/or keyboard and a touch screen 2.

The processing unit has a communication interface for connecting and exchanging data and command strings from remote servers or unit, such as a usual network interface. This interface can be a traditional network Ian interface for connecting to the web and/or for connecting to privates networks which is indicated by 7. A further communication interface indicated by 4 may be provided for communicating with one or more remote measurement units, sensors or other remote devices, like cameras which are distributed at different sites having determined geographical coordinates in a predetermined geographical territory.

With 3 there is indicated the graphic card controlling the touchscreen. Number 8 stands for one or more data input drive which is capable at least of reading data from readable memory supports, like CD or DVD or memory cards or pens. The drive may also be of the kind capable of writing data on the said supports.

Numeral 5 represents a memory in which control programs for the hardware functions are saved which are needed by the hardware to execute its operative tasks, while numeral 6 indicates a memory in which the evaluation and prediction programs are saved as well as the programs for transforming the processed data into a graphic representation displayable by the touch screen 2. With number 9 a wireless communication interface is indicated.

As it appears from the above description the hardware of the system according to the prese4nt invention is mainly the one which is present in a known computer using a touch screen as main interface with the user. The position sensors and other measurement sensors or other peripheral devices like cameras are specific peripherals used by the system and can communicate with the processing unit by means of one or more different communication interfaces, depending from case to case. Preferably the communication can be wireless or by means of cabled connections to local access pints or routers which then are connected as clients, either wirelessly or by means of cables, to a data collection network in which the processing unit has the role of data reading server.

The specific processing tasks are carried out on the input data by a certain number of processing software programs which are integrated in a processing suite allowing to carry out all of the possible processing functions or only some of the entire number of functions available.

As it appears each processing tool can be launched by touching with the hand or by means of a tool an specifically dedicated area of the touch-screen which has the function of a button. The screen may be provided with differently shaped areas which can be displayed with every possible design as represented in a simple way by the different diameters of the circular areas indicated by 102, 202, 302 in figure 2. Touching on an area will start the execution of a corresponding program which will then process in a certain specific way the input data.

The input data can be in the form of a database which is on a readable memory support or the database is created by the system itself due to the ability of communicating directly with the remote sensors, measuring devices, cameras or similar.

Relating to the different processing software programs which can be executed by the processing unit in order to generate the status and the predictive evaluation of the dynamics of a landslide in a certain restricted geographical territory or area, each of these software is generate for instructing the processing unit to carry out a particular method of processing the input data.

One routine is for generating the evaluation of the status of the landslide and of the evolution of the landslide dynamics in time and space basing on a virtual model for simulating the evolutionary dynamics of events or processes.

The virtual model is obtained by using at least two measurements of values of parameters describing a process which two measurements are carried out a different times for calculating the dynamic evolution of the event or process in time and space in the period over which the said measurements has been made and also in future times.

With the term evolution in the present description and in the claims it is meant prediction and evolution of the dynamic behaviour of a system.

The measurements of the parameters describing the event or process can be taken at more than two different times so that for each parameter a sequence of measurement values taken at different times is provided which sequence is used for generating the model.

The model according to the present invention consists in a non linear adaptive mathematical system simulating the spatial and temporal dynamics of the event or processes by using measured values of a certain number of parameters describing the evolutionary condition of the event or process at certain different times;

The values of the said parameters being measured at a first time and at least a second time different from and following the said first time or at several times of a sequence of times of measurement;

the said model defining a n-dimensional array of points in a n- dimensional reference system whose axis represents the values of the parameters being measured and in which array the said parameters are represented by special points in the said array of points; the displacements of each one of the points of the said array of points being computed as a function of the displacements in the said array of points of each of the points representing the said measured parameter values between a first time of measurement and at least a following second time of measurement and

as a function of the distance of each of the points of the array of points from each of the points representing the measured parameters; the evolution of the event and or the model in time being visualized by displaying the points of the array of points at different times.

According to a further feature the n-dimensional array of points is represented by n-dimensional grid in which the points of the array of points are the crossing points of the lines delimiting the meshes of the grid and the evolutionary condition of the event or process at a certain time is visualized as the distortion of the grid determined by the changes in relative position of the points of the array from the starting position in which the points of the array are equally spaced one from the other to the position of the said points of the array of points computed at the said certain time.

For the grid a certain mesh size can be set while for the array of points the distance of a point in the array from the neighbour points directly beside the said point can also be set among several different sizes.

Particularly the array of points is two or three dimensional array. Similarly the grid is two or three dimensional.

The above model is able to infer how each point of the array or of the grid will modify its coordinates at each temporal step when any point in the grid representing a measured parameter will move toward its new position.

The model is particularly designed and useful for describing the evolution in time and space of events or processes on a geographical region and the space being the three dimensional geophysical space of the territory of the said geographical region.

I relation to the above features of the model and of the method according to the present invention it is to consider that as already said instead of measuring the parameters at least some of the said parameters can be set by the user at a certain value. This allows to test the evolution of the behaviour of a process or of the event in certain conditions which are virtually set by the user. In this way it is possible to predict how the process, the event will behave if such imposed conditions will occur.

Furthermore in relation to the above and also to the following description, each point representing a measured condition of the event or process in the n-dimensional map can be described by a vector or by a matrix of parameters.

The model according to the present invention, not only helps in predicting the evolution of the dynamic behaviour of the system represented by the model, but also it give information about where the event or process will occur and to determine the limits of the effects of this significant behaviour

The model and the method according to the invention operates by means of a mathematical system of equation which will be described hereinafter with the help of figures 19 to21 .

The evolution in time and space of a process or event can be described as the displacement of points representing certain values of parameters in a certain space.

The mathematical model can be best understood by analysing at first the two dimensional embodiment. The three dimensional embodiment represents nothing more than a obvious extension of the equations in three dimensions.

Let us suppose a two dimensional finite and regular grid of P discrete points of a discrete geometry. The points P forms an array of points. Let us suppose a set M of these points, each one able to follow within the grid a discrete path in T temporal steps. These points are the points representing measured parameters at least at two different times or the points at which at least at two different times a certain parameters are measured. The said parameters being specific parameters for describing the process or event.

Let us name the moving points of the set M Entities (E) and all the points of the grid Geometrical points (G).

We define trajectory the minimal path at each temporal step. Each trajectory of each Entity is assumed to be linear. The whole path of each Entity has no constraints, but it has to work within the grid boundaries.

The object of the invention can be reformulated as defining a Model able to infer how each geometrical point of the grid will modify its coordinates at each temporal step when any Entity of the grid will move toward its new position.

Figure 19 try to visualize the above definitions.

The two dimensional space is represented by the grid 1 . The geometrical points P which are the points of the array of points, are the crossing points of the horizontal lines with the vertical lines of the grid 1 . Five entity points E1 to E5 are illustrated with the position on the grid at a first time of measurement of specific parameters of the event at the corresponding entity E1 , to E5 and at a second time of measurement of the said parameter. The displacement of each entity on the grid resulting form the results of the two measurements of the parameters is the trajectory represented by the arrow A1 to A5.

According to figure 20, any trajectory of each Entity is divided in N linear under-steps of equal length.

Furthermore each entity within its trajectory is defined by one Origin location (its original X and Y coordinates) and a Moving Local Target, defined by each under-step. Figure 21 illustrates the division of the trajectory from the origin to the target of the entity point 1 in 7 under-steps.

In the present model the distances of each geometrical point G from the Origin and from the Local Target of any Entity at each under step (n) is considered for calculating the dynamics of the event or process in space and time.

In the two dimensional model and according to the above definitions such distances are defined b the following equations: dl (n) = ^(* («) - x] (n)f + (tf (n) - y] (n)f . where:

f (ⁿ y (ⁿ) are the coordinates of a generic point Pi of the grid at the understep (n), when n=o the point Pi is lined up with the regular grid.

s s

% j ·> y j are the origin coordinates of each entity point (j), which means the parameter values at the time of the first measurement or the point at which the parameter values have been measured at the time of the first measurement; ^x _j (ⁿ)> y _j (ⁿ) are the local target coordinates of each entity point (j), at any understep (n). When n=0 the entity point lies on its origin, while when n=N the entity point has completed its trajectory. is the distance of a generic point Pi from the origin of any entity point j at the understep (n) (») is the distance of a generic point (i) from the local target (n) of any entity point j at the understep (n). The model further considers that at each understep (n) a quantity of Potential energy A(n) is computed according to the following equations:

Where i(n) ~ y

P p

z(») O) ;

n ) ^ ^{1 7} '

During the evolution of the event or process it is considered that the potential energy defined by the above equation is converted in kinetic energy so that the coordinates of the points Pi will be updated with the A(n) quantity according to the versus along the x and y axis defining the two dimensional space of the grid.

The computation of the position of the points of the array of points or of the grid at a certain time as a function of the measured values of the parameters at least at a first and at a second following time carried out according to the following equations:

In which

(d; d .

Δ ∑ ^exP d d :

a (2B)

And in which

are the coordinates of a point P indexed (i) of the array of points at the understep (n)

X [p] _v [p]

<(»+!) (»+l) are the coordinates of a point P indexed (i) of the array of points at the understep (n+1 ) _ys s [s] [s]

j ·> j or j ·> y j are the coordinates at the first time of measurements of the points representing the values of the parameters at the first time of measurement (time T=0);

y J{n) are the coordinates at the second time of measurements of the points representing the values of the parameters at the second time t of measurement (time T=t) and at the understep n;

< (») or dj - is the distance of a point (i) of the array of points from the point in the said array representing a measured parameter value at the initial instant of the understep (n) which point is defined as Source point of the understep (n);

< (») or dj - is the distance of a point (i) of the array of points from the point in the said array representing a measured parameter value at the end instant of the understep (n) and which point is defined as Target point of the understep (n);

And where:

^ i_{( n )} has the meaning of a quantity of potential energy accumulated by each point Pi at each understep n, X j ^P and tfy . ^p j_{s a} function for determining the sign of the potential

'(») energy contribution at each understep n.

The displacement of the points of the array which are equivalent of the points defined by the crossing points of the grid can be visualized by displaying the deformation of the grid due to the displacement of the sad points according to the above equations.

