EP0995156A2

EP0995156A2 - Method and structure for the neural modelling of a dynamic system in a computer

Info

Publication number: EP0995156A2
Application number: EP98943653A
Authority: EP
Inventors: Hans-Georg Zimmermann; Ralf Neuneier
Original assignee: Siemens AG
Current assignee: Siemens AG
Priority date: 1997-07-09
Filing date: 1998-07-08
Publication date: 2000-04-26
Also published as: WO1999003043A3; WO1999003043A2; JP2001509623A

Abstract

The invention relates to a method and a neurone layer structure for the neural modelling of dynamic systems. To this end, parameters describing inertia and parameters describing acceleration of the system's time series are trained and processed separately in the network. The prognostic values thus obtained are combined to give a desired prognostic quantity. Different target quantities in the form of average values with bases of different widths can be obtained by defining different indicators for each dynamic parameter. A greater fault current for returning to the network is generated by training these values. This makes possible exact simulation of the different dynamic parameters. The inventive structure and method are preferably used for stock exchange forecasts and for other dynamic systems.

Description

description

Method and structure for neural modeling of a dynamic system on a computer

The invention relates to a method and a layer arrangement for a neural network, with which in particular dynamic systems can be modeled well, such as technical systems or economic systems.

When modeling dynamic systems using neural networks, there is generally the problem that the information about the dynamics of the system is contained in the temporal / dependence of adjacent patterns of time series. Most common learning methods of neural networks present the patterns to the neural networks in a random arrangement in order to avoid local minima and to increase the learning speed. In this way, the network obtains its knowledge of the coupling of the individual temporal patterns only implicitly from the slowly changing neuron weights. It is particularly difficult to model a dynamic system when many input variables, i.e. on the order of e.g. 30 input variables (but there can also be several hundred) to a few, i.e. a single output variable or optionally two output variables are to be processed. In order to get a good picture of the system behavior through the neural network, a lot of time series have to be presented to the network, which are often not available in reality and especially with economic data.

In order to get a grip on this problem, there are approaches in the state of the art to use the inherent structure of dynamic systems for their neural modeling. In the dynamic systems to be modeled, it is particularly important on the target side that a sufficient number of output variables in the form of different Targets are available to describe successive states of the system. In this way, more error information flows back from the target side to the input side of the network and the system can thus be described in more detail. Further details can be found in Hans Georg Zimmermann and Andreas S. Weigend, "How To Represent Dynamical Systems In Feed Forward Networks: A Six Layer Architectuie" Proceedings of the Fourth International Conference on Neural Networks in the Capital Market (NNCM-96), page ^" 1-18, published in Decision Technologies for Financial Engineering. This publication proposes a six-layer model for a neural network to measure the dynamics of a technical system, or a system that predicts stock data by means of a dynamic characterization of the For the purpose of better modeling of a time series, several neighboring values of the time series are trained there separately in different branches of the neural network as targets and later combined by averaging to the desired output quantity Net at the exit dur ch imprinted a so-called interaction layer.

In this context, a branch is to be understood as a part of the neural network, which is itself an artificial neural network with inputs, at least one output and adaptable weights when individual neurons are coupled.

DE 195 37 010 AI discloses a learning method and a learning arrangement for emulating a dynamic process by learning at least two time series together. A separate learnable component is provided for each time series, to which historical values of the time series used are added. A present component of a

Time series is decorrelated from its historical values and the historical values of the other time series. From US 5 479 571 A a neural network with two hidden layers is known.

The object on which the invention is based is to specify a further method and a further structure with which dynamic systems can be modeled neuronally on a computer.

This object is achieved according to the features of claim 1 for the method and according to the features of claim 8 for the structure.

The method for neural modeling of a dynamic system on a computer comprises the following features: a) Influencing variables of the dynamic system are used to emulate at least one first output variable into at least one first influencing variable, which determines the inertia of the dynamic system and into at least a second influencing variable, which determines the acceleration of the dynamic system groups; b) in a neural network (NN) at least a first (ZI) and a second (Z2) parallel branch of the neural network (NN) are trained separately with the behavior of the first influencing variable or second influencing variable; c) to form a first output variable (AD) depending on the influencing variables (ED), the or all outputs of the parallel branches (ZI, Z2) of the neural network (NN) are combined.

