WO2016031174A1 - シミュレーション装置、シミュレーション方法、および、記憶媒体 - Google Patents
シミュレーション装置、シミュレーション方法、および、記憶媒体 Download PDFInfo
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- G06F30/20—Design optimisation, verification or simulation
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01W—METEOROLOGY
- G01W1/00—Meteorology
- G01W1/10—Devices for predicting weather conditions
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/17—Function evaluation by approximation methods, e.g. inter- or extrapolation, smoothing, least mean square method
- G06F17/175—Function evaluation by approximation methods, e.g. inter- or extrapolation, smoothing, least mean square method of multidimensional data
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis
Definitions
- the present invention relates to a simulation technique for mathematically modeling phenomena and hypothetical situations occurring in the real world and calculating them numerically on a computer.
- Simulation is a mathematical model of a phenomenon or hypothetical situation that occurs in the real world and numerically calculated on a computer.
- time and space can be freely set and calculated.
- By such a simulation it is possible to predict a situation where it is difficult to obtain an actual result (for example, a situation in a place where observation is difficult) or a situation that may occur in the future.
- an actual result for example, a situation in a place where observation is difficult
- a situation that may occur in the future for example, a situation in a place where observation is difficult
- simulation results can be used as indicators for theoretical clarification of causal relations, design, planning, and the like.
- simulation is effective when you want to grasp and understand the state continuously over a wide area in a situation where the number of observation data actually obtained is small and the distribution is spatially and temporally biased.
- the simulation is merely a mathematical simulation of reality, its accuracy depends on how well the reality is understood and faithfully simulated. Therefore, when the actual observation data is small as described above and the phenomenon is incompletely understood, the model includes imperfections.
- the calculation is performed discretely, in order to grasp continuously over a wide area, it is necessary to subdivide the target region and perform a large amount of calculation.
- incomplete calculation conditions must be set according to the allowable calculation time and computer resources. These imperfections degrade the accuracy of the simulation.
- Data assimilation is known as a mechanism for improving the accuracy of simulation under such imperfect conditions.
- Data assimilation is a method of incorporating observation data obtained in reality into numerical simulation. Even when simulations using the same mathematical model are used, various results appear depending on the above-described inherent imperfections, given initial conditions, boundary conditions, and the like. Data assimilation searches the simulation results for the best explanation of observation data obtained in reality, and simultaneously updates the model and conditions.
- a weather prediction device described in Patent Document 1 uses precipitable water data by a GPS receiver that is installed many on the ground and can be observed frequently, wind direction and wind speed data by Doppler radar, and rainfall intensity data by radar AMeDAS. And this weather prediction apparatus takes in these data measured in real time or near real time, and assimilates data by a three-dimensional variational method. Further, as another related technique for dealing with such a problem, a synchronization device and a meshing device described in Patent Document 2 are known.
- this synchronizer When the data from multiple observers are asynchronous, this synchronizer is synchronized to show the observation data at the same time by reconstructing these observation data on the time axis by interpolation processing. To do.
- this meshing device rearranges the synchronized observation data of a plurality of points so as to be positioned on mesh points (lattice points) at regular distance intervals in the horizontal space in the target area.
- Patent Document 3 describes the soil salinity and drainage in the coastal area after the tsunami occurrence, the soil moisture index value for each satellite image of the three periods before, immediately after, and several months after the tsunami occurrence. An example of estimation based on change is described.
- Patent Document 4 describes an example of a method for performing yield prediction of a paddy rice field in a wide area using a satellite SAR image and a crop yield prediction model with low labor and high accuracy in the first half of the growing season. ing.
- a satellite-mounted optical sensor that observes the intensity of reflected sunlight in the visible or near-infrared region is greatly affected by the weather, such as being unable to observe in the presence of clouds. Therefore, this technique uses SAR image data in a microwave (X band: wavelength 3.1 cm) that is not affected by clouds.
- yield prediction is performed by obtaining a yield prediction formula by regression analysis from the correlation between the obtained SAR image data and the amount representing the growth state of the crop such as the plant height and the number of stems.
- mathematical models may be used for analysis of observation data, although it is different from real-world simulation.
- an application where it is determined whether or not an object exists within a predetermined area using a millimeter wave radar or the like, it is difficult to make an accurate determination using only observation data. This is because, especially when the object is a pedestrian, the reflection intensity of the radar is very small (the SN ratio: signal to noise ratio is small), and the reflection intensity varies from moment to moment with various posture changes of the pedestrian. Because it changes.
- a technique described in Patent Document 5 is known. In this method, a feature amount model of a pedestrian signal or a noise signal is created in advance from the distribution of the reflection intensity with respect to the detection position of the object.
- Patent Document 5 also describes a technique for integrating the probabilities of a plurality of states obtained from a plurality of sensors for various states that are present, absent, and unknown.
- Patent Document 1 describes an abnormal value removing device that removes abnormal values after obtaining observation data.
- This abnormal value removing apparatus determines that observation data having a difference of a certain level or more compared with a calculated value by a weather model at the same time is an abnormal value.
- this abnormal value determination based on local information of model calculation values, it is not possible to take into account rapidly changing states or unique environments / phenomena.
- the related technique described in Patent Document 5 integrates the observation data with the model after stochastic integration, and therefore estimates various states based on more information, including the possibility of specificity. Is possible.
- this related technique mainly uses a general weighted average as a probability integration method, and has a problem that the target is limited to observation data of the same type and the same dimension.
- this related technique has a problem that it does not consider a mechanism that enables determination and correction of the integration result.
- Patent Document 3 describes a method for estimating a land state by integrating satellite images from three different periods. However, Patent Document 3 does not mention a countermeasure when the satellite data cannot be acquired at an optimal time or when the data shows a specific value due to the influence of water accumulated on the soil surface.
- the related techniques described in Patent Documents 2 and 3 do not consider observation data having some discontinuity or specificity. Further, the related technology described in Patent Document 4 does not use optical sensor data whose ideal observation data acquisition time interval is unstable due to the influence of the climate, and prioritizes the certainty of data acquisition. Used. And since this related technology creates a yield prediction model recursively from the data obtained in this way, it generates an inappropriate model when there is discontinuity or specificity in the data. There is a concern that.
- FIG. 15 is a schematic diagram for explaining a simulation using typical data assimilation.
- the horizontal axis represents a time change
- the vertical axis represents an observed value.
- the observed value is a value actually measured by a sensor or the like.
- the state variable is a variable for calculating the time evolution on the simulation model.
- the observed value is not necessarily a true value of the target quantity because it is affected by the observation frequency and sensor accuracy. Therefore, in FIG. 15, this unknown true value is virtually represented by a broken line.
- observation value is related by the state variable and the observation model, the observation value can be simulated by calculating the time change of the state variable.
- the simulation it is difficult for the simulation to reproduce the true value when the incompleteness inherent in the model, the given initial condition, and the boundary condition are uncertain. Therefore, data assimilation is intentionally disturbed and stochastically simulated, and from the various simulation results obtained, the one that best explains the observation data actually obtained is searched.
- this process is schematically represented by solid lines representing a plurality of calculated values (simulations). Each simulation continues with the value corrected by the observed value as the initial value of the next step. As is clear from FIG.
- an object of the present invention is to provide a technique for performing high-resolution and high-accuracy simulation over a wide area while considering non-ideal observation data and observation data with discontinuity or specificity.
- the simulation apparatus of the present invention is based on the initial state and parameters of the state vector in the simulation and input means for acquiring a plurality of observation data as inputs, and based on the initial state and parameters.
- a system model for simulating the time evolution of a state vector, and a data selection processing means for selecting a plurality of observation data to be used from among the plurality of observation data based on information related to the state vector in the system model, and a selection A plurality of observation models respectively corresponding to the plurality of observation data, wherein a plurality of state vectors output from the system model are converted and output based on the relationship between the observation data and the state vectors.
- An observation model and the plurality of observation models A posterior distribution of the state vector is generated based on the output state vector and the observation data selected by the data selection processing means, and a posterior distribution based on all the observation data selected by the data selection processing means Integrating the first posterior distribution and the second posterior distribution, the posterior distribution generating means for outputting the posterior distribution based on one or more missing observation data as the second posterior distribution and outputting as one posterior distribution Posterior distribution integrating means, determining means for determining which of the second posterior distribution and the integrated posterior distribution to be used, the posterior distribution determined by the determining means, and the first posterior distribution Output means for inputting a state vector to the system model and outputting a time series of the state vector.
- the simulation method of the present invention when the initial state and parameters of the state vector in the simulation and a plurality of observation data are input, the time of the state vector using the system model based on the initial state and parameters.
- Simulation of development based on information related to the state vector in the system model, select a plurality of observation data to be used from among the plurality of observation data, a plurality of corresponding to each of the selected plurality of observation data
- the observation model select a plurality of observation data to be used from among the plurality of observation data, a plurality of corresponding to each of the selected plurality of observation data
- the state vector output from the system model is converted based on the relationship between the observation data and the state vector, respectively, and the state vector output from the plurality of observation models and the selected one
- the state vector A posterior distribution is generated, and the first posterior distribution based on all selected observation data and the second posterior distribution based on one or more missing observation data are integrated, and the second posterior distribution and the integration are integrated. Deciding which of the subsequent posterior distributions to use
- the storage medium of the present invention uses the input step of acquiring the initial state and parameters of the state vector in the simulation and a plurality of observation data as inputs, and the system model, based on the initial state and parameters.
- a system model calculation step for simulating the time evolution of a state vector; and a data selection processing step for selecting a plurality of observation data to be used among the plurality of observation data based on information related to the state vector in the system model; , Using a plurality of observation models respectively corresponding to the selected plurality of observation data, and converting and outputting the state vectors output from the system model based on the relationship between the observation data and the state vectors, respectively.
- An observation model calculation step A posterior distribution of the state vector is generated based on the state vector output from the number of observation models and the observation data selected in the data selection processing step, and all the observation data selected in the data selection processing step are Generating a posterior distribution as a first posterior distribution and outputting a posterior distribution based on one or more missing observation data as a second posterior distribution; the first posterior distribution and the second posterior distribution; A posterior distribution integration step of integrating the posterior distribution, a determination step of determining which of the second posterior distribution and the posterior distribution after integration is used, the posterior distribution determined in the determination step, and the first An output step of inputting a state vector consisting of a posterior distribution of the state vector to the system model and outputting a time series of the state vector Stores a computer program for causing a computer to execute the device.