Different zones of density of the points of the array and thus of the grid are generated by the displacement of the points Pi and the different densities are a visual and numerical value that indicates the evolutionary condition of the process at the different zones of the grid or of the array of points at a certain step which means at a certain time from the time of origin t=0, which is the time of the first measurements of the said parameters.

As it will appear more clearly in the following examples the parameters can be a position in space or any other kind of measurable entity which is typical for describing the process or the event or which is a typical consequence of a process or of an event.

The mathematical engine of the model is an adaptive non linear system which is good suited for simulating evolution of events or processes of the natural kind and in which the relation between the parameters and their evolution in space and time cannot be represented by equations which can be solved.

As already discussed above, practically any kind of event or process or any kind of device, plant or system can be represented by certain parameters which values are measurable and which parameters are typical for describing the status of the process of the event, or globally of the device, of the plant or of the system or of each one of the operative organs or units forming the said device, plant or system. Once such parameters has been determined a space can be always constructed in which the behaviour of the event, or the process or of the device, plant or system can be represented by a map in which the status of the process or event can be represented by a point and also the status or function of a device, a plant or a system or of certain selected operative organs or units can be represented by points in the said map. The said points having a certain position in the map as a function of the values of certain parameters.

Thus it appears clearly that the above general model and method for generating the model applies not only to events or processes or plants or systems having topographical representation, but also to any kind of event, process, device, plant or system which behaviour can be represented by a map.

Figures 3 to 18 illustrate the application of the above model to the present invention for simulating a landslide interesting a big part of a territory and particularly in the Alps at the town of Corvara (Italy). The landslide has been monitored for several years by considering the displacements of position sensors (GPS sensors) located in the territory at a certain number of different geographic points at the time t=0, (step n=0) of which points the geographic coordinates and the height has been measured.

At each following measurement steps at a second and further times the new geographic coordinate has been measured and the new height.

The map of figure 3 shows an aerial two dimensional image of the geographic region where the landslide is proceeding and the trajectory which the entity points, i.e. the points on the map at which the position sensors has been placed have run from the instant t=0 to an instant t=T, where t=0 corresponds to the first measurement step in 2001 and t=T to the last measurement step at t=T, where T is the year 2008.

The trajectory is in the form of an arrow. The origin of the arrow is the position of the entity point at t=0 and the apex of the arrow is the position of the entity point at t=T. The length of the arrow represents the distance from the position at t=0 from the position at t=T, and the thickness the mean velocity.

As it appears from the figure and from the legend there are entity points which have carried out very fast and long paths and other points which did not change position or only slightly changed their position. Since only a certain number of points distributed over a very large territory could be monitored, a complete picture or description of what will happen at different regions of the territory due to the measured displacements of the said specific entity points cannot be foreseen nor understood.

The measured data has been used to generate the model for simulating the event or process evolution in time and space.

A grid representing the geographic position of certain generic points of the territory is generated. In a first step the grid is two dimensional and the entity points at which the displacement has been measured are also represented on the grid. The grid defines at the crossings of the vertical and horizontal lines points forming an array of points which is regular, i.e. the points have an uniform distribution at time t=0.

Applying the model according to the above description in using the position data at different times of the entity points the grid is deformed as illustrated in figure 6 and 7 which is an enlarged view of figure 6. In the output examples of figure 6 and 7, the grid is shown overlapped to the two dimensional satellite map of the region. This is obtained by registering the grid and the maps by using the geographic position coordinates measured by the GPS unit present in each sensor or measuring unit of the sensors and measuring units distributed over the territory and the one determined by the model as the evolution, namely the displacement of the points at a certain time.

There are three typical areas of the grid:

An area where the line density is lowest (white area)

An area where the line density is maximum (black area)

An area at which the grid is not been deformed and has essentially maintained its regular shape.

All these areas are interconnected by areas where the density of the grid lines increases from the lowest density areas to the highest density areas or to the area where the grids has maintained essentially its original shape or areas where the density decreases from the highest density areas to the lowest density areas or to the areas where the grid has maintained essentially its original shape. As it appears clearly from the overlapping comparison between the grid and the map there is a congruence of the zones having the lowest density of lines of the grid in the output grid with the regions in the picture where the GPS sensors located at the entity points has undergone the strongest displacements.

The different densities of the grid lines and the essential invariance of the grid has been found out by comparing the area of the grid with the corresponding features of the territory and of the region interested by the landslide.

The regions having less density of the grid lines (white areas of the grid) are the regions where the strongest displacements have occurred.

The regions where the density of the grid lines has its maximum are the regions where there are boundaries of the landslide impeding any further displacement.

The regions where the grid is essentially identical to the one at the time t=0 are the regions where no displacement has occurred but where no natural boundary exists to a displacement.

As it appears clearly the regions of maximum strength of displacement (lowest density of the grid lines in the output grid of the model) are the ones having the strongest gravitational effect, so ripid descending slopes, while the regions where there are limits to the sliding and corresponding to the areas of the output grid of the model where the density of the grid lines is a maximum (black areas) the territory shows ripid rising slopes or rocks or other geological structures high resistant or also artificial limitations due to constructions made by man, such as roads, containment walls or other kind of constructions.

The above described examples are related to evaluation of the propagation or development of events or processes in time and space which have e geographical relation, in the sense that the points where the parameter are measured and the displacements of these points and equally the array of generic points are related to locations on a map of a territory defined by its geographic coordinates.

From the above description it is possible to extrapolate the more general equations of the model according to the present invention which describes the mathematical engine of the model for a n-dimensional case in which n is a natural number starting from 2.

The more generic expressions of the mathematical equations expressed with reference to the two dimensional case in the above description is a obvious extension of the said equations related to the two dimensional case:

According to this n-dimensional extension, the computation of the position of the points of the array of points at a certain time as a function of the measured values of the parameters at least at a first and at a second following time is carried out according to the following equations:

P_l (n + \) = P_l (n) + Delta_l (n) _{(1 )}

In which

P, ( ) is the position of the i-th point in the grid at the step n; n being the index number of a step of a certain number of steps in which it is divided the displacements of the points representing the measured parameters and the time interval between a first time of measurement and a second time of measurement and during which interval the said displacements has occurred;

P, (n + l) is the position of the i-th point in the grid at the step n+1 ;

Delicti ) is defined by the following equation: Delta_i (n) =

In which: s the distance of a point (i) of the array of points from the point in the said array representing a measured parameter value at the initial instant of the understep (n) which point is defined as Source point of the understep (n); s the distance of a point (i) of the array of points from the point in the said array representing a measured parameter value at the end instant of the understep (n) and which point is defined as Target point of the understep (n);

The maps of figures 8 and 9 show the output when different grid dimensions has been chosen.

Figure 3 illustrate a three dimensional view of the map or image of the territory on which the three dimensional map is superimposed.

The figures 1 1 and 12 illustrates a different graphical output still representing the aerial image with superimposed the registered grid but in which also the sensors or measurement points are indicated as small squares and in the correct position.

Here by clicking or tipping on the squares indicating the points the image of the landscape at the location of the corresponding sensor is opened in a similar way as illustrated in figures 3 and 18.

Still according to a further variant the grid alone can be displayed on the screen and on the grid the points for which the maximum of effect is expected are highlighted as illustrated by figures 13 and 14. In these representations sensors and thus points on then grid coinciding with the senor locations being subject to different effects can be highlighted or represented in a different way as for example different colors and or shapes. In the figures 13 and 14 round and square points are illustrated which indicate the points at which different behaviours of the process has been predicted or occurred. In the case of landslides typically these difference is related to points where bigger and less displacements are expected or has occurred.

Figure 15 illustrates a view similar of the one of figure 10, where the points on the map have all a square form but the squares are differentiated relatively to their colour, indicating differently affected points by the evolutionary story or prediction of the landslide or the geologic process.

A way of determining the features of the points consist in using a software program for carrying out a processing method on the measured data, namely in the displacement history of the sensors from a time t=0 to a following time. The said program is for carrying out a method for determining features of events or processes having a dynamic evolution in space and/or time and particularly a method for determining features of events or processes having a dynamic evolution in space and/or time which event or process takes place in a space which can be described by a map, particularly a two or three dimensional map and the behaviour of the said event or process is described by features or parameters which can be represented as points in the said map.

A method for determining features of events or processes having a dynamic evolution in space and/or time which events or processes can be represented by a topographic map or similar i.e. for example processes or events which take place in a geophysical territory, the territory being described by a two or three dimensional geometrical map.

The present method is particularly relevant for evaluating complex events or processes relatively to the consequences determined by the dynamical behaviour of the said events or processes.

Many events or processes can be described by a map in which characteristic data are represented by points in the said map and which data relates to the measured values of physical and or chemical parameters univocally describing the status at a certain time at which the said measure has been carried out.

During the evolution of the event or process the parameter changes and since no clear relationship can be determined between the single parameters it is not evident what consequences this changes will have in the future.

The method for determining features of events or processes having a dynamic evolution in space and/or time carried out by means of the program executed by the processing unit of the system according to the present invention consist in the following steps:

Defining a set of parameters describing the effects of the event or process which can be measured and are characteristic of the said event or process.

The values of the said parameters being measured;

defining a n-dimensional space in which the said parameters describing the event or process are represented by points defined as entity points; determining as a function of the measured values of the characteristic parameters describing the event or process a geometrical point in the said n-dimensional space in which geometrical point is the point of accumulation of forces generated by the evolution of the event of process in time;

displaying or printing the said n-dimensional space in which the said characteristic parameters are shown as entity points as well as the said geometrical point.

The said geometrical point being the point at which the probability is highest that there will occur further effects generated by the said event or process as a consequence of the development of the event or process described by the said measured values of the parameters.

The determination of the said geometrical point is carried out according to the following steps: Defining a n-dimensional array of points in the said n- dimensional space and determining the geometrical point as the geometrical points for which it is a minimum the sum of the rests of the divisions of the distance of each point of the grid with the distances that each geometric point has from each one of the entity points.