The layer arrangement for a neural network for simulating a dynamic system has the following features: a) for simulating at least one first influencing variable, which determines the inertia of the dynamic system, and a second influencing variable, which determines the acceleration of the dynamic system, there are at least one hidden first (4000) or second (4500) neuron layer, as well as a first (5000) or second (5500) output layer; b) there is a combination layer (6000) for combining the simulated first influencing variable (610) and second influencing variable (620) into output variables.

Advantageous developments of the invention result from the dependent claims.

In a further development different dynamic influencing variables of the dynamic system are distinguished which characterize the inertia and the acceleration of the system. Through separate modeling in different sub-branches of a neural network according to the method according to the invention, the neural network is forced to learn the target size on the basis of different dynamic characteristics, the same input time series being able to be used. The output variable to be simulated is only subsequently formed by superimposing the modeled target variables of these two different dynamic parameters.

Time series in the form of time series vectors of various influencing variables can advantageously be supplied to the neural network, and the output variable formed is combined into a single output variable by weighted averaging, since this reduces the noise component in the input variables and a more accurate replication by modeling different input variables the output size is possible.

In a further embodiment, it is particularly advantageously provided that the incoming signals are preprocessed by neuron-weighting them, these neuron weights being determined by subordinate positions of the neuron signals. len network can be set in order to filter out undesirable influencing variables that have nothing to do with the dynamic system to be modeled.

The branches of the neural network can radial through implementation ^'Ba are supplied, since thus the neural network to carry out different cases the possibility is also given in addition to determine sisfunktionen similarities within the pattern not only with linear predictors, but also with square weighted predictors.

Furthermore, for the dynamic parameter to be supplied to the respective neural network, i.e. In other words, inertia parameters or acceleration parameters, a plurality of indicators are formed, so that a larger amount of error return is generated within the network by a plurality of target variables, and thus a more accurate replication of the respective dynamic variable is possible. For this purpose, the mean value or the curvature is preferably modeled with several defined interval distances around the target value.

Furthermore, the input variables for the method can be prepared in the form of the selected indicators in order to show the network a clear picture of the internal state of the dynamic system to be modeled. A dynamic system is characterized by the momentarily acting inertia and influencing forces. From the input time series offered, one can now draw conclusions about the acting inertia and the forces by using the first and second differences of the time series. To normalize the order of magnitude of the input indicators, we also divide by the time series, which leads to relative changes.

In a further embodiment, some of the forces are not simply represented as second derivatives. In many processes, the dynamic system is movement characterized by a balance. Here the distance between a point in the time series and the equilibrium is a better characterization of the acting force than the description in the form of an acceleration. As a simple approximation to the description of the currently valid equilibrium point, the mean value of the last values of the time series can be used. If you now choose the difference between the current value of the time series and the mean value as equilibrium, you have used the latest point information but compared it with an outdated estimate of the equilibrium. It proves to be more advantageous in the difference to choose a past value of the time series such that the averaging for estimating the equilibrium is arranged symmetrically about this point. In this way, a better characterization of the tension between point and equilibrium of the dynamic system to be characterized is obtained.

Furthermore, a layer arrangement for a neural network for simulating a dynamic system can be provided, because there is a separate branch in the neural network for each dynamic parameter to be simulated, and an increased error reflux is generated by checking the hidden positions with an output layer, by means of which the The information about the dependence of neighboring time series values is imprinted on the neural network.

In a further development of the layer arrangement according to the invention, a preprocessing layer is provided which serves both or the respective network branches together, since, for example, no two different preprocessing stages have to be provided and since the weights in the preprocessing layer are set by the error feedback from the respective branches of the neural network, in order to filter out undesired influencing variables and thus a more precise filtering out of disturbance variables can take place. In a further development of the layer arrangement, a square layer is particularly advantageously provided, which square-weighted the input values or the values supplied by the preprocessing layer. This enables the subsequent layers to simulate radial basic functions and thus to establish similarity references and not just case distinctions of incoming patterns.

The combination layer, the individual branches of the layer arrangement, can be followed by a possibly weighted mean value layer in order to form an average value from the vectors of the prediction variable and thus to minimize the noise within the individual values.

Control layers, which model the interval distances of the individual indicators from the respective dynamic parameter to be reproduced and which prevent the neural network or the respective branch of the neural network from taking place, are particularly advantageous in the layer arrangement of the respective branches of the neural network as output layers different indicators modeled only one.

An exemplary embodiment of the invention is explained in more detail below with reference to figures.