- the present invention can provide a technique for performing high-resolution and high-accuracy simulation over a wide area while considering non-ideal observation data and observation data with discontinuity or specificity.
- the simulation apparatus 100 can be applied to a simulation that follows time evolution by solving a partial differential equation of continuous time and space based on a physical law.
- partial differential equations include, for example, a motion equation describing motion, a Navier-Stokes equation describing fluid, a thermodynamic equation describing thermal change, and a shallow water equation describing tsunami.
- the simulation apparatus 100 can also be applied to a simulation using a finite element method.
- the system to be simulated is a system in which a state vector that follows a time change is connected to actual observation data by some relational expression, that is, a system in which simulation results and observation data can be compared. It shall be.
- a simulation apparatus 100 includes a system model 21, a data selection processing unit 30, m observation models 31 (first observation model 31-1 to m-th observation model 31-m), and posterior distribution.
- a generation unit 40, a posterior distribution integration unit 50, and a determination unit 51 are provided.
- the simulation apparatus 100 includes an input unit 10 and an output unit 60.
- m is an integer of 2 or more and M or less, and M is an integer of 2 or more.
- the simulation apparatus 100 includes a prior distribution storage unit 22, a first posterior distribution storage unit 41 a, and a second posterior distribution storage unit as storage areas for data input / output between the functional blocks. 41b and the integrated posterior distribution storage unit 52.
- the prior distribution storage unit 22 constitutes an embodiment of a part of the system model of the present invention.
- the first posterior distribution storage unit 41a and the second posterior distribution storage unit 41b constitute an embodiment of a part of the posterior distribution generation unit of the present invention.
- the integrated posterior distribution storage unit 52 constitutes an embodiment of a part of the posterior distribution integration unit of the present invention.
- a simulation apparatus 100 includes a CPU (Central Processing Unit) 1001, a RAM (Random Access Memory) 1002, a ROM (Read Only Memory) 1003, a storage device 1004 such as a hard disk, an input device 1005, and an output.
- the input unit 10 includes an input device 1005 and a CPU 1001 that reads a computer program stored in the ROM 1003 or the storage device 1004 into the RAM 1002 and executes it.
- the system model 21, the data selection processing unit 30, the observation model 31, the posterior distribution generation unit 40, the posterior distribution integration unit 50, and the determination unit 51 are configured as follows.
- these functional blocks are constituted by a CPU 1001 that reads a computer program stored in the ROM 1003 or the storage device 1004 into the RAM 1002 and executes it.
- the output unit 60 includes an output device 1006 and a CPU 1001 that reads a computer program stored in the ROM 1003 or the storage device 1004 into the RAM 1002 and executes the computer program.
- the hardware configuration of the simulation apparatus 100 and each functional block thereof is not limited to the above-described configuration.
- the input unit 10 acquires the initial state and parameters of the state vector of the observation region handled in the simulation, and M types of observation data (first to Mth observation data).
- each of the M types of observation data is an observation value by a sensor or the like.
- each of the M types of observation data may have a different dimension or the same as some or all of the other observation data.
- the input unit 10 may acquire these pieces of information stored in the storage device 1004.
- the input unit 10 may acquire the information by acquiring the storage position information of the information in the storage device 1004 via the input device 1005.
- the system model 21 simulates the time evolution of the state vector based on the initial state and parameters acquired by the input unit 10.
- the time evolution of the actual phenomenon of interest is represented by a partial differential equation of continuous time / space, but in order to carry out the simulation, the region to be simulated is discretized in time / space.
- a state vector composed of a set of state variables is used in order to follow the time evolution of an actual phenomenon in the observation region.
- the number of state variables may be determined according to the purpose of the simulation, and may be any number.
- the discretization over time is realized by determining the state variable ⁇ t + 1 at time t + 1 by proceeding one step from the state variable ⁇ t at a certain time t.
- the time indicates one step in the simulation, and for example, time t ⁇ 1 means one step before time t.
- the steps in the simulation are also referred to as time steps.
- ⁇ represents various parameter vectors necessary for calculation of the model.
- V t represents system noise at time t. System noise V t in order to represent the effect of the imperfections in the model numerically, are introduced as a stochastic driving term act on the state vector.
- the mapping f may be linear or non-linear depending on the target phenomenon.
- the state vector X t at the time t need not be explicitly defined by the state vector X t-1 at the time t ⁇ 1. That is, the system model 21 of the present embodiment, as an input state vector X t-1 at time t-1, it is sufficient computing a state vector X t at time t.
- the probability distribution p (X t) of the state vector X t at time t is, N pieces of ensembles ... (5) Is approximated by
- the calculation of the ensemble represented by the equation (4) is characterized in that it is independent for each ensemble. Therefore, the system model 21 may be repeatedly calculated N times, or may be calculated at once by N parallel computers, and the calculation method can be flexibly changed according to the calculation resource. In the following, it shows the probability distribution of the state vector X t and p (X t), also referred to as a prior distribution.
- the probability distribution of the state vector at time t-1 p (X t- 1), the probability distribution p of the state vector at time t (X t ) can be calculated. Further, the system model 21 outputs the calculated probability distribution p (X t ) as a prior distribution to m observation models 31 described later. For example, the system model 21 may store the calculated prior distribution p (X t ) in the prior distribution storage unit 22 that can be read by the m observation models 31.
- the data selection processing unit 30 selects m types of observation data to be used among the first to Mth observation data based on information related to the state vector.
- the data selection processing unit 30 then outputs the selected m types of observation data to the posterior distribution generation unit 40 described later.
- control signal CTL0 information related to the state vector is input from the system model 21 to the data selection processing unit 30 as the control signal CTL0.
- Control signal CTL0 for example, the number of dimensions of the state vector X t and may include such other information about the state variables.
- the data selection processing unit 30 selects m types of observation data OBS 1 to OBS m to be used at time t. Then, the data selection processing unit 30 outputs the selected observation data OBS 1 to OBS m to the posterior distribution generation unit 40.
- the data selection processing unit 30 compares the state vector set in the system model 21 and information (for example, physical quantities and dimensions) regarding each observation data, so that m pieces respectively corresponding to the selected m kinds of observation data.
- the observation model 31 may be generated.
- the generation of the observation model 31 is to generate an observation model equation that relates the state vector Xt and the observation data OBS 1 to OBS m .
- the relationship between these state vectors and the observation data is schematically shown in FIG.
- An observation model expression representing such a relationship is expressed by, for example, the following expression (6). ... (6)
- the data selection processing section 30, (6) Information of the mapping h 1 ⁇ h m and the noise amount w 1 ⁇ w m to consider observational data in the expression, as the control signal CTL1 ⁇ CTLM, observation model 31 -1 to 31-m may be output. Thereby, m observation models 31 are generated.
- the noise amounts w 1 to w m and the observation data OBS 1 to OBS m in the equation (6) are assumed to be L-dimensional if the observation data is ideally obtained at all the lattice points 1 to L, respectively. It becomes a column vector.
- the data selection processing unit 30 may set the noise amount of the observation model 31 corresponding to the observation data based on the variance value and the noise amount of each observation data.
- the matrix E 2 is represented by a matrix in which the elements of the row corresponding to the lattice points that were not observed in Expression (7) are changed to zero.
- the dimension on which h 2 acts on the left side is smaller than L, and is the same dimension as the observation data OBS 2 .
- the expression (7) represents the ⁇ 1 + J (j ⁇ 1) ⁇ column in the j-th row.
- the matrices E 1 to E m can be expressed regardless of the number of state variables.
- the mapping h 1 ⁇ h m in equation (6) depending on the relation of the state variables and the observation data may be a linear or non-linear. Therefore, for example, in the case of the j-th observation model 31-j, the calculation represented by the equation (6) is performed when the state vector X t at the time t calculated by the equation (4) is input. ... (8) Can be output.
- the observation model 31 of all m species performs the operation of each (8) with respect to the state vector X t, the transformed state vector X t of the total m species, and outputs it to the posterior distribution generating unit 40.
- the group of (2) Formula or (4) Formula and (8) Formula is called a state space model.
- E 1 to E m it is assumed that the lattice point (L dimension) of the system model 21 matches the lattice point (L dimension) of the observation model. It is also assumed that no.
- the value of each element may be changed so that the observation points where the observation data is actually obtained are, for example, the weighted average or the weighted average of the values of neighboring grid points.
- E 1 to E m described above represent the state variable lattice points and the resolution of the observation points of the plurality of observation data for each observation data by one-to-one, weighted average, or weighted sum. Represents the relationship to
- the m observation models 31 correspond to m observation data selected by the data selection processing unit 30, respectively.
- Each observation model 31 converts the state vector output from the system model 21 into a predetermined state vector based on the equation (8) representing the relationship between the observation data and the state vector.
- Each observation model 31 outputs the converted state vector to the posterior distribution generation unit 40.
- State vector converted has a prior distribution of the m kinds of transformed state vector X t at time t.
- the posterior distribution generation unit 40 generates a posterior distribution of the state vector based on the state vector output from the m observation models 31 and the observation data selected by the data selection processing unit 30. Then, the posterior distribution generation unit 40 sets the posterior distribution based on all the m types of observation data selected by the data selection processing unit 30 among the generated posterior distributions as the first posterior distribution. Further, the posterior distribution generation unit 40 sets the posterior distribution based on the observation data missing one or more of the m types of observation data selected by the data selection processing unit 30 as the second posterior distribution. Further, the posterior distribution generation unit 40 outputs the generated first posterior distribution and second posterior distribution to the posterior distribution integration unit 50 and the like.
- the posterior distribution generation unit 40 may store the generated first posterior distribution in the first posterior distribution storage unit 41a that can be read by the posterior distribution integration unit 50 or the like. Further, the posterior distribution generation unit 40 may store the generated second posterior distribution in the second posterior distribution storage unit 41b that can be read by the posterior distribution integration unit 50 or the like. The posterior distribution generation unit 40 also outputs the generated first posterior distribution to the system model 21 and the output unit 60. In this case, for example, the posterior distribution generation unit 40 may store the generated first posterior distribution in the integrated posterior distribution storage unit 52 that can be read by the system model 21 and the output unit 60.
- the posterior distribution generation unit 40 is input with m types of X t prior distributions at time t and observation data OBS 1 to OBS m .
- y) when the prior distribution p (x) and the distribution p (y) of the observation data are input is obtained from Bayes' theorem as follows: ... (9) It is expressed.