A particular application of the present method is in a three or in a two dimensional space. In this special applications the space can be divided in voxels or pixels respectively for a three or for a two dimensional space. The above method can be very simply adapted to events which can be described by images or maps and in particular to events or processes which are described in a geographical space.

For a two dimensional application the above method computes the coordinates of the said geometrical point called Harmonic Centre the geometrical point whose distances from the points representing measured parameters at a certain time, so called assigned Entities, minimize the sum of the remainders of their reciprocal divisions.

In a two dimensional space represented as an array of pixels the following equations describes the said harmonic point:

dHarmonic = arg

Where N = Number of points relating to measured parameters, also called entity points;

M = Number of pixel points i.e. the points of the array of points.

A = set of assigned points

P = set of pixel points i, j { 2, ,N}

k e {l,2, ,M}

C = big integer positive constant;

D = Euclidean distance

dH = harmonic distance = linear scaling between

dHarmonic = harmonic centre or the geometrical point determined by the present method.

The above equation can be interpreted also as a geometrical point of maximum resonance of the effects of the event or process starting from the points in a photographs which are defined as the entity points or the points representing measured parameters.

According to a further step, the whole space can be transformed into a Harmonic scalar field, where each geometrical point presents a specific Harmonic value.

At this point according to a further improvement a segmentation of the whole space into a certain number of classes with different degree of Harmony, in relation with the assigned Entities can be carried out. The segmented harmonic scalar field can be represented by a two dimensional image in which the geometric points which are of the same class are indicated by means of an identical color or shade of a color which is different from the other colors or shades used for representing the pixels assigned to the other classes.

This representation can give a clear indication of where the effects of an event or process will concentrate their forces and so where this forces are accumulated and an unexpected effect is produced or will most probably produced in future times.

The Harmonic field segmentation is carried out according to the following equations starting from the above equations defining the harmonic centre:

1 M M

k

^M k=\.k P ^dHMAx, = k m,x_kaexA

dH, e H Max dH, > H Max

dH, e H High dH_N < dH_k < H_Max dH_k e H_Low dH_M < dH_k < dH_N ^dHk ^{e H}Nuii dH_k < dH_M

Where further to the above definitions the following definitions are valid: dH ^N is the harmonic distance mean of the entity points (assigned points);

d ^M is the harmonic distance mean of the Pixel points, i.e. the points of the array of points;

dH MAX_N j_{s t}^_e [\/|j_nj_ma| harmonic distance among the entity points (assigned points); Max j_{s se}t ₀f points with maximum harmony; H^lgh is the set of points with high harmony; L^ow is the set of points with low harmony; il j_{s se}t ₀f poin s with Null harmony;

In this set of equations the segmentation of the scalar harmonic field has been carried out considering four different level or classes which are defined mathematically above.

It has to be stressed out that the present method not only allows to let unknown features appear but also it might operate in order to evaluate the reliability of features which has been determined in other ways.

Furthermore it is also to be stressed out that time may be one of the measured parameter and thus one of the dimensions of the two, three or n-dimensional space in which the map is constructed.

In figure 22 there is shown a bird view picture of a region of the territory of commune of Corvara (Italy) where an landslide is monitored and in which bird view the points indicated by numerals 1 to 12 represents the monitored points by means of GPS sensors. The view further shows the Harmonic points 1 and 2 which are represented encircled and which position in the map has been determined by the present method. The said two points were not monitored but they have been determined by the method according to the present invention as points were the effect of the landslide are also to be expected.

An inspection on the territory at the said two points has revealed that there the trees were inclined relatively to the vertical direction as it is shown by the photograph of Fig. 23, thus demonstrating that the current method has correctly revealed an unknown feature of the process consisting in the landslide.

So in this case the processing routine executed by the hardware according to the above described method has helped to determine the features of certain pints in the geographical region for which certain effects have to be expected or has occurred. An alternative processing routine using a specific program for processing the measured position data in time of the sensors or measurement points is disclosed in the following documents:

The Topological Weighted Centroid and the Semantic of the Physical Space - Application, Enzo Grossi&, Massimo Buscema§, Tom Jefferson, 2009 Bentham Science Publishers Ltd., Artificial Adaptive Systems in Medicine, 79-89, chapter 9.

The Topological Weighted Centroid, and the Semantic of the Physical Space - Theory, Massimo Buscema^*, Marco Breda^*, Luigi Catzola, 2009 Bentham Science Publishers Ltd., Artificial Adaptive Systems in Medicine, 69-78, chapter 8.

The disclosure of which documents is incorporated in the preent description. The theory can be applied directly to the present application of geological process and events and particularly to the landslides.

The output of the processed data is the definition of starting points of the entire event. The figures 16 and 17 illustrates the points determined by the processing in a scalar field map by means of TWC and TWCab.

The causation process for the geological event may be also evaluated or inspected by an alternative method which is also carried out by the system in the form of a program routine loadable in the working memory of the processing unit and executable by the said processing unit on the data used by all the other above described processing programs.

The reconstruction of a causation process from time varying data describing an event or process and for predicting the evolution dynamics of the said event or process has a great technical importance in may technical fields. Practically if considering a control logic of a system or a plant, several parameters can be measured at different locations and at different times. A certain condition of operation of such a system can be analysed relating to the causation processes which has brought to the said condition by means of a method according to the present invention. Furthermore, a prediction of the evolutionary dynamics based on the entities and on the time varying quantities measured for one or more features of the entity may allow to evaluate the future evolutions of the system and to take the necessary measures in order to influence this evolution either positively or negatively.

The suite of programs may also comprise a program for carrying out a data processing according to a method for reconstructing a causation process from time varying data describing an event

Which data consist in a certain number of entities each one having a position in a space, and each one of the said entities being characterized by at least a quantity or value relatively to at least one feature and in the said quantity or value relatively to at least one of the said features of the said entities at least at two different times or at each time instant of a sequence of time instants;

The said location in space are here the geographic coordinates of the sensors or measuring points and the quantity or values are the displacements parameters from the position at a certain time t=0 to a further time of a sequence of time instants;

The method describing the more likelihood transition of all entities i, j from the time n to the time n+1 as a function of the position coordinate of the entity I and of the entity j and the quantity of the at least one feature of the entity I and of the entity j at the time n and at the time n+1 :

The said function determining the strength of the connection between each entity i at time n and each other entity j at time n+1 ;

The said method determining the source causing changes in quantity of the entity j from the time n to the time n+1 as the entity i for which the strength of connection is a maximum. According to a further feature, the said method is applied for each step from a time n to a time n+1 of the value of at least one quantity determined at each time instant of a sequence of time instants.

According to still a further improvement for each time step from time n to time n+1 , a data matrix is generated in which each element is the strength of the connection of each entity i at time n to each entity j at time n+1 .

According to a further improvement, from a data matrix of the strength of the connections a data matrix of the presence of a directed link is generated in which each element represents the presence value 1 or absence value 0 of a connection between en entity I at time n and an entity j at time n+1 and in which the said value 0 or 1 is given by determining the maximum strength among the strength of connection of each one of the entities i and one entity j.

More precisely the strength of the connection between a so called source entity i at time n and a destination or target entity j at time n+1 is determined accordin to the followin function:

Where

ΛΑ [„₊i]

are respectively the quantity in source place (entity i) at time n and the quantity inn source place (entity i) at time n+1 ; q^["^] q ^n+l

^J , ³ are respectively the quantity in destination place (entity j) at time n and the quantity in destination place (entity j) at time n+1 ; l is the distance between the source (entity i) and the destination (entity j) in the space or map;

^ is a tuned parameter connected to distance; is the strength of directed connection between source (entity i) at time n and destination (entity j) at time n+1 .

A matrix of the strength of connection can be constructed from the data of the strength of connection obtained from equation

The selection of the strongest connection for determining which source entity i has caused the changes in the quantity of the destination entity j in the time step from time n to time n+1 is determined as follows

from ^J

Where ArgMax is the maximum of the argument of the function ς» [«,« + ΐ] ς» [« ,« + ΐ]

i /^' Win i

^, and ^, determines this maximum among the strength of connection of the source entities i for each different destination entity j. The entity I for which the strength of connection ^{1 ,J} is maximum to a certain entity j is considered as the entity by which the event at entity j determining the changes in the value of the quantity at entity j from time n to time n+1 has been caused.

n [n ,n + l]

Win i

From ^, a numerical value of presence/absence of a directed link between a source entity I at time n and a destination entity j at time n+1 can be determined by the following equations:

The definition Win relates to the ith entity for which the equation is valid. is defined as the function indicating the presence of a link between a source entity I at time n and a destination entity j at time n+1 .

Similarly as for the strength of the connections, as for the presence of the links a matrix can be generated from the values , which matrix has values 1 for the elements I, j for which the

entity i satisfying the equation Sfe ^,J;^1] = f_{or a} destination entity j and zero values for all the entities i for which the said equation is not true.

According to still a further improvement the results of the above equations which are limited to the discrete entities i, j provided in the database and having a certain position in a map can be extended to the entire map by determining out of the values ^{1 ,J} a scalar field.

This scalar field defines the potential influence on the process or event of each place (entity) overall the global surface of the map.

In a two dimensional map, where each entity has a position defined by a pair of coordinates (x, y) the equation

Defines the potential influence of the i-th entity overall the global surface of the map.

And the equation

« j

Defines the cumulative potential Influence of the i-th assigned entity overall the global surface

Where

M is the number of the assigned entities N is the nubmer of time steps (Delta times) of the sequence of time instants from the first to the last time instant of the sequence.

The potentiality (U) of each point of the surface to influence the other point of the surface of the map and to be influenced is determined by the following equation:

Where

D(.) is the distance of a generic k-th point P from the i-th entity (E) in the map

M is the number of entities E

E x,y is the i-th entity E with the coordinate x, y in the map

P_k

x-^y is the k-th point P in the map with the coordinate x, y in the map.