FIG. 1 shows an example of a block diagram of a method according to the invention. FIG. 2 shows an example of a neural network with a neuron layer arrangement according to the invention.

As FIG. 1 shows, a method EV has, for example, processing blocks, a first processing block ZI and a second processing block Z2, and a further processing block 3000. The processing blocks ZI and Z2 denote two separate branches, a first branch ZI and a second branch Z2 of a neural network NN.

The first processing block ZI and the second processing block Z2 receive input data in the form of time series which are taken from a real system, i.e. were measured.

A plurality of processing layers, a first processing layer 1000 and a second processing layer 2000 of the first processing block ZI or a first processing layer 1500 and a second processing layer 2500 of the second processing block Z2 are provided in the first and second processing blocks ZI and Z2 in the neural network NN, respectively are interconnected by signal lines 110 and 120.

In the first processing block ZI, acceleration parameters, such as the force which causes a reset or a dynamic in the system, are described.

In the second processing block Z2, inertia parameters of the dynamic system are simulated. The input data of the time series with which these respective processing blocks are supplied identically according to the method are processed in relation to identical indicators for these respective dynamic parameters.

For the second processing block Z2, it is provided to emulate an average value around a prediction value by drawing time series values at various intervals around this value from this prediction value for averaging.

This applies analogously to the first processing block ZI, in which the curvature of the time series can be supplied for different curve sections around the predicted value. After the internal processing in the various branches of the neural network, or the processing blocks ZI and Z2, the output variables are fed via connecting lines 210 and 220 to a combination module 3000, which uses them to generate output data, ie the prediction value. It is achieved by the method that separate target sizes are defined for a respective dynamic parameter and these are simulated in different branches of a neural network. In this way, a strict separation of these dynamics-characterizing variables is achieved in the modeling, in that separate indicators are also learned during the training by the neural network. By forming a plurality of indicators per processing block ZI, Z2 it is achieved that a plurality of target sizes must be learned and thus the respective dynamic variable to be reproduced by the processing block is better simulated by an increased error feedback within the processing branch because the error feedback increases leads to a more precise adjustment of the weights in the neural network.

As FIG. 2 shows, a neural layer model for the neural modeling of a dynamic system has a plurality of layers 1000, 2000, 3000, 4000, 4500, 5000, 5500, 6000, 7000, 75000, the respective thousands indicating the numbering of the layers .

The connections between the individual layers are described by thick and thin arrows, the thick arrows indicating that a weight adjustment can be carried out, while the thin arrows indicate that predefined weights are set.

Although seven layers are shown in this exemplary embodiment, it is not necessary for the invention that all layers are present for the implementation of the invention are. The basic principle of the invention can also be represented by layers 4000 to 6000.

A preprocessing of the time series data of the dynamic system is carried out in front of the input neuron layer 1000 of the neural network NN. With regard to economic data, the preprocessing shows the network a picture of the momentum and forces currently effective in the markets.

In particular, individual sub-dynamics, expressed by the various input variables, by their inertia and the forces associated with them, should be characterized. The relative change in an input variable is preferred as a measure of the inertia. In this way, the speed in the change of this input variable is represented and the magnitude of the input variable is standardized.

The second derivative of the input variable is used to characterize a force. However, input variables can optionally be equilibrium variables, the restoring force of which depends on a distance between the current state and the respective state of equilibrium. In a mechanical system, this is the deflection of a spring pendulum from the idle state. In an economic system, for example, this observation quantity is a price that is derived from a process of equilibrium between supply and demand.

For the characterization of this, a different approach offers a description of the driving force. With such dynamics, the distance from the current value to the equilibrium value is a better measure of the force which the system retracts towards the equilibrium state. A simple estimate of the equilibrium position can be calculated by averaging the last values in the time series. However, this procedure has the disadvantage that the current value of the time series contrasts with an outdated estimate of the equilibrium value.

Therefore, the following way is preferred to reset the point value to be predicted to such an extent that it becomes possible to compare a central mean value of the point information. This concept can be understood using the following examples, where the index t denotes the current period, t-6 e.g. the time 6 steps earlier and aver (x (t), 12) indicates the averaging over the most recent 12 data.