- x) of the numerator is called a likelihood that is an index of the degree of fit of the state variable x to the observed value y.
- x) can be separated into the mapping h and the noise amount w as shown in the equation (8). ... (10)
- the quantity calculated by can be used.
- r is a density function of the noise amount w.
- the right side is redefined as a function LH using y and h (x).
- y 1: 0 , x) of one item in the equation (11) is a probability of y 1 when there is no observation data, that is, x of y when y 1 is obtained.
- y 1: 1 , x) is the probability of y 2 when y 1 is obtained.
- each observation data is acquired by a different sensor or the like, and there is no simultaneous distribution of y 1 and y 2 . Therefore, the second term results in the likelihood p (y 2
- the denominator Z is a normalization constant. Using this relationship, since the posterior distribution of the state variable U k at the lattice point k is expressed as p (U k ), m types of observation data y are obtained as OBS 1 to OBS m . ... (13) It is expressed.
- the numerator is the product of the likelihood product of each observation data and the prior distribution p (U k ), as expressed by equation (12). Furthermore, since each likelihood is expressed by equation (10), the posterior distribution of equation (13) is (14) It is expressed.
- the posterior distribution generation unit 40 calculates m kinds of likelihoods, which are calculated from the m observation data OBS 1 to OBS m and the mappings h 1 to h m , based on the posterior distribution of the state variable Uk at the lattice point k. Calculated from LH and prior distribution p (Uk). Similarly, the posterior distribution generation unit 40 calculates the posterior distribution with respect to all of the lattice points 1 to L by the expression (13), that is, the expression (14).
- the posterior distribution generation unit 40 uses the following equation (15) instead of the equation (13) for lattice points that are missing at one or more points among the m types of observation data. For example, as in the case of OBS 2 shown in FIG. 3, observation data may be obtained only at some lattice points. In this case, the posterior distribution generation unit 40 cannot calculate the product of likelihoods for all the observation data represented by the numerator of equation (13). For example, assuming that only m ⁇ 1 types of observation data can be obtained at the lattice point k ′, the posterior distribution is ... (15) That is, ... (16) And the number of likelihoods constituting the numerator is reduced to m-1. In the equations (15) and (16), “m ⁇ 1” indicates that at least one observation data out of the m species is not obtained, and is not obtained (missing). ) The number of observation data is not limited to one.
- the posterior distribution generation unit 40 generates a posterior distribution for each lattice point for each state variable.
- the posterior distribution for each grid point for each state variable is also referred to as the posterior distribution for each state variable / grid point.
- the posterior distribution generation unit 40 outputs the posterior distribution calculated using the expression (13) based on all the observation data as the first posterior distribution.
- the posterior distribution generation unit 40 outputs the posterior distribution calculated using the equation (15) from the observation data lacking at least one of the m types as the second posterior distribution.
- a certain prior distribution p (x) follows a normal distribution having an average ⁇ 0 and a variance V prio , and n observation values y 1 , y 2 ,. . . y n the average mu, assumed to follow a normal distribution of variance V.
- y) calculated by Bayes' theorem (9) is also a normal distribution, and the variance V post is ... (17) It is expressed. From this, it can be seen that the greater the number of observations used in the calculation of the posterior distribution, the smaller the variance, that is, the more accurate the posterior distribution.
- each of the first and second posterior distributions is not necessarily a normal distribution, but the second posterior distribution has a smaller number of acquired observation data than the first posterior distribution. Therefore, the variance of the first posterior distribution p (U k
- the posterior distribution integration unit 50 calculates a new posterior distribution by integrating the first posterior distribution and the second posterior distribution for each state variable / grid point for which the second posterior distribution is calculated. To do. Further, the posterior distribution integration unit 50 outputs the new posterior distribution after integration to the determination unit 51. In the present embodiment, since the posterior distribution is approximated by a set of ensembles, the posterior distribution integration unit 50 calculates an ensemble that approximates the first posterior distribution and an ensemble that approximates the second posterior distribution as a predetermined number. What is necessary is just to integrate by overlapping in a ratio.
- the posterior distribution integration unit 50 acquires the above-described first posterior distribution and second posterior distribution as inputs from the first posterior distribution storage unit 41a and the second posterior distribution storage unit 41b.
- OBS 1: m ⁇ 1 ) is at least one p (U k
- Dispersion is larger than m ) (ie, the accuracy is low). Therefore, the posterior distribution integration unit 50 integrates the first posterior distribution and the other second posterior distributions for each state variable / grid point for which the second posterior distribution is calculated, and calculates a new posterior distribution. .
- the posterior distribution integration unit 50 calculates a new posterior distribution p ′ (U j
- ⁇ represents a parameter set that determines the function g.
- k represents a lattice point where the first posterior distribution is generated.
- I represents another lattice point where the second posterior distribution is generated. Note that i ⁇ j.
- the dash (′) of the probability distribution p ′ in the equation (19) indicates that it is a probability distribution after integration in the posterior distribution integration unit 50.
- the posterior distribution integrating unit 50 newly calculates the posterior distribution p ′ (U j
- the determination unit 51 determines which one of the second posterior distribution and the integrated posterior distribution is used. Specifically, the determination unit 51 uses which of the original second posterior distribution and the integrated posterior distribution as the posterior distribution for the state variable / grid point for which the second posterior distribution is generated. To decide. Specifically, the determination unit 51 may store the determined posterior distribution in the integrated posterior distribution storage unit 52.
- the integrated posterior distribution storage unit 52 stores the first posterior distribution as described above. As a result, the integrated posterior distribution storage unit 52 stores the first posterior distribution or the determined posterior distribution for each state variable / grid point.
- the determination unit 51 may determine which to use based on each variance value of the second posterior distribution and the posterior distribution after integration. Specifically, the determination unit 51 includes the post-integration posterior distribution p ′ (U j
- the determination unit 51 determines that the variance of the posterior distribution after integration is smaller than the variance of the original second posterior distribution. Until this is true, the calculation may be repeated by changing the parameter ⁇ of the function g in the equation (19). For example, when the function g is a weighted average, the determination unit 51 may change the weighting coefficient. Further, the determination unit 51 assumes a certain prior distribution p ( ⁇ prior ) as the parameter ⁇ , and uses the Bayes's theorem (9) with the variance value of the equation (4) as an observation value, thereby minimizing the variance.
- a posterior distribution p ( ⁇ post ) of the parameter ⁇ may be obtained.
- the determination unit 51 selects the posterior distribution after integration and selects the integrated posterior distribution. Save in the storage unit 52. If the variance does not decrease even when the parameter ⁇ is changed, the determination unit 51 selects the original second posterior distribution and stores it in the integrated posterior distribution storage unit 52.
- all the lattice points k at time t are determined by the first posterior distribution and the integrated posterior distribution or second posterior distribution selected by the determination unit 51.
- the output unit 60 When continuing the simulation, the output unit 60 inputs the state vector at the time t, which includes the posterior distribution selected by the determination unit 51 and the first posterior distribution, to the system model 21. Then, the system model 21 calculates a prior distribution at time t + 1, which is the next time step, using the posterior distribution at time t. In addition, the output unit 60 outputs, to the output device 1006 and the like, a time series of state vectors including the posterior distribution and the first posterior distribution selected by the determination unit 51 as a result of the simulation.
- all lattice points k at time t are determined by the first posterior distribution and the integrated posterior distribution or second posterior distribution selected by the determination unit 51.
- the output unit 60 may input the posterior distribution at each state variable / grid point stored in the integrated posterior distribution storage unit 52 to the system model 21 and output the time series.
- the system model 21 determines time steps, lattice points, and state variables for obtaining time evolution in order to perform a discretized simulation in time and space (step S101).
- the time step and the grid point may be based on required accuracy or may be selected appropriately so that the calculation converges.
- the input unit 10 acquires the first to Mth observation data (step S102).
- the data selection processing unit 30 refers to the information on the state variables set in the system model 21, and selects m types of observation data to be used among the first to Mth observation data (step S103). .
- the data selection processing unit 30 sets a relational expression for associating the state variable with the m types of observation data, and the amount of noise included, and generates observation models 31-1 to 31-m (step S104). ).
- the data selection processing unit 30 may set the relational expression and the amount of noise based on the type, nature, physical quantity, observation data, number of dimensions of the state variable, and the like. Thereby, m observation models 31 are generated.
- the simulation apparatus 100 ends the operation at the start of the simulation.
- the input unit 10 acquires an ensemble and parameters indicating the initial state of the state vector, and outputs them to the system model 21 (step S201).
- the system model 21 calculates an ensemble of the next time step, that is, a prior distribution, and stores it in the prior distribution storage unit 22 (step S202).
- the input unit 10 determines whether or not at least one of the first to m-th observation data is obtained at the time of this time step (step S203).
- step S203 the system model 21 executes step S202 again using the prior distribution of the next time step stored in the prior distribution storage unit 22. , Perform a calculation that advances the time step one more time.
- step S203 even if any observation data is obtained, it is determined as No in step S203 even if it is specified that the data is not corrected at this time step.
- the observation models 31-1 to 31-m are stored in the prior distribution storage unit 22. Each prior distribution is converted (step S204).
- step S104 the observation models 31-1 to 31-m that are generated in step S104 at the start of the simulation are basically used.
- the above-described step S104 may be newly executed when the behavior of the observation data changes greatly or when the simulation calculation is not successful.
- step S204 conversion may be performed using the m observation models 31 that are newly generated.
- the posterior distribution generation unit 40 generates a posterior distribution for each state variable / grid point based on the generated m types of converted prior distributions and the m types of observation data at the time of this time step. (Step S205). This corrects the original prior distribution.
- the posterior distribution generation unit 40 determines whether the posterior distribution for each state variable / grid point generated in step S205 is the posterior distribution based on all the m types of observation data selected in step S103, or a part thereof is missing. It is determined whether the posterior distribution is based on the observation data (step S206).
- the posterior distribution generation unit 40 stores the posterior distribution as the first posterior distribution in the first posterior distribution storage unit 41a. (Step S207).
- the posterior distribution generation unit 40 also saves the first posterior distribution in the integrated posterior distribution storage unit 52 as the posterior distribution at the state variable / grid point (step S208).