According to a further feature the present method may be applied for predicting the evolution dynamics of the said event or process starting from the information about the causation process. In this case the method for predicting the evolution dynamics of the said event or process comprises the following steps:

Providing data which data consist in a certain number of entities each one having a position in a space, and each one of the said entities being characterized by at least a quantity or value relatively to at least one feature,

The said data comprising for each of the said entity i, j and for at least

Q

one of the features the quantity or value ^{1 1} at different time instants n of a sequence of time instants comprising N time steps;

Determining for each step from one time instant n to the following time instant n+1 in the said sequence of time instants the matrix of the strength of connections from a source entity i at time n to a

£f [w ,w + l] destination entity j at time n+1 and the connection matrix ^{1 ,J} , i.e. the matrix of absence or presence of a link between a source entity i at time n and a destination entity j at time n+1 ,

Generating a new dataset by joining the data of the connection matrix

£f [w ,w + l]

^{1 ,J} of all the N time steps of the sequence of time instants;

Training a predictive algorithm with at least part of the data of the said new dataset;

determining the quality of the entities as source entities i at a first time instant at which the quality or value of the at least one feature is known for destination entities j at a following future time instant by feeding the said known data at the first time instant to the trained predictive algorithm.

Using a more strength mathematical formalism the above can be expressed as follows:

The new dataset is generated by joining an rewriting the connection matrices with a moving windows where each connection vector x of each place P of the entity at the time n points out to the connection vector x of the same pla t time n+1

New Dataset:

Where P is the number of places where the entities are

N is the number of time steps

According to a particular embodiment the predictive algorithm is a Artifical Neural Network ANN with the following model: x(n)→ x(n + 1) = f(x(n), w^* ) + s

Where *

^ is the weight matrix of the trained Artificial Neural Network which approximate the optimal parameters to model the global temporal

£f [w ,w + l] process obtained by the known connection matrices ^{1 ,J} so defining the local laws of the process itself.

According to an improvement a special way to use the new dataset for training and testing the predictive algorithm, i.e. the artificial neural network is chosen which consist in the fact that

For training set and testing set each record is composed by P+1 input variables consisting in:

the connectivity values (1/0) of each place from the time (n) to the time

(n+1 ) according to the corresponding connection matrix ^{1 ,J} and the connectivity values (1/0) of each place from the time (n+1 ) to the time (n+2) according to the corresponding connection matrix

[« + l,« +2] while none of the sets has the same input vector but a different target vector.

Referring to figure 24, the table illustrated is a scheme of the structure of typical data for which the present method can be used for reconstructing a causation process and for predicting future evolution.

The present example is limited to a two dimensional case but the process may be also extended to a thee dimensional or n dimensional case.

The structure of the data comprises entities having stable positions in a map. This means constant coordinates in time.

Each entity is further characterized by a feature which changes in time and can be represented by a quantity such as a numerical value. The data of the said quantity is provided at least for two, generally for a certain number of time instants of a sequence of time instants.

Starting from the knowledge of this kind of data the question to which the method according to the present invention gives an answer is how to reconstruct the global causation process.

This causation process can be defined also as the information about which entity provided in the data at a certain time (n) influences which other of the entities at the time (n+1 ) causing the variation of the quantity observed. Furthermore is also relevant to determine the strength of the said influence.

As it will be seen in the following description the further improvement step of the method according to the present invention is also to determine the invariants of the causation process and thus be able to predict which of the entities at a certain time (n) will influence which other entities at the time (n+1 ) in a blind way, i.e. without knowing the data at the time (n+1 ).

The method according to the present invention is explained in the following according to different examples.

EXAMPLE I

Example 1 is based on the data reported in the table of figure 25. The entities are in then form of five places (place 1 to Place 5) for which the coordinate are known in a two dimensional map. For each of the said places a quantity corresponding to a certain feature related to the places and representing a certain process or event are provided in a numerical value form and for three different time instants of sequence of time instants. The time instants being defined as time n=0, time n=1 and time n=2. The places are placed in a map illustrated in figure 3 and the position of the places in the map is determined by using their coordinates.

Starting from the data of figure 2 the causation process is then reconstructed by considering each time step separately: the first time steps from time n=0 to time n=1 and the second time step from time n=1 and time n=2.

For both time steps the strength of the connection between each place 1 to 5 versus each other of the places 1 to 5 is determined means of the followin equation:

Where

, ^l are respectively the quantity in source place (entity time n and the quantity inn source place (entity i) at time n+1 ; q^["^] q ^n+l

^J , ³ are respectively the quantity in destination place (entity j) at time n and the quantity in destination place (entity j) at time n+1 ; da

is the distance between the source (entity i) and the destination (entity j) in the space or map;

^ ned parameter connected to distance; is the strength of directed connection between source (entity i) at time n and destination (entity j) at time n+1 .

A matrix of the strength of connection can be constructed from the data of the strength of connection obtained from equation ^{1 ,J}

In figure 27 the flux of the reconstruction process is illustrated starting from the data of figure 25 and for both the time steps defined above. The first line of tables below the starting data represents the matrix of the strength of connections between the places considered at source entities at time n (rows) and the places considered as destinations at time n+1 (columns).

Once the said data is available, for each time step and for each place as source entity the maximum strength value is determined and this is taken as an indication that a direct link is present for the place representing the source entity and the place representing the destination entity for which the strength of connection is a maximum. This steps are carried out applying to the data of figure 25 and for each time step the following steps:

Where ArgMax is the maximum of the argument of the function

Qr [« ,« + l] Qr [« ,« + l]

i /^' Win i

^, and ^, determines this maximum among the strength of connection of the source entities i for each different destination entity j. The entity I for which the strength of connection is maximum to a certain entity j is considered as the entity by which the event at entity j determining the changes in the value of the quantity at entity j from time n to time n+1 has been caused.

n [n ,n + l]

Win i

From ^, a numerical value of presence/absence of a directed link between a source entity I at time n and a destination entity j at time n+1 can be determined by the following equations: e definition Win relates to the ith entity for which the equation l is defined as the function indicating the presence of a link between a source entity I at time n and a destination entity j at time n+1 .

Similarly as for the strength of the connections, as for the presence of the links a matrix can be generated from the values , which matrix has values 1 for the elements I, j for which the entity i satisfying the equation for a destination entity j and zero values for all the entities i for which the said equation is not true.

In the above indicated equations the term entity corresponds in the present example to the places 1 to 5.

The matrix of connections for the two time steps are reported in figure 4 in the last line. As it appears clearly for each place 1 to 5 considered as a source entity the maximum values of the strength of connection are determined so that the matrix of connection is formed by "0" or "1 " indicating respectively absence and presence of a direct link between the place considered as a source entity and the place considered as the destination entity.

From the said matrix of connections it appears that in the first time step from time instant n=0 to time instant n=1 , the source entity Place4 has caused a variation of the quality at the destination entities place3 and place5 and the source entity place5 has caused a variation of the quality for the destination entity place4. All the other places are not involved in the causation process of the evolution of the event in the said time step 1 .

In the second time step from n=1 to n=2, the connection matrix indicates as source entity Place3 which has caused a variation of the quality at the destination entities placel , place4 and place5 and place4 which has caused a variation of the quality for the destination entity place2.

In figures 28 and 29 the said results are represented as a first transfer step from a status 1 at time n=0 to a status 2 at time n=1 and as a second transfer step from a status 2 at time n=1 to a status 3 at time n=2.

The tables indicate the time step to which the data refer. In the left column there is indicated the source entity, in the following column the direction and in the third column the destination entity on which the source entity has a direct link , i.e. has cause the variation in the monitored quantity from tine n to time n+1 . The last right column indicates the strength of the connection between the source and the destination entity.

So if considering the table of figure 27, the source entity place 3 at time n=0 has caused the variation of the quantity at the value of time n=1 of the destination entity Place 3, similarly the source entity Place 5 has caused the variation of the quantity at the value of time n=1 of the destination entity Place 4, which place 4 is as the same time source entity influencing the quantity at time n+1 of the destination entity Place5. the strength of the influence for each couple of source and destination entity is given in the right column as a numerical parameter.

In the table of figure 29, the results are that in the second time step, the source entity place 3 at time n=1 has caused the variation of the quantity at the value of time n=2 of the destination entity Place 1 , similarly the source entity Place 4 has caused the variation of the quantity at the value of time n=2 of the destination entity Place 2. the source entity Place 3 has also influenced the quantity at time n=2 of the destination entities Place 4 and Place 5.

The right column indicates the strength of the influence for each couple of source and destination entity.

Figure 30 represents the matrix of connection among the 5 places as source entities and the five places as destination entities at the first time step from time n=0 to time n=1 . Figure 31 is a graphic representation of the said connection matrix with vectors connecting the source entities and the corresponding destination entities for which a direct link is present according to connection matrix of figure 30. Since for the two entities place 4 and 5 the situation is that they are alternatively source and destination entities of each other, there is only a line for which the arrow changes direction depending on the source entity considered. Figure 32 represents the matrix of connection among the 5 places as source entities and the five places as destination entities at the first time step from time n=1 to time n=2. Figure 33 is a graphic representation of the said connection matrix with vectors connecting the source entities and the corresponding destination entities for which a direct link is present according to connection matrix of figure 32.

In figure 34, on the left hand side there are shown the table of the data, i.e. the entities and the corresponding quantities at the time n=0, n=1 and n=2, the connection matrix for the first time step from time n=0 to n=1 and the connection matrix for the second time step from tine n=1 to n=2.

The right hand graphic representation corresponds to the graphic representations of figures 31 and 33 overlapped one on the other.

Starting from the data of the computed strength of connection between the source entities and the destination entities at a time step and to the corresponding connection matrix, it is possible to extend the reconstruction of the causation process over the entire plane by determining scalar field.

The said scalar field represents the potential influence on the process or event of each place (entity) overall the global surface of the map.

The following formalism is used to determine the scalar field in a map, which field represents the potentiality (U) of each point of the surface of the map to influence the other points of the surface of the map and to be influenced.

Defines the potential influence of the i-th entity overall the global surface of the map. And the equation

Defines the cumulative potential Influence of the i-th entity overall the global surface where

M is the number of the assigned entities

Ν is the nubmer of time steps (Delta times) of the sequence of time instants from the first to the last time instant of the sequence.