1.x = inflation indicator (e.g. a time series that does not originate from an equilibrium process) INPUT = (x (t) - x (t-6)) / x (t-6) INPUT = (x (t) - 2 * x (t-6) + x (t-12)) / x (t-6) y = US- $ (example of a time series defined by a supply - demand balance) INPUT = (y (t) - y ( t-6)) / y (t-6)

INPUT = (y (t-6) - aver (y (t), 12)) / y (t-6)

However, this external preprocessing in front of the input layer 1000 cannot completely solve an urgent problem, which arises, for example, in economic analyzes. This involves limiting outliers, or rather filtering larger movements of economic time series, which were not brought about by the economy but by political decision-making. Here, however, the problem arises of specifying the unknown size from which the damping of the input variables is to be carried out.

For this purpose, a preprocessing layer 2000 is provided for the neural layer arrangement, with which the problem caused by the neural network NN interna- is achieved by the unknown damping constants appearing as learnable parameters in the network.

The internal preprocessing of the signals offered to the neural network NN is carried out by means of a weight matrix between the input layer 1000 and the preprocessing layer 2000, which consists of a diagonal matrix, which is denoted by 200.

The hyperbolic tangent (tanh) is used for the activation function of the first inner layer. This procedure and layer arrangement limit outliers in the values. Weight-based checking of inputs is also advantageously supported by this weight matrix. The weights should preferably be initialized with 1 in the preprocessing layer 2000 and the weights should preferably be limited to values between 0 and 1.

In the neuron layer arrangement, the output signals of the preprocessing layer 2000 are forwarded to three further neuron layers 3000, 4000 and 4500. While a pure copy of the signals is forwarded to layer 3000, so that 300 denotes an identity image, the subsequent layers 4000 and 5000 or 4500 and 5500 receive the signals derived from preprocessing layer 2000 and transforms them linearly and squared, which is indicated by arrows 400 to 450 is indicated.

By using a quadratic activation function on the data output by the preprocessing layer 2000 in the neuron layer 3000, it is achieved that the neural network can also implement radial basic functions and thus can not only make case distinctions, but can also learn similarities in the patterns offered. The signals 400, 410 or 420 and 450 generated in this way are then weighted in the neuron layers 4000 and 5000 or 4500 and 5500 multiplied, the layers 5500 and 5000 representing output layers of the neural network NN, while the layers 4000 and 4500 represent hidden neuron layers.

This part of the neural layer arrangement combines the classic concepts of a multilayer perceptron with a sigmoid inner layer of neurons and a classic radial basis function network. This connects the global and local approaches to these approximation approaches. As

The activation function for the preprocessing layer 2000 and the hidden layer 4500 is chosen as the hyperbolic tangent. It may be helpful to add a Softmax function to the activation function.

Layers 5000 and 5500 identify the underlying dynamic system. For this purpose, these two layers are provided as the first starting layers in the neural layer arrangement and have target values that are to be learned. The weights of layers 4000 to 5500 can be adapted here, as already indicated in the explanation of the arrow strengths. For the layer 5500, which is intended to model, for example, the inertia component of the dynamic system, 3-point averages and balance information of the time series to be approximated are offered as target values. Some examples of such target values are given below.

TARGET = (x (t + 5) + x (t + 6) + x (t + 7)) / (3 * x (t)) - 1) TARGET = (x (t + 4) + x (t + 6) + x (t + 8)) / (3 * x (t)) - 1) or

TARGET = (aver (x (t + 7), 3) - x (t)) / x (t)

TARGET = (aver (x (t + 8), 5) - x (t)) / x (t)

These embeddings are preferably arranged symmetrically around the value to be predicted here, for example x (t) +6. As averages, they also show the advantageous property to attenuate noise in the data. Layer 5000, on the other hand, which acceleration properties of the system should learn, is offered so-called forces or mean-inverting information. The following characterizations are available for the forces that are offered as target or target values of the output layer 5000:

1.TARGET = (-x (t + 5) + 2 * x (t + 6) - x (t + 7)) / (3 * x (t)))

TARGET = (-x (t + 4) + 2 * x (t + 6) - x (t + 8)) / ^' (3 * x (t))) or

TARGET = (x (t + 6) - aver (x (t + 7), 3)) / x (t)

TARGET = (x (t + 6) - aver (x (t + 8), 5)) / x (t)

These are force characterizations in the form of accelerations, or in the form of reversal forces in

Balance situations. A crucial point is that the embeddings and the associated forces are simply added in pairs to the target value desired in the end