- this posterior distribution is a posterior distribution based on observation data that is partially missing among the m types of observation data
- the posterior distribution generation unit 40 determines the posterior distribution as the second distribution. And the variance value V0 is calculated (step S209). Then, the posterior distribution generation unit 40 stores the second posterior distribution and its variance value V0 in the second posterior distribution storage unit 41b.
- the posterior distribution integration unit 50 integrates the first posterior distribution and the second posterior distribution for each state variable / grid point for which the second posterior distribution is generated, so that the variance value V is minimized.
- a new posterior distribution (integrated posterior distribution) is calculated (step S300).
- the posterior distribution integration unit 50 repeatedly calculates the posterior distribution after integration using the equation (19) while changing the parameter set ⁇ for the target state variable / grid point. What is necessary is just to search for the minimum ⁇ .
- the posterior distribution integration unit 50 may perform a search using the least square method or the Bayes theorem.
- the minimum value of the found variance is assumed to be Vmin.
- the determination unit 51 compares the minimum variance value Vmin with the variance value V0 before integration (step S301).
- the determination unit 51 sets the post-distribution after integration as a new post-distribution at the state variable / grid point (step S302), and the post-integration post-event.
- the distribution is stored in the distribution storage unit 52 (step S208).
- the determination unit 51 interrupts the integration and sets the second posterior distribution as the posterior distribution at the state variable / grid point (step S303), It preserve
- step S304 the simulation apparatus 100 repeats the operation from step S202. That is, the system model 21 executes step S202 with the posterior distribution of each state variable / grid point stored in the integrated posterior distribution storage unit 52 as input, and starts calculation of the next step.
- step S304 the output unit 60 performs the posterior distribution of each state variable / grid point stored in the integrated posterior distribution storage unit 52.
- the series is output and the simulation operation ends.
- the simulation apparatus performs high-resolution and high-precision simulation over a wide area while considering non-ideal observation data and observation data with discontinuity and specificity. Can do.
- the system model simulates the time evolution of the state vector.
- the data selection processing unit selects m types of M types of observation data.
- m observation models respectively corresponding to m types of observation data transform the prior distribution of the state vector of the next step calculated by the system model based on the relationship between the observation data and the state vector.
- the posterior distribution generation unit generates a posterior distribution for each state variable / grid point based on the converted m types of prior distributions and the selected m types of observation data.
- the posterior distribution generation unit sets the first posterior distribution based on all the m types of observation data among the generated posterior distributions as the first posterior distribution.
- the posterior distribution is 2.
- the posterior distribution integration unit generates a new posterior distribution by integrating the first posterior distribution and the second posterior distribution with respect to the state variable / grid point where the second posterior distribution is generated. Then, the determination unit determines which of the second posterior distribution and the new posterior distribution is to be selected, and sets the determined posterior distribution as the posterior distribution after the integration of the state variables and grid points. This is because the system model calculates the state vector of the next step using the posterior distribution of the state vector consisting of the first posterior distribution and the integrated posterior distribution as input.
- observation data with a low measurement frequency can be corrected in consideration of observation data with a high measurement frequency, so that a more accurate simulation is possible.
- FIG. 6 shows a case where there are two types of observation values (observation value 1 and observation value 2) selected by the data processing unit.
- observation value 1 and observation value 2 different types of observation data can be related to the same type of state variables by using different types of observation models corresponding to the m types of observation data.
- observation model corresponding to observation value 1 is represented as observation model 1
- observation model corresponding to observation value 2 is represented as observation model 2. Note that it is assumed that the observed value 1 is the same type as the observed value in the simulation of FIG.
- an observed value (observed value 1 indicated by ⁇ in FIG. 6) including a lot of inappropriateness or error is obtained as compared with the related technology of FIG.
- the present embodiment can correct the simulation value of the observed value 1 in consideration of the other observed value 2 by integrating the posterior distribution. Observed observation value 1 is no longer used for correction. For this reason, this embodiment can prevent an increase in error.
- the present embodiment is a simulation that uses a plurality of types of observation data, even if the observation data has a small amount of data or has a spatially and temporally biased distribution. Can be made to have high resolution and high accuracy over a wider area. In the future, it is expected that a large amount of observation data will be gathered in a wider variety by gathering information from a large amount of sensors such as M2M (Machine-to-Machine). In this embodiment, in a situation where a large amount of data is gathered in such a wider variety, information from a plurality of observation data is used in an integrated manner as compared with related technology in which accuracy is limited by the characteristics of the observation data. Thus, more effective simulation can be performed.
- M2M Machine-to-Machine
- a simulation apparatus 200 has a configuration in which a soil model 221 is applied as the system model 21 in the simulation apparatus 100 as the first embodiment of the present invention.
- the simulation apparatus 200 includes two observation models 231-1 to 231-2 corresponding to two types of observation data as m observation models 31 in the simulation apparatus 100 according to the first embodiment of the present invention. It is the structure which applied.
- the simulation apparatus 200 is different from the simulation apparatus 100 according to the first embodiment of the present invention in that a posterior distribution integration unit 250 is provided instead of the posterior distribution integration unit 50.
- the soil initial state is applied as the initial state in the present invention
- the terrain / weather parameter is applied as a parameter in the present invention
- FIG. 8 schematically shows the time series change (4 steps from t-3 to t) of the target calculation grid space (9 grids from 1 to 9) for the soil moisture data OBS 1 and the satellite data OBS 2. Show.
- the filled portions indicate lattice points from which observation data is acquired.
- the spatial acquisition range and interval of these two types of observation data are considered to be the same as the calculation grid space. Further, even if the data acquisition point is local in the grid, the value in each grid is considered to be uniform.
- the soil moisture data OBS 1 may be, for example, an observation value obtained from a dielectric constant soil moisture sensor that is buried in the ground and calculated from the dielectric constant.
- the soil moisture data OBS 1 may be obtained from another sensor.
- the feature of this soil moisture data OBS 1 is that it can measure only the value of the point where the sensor is installed, so it is discrete in space, but it is highly accurate because it directly measures the physical quantity corresponding to soil moisture. Is a point. In FIG. 8, it is assumed that sensors are installed only at three points of grid point numbers 1, 3, and 8.
- the satellite data OBS 2 may be, for example, remote sensing data obtained from a sensor ASTER (Terra / ASTER) mounted on the Terra satellite. Specifically, the intensity of reflected light with respect to sunlight at the near infrared (band 3, 0.78-0.86 ⁇ m) and short wavelength infrared (band 4, 1.600-1.700 ⁇ m) wavelengths according to Terra / ASTER.
- the data is applicable as satellite data OBS 2 .
- data of other methods and wavelengths may be applied to the satellite data OBS 2 .
- the feature of the satellite data OBS 2 is that the reflected light intensity on the ground surface with respect to sunlight in the near-infrared and short-wavelength infrared wavelength regions can be acquired as two-dimensional image data.
- the satellite data OBS 2 is estimated using a significant correlation between the reflected light intensity and reflectance at these wavelengths and the water content of the ground surface soil based on the obtained data. Therefore, it becomes an indirect value and the accuracy may be insufficient.
- the soil model 221 is an example of the system model 21 in the first embodiment of the present invention.
- the soil model 221 calculates temporal and spatial changes such as soil moisture, using the physical properties of the target soil, for example, the degree of slope and drainage, and the weather conditions such as precipitation as parameters.
- LSM LAND-SURFACE MODEL
- the soil model 221 may be applied with a soil module of a decision support system DSSAT (Decision Support System for Agrotechnology Transfer) for agriculture.
- DSSAT Decision Support System for Agrotechnology Transfer
- the posterior distribution integration unit 250 integrates the first posterior distribution and the second posterior distribution with respect to the state variable / grid point where the second posterior distribution is generated. To calculate a new posterior distribution.
- the posterior distribution integration unit 250 may use a model generated based on the spatial correlation of each calculated posterior distribution during the integration process. As the model, for example, a covariance function or a variogram function can be applied.
- the posterior distribution integration unit in the present invention may use another model based on the spatial correlation of each posterior distribution.
- the posterior distribution integration unit 250 may update the parameters characterizing the calculation of the model used for integration based on the spatial correlation of each calculated posterior distribution. Processing using a model based on spatial correlation and processing for Bayesian updating of its parameters will be described together with specific examples in the following description of operations.
- the soil model 221 acquires the initial soil state and topographic / meteorological parameters via the input unit 10, and sets the soil moisture amount SM k at the lattice point k as a state variable (steps S101 and FIG. 5 in FIG. 4). S201).
- the state variable at one grid point is set to only the soil moisture amount will be mainly described.
- a static variable can be applied in addition to a dynamic variable that changes with time or a quantity whose value is to be estimated.
- the state variables may be selected according to the phenomenon to be simulated, the system model, the purpose, and the like.
- the state variable only needs to be able to generate a state vector at a certain time by the state vector and the soil model 221 one step before. Moreover, since the amount of calculation increases as the number of state variables increases, the state variables should be set appropriately according to the permitted computing resources.
- the data selection processing unit 30 acquires two types of observation data (step S102 in FIG. 4), and selects soil moisture data OBS 1 and satellite data OBS 2 as m types of observation data to be used (step S102). S103).
- the data selection processing unit 30 generates two, a first observation model 231-1 corresponding to the soil moisture data OBS 1 and a second observation model 231-2 corresponding to the satellite data OBS 2 ( Step S104).
- the soil moisture data OBS 1 has the same dimension as the state variable SM and the observed noise follows a Gaussian (normal) distribution.
- the matrix represented by Equation (7) is a unit matrix. Therefore, the observation data OBS 1 and the state variables are based on the observation model equation of the equation (8), (21) It is expressed by the linear relationship.
- the observation noise w 1 can be a Gaussian distribution with an average of 0 and a variance ⁇ 1 , for example.
- the data selection processing unit 30 generates the first observation model 231-1 represented by the equation (21).
- the satellite data OBS 2 it is assumed that the reflected light intensity or reflectance at the near-infrared and short-wavelength infrared wavelengths and the soil moisture content are related by a nonlinear function h 2 .
- the observation lattice points coincide with the calculation lattice.
- the observation data OBS 2 and the state variable are based on the observation model equation of the equation (8), (22) It is expressed by the nonlinear relationship.
- the observation noise w 2 can be, for example, a Gaussian distribution with an average of 0 and a variance ⁇ 2 .
- the data selection processing unit 30 generates the second observation model 231-2 represented by the equation (22).
- the posterior distribution generation unit 40 calculates the posterior distribution for each lattice point according to the Bayes' theorem of equation (9) (step S205).