The potentiality (U) of each point of the surface to influence the other point of the surface of the map and to be influenced can be determined using the following equation:

Where

M is the number of entities E x-^y is the i-th entity E with the coordinate x, y in the map

P_k

x-^y is the k-th point P in the map with the coordinate x, y in the map. Applying the above equations to the data set of the above described example and represented in the table of figure 2, the scalar field computed is represented in the figures 35 to 37.

Figure 35 represents graphically the scalar field for the first time step from time n=0 to n=1 and figure 36 represents graphically the scalar field for the second time step from time n=1 to n=2.

In figure 37 the scalar field is illustrated resulting from overlapping the scalar fields of the first and of the second time steps represented in figure 35 and 36.

A further improvement of the method according to the present invention allows to use the output data consisting in the connection matrices for the different time steps for predicting which are the invariants of the process in order to render possible to predict which entities at a certain time (n) will influence which other entities at the time (n+1 ) without knowing the quantities for the said entities at the said time (n+1 ).

Figure 38 shows a table of the dataset which will be used for carrying out an example of the prediction method steps. This data set is the original dataset used for the previous example and shown in the table of figure 25 which is further expanded by adding the quantity for each of the places 1 to 5 for further time instants n=3 and n=4. The sequence of time instants for which the value of the quantity is given are now four time steps.

In relation the dataset of figure 38 it has to be noticed that the number of records are few in relation to the records which are too many. The prediction of real/interger number (approximation function) is much harder than to perform a patter recognition task (classification). For the above reasons, from a statistical viewpoint the said dataset is not ideal for building a predictive model from the step of a previous time (n) to a following time (n+1 ) and the conditions make the prediction model impossible to built up, especially using artificial neural networks.

In order to overcome the above difficulties the present method provides the step of using the connection matrices for each time step from time n to time n+1 for generating a new dataset which allows the construction of a predictive model.

The new dataset is generated by the steps of joining and rewriting the data of the connection matrices computed for all of the time steps or for a certain number of time steps with a moving window where each connections vector of each entity Place 1 to place 5 at the time (n) points out to the connection vector of the same entity (Place 1 to Place 5) at the time (n+1 ).

This steps may be expressed in a more precise formalism by the

Where P is the number of places where the entities are

N is the number of time steps

According to a particular embodiment the predictive algorithm is an Artifical Neural Network ANN with the following model: x(n)— x(n + 1) = / (x(n), w^* ) + ε

Where

*

^ is the weight matrix of the trained Artificial Neural Network which approximate the optimal parameters to model the global temporal process obtained by the known connection matrices ^{1 ,J} so defining the local laws of the process itself.

Applying the above steps to the dataset of figure 38 as illustrated in figure 39, the reconstruction steps of the causation process provide four matrices, one for each time step and each matrix being a 5x5 matrix in which the strength of the connections for the source entities (place 1 to Place5) at step(n) to the destination entities (place 1 to Place5) at step (n+1 ) are given and a set of further four connection matrices defining the possible oriented link between the source entities (pace 1 to Place 5) from step (n) to step (n+1 ).

Figure 40 illustrates the results of the causation process for each step (1 to 4) defined as trans 0-1 , trans 1 -2, trans 2-3 trans 3-4 in a table and in the graphic form as already shown in the previous example of figures 25 to 33.

Applying the joining and rewriting process of the connection matrices for obtaining the new database described above to the connection matrices determined for each time step of the present example, the new dataset obtained is illustrated in figure 41 .

On the left hand side the braces indicates the part of the records of the dataset which are used for carrying out training, testing of an artificial neural network and a prediction experiment.

With tuning the records are indicated which are used for training an blind testing the trained artificial neural network. The last five records relating to the source entities Place 1 and Place 5 at step n=3 (fourth step) are the records on which the prediction algorithm is used for determining at time (n+1 ), the connection matrix relating to this time step.

For the Training set and for the Testing set, each record is composed by P+1 input variables:

1 . The connectivity (1/0) of each place from the time (n) to the time (n+1 ), according to the TDM Output;

2. An identification number for each place (an integer).

And P target variables:

1 . The connectivity (1/0) of each place from the time (n+1 ) to the time (n+2), according to the TDM Output.

The best condition for the Training and for the Testing set is a situation where none of the patterns has the same input vector but a different target vector. When this situation occurs, the patterns with these features are not trainable or testable. A solution can be to augment the memory window, if the amount of data allow this coding, until every ambiguity disappear. In the other cases, the ANNs will treat these situations as "noise".

In the present example there are some cases of ambiguity, but the data are too few for an augmented Coding.

The training set is composed of 10 patterns: 6 input and 5 target each one;

The testing set is composed of 5 patterns, with the same input- target structure.

An artificial neural network, particularly a so called Sine Net according to document US 7,788, 196 is used for training. Its weights are tested in blind way (the ANN will see only the input vector of the 5 patterns) using the testing set. The artificial neural network prediction capability are measured in an experiment in terms of

1 . Sensitivity =Number of real connections correctly predicted,

2. Specificity =Number of real non connections correctly predicted,

3. Accuracy= Number of correct predictions.

The artificial neural network, consequently, will generate 25 (5x5) independent estimations (predictions).

After 43989 epochs the Sine Net artificial neural network, with 24 hidden units, has terminated its training, with no further possibility to reduce its learning error (RMSE=0.21505214).

Figure 42 illustrates the results of the prediction for each place by comparing the real known connection matrix with the predicted/estimated one by the artificial neural network.

As it is indicated the light grey areas indicate the results which are missing connection relating to the real known data while the dark grey area the false connection relatively to the real known data.

The table of figure 43 indicates the performances of the artificial neural network in terms of sensitivity, specificity and accuracy. As it appears the sensitivity is 60,00%, the specificity is 90,00%, and the accuracy is 84,00%.

Figures 44 and 45 illustrates the graphical representations respectively of the known real dynamics and of the dynamics predicted with the artificial neural network.

Although the terminology used in the discussion of the processing method is generic, it is a plain operation for the skilled person to consider that the input data in the present application are geographical coordinates and their change in time, so that the method can be directly applied to the application of the landslides or of geological processes and events without any inventive step being needed. The displayed output can be of similar kind as for the previous processing method and illustrated in figures and such as the one disclosed in the figures 16 and 17 or it can be also one of the outputs illustrated in the figures 28 to 33 and 36 and 40.

A further possible processing routine for which the software program suite may comprise a dedicated software program loadable and executable by the system Hardware allows to determine implicit hidden features of phenomena which can be represented by a point distribution in a space. This can be achieved by providing a software program which carries out a processing method for determining hidden features of phenomena which takes place in a space and the effect of the said phenomena being described by value of parameters which can be measured and which can be represented by points in a map, particularly a two or three dimensional map.

According to a further specific application of the invention, the method is for determining hidden features of phenomena which are georeferentiated i.e. which take place in a geophysical territory, the territory being described by a two or three dimensional geometrical map which is the specific kind of problems to which the system according to the present invention applies i.e. more generally geological events and more specifically landslides.

The present processing method is particularly relevant for evaluating complex phenomena which phenomena can include physical processes or events.

Events or processes are observed and described by effects which can be described by measuring the values of certain physical or chemical parameters at a certain time and at certain locations in space. Generally the data acquired from this measurements is useful for determining the current condition of the event or process or generally speaking of the phenomena. When complex phenomena are considered it may not be at once clear if all the possible effects have been considered or if further effect derives or are related to the phenomena under study. Furthermore if the phenomena is distributed over a certain area than it is possible that not every location has been considered or is known or appears to be relevant for measuring the parameters describing the consequences of the phenomenon.

The possible further parameters and/or the locations at which the effects of the phenomenon will arise may in general not be determined directly by analysing the phenomenon due to the high degree of complexity and non linearity of the laws governing the phenomenon.

Giving an answer to the above problem is relevant for generating a machine allowing to analyze and describe phenomena in an automatic and objective way without the need of entering the in the highly complex and non linear mechanism ruling the phenomena and also for enhancing the cognitive capacities of devices having a certain artificial intelligence.

Currently there exists a method for determining the relationships between the said points which method is known with the denomination of Minimum Spanning Tree. According to this method for every distribution of Points in a D-dimensional space it is possible to determine at least one minimum spanning tree. The minimum spanning tree is the smallest sum of the distances of the points according to certain connections between each point and another point of the map.

A more rigorous mathematical definition is the following:

Given a connected, undirected graph, a spanning tree of that graph is a sub graph which is a tree and connects all the vertices together. A single graph can have many different spanning trees. It is possible to assign a weight to each edge, which is a number representing how unfavorable it is, and use this to assign a weight to a spanning tree by computing the sum of the weights of the edges in that spanning tree. A minimum spanning tree (MST) or minimum weight spanning tree is then a spanning tree with weight less than or equal to the weight of every other spanning tree.

The MST and several algorithm are well known in the art and are common general knowledge of the skilled person.

The object of the present processing method is to determine implicit hidden features of phenomena which can be represented by a point distribution in a space in an automatic and simple way and to represents the said hidden features graphically.

Surprisingly it has been found that starting from a certain distribution of measured parameters which describes the phenomenon and which are represented in a map in an n-dimensional space, particularly in two or three dimensional space, it is possible to extract from the distribution of the said points information on other points having different position in the said map and representing further parameters or further locations which has a relevance for the phenomenon or at which the effects of the phenomenon has or will appear.

It seems that the distribution of the measured points implicitly includes the presence of the hidden points.

The processing method carried out by the system according to the present invention comprises the following steps:

Defining a set of first parameters describing the effects of the phenomenon such as an event or process which first parameters can be measured and are characteristic of the said event or process.

defining a n-dimensional space in which the said first parameters describing the event or process are represented by points defined as entity points;

determining as a function of the measured values of the said first characteristic parameters describing the event or process further geometrical points in the said n-dimensional space which geometrical points are expected to be further characteristic parameters describing the phenomenon or further locations at which the phenomenon will produce its effects;

the said further parameters or points are added, in a recurrent sequence, to the first parameters or points so to have at each iterative step a shorter minimum spanning tree than at the step before.

displaying or printing the said n-dimensional space in which the said further characteristic parameters or points are shown together with the said first parameters as well as the said geometrical point.