TARGET = (x (t + 6) - x (t)) / x (t)

complete. You can understand this by simply adding up the two formulas that are adjacent to each other and adjacent. Of course, it should not be indicated here that this procedure is the only way to implement the invention. With the teaching given, each average specialist can select other averages or other target sizes and combine them accordingly in order to emulate a predicted target value without being inventive or without proceeding in the sense of the invention. Since many characterizations of the dynamics can preferably be represented and thus learned through different embeddings and different ranges of the associated forces, 4500, 5500 or 4000 and 5000 are created in the replication of the dynamic branches. co co MM I- ¹ P ¹

Cπ o cπ O Cπ o cn tr φ Φ 52 O CL 3 52 UI- ^{1 y} QP "<^ Q CΛ 3 DJ g IS ⁾ CΛ ιQ S yQ i ^ - P CL CL cπ p- 52 tt CΛ

NP P- φ P d φ φ φ φ DJ DJ φ φ Φ Φ Φ Di 3 3 Z rt Φ φ Ci DJ Φ Φ d P CL Dl Hi CL Ό z 3 rt CL 3 rt tr ZP 3 PP rt P rt n CL Φ P- CΛ P- P "3 3 P d Φ rt Φ CL P

• DJ Φ N 3 yQ er Φ Φ PP "ιQ 3 er ιQ CΛ N er Φ CL P- ω rt CΛ rt 3 n 3 3 d: P- P- φ d 3 DJ d cn DJ 3 P- = φ rt P - P n rt ^y QP P- o DJ Φ P- P- tr et rt P "rt n

CΛ tr P 3 ιQ 3 O tr 3 O: er ^ φ Φ Z er rt Q P- DJ φ ^y Q p- P- Φ P- er

^• <rt PO yQ Φ P- CL P- fr P- φ d α εo P- o Φ Φ rt P- Φ 3 tr P d Φ CΛ P- O Φ ω φ er 3 cn Φ vQ Hi 3 1-1 3 Φ Φ φ d P tr P- P Φ 3 3 ^y Q φ 3 et O o σ> 3 rt t DJ tr er P> v

Ct P- P- D: OP Φ: et P 3 α 3 CL N 3 rt rt φ 3 r CL φ P- n rt P- So er P er tsi O 3 Φ 3 z rt Φ α Φ tt & Z Φ 3 Φ o P-

3 φ er Φ cn Φ Φ Φ pd ^ 3 _^ Hi 3 CL φ • Φ P 3 CL P- P cn P- d P ^ CΛ 3 <cn Φ W rt PX • -3 d cn cn P- d = Φ d rt P Φ CΛ P- 3 O rt n 3 cn φ s P- d P-

52 3 rt <J ^• o DJ 3 DJ p- n CL P 3 P Φ CL cn P- Φ φ »Q er 3- CL n 3 3 3 Φ φ

Φ P- d Φ Φ tr P ιQ a n er DJ O 3 Φ O> n CΛ P 3 Φ er tr CL CL P- P "

P- o tt P cn P N P- ιQ p er rt G> ^ H er P er d tr O d 3 DJ P- CL P- 3 φ

3 er Φ Hi z N Φ Φ Φ rt P 3 CΛ P- CΛ Φ CJ 52 CΛ tP 3 Φ Φ P ¹ φ σ »Φ

N rt he CL Φ DJ • P- rt P 3 p- DJ CL ß ^: rt Φ n φ »QP tr Φ Φ Z cn CL P CL tr NJ PN d P * φ P- tT rt ZP er vQ P ¹ DJ a Φ P- he P CL DJ er Φ d P- n P- d Φ o Z

Hi P- φ 3 3 H Ό φ φ Φ DJ rt cn 3 P 3 P- Di: φ 3 Φ P P N d P er P- tt 3 3 Z P-

DJ 3 P Φ er 3 P P- 3. φ d Φ n Hi ^y Q P- od P et * n P ιQ H) er φ cn

3 Φ cn t- <Z 3 • rt n ^y Q 52 3 DJ er rt CL cn rt DJ 3 CΛ n P- er Pi DJ φ P- n ^y Q DJ rt Φ φ cn S Φ e ö <Φ ιQ £ rt Φ φ cn Φ ^y Q φ DJ er φ Φ P- cn P- a rt er