- two observation values OBS 1 and OBS 2 are obtained for lattice points 1, 3, and 8, whereas lattice points 2, 4, 5, 6, 7, For 9, only one observed value OBS 2 is obtained. Therefore, the posterior distribution generation unit 40 uses the observation data selected by the data selection processing unit 30 for the former grid points 1, 3, and 8, and uses the following expression (23) based on the expression (13). To calculate the first posterior distribution. ... (23)
- i 1, 3, and 8.
- OBS1i, OBS2i denote the observation data OBS 1 and OBS 2 obtained in the lattice point i, respectively.
- the first posterior distributions of the lattice points 1, 3, and 8 calculated by the equation (23) are stored in the first posterior distribution storage unit 41a (Y in step S206, S207).
- the first posterior distributions of these grid points 1, 3, and 8 are also stored in the integrated posterior distribution storage unit 52 (step S208).
- the posterior distribution generation unit 40 lacks one of the observation data selected by the data selection processing unit 30 for the latter lattice points 2, 4, 5, 6, 7, and 9, so
- the second posterior distribution is calculated using the following formula (24) based on the formula (4). ... (24)
- j 2, 4, 5, 6, 7, and 9.
- Each second posterior distribution of the grid points 2, 4, 5, 6, 7, 9 calculated by the equation (24) is stored in the second posterior distribution storage unit 41b (N and S209 in step S206). .
- the posterior distribution integration unit 250 integrates the first and second posterior distributions calculated by the equations (23) and (24) (step S300).
- a linear combination of the posterior distributions of the peripheral grid points is considered as the function g of the posterior distribution integration shown in the equation (19).
- the second posterior distribution represented by the equation (24) is stored in the second posterior distribution storage unit 41b. Yes.
- this posterior distribution is expressed by a linear combination of posterior distributions of lattice points other than lattice point 2, ... (25) It is expressed.
- ⁇ 1 to ⁇ 9 are weighting coefficients corresponding to the parameter set ⁇ in the equation (19).
- the dash (′) of the probability distribution p ′ in the equation (25) indicates the probability distribution after integration by the posterior distribution integration unit 250.
- Expression (25) is similar to the so-called Kriging method in which the value at the unknown lattice point 2 is determined based on a certain stochastic correlation with the value of the surrounding lattice points, that is, the spatial correlation. Can be considered.
- the value at each lattice point is not a definite value, but a posterior distribution obtained from equations (23) and (24). That is, between the position r k and the distance gamma distant point r k + gamma lattice points k, soil moisture of the posterior distribution p
- Equation (26) represents the state variable SM of the lattice point at the position x.
- OBS represents m kinds of observation data. This can be obtained, for example, by solving a simple Kriging equation as shown in the following equation (27).
- the method for obtaining the parameter ⁇ of the function g used when the posterior distribution integration unit integrates the posterior distribution is not limited to this method, and may be another method. ... (27) Next, the operation for obtaining the covariance function of equation (26) will be described.
- the posterior distribution integration unit 250 obtains the variogram function V ( ⁇ ) first.
- the variogram represents a stochastic interaction between the position r k of the lattice k and a point r k + ⁇ that is a distance ⁇ away, that is, a spatial correlation.
- An example of the variogram estimation result is shown on the left side of FIG. This example shows an exponential variogram model for the results of calculating variograms of grid points other than those calculated by integration. ... (29) And ⁇ which is the parameter was estimated.
- ⁇ represents three parameter sets that characterize the variogram, and is generally called nugget ⁇ 2 , range ⁇ , and sill ⁇ 2 .
- the range ⁇ and nugget ⁇ 2 are estimated using Bayes' theorem (9). Specifically, since the uniform prior distribution in the range ⁇ and the nugget ⁇ 2 were predicted to be close to 0, an exponential prior distribution was assumed, and the Bayes' theorem was calculated from the results of the variogram actually calculated. The posterior distribution was obtained by An example of the result is shown on the right side of FIG. As is clear from this figure, the maximum value is seen in the posterior distribution, and this maximum value can be regarded as the parameter value and the maximum likelihood value that best reproduces the calculated variogram.
- the posterior distribution integration unit 250 performs the posterior distribution p ′ (SM 2
- FIG. 10 shows details of the integration operation of the posterior distribution integration unit 250 in step S300.
- FIG. 10 shows an integration operation for a certain grid point for which the second posterior distribution is calculated.
- the posterior distribution integration unit 250 calculates a variogram or covariance for grid points other than the target grid point (step S401).
- the posterior distribution integration unit 250 defines a function applicable to the variogram or covariance calculated in step S401 (step S402).
- the posterior distribution integration unit 250 assumes a prior distribution for the function parameter defined in step S402 (step S403).
- the posterior distribution integration unit 250 obtains the posterior distribution of the parameters by updating the parameter pre-distribution assumed in step S403 by using Bayes' theorem based on the variogram or covariance calculation result (step S404). ).
- the posterior distribution integration unit 250 derives a covariance function using the parameter posterior distribution obtained in step S404 (step S405).
- the posterior distribution integration unit 250 obtains a weighting coefficient (parameter set ⁇ ) for integrating the posterior distribution of the lattice points other than the target lattice point by the Kriging equation (step S406).
- the posterior distribution integration unit 250 integrates the posterior distribution of grid points other than the target grid point using the parameter set ⁇ used in step S406 (step S407).
- the simulation apparatus 200 executes steps S301 to S304 and S208 in the same manner as in the first embodiment of the present invention.
- the integrated posterior distribution or the second posterior distribution is stored in the integrated posterior distribution storage unit 52 for each grid point where the second posterior distribution is generated.
- the soil model 221 continues calculation of the next time step using the state vector which consists of the posterior distribution of this time step preserve
- the simulation apparatus performs high-resolution and high-precision simulation over a wide area while considering non-ideal observation data and observation data with discontinuity and specificity. Can do.
- the present embodiment includes the following configuration in addition to the same configuration as the first embodiment of the present invention. That is, when the posterior distribution integration unit integrates the first posterior distribution and the second posterior distribution with respect to the grid point where the second posterior distribution is generated, the spatial correlation of the calculated posterior distributions. This is because a model generated based on the above is used. In addition, the posterior distribution integration unit updates the parameters that characterize the calculation of the model used for integration based on the spatial correlation of each calculated posterior distribution.
- the simulation can be performed with high resolution and high accuracy over a wider area.
- a soil model is applied to a system model
- soil sensor data and satellite data are applied to a plurality of observation data
- a soil moisture amount is simulated.
- this embodiment can also be implemented using other system models and observation data for other objects.
- a weather model may be applied to the system model
- weather sensor data and satellite data may be applied to a plurality of observation data.
- a simulation apparatus 300 has a configuration in which a crop model 321 is applied as the system model 21 in the simulation apparatus 100 as the first embodiment of the present invention.
- the simulation apparatus 300 includes two observation models 331-1 to 331-2 corresponding to two types of observation data as m observation models 31 in the simulation apparatus 100 according to the first embodiment of the present invention. It is the structure which applied.
- the simulation apparatus 300 is different from the simulation apparatus 100 according to the first embodiment of the present invention in that a posterior distribution integration unit 350 is provided instead of the posterior distribution integration unit 50.
- the soil initial state is applied as the initial state in the present invention
- the terrain, weather, and crop parameters are applied as the parameters in the present invention.
- the first satellite data has high frequency and low spatial resolution
- the second satellite data has low frequency and high spatial resolution
- the first satellite data OBS 1 and the second satellite data OBS 2 are time-series changes (t ⁇ 3 to t) in the target calculation lattice space (16 lattices 1 to 16). 4 steps) are schematically shown.
- the filled portion indicates the lattice point from which data is acquired.
- the first satellite data with high frequency and low spatial resolution may be data obtained from, for example, a sensor MODIS (Terra AQUA / MODIS) mounted on a Terra satellite or an AQUA satellite.
- MODIS Triang AQUA / MODIS
- the reflected light intensity data for sunlight in the visible red band (wavelength 0.58-0.86 ⁇ m) and near-infrared band (wavelength 0.725-1.100 ⁇ m) by Terra AQUA / MODIS are as follows: It can be applied as the first satellite data.
- Such first satellite data can basically be acquired every day, depending on the latitude of the area to be acquired. However, such first satellite data has a low spatial resolution of about 250 m on the ground.
- the second satellite data with low frequency and high spatial resolution includes observation data obtained from, for example, a LANDSAT satellite, a PLEIADES satellite, or an ASNARO satellite.
- the wavelength range acquired by these is substantially the same as the wavelength acquired as the first satellite data.
- the acquisition frequency and the ground resolution of such second satellite data are about 30 m at intervals of 8 to 16 days for the LANDSAT satellite, and about 2 m at intervals of 2 to 3 days for the PLEIADES satellite and ASNARO satellite.
- NDVI Normalized Difference Vegetation Index
- LAI leaf area index
- the lattice spacing between the two types of observation data OBS 1 and OBS 2 is different. Therefore, the calculation grid of the crop model 321 is set so as to match the observation data of at least one of OBS 1 and OBS 2 .
- the vector in the observation model equation shown in equation (7) may be changed to be, for example, a weighted average or a weighted average of the values of neighboring grid points.
- the acquisition time intervals of the two types of observation data OBS 1 and OBS 2 are different. Therefore, the posterior distribution integration unit 350 is obtained from the observation data OBS 1 having a high acquisition frequency by estimating the posterior distribution obtained from the observation data OBS 2 having a low acquisition frequency based on the temporal correlation. Integrate according to the acquisition time of the posterior distribution.
- the setting of the state variable at one grid point may be selected according to the dependence of the variable on the time and the number of unknowns to be estimated.
- the data selection processing unit 30 acquires two types of observation data (step S102), and selects the first satellite data OBS 1 and the second satellite data OBS 2 as m types of observation data to be used. (Step S103).
- the data selection processing unit 30 performs the first observation model 331-1 corresponding to the first satellite data OBS 1 and the second observation model 331-2 corresponding to the second satellite data OBS 2. Are generated (step S104).
- observation model 331-2 has a one-to-one correspondence between the lattice point from which the second observation data OBS 2 is acquired and the calculation lattice point, ... (31) It is expressed.
- H 1 and H 2 are a mapping h that associates each observation data with the state variable LAI, and a mapping that includes a matrix that associates lattice points.