The method steps are easily understood since at each step one point or parameter is added to the first ones which reduces the length of the minimum spanning tree. At each following step the points or parameters determined in the preceding steps are maintained and a new point or parameter is searched that further educes the length of the minimum spanning tree.

As already indicated the new set of points are somehow implicit points of the original map of the points corresponding to the first parameters and the method according to the invention defines the set of this implicit points/parameters of any map in a D-dimensional space.

Since considering the said d-dimensional space a continuum would lead to infinite minimum spanning trees, in order to have a finite number of steps the space is quantized in pixels or voxels, and a certain minimum pixel or voxel distance is defined.

A preferred pixel or voxel distance is about 0,5mm.

The method according to the present invention determines the coordinates of the further points and the presence of further parameters of a phenomenon in a quantized space as defined above according to the following algorithm:

The Minimum Spanning Tree problem is defined as follows: find an acyclic subset T of E that connects all of the vertices V in the graph and whose total weight is minimized, where the total weight is given by

T is called spanning tree, and MST is the T with the minimum sum of its edges weigthed.

And the number of its possible tree is :

T = v^v~1

Here da ^,J is the Euclidean distance of each point i from each point j;

d(T) is the length of sum of the edges.

V are the vertices, i.e. the points in the map.

The above step is repeated for determining in sequence a new point or parameter which when added to the other points or parameters allows to obtain a smaller minimum spanning tree.

An array of generic points in the d-dimensional space is defined and in which array the points are equally spaced one from the other along each of the d-dimensions and at each step the minimum spanning tree is calculated for a distribution of points comprising the first points and one of the points of the said array of generic points. The generic point of the array for which the smallest minimum spanning tree results is then taken as the further unknown implicit point or parameter and added to the set of the first points. This amended set of first points is then used for repeating the above steps. This steps are repeated cyclically until no further generic point of the remaining points in the array is found fro which a smaller MST can be computed as the one computed in the last step. At every step the further point determined in the previous step is maintained and the new MST is determined using all the first points and the each one of the further points added in each one of the preceding steps of the sequence of steps.

The added further points/parameters are then displayed on a graphical representation together with other first points or parameters or the values representing the coordinate of these further points are saved and/or printed.

Graphical representation may be the best way of presenting the further points or parameters when the space is two or three dimensional.

The example of figure 46 relates to the comparison of the determination of MST of a grid of points having a 5x5 dimension according to the known methods and to the method of the present invention.

On the left side of figure 46 the 5x5 array of points coinciding with the crossing points of the lines of the grid are shown in a two dimensional space. The minimum spanning tree determined by the current known algorithm is formed by horizontal lines each one connecting a line of points of the grid and a vertical line connecting the points of the first column of the grid.

The map of the right side illustrates the MST determined recurrently according to the present invention. In the map showing the grid or array of the said initial points, further points has been added which are displayed in the map. These further points lead to a different configuration of the MST which is smaller than the one on the map of the left side of figure 46 and which is calculated by the known algorithm.

The points represented by the small squares are the points added according to the present method.

At each step a point is added and a new minimum spanning tree is determined which is smaller than the one of the previous distribution of points. In order to carry out this task, the space defined by the map is quantized by mean of an array of point. In the present example the array of points is two dimensional so that the space of the map can be described as an array of pixels having a certain distance one from another along the two directions.

At a first step the method computes the minimum spanning tree for each distribution of point including one of the points of the said array of points in which the space is quantized. The smallest minimum spanning tree is determined and the added point for which this smallest minimum spanning tree has been computed is added to the map.

In the following step the same process is repeated but this time the initial distribution of points for the step comprises the original initial distribution of points and the one calculated in the first step.

This mechanism is repeated for each step each time defining a new distribution of points comprising the original one and each one of the points added in the previous steps. The iteration is stopped when the step does not lead to an MST which is smaller than the one determined in the previous steps.

In figure 47 the program steps describing the algorithm for carrying out computations according to the equations describing the present method are reported.

As it appears clearly the computations for each step of the recurrent MST. The last lines describes the verification if a further step is needed for determining a further hidden point or if no further point is needed. If a further point has to be determined the steps are repeated by maintaining all the other points determined in the previous steps as points in the map on which the calculation of the coordinates of the further point has to be based.

Further features of the system according to the present invention are disclosed in figures 3, 4 and 13.

In figure 3 and 13 it is possible to appreciate the fact that by tapping, clicking or touching on the points highlighted in a grid or in an image this action corresponds to the requests of providing images of the real condition of the site at which the position of the point on the map corresponds to a sensor on the territory at the location having identical geographical coordinates. This functionality helps in considering the appearance of the territory for evaluating signs or visual indicia on the territory of effects of a landslides process. This images can be loaded already in a database or can be achieved directly on site by means of remote cameras which registers the images and send the images to the processing unit of the system Hardware working as a server collecting the images or requesting the images.

According to still another feature which appears clearly from figure 4, the user of the system, may use the touch screen for selection from the map of one bigger geographical territory smaller territories and put this selections as different images on the said map bringing the selections manually or automatically in registration with the general map. So on the general map the different areas can be placed and also in matching condition with the general map and one with the other. This helps in studying different regions of a territory and to graphically display the results of different regions together and in thee correct geographic relation the maps of the results.

Claims

1. A system for evaluating the current evolutionary status of events or processes in a geographical region and for generating and s visualizing predictions of the evolutionary dynamics in time and space the said system operates by means of a virtual model which is directed to the simulation of a process or of an event which takes place in a geophysical territory, the territory being described by a two or three dimensional geometrical map, the said virtual model is in the form of a0 suite of executable programs which can be loaded in the working memory of a processing unit and executed by the said processing unit on demand; a representation of the status and of the evolution of the process at certain time being in the form of a graphical representation displayed on a screen;

5 The event or process which the system evaluates and for which the said system generates and visualizes the evolutionary dynamics in time and space is the landslide in a certain geographical territory;

The computed current condition of the landslide dynamics in whole territory based on the data obtained for certain geographical points distributed on the territory and highlight the said status by means of one or more graphical outputs or the computed evolution of the process or event at a certain time instant is visualized as a grid which is deformed according to the geographical positions of the points in time and which is registered and superimposed to a two or three dimensional map or aerial or satellite image of the territory;

the condition of the event or process, namely of the landslide, is determined by means of the displacements measures of certain number of sensors placed on the territory taken at different time.

2. A system according to claim 1 in which the suite comprises one or more routines or interoperative programs each one carrying out a specific processing task on the input data which consist in the measurement of the displacement in time of a certain number of points distributed on a certain geographical territory and thus on a two or three dimensional map of the said territory, as well as routines for graphically representing the outputs of the predicted evolutionary dynamics in relation to the map of the geographical territory or satellite or aerial images of the said territory.

3. A system according to claim 1 or 2, characterized in that said system consists in a hardware device comprising a processing unit with means for loading and executing software programs, one or more user interfaces for inputting data and commands;

one or more means for displaying the output data, i.e. the results of the processing tasks carried out on the input data by executing one or more software programs;

means for inputting measured data in the form of data strings or a database; interface means for connecting to one or more measuring units and directly inputting data measured by the said measurement units; one or more communication ports for connecting and exchanging data with remote devices through a public or private network, such as remote servers;

4. A system according to one or more of claim 1 to 3, in which the measuring units are a certain number of position sensors each of which is placed on a certain location of the geographical territory and each one of which measures at certain times of a predetermined sequence of time instants the changes in its position or the displacement relatively to the position determined at the preceding time instant in the predetermined sequence of time instants;

The measured data are position data of each sensor and time data at which the position data has been determined;

5. A system according to one or more of the preceding claims in which the software programs are:

6. A system according to one or more of the preceding claims in which the software programs comprise a database of images of the site on the territory at which the sensors or measurement points are located in order to allow to monitor the appearance of the territory at this sites which images are retrieved and displayed by clicking on the representations of the corresponding point.

7. A system according to claim 6 in which in combination or alternatively In place of the database of images the zoomed satellite images of the site of location of the sensor or the measurement point is downloaded and displayed.

8. A system according to claim 6 or 5 in which alternatively or in combination the images are images registered by remote cameras placed at the said sites, such as web cams or similar devices which are connected by a private network.

9. A system according to one or more of the preceding claims in which the hardware of the present system is in the form of a table computer or of a so called wall computer while the software programs are loaded or loadable in the memory of the said devices and are executable on demand by the said hardware while the outputs are displayed on the touch screen.

10. A system according to the preceding claims in which one of the programs is a program for generating a model for simulating the evolutionary dynamics of events or processes the said model consisting in a non linear adaptive mathematical system simulating the spatial and temporal dynamics of the event or processes by using measured values of a certain number of parameters describing the evolutionary condition of the event or process at certain different times;

The values of the said parameters being measured at a first time and at least a second time different from and following the said first time;

the said model defining a n-dimensional array of points in a n- dimensional reference system whose axis represents the values of the parameters being measured and in which array the said parameters are represented by special points in the said array of points;

the displacements of each one of the points of the said array of points being computed as a function of the displacements in the said array of points of each of the points representing the said measured parameter values between a first time of measurement and at least a following second time of measurement and

11. A system according to claim 10 in which the n-dimensional array of points is represented by n-dimensional grid in which the points of the array of points are the crossing points of the lines delimiting the meshes of the grid and the evolutionary condition of the event or process at a certain time is visualized as the distortion of the grid determined by the changes in relative position of the points of the array from the starting position in which the points of the array are equally spaced one from the other to the position of the said points of the array of points computed at the said certain time.

12. A system according to claim 10 or 11 , in which the a certain mesh size can be set.

13. A system according to one or more of the preceding claims 10 to 12, in which the array of points is two or three dimensional.

14. A system according to one or more of the preceding claims 10 to 13, in which the grid is two or three dimensional.

15. A system according to one or more of the preceding claims 10 to 14, in which the evolution between a first time at which a parameters are first measured and a second time at which the parameters are measured a further time is divided in a certain number of steps, the displacements of the points representing the measured parameters and the time interval during which the said displacements has occurred being divided by the said certain number of steps.