Φ HHP cn tr P- O rt 3 d φ d P ^J o Φ P n 3 Φ 3 a σ tP 3 rt Φ Φ φ

3 P- O 3 φ N f ιQ - p- P P P d ιQ CL 3 d er • P CΛ a φ P- φ IS! CL DJ CΛ d P 3

• rt 3 φ 3 z DJ Φ Φ rt o cn o 3 P φ 3 <P- d n Φ P- Φ 3 z d rt rt Φ Ό

DJ: 3 rt P "P" α er O 3 et O: P ¹ ^] rt φ o 3 er 3 3 cn CL φ 3 rt tt Φ 3 P ec rt NP ¹ P- P ¹ Φ DJ CL er DJ EP P "o Φ P er ^y Q P- ιQ φ φ P- ^y Q Hi DJ: 3 o

P- d CL P- CL cn P- ι-f EP Φ et P- P- s Φ P- o P cn rt o Φ N iQ p- P "2 iQ φ CL P dn P- n φ 3 3 DJ Φ φ P- 3 φ o Φ rt Φ N er CΛ £ <d Φ <3 P ¹ P- Φ 3

P Φ P er Φ er P rt Φ cn CL rt P P- 3 d rt φ P- P- Φ CL Φ 3 do tr CΛ <n Φ Φ d P- ι-3 φ 52 rt d 3 P- CΛ rt rt φ Φ P- P Φ P CΛ

Φ φ er cn Φ P 3 ∑: 3 DJ tz 3 Φ Φ et 3 -J Di φ DJ: s N rt} - ^• P- 3 cn rt CL et o Φ

P- NPP ^y Q P- H Φ φ rt P- ιQ cπ 3 CL o rt _§ rt Φ N 3 rt - Φ P- 3 3 d Hi s Hi σ H CL ιQ P 3 N s: Φ o CL φ o N tt P ^J DJ Φ Φ tr 3 Φ Φ

CΛ P- * <o- CL φ Φ 3 Φ CL o Φ 3 o ZS er 3 P- P- of cn Cn d: P- φ 3 Φ od vQ φ P 3 3 fr • 3 rt Φ P tr φ P Φ P- CΛ Φ Φ P ¹ 3 Φ er tr φ cn P

P ^> 3 d CL

B ^* DJ o iQ 3 3 Φ rt Φ PZ 3 dn rt PPH Φ Ct 3 DJ 3 n 3 ^{^}

P ^J rt 3 <J d 3 3 H CL CL P- Φ N 3 er DJ CL rt D> 3 Φ φ P er DJ rt Φ ^y Q P- DJ 3 P- O 3 O: et P- P- Φ P d W CL rt φ tr OP 3 _^ W P- P "

Φ P φ P- yQ fr 3 rt ϊ> Φ ^y Q P- CL 3 CL P- Φ rt 3 P- 3 uq 52 Φ CL Φ n rt

CΛ NP ¹ cn Φ P- Φ Φ P DJ 3 φ rt φ? ^ 3 -J P- Hi φ Φ DJ P- P- er Φ tr dd φ ^y Q 3 cn P 3 rt P- Φ P Φ 3 o tr Cπ 3 P- Ct CS3 rt d σ tP 3 cn rt 3

Φ π 3 φ rt <UI- O Cl P 3 φ o Φ 3 z d Z Z P Ό ^

<! er cn Φ 3 CL he DJ Z Φ P er *> w CΛ tr rt rt o 3 α φ 3 P- Φ o et CL P- σι o Φ rt> ^■ P DJ: d φ P ¹ P- £ Φ O P - rt Φ P rt Φ P ^« iQ CΛ P 3 DJ D» Φ φ o Z

P 3 Φ d S> P. PP ^J P Φ 3 φ P * er <! O d ω rt rt n rt DJ 3 tr 3 o Φ

N CL P "CΛ <5 Φ n Φ t p- P- P ¹ Ct P- o 3 P- d • er N er P- P- Φ Φ o P" d φ P ^J ιQ o er σ 3 P "tr 3 Φ d φ PP ^{1 y} Q 3 CΛ φ d Φ - N φ fr P- 3 et n vq 3 Φ Dl P CΛ tr p- φ φ 3 CL N P- Φ CL ιQ <5 3 d 3 T P- φ he rt

3 3 iQ n CL N Φ ^y Q P- 3 cn ^y Q φ d Φ 3 H o tr φ Ό DJ UI. tr Φ P φ

3 iQ Φ er J DJ d P- Φ 3 TJ yQ P <1 Φ P Φ P- P fr 52 P φ P- yQ tr DJ cn cn P- cn 3 iQ 3 S P- Ct CL rt Φ d O P- rt P- 3 O o Φ DJ et Φ Φ cn