- W 1 and w 2 are observation noises, and can be set to, for example, a Gaussian distribution with an average of 0 and a variance ⁇ .
- the observation models 331-1 and 331-2 in the equations (30) and (31) are specific examples of the observation model equations represented by the equation (8).
- the crop model 321 acquires the initial soil state and topography / weather / crop parameters, and calculates the prior distribution of the state vector in the next step in the simulation (steps S201 and S202 in FIG. 5). Then, the observation models 331-1 and 331-2 convert the prior distribution by the equations (30) and (31) (step S203). Here, it is assumed that the converted prior distribution p (LAI k ) at time t ⁇ 1 in FIG. 12 is calculated in step S203 after the operations shown in FIG. 5 are appropriately repeated.
- the posterior distribution generation unit 40 sets the first posterior distribution as ... (32) Is stored in the first posterior distribution storage unit 41a (Yes in steps S205 and S206, S207).
- LH is a function for calculating the likelihood expressed by equation (13)
- Z of the denominator is a normalization constant.
- the posterior distribution generation unit 40 sets the second posterior distribution as ... (33) Is stored in the second posterior distribution storage unit 41b (No in steps S205 and S206, S209).
- the posterior distribution integration unit 350 integrates the first posterior distribution represented by the first and third expressions represented by the expression (32) and (33). Specifically, as the function g of the posterior distribution integration shown in the equation (19), here, based on the temporal correlation from the second posterior distribution at the current time and the first posterior distribution at different times. A linear combination with the estimated posterior distribution is applied. For example, since the posterior distribution at time t in FIG. 12 is only the first satellite data OBS 1 as described above, the second posterior distribution represented by the equation (33) is the second posterior distribution. Is stored in the posterior distribution storage unit 41b. Therefore, the posterior distribution integration unit 350 generates a first posterior distribution at time t for integration with the second posterior distribution at time t from the posterior distribution generated at a past time before time t.
- the posterior distribution integration unit 350 uses the second posterior distribution p (LAI k
- OBS 1 , OBS 2 ) 1: t ⁇ 1 is integrated by the following equation (34). ... (34)
- ⁇ 0 and ⁇ 0 are weighting coefficients corresponding to the parameter set ⁇ in the equation (19).
- the dash (′) of the probability distribution p ′ indicates the probability distribution after integration by the posterior distribution integration unit 350.
- Equation (35) in the case of estimating only from the first posterior distribution at time ti is specifically: ... (36) It is expressed.
- the second observation data OBS 2 is not obtained, and the posterior distribution at the time when the second posterior distribution is generated (in FIG. 12, t ⁇ 2, t ⁇ 4,...) Is also considered.
- the post-integration post-integration stored in the integrated post-post-distribution storage unit 52 for a time prior to time t (35) ... (37) It is expressed.
- time ti represents the time at which the first posterior distribution is calculated
- the posterior distribution integration unit 350 uses the posterior distribution p (LAI k
- the simulation apparatus 300 executes steps S301 to S304 and S208 in the same manner as in the first embodiment of the present invention.
- the integrated posterior distribution or the second posterior distribution for each lattice point is stored in the integrated posterior distribution storage unit 52 at time t when the second posterior distribution is generated at each lattice point.
- the crop model 321 continues the calculation of the next time step by using the state vector composed of the posterior distribution at the time t stored in the integrated posterior distribution storage unit 52.
- the simulation apparatus 300 ends the operation.
- the simulation apparatus performs high-resolution and high-precision simulation over a wide area while considering non-ideal observation data and observation data with discontinuity and specificity. Can do.
- the present embodiment includes the following configuration in addition to the same configuration as the first embodiment of the present invention. That is, when the posterior distribution integration unit integrates the posterior distribution with respect to the grid point where the second posterior distribution is generated, the model generated based on the temporal correlation of the posterior distribution calculated in the past is used. It is because it uses.
- the present embodiment estimates the posterior distribution at time t based on the temporal correlation from the posterior distribution calculated in the past from the time t at which the second posterior distribution was generated, and the estimated posterior distribution.
- the posterior distribution after integration at time t is calculated using the distribution.
- a crop model is applied to a system model and satellite data is applied as a plurality of observation data.
- the type and contents of the system model and observation data are not limited.
- the present embodiment can be applied to a combination of high-frequency but locally discrete observation data and low-frequency but high-resolution and planar observation data using a corresponding system model as appropriate. .
- FIG. 13 shows the configuration of a simulation apparatus 400 as the fourth embodiment of the present invention.
- a simulation apparatus 400 has a configuration in which a weather model 421 is applied instead of the soil model 221 in the simulation apparatus 200 as the second embodiment of the present invention.
- the simulation apparatus 400 uses two observation models 431-1 and 431-2 instead of the two observation models 231-1 and 231-2 in the simulation apparatus 200 according to the second embodiment of the present invention. It is an applied configuration.
- the weather value initial state is applied as an initial state in the present invention, and the terrain parameter is applied as a parameter in the present invention.
- the M 2 observation data
- the GPS precipitable water data OBS 1 and the sonic radar data OBS 2 are applied.
- GPS precipitable water amount data OBS 1 uses the property that the arrival time is delayed as the amount of water vapor in the atmosphere increases until the radio wave radiated from the GPS (Global Positioning System) satellite reaches the GPS receiver. This is data that estimates the vertical integrated amount.
- GPS precipitable water is useful for estimating the timing of occurrence of local heavy rain and improving the accuracy of estimation of total rainfall in a single rainfall.
- the GPS precipitable water has a feature that it is easy to increase the density relatively on the land surface because a GPS receiver may be provided on the ground side.
- the GPS precipitable water amount is an integrated value in the vertical direction only in the vertical direction, it is difficult to appropriately express the spatial distribution.
- an acoustic radar if an acoustic radar is used, the altitude dependence of the water vapor amount can be measured. For example, when a sound wave is emitted vertically upward and an atmospheric turbulent scattering echo is received, the echo depends on the altitude gradient of the atmospheric refractive index. Further, the altitude gradient of the atmospheric refractive index is strongly dependent on the altitude gradient of the water vapor amount. Therefore, by observing this echo, the altitude dependence of the water vapor amount can be measured.
- calculation grid points 1 to 8 are arranged in a three-dimensional space.
- the value at one observation grid point is associated with the integrated value of two calculation grid points having the same coordinates on the xy plane and different z (vertical) coordinates.
- OBS 1 is acquired at each observation lattice point that can be associated with the integrated values of calculation lattice points 1 and 5 having the same xy coordinates, the integrated values of 2 and 6, and the integrated values of 4 and 8, respectively.
- the value of one observation data acquisition grid point can be associated with the average value of four calculation grid points in the same plane, that is, the same z (vertical) coordinate.
- Equation (39) is a specific example of the observation model represented by Equation (8). ... (39)
- the simulation apparatus 400 configured as described above operates in substantially the same manner as the simulation apparatus 200 as the second embodiment of the present invention.
- the weather model 241 calculates the prior distribution of the state vector at the next time step calculated based on the initial state of the weather value and the topographic parameters (steps S201 to S202 in FIG. 5). Then, the two observation models 431-1 to 431-2 described above convert the prior distributions (steps S203 to S204). Then, the posterior distribution generation unit 40 generates the first posterior distribution or the second posterior distribution at each lattice point (steps S205 to S207, S209). At this time, since the first observation data OBS 1 is not observed at the lattice points 3 and 7, the second posterior distribution is generated. In addition, the first posterior distribution is generated at other lattice points.
- the posterior distribution integration unit 250 and the determination unit 51 generate an integrated posterior distribution for the grid points 3 and 7 where the second posterior distribution is generated, and generate the integrated posterior distribution or the original second distribution. Is determined (steps S300 to S303).
- the meteorological model 421 continues the simulation using a state vector composed of the first posterior distribution or the determined posterior distribution for each grid point.
- the output unit 60 outputs a time series of state vectors and ends the operation.
- the simulation apparatus can be applied even when the observation data cannot simply have a one-to-one correspondence with the lattice points, or even in a three-dimensional space simulation. It is. Even in such a case, the present embodiment uses a suitable observation model, so that non-ideal observation data and observation data with discontinuity and specificity are taken into account. It is possible to perform a simulation with high resolution and high accuracy.
- each functional block of the simulation apparatus has been mainly described as being realized by a CPU that executes a computer program stored in a storage device or a ROM.
- the present invention is not limited to this, and some, all, or a combination of each functional block may be realized by dedicated hardware.
- the functional blocks of the simulation apparatus may be realized by being distributed among a plurality of apparatuses.
- the operation of the simulation apparatus described with reference to each flowchart may be stored in a computer storage device (storage medium) as a computer program of the present invention. . Then, the computer program may be read and executed by the CPU. In such a case, the present invention is constituted by the code of the computer program or a storage medium.