16. A system according to one or more of the preceding claims 10 to 15 in which the computation of the position of the points of the array of points at a certain time as a function of the measured values of the parameters at least at a first and at a second following time is carried out according to the following equations:

P n + l) = P_i(n)+ Delta _t(n) _{( )}

In which

Pi {ⁿ ) is the position of the i-th point in the grid at the step n; n being the index number of a step of a certain number of steps in which it is divided the displacements of the points representing the measured parameters and the time interval between a first time of measurement and a second time of measurement and during which interval the said displacements has occurred;

/> (« + i ) is the position of the i-th point in the grid at the step n+1 ;

Delt _i {n) j_s defined by the following equation:

Delta i ( ) =

In which: d_j (^M)is the distance of a point (i) of the array of points from the point in the said array representing a measured parameter value at the initial instant of the understep (n) which point is defined as Source point of the understep (n); is the distance of a point (i) of the array of points from the point in the said array representing a measured parameter value at the end instant of the understep (n) and which point is defined as Target point of the understep (n);

17. A system according to one or more of the preceding claims 10 to 16, in which the model is a two dimensional model and in which the computation of the position of the points of the array of points at a certain time as a function of the measured values of the parameters at least at a first and at a second following time is carried out according to the following equations:

In which

And in which are the coordinates of a point P indexed (i) of the array of points at the understep (n)

^'„₊i) are the coordinates of a point P indexed (i) of the array

*(»+!)

of points at the understep (n+1 )

X ^s V ^s r^[s] v ^[s

-^j > j j or ^j y are the coordinates at the first time of measurements of the points representing the values of the parameters at the first time of measurement (time T=0); ^xj (ri)> y j (ⁿ ) or ^Xj_(n) ' y j_{{ n )} are the coordinates at the second time of measurements of the points representing the values of the parameters at the second time t of measurement (time T=t) and at the understep n; dj in) or ^i[y|_n) is the distance of a point (i) of the array of points from the point in the said array representing a measured parameter value at the initial instant of the understep (n) which point is defined as Source point of the understep (n); dg {n) or dj is the distance of a point (i) of the array of points from the point in the said array representing a measured parameter value at the end instant of the understep (n) and which point is defined as Target point of the understep (n);

And where:

^/_(n) has the meaning of a quantity of potential energy accumulated by each point Pi at each understep n,

[p]

,^Wa anndd #,^W tion for determining the sign of the potential

'(") °y is a func

'(«) energy contribution _(n) at each understep n.

18. A system according to one or more of the preceding claims 10 to 17, in which the model describes a landslide, the measured values of parameters being points of measurements of displacement of a certain number of geographical points in a certain region each of these points having known coordinate at time t=o and new coordinates at each of one or more following measurement times, while the array of points is formed by generic geometrical points of the same territory forming the crossing points of the lines of a grid describing generic points of the said territory.

19. A method for generating a model for simulating the evolutionary dynamics of events or processes the said model consisting in a non linear adaptive mathematical system simulating the spatial and temporal dynamics of the event or processes by using measured values of a certain number of parameters describing the evolutionary condition of the event or process at certain different times;

defining a n-dimensional array of points in a n-dimensional reference system whose axis represents the values of the parameters being measured and in which array the said parameters are represented by special points in the said array of points;

computing the displacements of each one of the points of the said array of points as a function of the displacements in the said array of points of each of the points representing the said measured parameter values between a first time of measurement and at least a following second time of measurement and

as a function of the distance of each of the points of the array of points from each of the points representing the measured parameters; visualizing the evolution of the event and or the model in time by displaying the points of the array of points at different times.

20. A method according to claim 19, in which the n-dimensional array of points is represented by n-dimensional grid in which the points of the array of points are the crossing points of the lines delimiting the meshes of the grid and the evolutionary condition of the event or process at a certain time is visualized as the distortion of the grid determined by the changes in relative position of the points of the array from the starting position in which the points of the array are equally spaced one from the other to the position of the said points of the array of points computed at the said certain time.

21. A method according to claim 19 or 20, in which the a certain mesh size can be set.

22. A method according to one or more of the preceding claims

19 to 21 , in which the array of points is two or three dimensional.

23. A method according to to one or more of the preceding claims 19 to 22, in which the grid is two or three dimensional.

24. A method according to one or more of the preceding claims 19 to 23, in which the evolution between a first time at which a parameters are first measured and a second time at which the parameters are measured a further time is divided in a certain number of steps, the displacements of the points representing the measured parameters and the time interval during which the said displacements has occurred being divided by the said certain number of steps.

25. A method according to one or more of the preceding claims 19 to 24 in which the computation of the position of the points of the array of points at a certain time as a function of the measured values of the parameters at least at a first and at a second following time is carried out according to the following equations:

P^n + l) = Ρ η)+ Delta ,.(«) _{( )}

In which

n being the index number of a step of a certain number of steps in which it is divided the displacements of the points representing the measured parameters and the time interval between a first time of measurement and a second time of measurement and during which interval the said displacements has occurred; is the position of the i-th point in the grid at the step n+1 ;

Delt _; [n ) j_S defined by the following equation:

Delta ₍(η) =

In which: d yl)\s the distance of a point (i) of the array of points from the point in the said array representing a measured parameter value at the initial instant of the understep (n) which point is defined as Source point of the

(n); the distance of a point (i) of the array of points from the point in the said array representing a measured parameter value at the end instant of the understep (n) and which point is defined as Target point of the understep (n);

26. A method according to one or more of the preceding claims 19 to 25 in which the model is a two dimensional model and in which the computation of the position of the points of the array of points at a certain time as a function of the measured values of the parameters at least at a first and at a second following time is carried out according to the following equations:

In which

And in which

^Λϊ \^η )·> ^ ί ⁿJ or i,

(n ) ' ·^ϊ(_Π) are the coordinates of a point P indexed (i) of the array of points at the understep (n) ^{9 l'}<"⁺¹> ^{are tne coordinates} °f ^a P°^{int p} indexed (i) of the array of points at the understep (n+1 )

> y v j^[s are the coordinates at the first time of measurements of the points representing the values of the parameters at the first time of measurement (time T=0); xj (ⁿ)> j (Ό or ^Xj_{( n )} ' y are the coordinates at the second time of measurements of the points representing the values of the parameters at the second time t of measurement (time T=t) and at the understep df_j {n) or is the distance of a point (i) of the array of points from the point in the said array representing a measured parameter value at the initial instant of the understep (n) which point is defined as Source point of the understep (n); dy (w) or dl,)_(n) is the distance of a point (i) of the array of points from the point in the said array representing a measured parameter value at the end instant of the understep (n) and which point is defined as Target point of the understep (n);

And where: has the meaning of a quantity of potential energy accumulated by each point Pi at each understep n, is a function for determining the sign of the potential energy contribution ^ _(n) at each understep n.

27. A method according to one or more of the preceding claims 19 to 26 in which the model is used for calculating and displaying the s evolution of a landslide, by means of displacement measurements of a certain number of points on the territory ad at a sequence of following times, while the array of points is formed by generic geometrical points of the same territory forming the crossing points of the lines of a grid describing generic points of the said territory.

0 28 A system according to one or more of the preceding claims comprising a software program which can be loaded and executed by a hardware processing unit which program provides the said hardware unit to process input data according to the a method for determining features of events or processes having a dynamic evolution in spaces and/or time using measurements of values of parameters describing a process which can calculate the most probable consequences of the event or process at a certain time, the method comprising the following steps:

The values of the said parameters being measured at a certain time;

defining a n-dimensional space in which the said parameters describing the event or process are represented by points defined as entity points;

determining as a function of the measured values of the characteristic parameters describing the event or process at the said certain time a geometrical point in the said n-dimensional space which geometrical point is the point of accumulation of forces generated by the evolution of the event of process in time; displaying or printing the said n-dimensional space in which the said characteristic parameters are shown as entity points as well as the said geometrical point.

29. A system according to claim 28 in which the events or processes has a dynamic evolution in space and/or time which event or process takes place in a space which can be described by a map, particularly a two or three dimensional map and the behaviour of the said event or process is described by features or parameters which can be represented as points in the said map.

30. A system according to claim 28 or 29 in which the events or processes are topographically representable events or processes i.e. which take place in a geophysical territory, the territory being described by a two or three dimensional geometrical map.

31. A system according to one or more of the preceding claims 28 to 30 in which the said geometrical point are the point at which the probability is highest that there will occur further effects generated by the said event or process as a consequence of the development of the event or process described by the said measured values of the parameters at the first and at least at a second time.

32. A system according to one or more of the preceding claims

28 to 31 in which the determination of the said geometrical point is carried out according to the following steps:

Defining a n-dimensional array of points in the said n-dimensional space and determining the geometrical point as the geometrical points for which it is a minimum the sum of the rests of the divisions of the distance of each point of the grid with the distances that each geometric point has from each one of the entity points.

33. A system according to one or more of the preceding claims 28 to 32 in which the space is a three or in a two dimensional space and the array of points is a two or three dimensional array of points.

34. A system according to one or more of the preceding claims 28 to 33 in which the space is divided in voxels or pixels respectively for a three or for a two dimensional space, the array of points being the said array of pixels or voxels.

35. A system according to one or more of the preceding claims 28 to 34 in which for a two dimensional application the coordinates of the said geometrical point called Harmonic Centre is determined as the geometrical point whose distances from the points representing measured parameters at a certain time, so called assigned Entities, minimize the sum of the remainders of their reciprocal divisions.

36. A system according to one or more of the preceding claims 28 to 35 in which in a two dimensional space represented as an array of pixels the following equations describes the said harmonic point:

dHarmonic = arg

Where

N = Number of points relating to measured parameters, also called entity points;

M = Number of pixel points i.e. the points of the array of points.

A = set of assigned points

P = set of pixel points

e {l, , ,N}

k e {l,2, M}

C = big integer positive constant; D = Euclidean distance

= harmonic distance = linear scaling between I ' J

37. A system according to one or more of the preceding claims 28 to 36 in which the whole space is transformed into a Harmonic scalar field, where each geometrical point presents a specific Harmonic value.