Φ p et 3 on P- Φ tr ¹ P- φ φ • 3 3 P n Φ cn Φ »Q rt 3 o P CL σ P- J fr Φ Φ er er φ ^ - o Φ M Φ rt P er Φ • rt iQ er P- τ P 3 & N φ n Φ Φ on rt P d P ^J rt H φ PP 3 P rt φ • P- Φ Φ P- P- O P- rt er i 3 3 er er φ P DJ Φ Hi 3 CL rt 3 Φ 3 t-3 3 σ P cn Λ er φ Φ Cn 3 N Φ φ rt • rt cn Φ O ιQ 3 P- 3 tt Φ <! - DJ CL vQ P- Φ φ rt DJ P ¹ 3 Φ P- d <P- P- C

Φ cn 3 Φ DJ 3 d φ Φ PO s: NP Φ Φ Φ P- er DJ Hi CΛ CL 3 φ o 3 rt ö d rt Φ 3 3 1 3 rt er 1 P Φ d 1 P 1 CΛ 3 Φ rt rt 1 1 3 3 Φ D: P- P 3 Φ 1 et Φ 1 1 P Φ 1 3 P- o rt φ 3 P rt 1 1 • o er

Cπ

Claims

Claims:

1. Method for neural modeling of a dynamic system on a computer with the following features: a) Influencing variables of the dynamic system are used to simulate at least a first output variable in at least one first influencing variable, which determines the inertia of the dynamic system and in at least a second influencing variable, which determines the acceleration of the dynamic system, groups; b) in a neural network (NN) at least a first (ZI) and a second (Z2) parallel branch of the neural network (NN) are trained separately with the behavior of the first influencing variable or second influencing variable; c) to form a first output variable (AD) depending on the influencing variables (ED), the or all outputs of the parallel branches (ZI, Z2) of the neural network (NN) are combined.

2. The method according to claim 1, in which the influencing variables of the dynamic system for emulating at least one first output variable are grouped into a plurality of first influencing variables which determine the inertia and a plurality of second influencing variables which determine the acceleration of the dynamic system.

3. The method according to claim 1 or 2 a) in which the influencing variables (ED) are fed to the neural network (NN) in the form of time series vectors and thus a

Output variable vector is formed from first output variables (AD), b) and in which the mean value of its vector components is formed to form the first output variable.

Method according to one of claims 1 to 3, in which an intra-network preprocessing of the branches supplied Variables (ED) for damping disturbances contained in the influencing variables (ED) is carried out.

5. The method according to any one of claims 1 to 4, ^' in which the parallel branches (ZI, Z2) are supplied in parallel with linear and square-weighted influencing variables (ED).

6. The method according to any one of claims 1 to 5, in which at least two indicators with which the branches are trained as separate targets are formed from at least the first and / or the second or the second influencing variable or influencing variables.

7. The method according to any one of claims 3 to 6, wherein the first influencing variable as the embedding of a value in the

Time series and the second influencing variable is used as the curvature of the time series ..

8. The method according to any one of claims 3 to 6, in which the time series are prepared according to the indicators.

9. Layer arrangement for a neural network for simulating a dynamic system with the following features: a) for simulating at least one first influencing variable, which determines the inertia of the dynamic system, and a second influencing variable, which determines the acceleration of the dynamic system, are at least one hidden first (4000) or second (4500) neuron layer, as well as a first (5000) or second (5500) output layer; b) there is a combination layer (6000) for combining the simulated first influencing variable (610) and second influencing variable (620) into output variables.

10. Layer arrangement according to claim 9, in which a preprocessing layer (2000) for filtering out the first (4000) and second (4500) hidden neuron layers (2000) a disturbance variable and generation of filter data for supplying the first and second hidden neuron layers (4000, 4500) is present.

11. Layer arrangement according to one of claims 9 to 10, in which a squaring layer is provided between the first and second hidden neuron layers (4000, 4500) and the preprocessing layer (2000) for generating square-weighted filter data or input data.

12. Layer arrangement according to one of claims 9 to 11, in which the combination layer (6000) is followed by an averaging layer (MWF), for generating averaged output variables.

13. Layer arrangement according to one of claims 9 to 11, in which the first or second output layer (5000, 5500) is followed by an output layer (7000, 7500) in the form of a control layer, for checking properties of several each of the first and second influencing variables.