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Abstract
Description
本発明の第1の実施の形態としてのシミュレーション装置100について説明する。シミュレーション装置100は、物理法則に基づいた連続時間・空間の偏微分方程式を解いて時間発展を追うシミュレーションに適用可能である。そのような偏微分方程式には、例えば、運動を記述する運動方程式、流体を記述するナビエーストークス方程式、熱変化を記述する熱力学方程式、津波を記述する浅水波方程式などがある。また、シミュレーション装置100は、有限要素法を用いたシミュレーションにも適用可能である。なお、本実施の形態では、シミュレーション対象となる系は、時間変化を追う状態ベクトルが、実際の観測データと何らかの関係式で結ばれる系、すなわち、シミュレーション結果と観測データとが比較可能な系であるものとする。
・・・(1)
なお、式中の記号Tは、転置を意味する。この状態ベクトルの次元は、1格子点あたりの状態変数の数と格子点数Lとの積となる。(1)式の場合は、2L次元となる。
・・・(2)
という関係式で記述される。ここで、θは、モデルの計算に必要な各種パラメータベクトルを表す。また、Vtは、時刻tでのシステムノイズを表す。システムノイズVtは、モデル内の不完全性の効果を数値的に表すために、状態ベクトルに作用を及ぼす確率的な駆動項として導入される。また、写像fは、対象とする現象によって線形、または非線形であっても良い。また、(2)式から明らかなように、時刻tでの状態ベクトルXtが時刻t-1の状態ベクトルXt-1で陽に定義されている必要はない。すなわち、本実施の形態のシステムモデル21は、時刻t-1での状態ベクトルXt-1を入力として、時刻tでの状態ベクトルXtを計算できれば良い。
・・・(3)
によって近似することを、アンサンブル近似という。したがって、実際のシステムモデル21は、この各アンサンブルiの時間発展
・・・(4)
をすべてのアンサンブルについて求める。これによって、時刻tでの状態ベクトルXtの確率分布p(Xt)は、N個のアンサンブル
・・・(5)
によって近似される。この(4)式で表されるアンサンブルの計算は、アンサンブルごとに独立している点が特徴である。したがって、システムモデル21は、N回繰り返して計算をしても良いし、N個の並列計算機によって1度に計算を行ってもよく、計算リソースに応じて柔軟に計算方法を変えることが出来る。なお、以降では、状態ベクトルXtの確率分布をp(Xt)と示し、事前分布とも呼ぶ。
・・・(6)
この場合、データ選択処理部30は、(6)式における写像h1~hmおよび各観測データで考慮すべきノイズ量w1~wmの情報を、制御信号CTL1~CTLmとして、観測モデル31-1~31-mにそれぞれ出力すればよい。これにより、m個の観測モデル31が生成される。
・・・(7)
この行列は、j(jは1以上L以下の整数)行目の{1+2(j-1)}列目の要素のみ1を持つ。
・・・(8)
が出力される、と表すことができる。したがって、全m種の観測モデル31は、状態ベクトルXtに対してそれぞれ(8)式の演算を行い、全m種の変換された状態ベクトルXtを、事後分布生成部40へ出力する。なお(2)式または(4)式、および、(8)式の組は、状態空間モデルと呼ばれる。
・・・(9)
と表される。ここで、分子のp(y|x)は、状態変数xの観測値yへの当てはまり度合の指標である尤度と呼ばれる。尤度p(y|x)は、観測モデル31が(8)式で表されるように写像hとノイズ量wに分離できる場合は、
・・・(10)
によって計算される量を用いることができる。ただし、rは、ノイズ量wの密度関数である。なお、(10)式において、右辺を、yとh(x)を用いた関数LHとして再定義した。さらに、m種類の観測値y={y1,y2,・・・ym}が得られた場合の尤度p(y1:m|x)は、乗法定理を再帰的に使うことで、
・・・(11)
と積の形で表される。ここで、(11)式における1項目のp(y1|y1:0,x)は、観測データがないときのy1の確率であり、すなわち、y1が得られたときのxの尤度p(y1|x)となる。また、第2項のp(y2|y1:1,x)は、y1が得られたときのy2の確率である。ただし、それぞれの観測データは、異なるセンサなどで取得されており、y1とy2の同時分布が存在しない。このため、第2項は、結果的に、y2が得られたときのxの尤度p(y2|x)となる。したがって、この場合の(9)式で表される事後分布は、
・・・(12)
と表される。ここで分母のZは規格化定数とする。この関係を用いると、格子点kにおける状態変数Ukの事後分布は、事前分布をp(Uk)と表すと、観測データyがOBS1~OBSmとm種得られていることから、
・・・(13)
と表される。分子は、(12)式で表されるとおり、各観測データでの尤度の積と、事前分布p(Uk)との積である。さらに、それぞれの尤度は(10)式で表されるので、(13)式の事後分布は、
・・・(14)
と表される。このように、事後分布生成部40は、格子点kにおける状態変数Ukの事後分布を、m個の観測データOBS1~OBSmと写像h1~hmとにより計算されるm種の尤度LHと、事前分布p(Uk)とから算出する。同様にして、事後分布生成部40は、格子点1~Lの全てについて、(13)式すなわち(14)式により事後分布を計算する。
・・・(15)
すなわち、
・・・(16)
と表され、分子を構成する尤度の数がm-1に減少する。なお、(15)式および(16)式において、“m-1”は、m種のうち少なくとも1種の観測データが得られていないことを表しており、得られていない(欠損している)観測データの数を1つに限定するものではない。
・・・(17)
と表される。これより、事後分布の計算に用いられる観測値の数が多いほど、分散は減少する、すなわち事後分布の確度が向上することがわかる。
・・・(18)
次に、事後分布統合部50について説明する。事後分布統合部50は、第1の事後分布と第2の事後分布とを統合する。詳細には、事後分布統合部50は、第2の事後分布が算出された状態変数・格子点のそれぞれについて、第1の事後分布および第2の事後分布を統合して新たな事後分布を算出する。また、事後分布統合部50は、統合後の新たな事後分布を判定部51に出力する。本実施の形態では、事後分布は、アンサンブルの集合によって近似されているため、事後分布統合部50は、第1の事後分布を近似するアンサンブルおよび第2の事後分布を近似するアンサンブルを、所定の割合で重ねあわせることにより統合すればよい。
・・・(19)
ここで、πは、関数gを決定付けるパラメータセットを表す。また、kは、第1の事後分布が生成された格子点を表す。また、iは、第2の事後分布が生成された他の格子点を表す。なお、i≠jである。以降、(19)式における確率分布p’のダッシュ(’)は、事後分布統合部50での統合後の確率分布であることを示す。事後分布統合部50は、このようにして新たに算出された事後分布p’(Uj|OBS1:m)と、元の第2の事後分布p(Uj|OBS1:m-1)とを、判定部51に出力する。
次に、データ選択処理部30は、システムモデル21で設定された状態変数に関する情報を参照し、第1~第Mの観測データのうち、利用するm種の観測データを選択する(ステップS103)。
次に、本発明の第2の実施の形態について図面を参照して説明する。本実施の形態は、空間上は離散的だが値の精度が高い観測データと、空間上は連続的だが精度が十分でない観測データを利用したシミュレーションに適用できる。以下では、本発明のシミュレーション装置を用いて、土壌水分量のシミュレーションを行う具体例について説明する。なお、本発明の第2の実施の形態において参照する各図面において、本発明の第1の実施の形態と同様の構成およびステップには同一の符号を付して、本実施の形態における詳細な説明を省略する。
・・・(20)
と表せる。ここでは、1格子点における状態変数を土壌水分量のみと設定した例を中心に説明する。ただし、状態変数としては、時間変化する動的な変数や、値を推定したい量に加えて、静的な変数を適用可能である。また、状態変数は、シミュレーション対象の現象やシステムモデル、目的などに応じて選べばよい。状態変数は、(2)式に示したように、ある時刻の状態ベクトルが1ステップ前の状態ベクトルおよび土壌モデル221によって生成可能であればよい。また、状態変数が増えると計算量が増加するため、状態変数は、許された計算資源に応じて適切に設定すべきである。
・・・(21)
という線形な関係で表される。ここで観測ノイズw1は、例えば平均0、分散σ1のガウス分布とすることが出来る。このように、データ選択処理部30は、(21)式で表される第1の観測モデル231-1を生成する。
・・・(22)
という非線形な関係で表される。ここでも観測ノイズw2は、例えば平均0、分散σ2のガウス分布とすることが出来る。このように、データ選択処理部30は、(22)式で表される第2の観測モデル231-2を生成する。
・・・(23)
ここで、(23)式では、i=1、3、8である。また、OBS1i、OBS2iは、格子点iで得られた観測データOBS1およびOBS2をそれぞれ表すものとする。(23)式により計算された格子点1、3、8の各第1の事後分布は、第1の事後分布記憶部41aに保存される(ステップS206でY、S207)。また、これらの格子点1、3、8の各第1の事後分布は、統合後事後分布記憶部52にも保存される(ステップS208)。
・・・(24)
ここで、(24)式では、j=2、4、5、6、7、9である。(24)式により計算された格子点2、4、5、6、7、9の各第2の事後分布は、第2の事後分布記憶部41bに保存される(ステップS206でN、S209)。
・・・(25)
と表される。ここで、α1~α9は(19)式におけるパラメータセットπに相当する重み係数である。以降、(25)式における確率分布p’のダッシュ(’)は、事後分布統合部250での統合後の確率分布であることを示す。このとき、(25)式は、未知の格子点2における値を、周辺格子点の値とのある確率的相互関係、すなわち空間的相関性に基づいて決定する、いわゆるクリギング(Kriging)法と同様とみなすことが出来る。ただし、各格子点における値は確定値ではなく、(23)式および(24)式から求まる事後分布である。すなわち、格子点kの位置rkと距離γ離れた点rk+γとの間の、土壌水分量の事後分布p(SM|OBS)の空間的な相関性を表す共分散関数
・・・(26)
が求まれば、(25)式の重み係数α1~α9、すなわちパラメータセットπも求まる。なお、(26)式において、SM(x)は、位置xにおける格子点の状態変数SMを表す。また、OBSは、m種の観測データを表す。これは、例えば次式(27)に示すような、単純型クリギング方程式を解くことで求めることができる。なお、本発明において、事後分布統合部が事後分布を統合する際に用いる関数gのパラメータπを求める手法は、この手法に限定されず、他の手法であってもよい。
・・・(27)
次に(26)式の共分散関数を求める動作を説明する。共分散関数C(γ)とバリオグラム関数V(γ)の間には簡単な関係
・・・(28)
が成り立つため、いずれか一方を求めれば良い。以下では、事後分布統合部250において、バリオグラム関数V(γ)を先に求める場合について説明する。バリオグラムも、共分散関数と同様に、格子kの位置rkと距離γ離れた点rk+γとの間の確率的相互作用、すなわち空間的な相関性を表す。図9の左側に、バリオグラム推定結果の一例を示す。この例は、統合によって算出する格子点以外の格子点のバリオグラムを算出した結果に対し、指数型のバリオグラムモデル
・・・(29)