38. A system according to one or more of the preceding claims 29 to 38 in which a segmentation of the whole space into a certain number of classes with different degree of Harmony, in relation with the assigned Entities is carried out.

39. A system according to one or more of the preceding claims 28 to 38 in which the segmented harmonic scalar field is represented by a two dimensional image in which the geometric points which are of the same class are indicated by means of an identical color or shade of a color which is different from the other colors or shades used for representing the pixels assigned to the other classes.

40. A method according to claim 35 in which the Harmonic field se mentation is carried out according to the following equations:

AT ' ^k

^I k=l,keP

dH_k G H_Max dH_k > H_Max

d _k e H_High dH_N < dH_k≤H_Max dH^ H^ dH_M < dH_k≤ dH_N H_k < dH_M

Where further to the above definitions the following definitions are valid: dH

^N is the harmonic distance mean of the entity points (assigned points); dH_{M js t}^_{e narmon}j_C distance mean of the Pixel points, i.e. the points of the array of points;

dH MA Y

^{ΜΛΛ ν} is the Minimal harmonic distance among the entity points (assigned points);

^Max is the set of points with maximum harmony; H^igh is the set of points with high harmony; is the set of points with low harmony;

H ^Nu" is the set of points with Null harmony;

and considering four different level or classes which are defined mathematically above.

41. A system according to one or more of the preceding claims

28 to 40 in which time is set equal to one of the dimensions of the space in which the process or event is represented as a map.

42. A system according to one or more of the preceding claims

28 to 41 in which the method is used for verifying the reliability of possible features of a process or event which have been determined in a different way.

43 A method for determining features of events or processes having a dynamic evolution in space and/or time using measurements of values of parameters describing a process which can calculate the most probable consequences of the event or process at a certain time, the method comprising the following steps: Defining a set of parameters describing the effects of the event or process which can be measured and are characteristic of the said event or process.

The values of the said parameters being measured at a certain time;

determining as a function of the measured values of the characteristic parameters describing the event or process at the said certain time a geometrical point in the said n-dimensional space which geometrical point is the point of accumulation of forces generated by the evolution of the event of process in time;

44. A method according to claim 43, which method comprises the features of one or more of the preceding claims 28 to 42.

45. A system according to one or more of the preceding claims comprising a software program which can be loaded and executed by a hardware processing unit which program provides the said hardware unit to process input data according to a method for reconstructing a causation process from time varying data describing an event

the method describing the more likelihood transition of all entities i, j from the time n to the time n+1 as a function of the position coordinate of the entity I and of the entity j and the quantity of the at least one feature of the entity I and of the entity j at the time n and at the time n+1 : the said function determining the strength of the connection between each entity i at time n and each other entity j at time n+1 ;

the said method determining the source causing changes in quantity of the entity j from the time n to the time n+1 as the entity i for which the strength of connection is a maximum.

46. A system according to claim 45 in which the method steps are applied for each step from a time n to a time n+1 of the value of at least one quantity determined at each time instant of a sequence of time instants.

47. A system according to claim 45 or 46 in which for each time step from time n to time n+1 , a data matrix is generated in which each element is the strength of the connection of each entity i at time n to each entity j at time n+1.

48. A system according to claim 47 in which from a data matrix of the strength of the connections a data matrix of the presence of a directed link is generated in which each element represents the presence value 1 or absence value 0 of a connection between en entity I at time n and an entity j at time n+1 and in which the said value 0 or 1 is given by determining the maximum strength among the strength of connection of each one of the entities i and one entity j.

49. A system according to claim 47 or 48, in which the strength of the connection between a so called source entity i at time n and a destination or target entity j at time n+1 is determined according to the followin function:

Where

^Ί' , ^¾l are respectively the quantity in source place (entity i) at time n and the quantity inn source place (entity i) at time n+1 ;

¹ , ^J are respectively the quantity in destination place (entity j) at s time n and the quantity in destination place (entity j) at time n+1 ;

d. .

l^,J is the distance between the source (entity i) and the destination (entity j) in the space or map;

a is a tuned parameter connected to distance; is the strength of directed connection between source (entity0 i) at time n and destination (entity j) at time n+1.

50. A system according to claim 49 in which a matrix of the strength of connection can be constructed from the data of the strength of connection obtained from equation

51. A system according to claim 49 in which the selection of the5 strongest connection for determining which source entity i has caused the changes in the quantity of the destination entity j in the time step from time n to time n+1 is determined as follows from

Where ArgMax is the maximum of the argument of the function i i Win i

'^J and ^,J determines this maximum among the strength of connection of the source entities i for each different destination entity j and the entity i for which the strength of connection is maximum to a certain entity j is considered as the entity by which the event at entity j determining the changes in the value of the quantity at entity j from time n to time n+1 has been caused.

o[n,n+l]

Win i

52. A system according to claim 51 , in which from ^,J a numerical value of presence/absence of a directed link between a source entity i at time n and a destination entity j at time n+1 can be determined by the following equations:

Where

The definition Win relates to the ith entity for which the equation

S Win",j = Arg oMax{ isl i,"j:"^+l]} ) _{js va|jd}

£>[n,i+l]

^,,J is defined as the function indicating the presence of a link between a source entity I at time n and a destination entity j at time n+1.

53. A system according to claim 52 in which a matrix is generated from the values , which matrix has values 1 for the elements I, j for which the entity i satisfying the equation ^,J ' for a destination entity j and zero values for all the entities i for which the said equation is not true.

54. A method according to claim 49 in which the results of the equation

are extended to the entire map by determining out of the values a scalar field

55. A system according to claim 54 in which the scalar field is given by the potentiality (U) of each point of the surface to influence the other point of the surface of the map and to be influenced is determined by the following equation:

Where

P_k

x^,y is the k-th point P in the map with the coordinate x, y in the map and where

56. A system according to one or more of the preceding claims for predicting the evolution dynamics of an event or process starting from the information about the causation process which comprises the following steps:

The said data comprising for each of the said entity i, j and for at least one of the features the quantity or value at different time instants n of a sequence of time instants comprising N time steps;

£»[n,n+l] destination entity j at time n+1 and the connection matrix ^l,J , i.e. the matrix of absence or presence of a link between a source entity i at time n and a destination entity j at time n+1 ;

Where

Where are respectively the quantity in source place (entity i) at time n and the quantity inn source place (entity i) at time n+1 ;

q ^J["^] , g ^J[n+]] are respectively the quantity in destination place (entity j) at time n and the quantity in destination place (entity j) at time n+1 ;

d. .

^, is the distance between the source (entity i) and the destination (entity j) in the space or map;

a is a tuned parameter connected to distance; is the strength of directed connection between source (entity i) at time n and destination (entity j) at time n+1.

And where the elements of the connection matrix ^l'^J for each time step is determined from the strength of connections for each time step according to the following steps

presence/absence of a directed link between a source entity i at time n and a destination entity j at time n+1 is determined by the following equations:

Generating a new dataset by joining the data of the connection matrix of all the N time steps of the sequence of time instants;

57. A system according to claim 56, in which the new dataset is generated by joining an rewriting the connection matrices

a moving windows where each connection vector x of each place P of the entity at the time n points out to the connection vector x of the same place P at tim

New Dataset:

Where P is the number of places where the entities are

N is the number of time steps

58. A system according to claim 56 or 57 in which the predictive algorithm is a Artificial Neural Network ANN with the following model: x(n) - x(n + 1) = / (x(n), w^*) + ε

Where ^ is the weight matrix of the trained Artificial Neural Network which approximate the optimal parameters to model the global temporal process obtained by the known connection matrices so defining the local laws of the process itself.

59. A system according to claim 58, in which for the training set and the testing set of the artificial neural network each record of the said training and testing set from the new database is composed by P+1 input variables consisting in:

the connectivity values (1/0) of each entity from the time (n) to the time (n+1 ) according to the corresponding connection matrix and the connectivity values (1/0) of each entity from the time (n+1 ) to the time (n+2) according to the corresponding connection matrix

while none of the sets has the same input vector but a different target vector.

60. A method for reconstructing a causation process from time varying data describing an event

61. A Method according to claim 60, which method has the features of one or more of the preceding claims 45 to 55.

62. A system according to one or more of the preceding claims and which system provides a software program for carrying out a processing method for determining implicit hidden features of phenomena which can be represented by a point distribution in a space which method comprises the following steps:

Defining a set of first parameters describing the effects of the phenomenon such as an event or process which first parameters can be measured and are characteristic of the said event or process,

63. A system according to claim 62 in which an array of generic points in the d-dimensional space is defined and in which array the points are equally spaced one from the other along each of the d-dimensions and at each step the minimum spanning tree is calculated for a distribution of points comprising the first points and one of the points of the said array of generic points;

the generic point of the array for which the smallest minimum spanning tree results is then taken as the further unknown implicit point or parameter and added to the set of the first points forming an amended set of first points;

this amended set of first points is then used for repeating the above steps;

the said steps are repeated cyclically until no further generic point of the remaining points in the array is found fro which a smaller MST can be computed as the one computed in the last step.

64. A system according to claim 63, in which at every step the further point determined in the previous step is maintained and the new MST is determined using all the first points and the each one of the further points added in each one of the preceding steps of the sequence of steps.

65. A System according to one or more of the preceding claims claim 62 to 64 in which at each step the minimum spanning tree is determined according to the following algorithm:

find an acyclic subset T of E that connects all of the vertices V in the graph and whose total weight is minimized, where the total weight is given by

T is called spanning tree, and MST is the T with the minimum sum of its edges weigthed. Mst = Min{d(T)}

And the number of its possible tree is :

T = v^v~2

da

Here ^,J is the Euclidean distance of each point i from each point j; d(T) is the length of sum of the edges.

V are the vertices, i.e. the points in the map.

66. A System according to one or more of the preceding claims claim 62 to 65 in which the d-dimensional space of the map is quantized in pixels or voxels, and a certain minimum pixel or voxel distance is defined.

67. A method for determining implicit hidden features of phenomena which can be represented by a point distribution in a space which method comprises the following steps:

68. A method according to claim 67, which method comprises the features of one or more of the claims 62 to 67