にあてはめて、そのパラメータであるζを推定した。ここで、ζは、バリオグラムを特徴付ける3種のパラメータセットを表しており、一般にナゲットτ2、レンジφ、シルσ2と呼ばれる。ここでは、これらのパラメータのうち、レンジφとナゲットτ2について、ベイズの定理(9)式を用いて推定を行った結果を示している。具体的には、レンジφに一様な事前分布、ナゲットτ2は0に近い値が予想されたため、指数型の事前分布をそれぞれ仮定し、実際に算出されたバリオグラムの結果から、ベイズの定理によって事後分布をそれぞれ求めた。その結果の例を図9の右側に示した。この図から明らかなように、事後分布には最大値が見られ、この最大値は、算出されたバリオグラムを最も良く再現するパラメータの値、最尤値とみなすことができる。図9左側の曲線(推定値)は、このパラメータの下で(29)式に基づいて描いたものである。以上より、バリオグラムV(γ)の関数が算出できたので、(28)式より共分散関係も算出できる。なお、ここではベイズの定理を使ったパラメータ推定方法を示したが、あくまでも例示であって他の方法を用いても良い。また、図9は推定結果の一例であって、図8に記載の格子空間(1~9)に対応するものではない。
次に、本発明の第3の実施の形態について図面を参照して説明する。本実施の形態は、複数の観測データ間で観測格子間隔が異なる場合や、取得時間間隔が異なる場合のシミュレーションに適用できる。以下では、本発明のシミュレーション装置を用いて、作物生育(成長)についてシミュレーションを行う具体例について説明する。なお、本発明の第3の実施の形態において参照する各図面において、本発明の第1の実施の形態と同様の構成およびステップには同一の符号を付して、本実施の形態における詳細な説明を省略する。
・・・(30)
と表される。
・・・(31)
と表される。ここで、H1およびH2は、それぞれの観測データと状態変数LAIとを対応づける写像hおよび格子点を対応づける行列を含む写像である。また、w1およびw2は、観測ノイズであり、例えば平均0、分散σのガウス分布などに設定可能である。なお、(30)式および(31)式の観測モデル331-1および331-2は、(8)式で表される観測モデル式の具体例である。
・・・(32)
を計算し、第1の事後分布記憶部41aに保存する(ステップS205、S206でYes、S207)。ここで、LHは(13)式で表される尤度を計算する関数で、分母のZは規格化定数である。
・・・(33)
を計算し、第2の事後分布記憶部41bに保存する(ステップS205、S206でNo、S209)。
・・・(34)
ここで、α0、β0は、(19)式におけるパラメータセットπに相当する重み係数である。また、(34)式において、確率分布p’のダッシュ(’)は、事後分布統合部350での統合後の確率分布であることを示す。
・・・(35)
を適用することができる。ここで、例として、ARモデルfARが線形に記述される場合を考える。また、第1の衛星データOBS1および第2の衛星データOBS2のいずれもが観測されて第1の事後分布が生成されている時刻で、かつ、時刻tより前の時刻をt-iとする(図12ではi=1,3)。このような時刻t-iにおける第1の事後分布からのみ推定する場合の(35)式は、具体的に、
・・・(36)
と表される。
・・・(37)
と表される。ただし、(37)式において、時刻t-iは、第1の事後分布が算出されている時刻、時刻t-jは、第2の事後分布が算出されている時刻をそれぞれ表す。図12の場合、i=1,3、j=2であり、i≠jである。本実施の形態では、(37)式において、統合後事後分布記憶部52に保存されている統合後の事後分布を用いる場合を想定している。このため、図11において、統合後事後分布記憶部52から事後分布統合部350に対して、統合後の事後分布に関する情報を伝達するデータ経路を矢印で示している。
次に、本発明の第4の実施の形態について図面を参照して説明する。本実施の形態では、本発明のシミュレーション装置を用いて、降水量についてシミュレーションを行う具体例について説明する。なお、本発明の第4の実施の形態は、本発明の第2の実施の形態における計算格子空間を3次元に拡張したものである。また、本発明の第4の実施の形態において参照する各図面において、本発明の第2の実施の形態と同様の構成およびステップには同一の符号を付して、本実施の形態における詳細な説明を省略する。
・・・(38)
次に、音波レーダデータOBS2については、1つの観測データ取得格子点の値は、z(鉛直)座標が同じ、すなわち同一平面内の4つの計算格子点の平均値と対応づけることができる。図14では、OBS2は、z座標が同一の計算格子点1~4の平均値と、5~8の平均値とそれぞれ対応付け可能な観測点で取得されたデータである。したがって、第2の観測データOBS2と、状態変数RAINk(k=1~8)との関係を表す観測モデル431-2は、次式(39)で表される。なお、(39)式は、(8)式で表される観測モデルの具体例である。
・・・(39)
以上のように構成されたシミュレーション装置400は、本発明の第2の実施の形態としてのシミュレーション装置200と略同様に動作する。
10 入力部
21 システムモデル
221 土壌モデル
321 作物モデル
421 気象モデル
22 事前分布記憶部
30 データ選択処理部
31、231、331、431 観測モデル
40 事後分布生成部
41a 第1の事後分布記憶部
41b 第2の事後分布記憶部
50、250、350 事後分布統合部
51 判定部
52 統合後事後分布記憶部
60 出力部
1001 CPU
1002 RAM
1003 ROM
1004 記憶装置
1005 入力装置
1006 出力装置
Claims (10)
- シミュレーションにおける状態ベクトルの初期状態およびパラメータと、複数の観測データとを入力として取得する入力手段と、
前記初期状態およびパラメータを基に、前記状態ベクトルの時間発展をシミュレーションするシステムモデルと、
前記システムモデルにおける前記状態ベクトルに関連する情報に基づいて、前記複数の観測データのうち利用する複数の観測データを選択するデータ選択処理手段と、
選択された複数の観測データにそれぞれ対応する複数の観測モデルであって、それぞれ、前記システムモデルから出力される状態ベクトルを、前記観測データおよび前記状態ベクトルの関係性に基づき変換して出力する複数の観測モデルと、
前記複数の観測モデルから出力される状態ベクトルおよび前記データ選択処理手段で選択された観測データに基づいて、前記状態ベクトルの事後分布を生成し、前記データ選択処理手段で選択された全ての観測データに基づく事後分布を第1の事後分布として出力し、1つ以上欠如した観測データに基づく事後分布を第2の事後分布として出力する事後分布生成手段と、
前記第1の事後分布と前記第2の事後分布とを統合する事後分布統合手段と、
前記第2の事後分布および前記統合後の事後分布のいずれを用いるかを決定する判定手段と、
前記判定手段によって決定された事後分布および前記第1の事後分布からなる状態ベクトルを前記システムモデルに入力するとともに、該状態ベクトルの時系列を出力する出力手段と、
を備えたシミュレーション装置。 - 前記データ選択処理手段は、前記システムモデルで設定された状態ベクトルおよび前記各観測データにそれぞれ関する情報を比較することにより、前記各観測データに対応する前記観測モデルを生成することを特徴とする請求項1に記載のシミュレーション装置。
- 前記データ選択処理手段は、前記各観測データに対応する前記観測モデルのノイズ量を設定することを特徴とする請求項1または請求項2に記載のシミュレーション装置。
- 前記事後分布統合手段は、前記第1の事後分布および前記第2の事後分布を統合する処理において、算出済みの各事後分布の相関性に基づいて生成されたモデルを用いることを特徴とする請求項1から請求項3のいずれか1項に記載のシミュレーション装置。
- 前記事後分布統合手段は、前記統合に用いる前記モデルの演算を特徴付けるパラメータを、算出済みの各事後分布の相関性に基づいてベイズ更新することを特徴とする請求項4に記載のシミュレーション装置。
- 前記判定手段は、前記第2の事後分布および前記統合後の事後分布の各分散値に基づいて、いずれを用いるかを決定することを特徴とする請求項1から請求項5のいずれか1項に記載のシミュレーション装置。
- 前記状態ベクトルは、シミュレーションの対象領域内で離散化された格子点ごとの状態変数からなり、
前記観測モデルは、前記状態変数の格子点と、前記複数の観測データの観測点の解像度とを、前記観測データ毎に関係付けることを特徴とする請求項1から請求項6のいずれか1項に記載のシミュレーション装置。 - 前記各状態変数の確率分布が、離散化されて独立に計算されるアンサンブルの集合によってそれぞれ近似され、
前記事後分布統合手段は、前記アンサンブルの集合によって近似される前記各状態変数の確率分布を、所定の割合で重ねあわせることにより統合することを特徴とする請求項1から請求項7のいずれか1項に記載のシミュレーション装置。 - シミュレーションにおける状態ベクトルの初期状態およびパラメータと、複数の観測データとが入力されると、
前記初期状態およびパラメータを基に、システムモデルを用いて前記状態ベクトルの時間発展をシミュレーションし、
前記システムモデルにおける前記状態ベクトルに関連する情報に基づいて、前記複数の観測データのうち利用する複数の観測データを選択し、
選択された複数の観測データにそれぞれ対応する複数の観測モデルを用いて、それぞれ、前記システムモデルから出力される状態ベクトルを、前記観測データおよび前記状態ベクトルの関係性に基づき変換し、
前記複数の観測モデルから出力される状態ベクトルおよび選択された前記観測データに基づいて、前記状態ベクトルの事後分布を生成し、
選択された全ての観測データに基づく第1の事後分布と、1つ以上欠如した観測データに基づく第2の事後分布とを統合し、
前記第2の事後分布および前記統合後の事後分布のいずれを用いるかを決定し、
決定した事後分布および前記第1の事後分布からなる状態ベクトルを前記システムモデルに入力し、
決定した事後分布および前記第1の事後分布からなる状態ベクトルの時系列を出力するシミュレーション方法。 - シミュレーションにおける状態ベクトルの初期状態およびパラメータと、複数の観測データとを入力として取得する入力ステップと、
システムモデルを用いて、前記初期状態およびパラメータを基に、前記状態ベクトルの時間発展をシミュレーションするシステムモデル計算ステップと、
前記システムモデルにおける前記状態ベクトルに関連する情報に基づいて、前記複数の観測データのうち利用する複数の観測データを選択するデータ選択処理ステップと、
選択された複数の観測データにそれぞれ対応する複数の観測モデルを用いて、それぞれ、前記システムモデルから出力される状態ベクトルを、前記観測データおよび前記状態ベクトルの関係性に基づき変換して出力する観測モデル計算ステップと、
前記複数の観測モデルから出力される状態ベクトルおよび前記データ選択処理ステップで選択された観測データに基づいて、前記状態ベクトルの事後分布を生成し、前記データ選択処理ステップで選択された全ての観測データに基づく事後分布を第1の事後分布として出力し、1つ以上欠如した観測データに基づく事後分布を第2の事後分布として出力する事後分布生成ステップと、
前記第1の事後分布と前記第2の事後分布とを統合する事後分布統合ステップと、
前記第2の事後分布および前記統合後の事後分布のいずれを用いるかを決定する判定ステップと、
前記判定ステップで決定された事後分布および前記第1の事後分布からなる状態ベクトルを前記システムモデルに入力するとともに、該状態ベクトルの時系列を出力する出力ステップと、
をコンピュータ装置に実行させるコンピュータ・プログラムを記憶した記憶媒体。
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