TW201322149A - Method of establishing system equivalent model combined with Volterra system and its computer program product - Google Patents

Abstract

This invention discloses a method of establishing a system equivalent model combined with Volterra system and its computer program product. In this method, a neural network system model is first provided, which is combined with a Volterra system model and a feed-forward neural network model. A digital input signal is inputted into the neural network system model and the target system model at the same time to obtain a neural network system output signal and a target system output signal. According to the neural network system output signal and the target system output signal as the conditions, a differential evolution algorithm is used to calculate a neural network system coefficient, which is introduced into the neural network system model, so as to allow the neural network system model to be equivalent to the target system.

Description

Method for establishing system equivalent model of Votra system and its computer program product

The invention relates to a modeling method of an equivalent system model, and in particular to a modeling method for establishing an equivalent system model of an unknown target system by using a differential evolution algorithm.

In the prior art, system identification is a very important key in the field of automatic control. Based on this identified system model, we can further design the appropriate controller using various control techniques. In order to effectively identify unknown systems, the traditional prediction models include autoregressive time series patterns, autoregressive modes with external input variables, and autoregressive moving average modes. Nowadays, methods of artificial intelligence technology for system identification are increasingly valued, including: neural networks, fuzzy systems and a combination of fuzzy neural networks. These types of modes have considerable adjustable weight parameters. The ability to recognize far exceeds the traditional mathematical models. Traditionally, the correction of tunable parameters within these networks often utilizes the so-called gradient correction method.

However, system identification models built using artificial intelligence techniques, such as neural network models, require complex mathematical derivations and lengthy numerical operations. Excessive data operations can increase the computer or other similar electronic operators. The burden of software and hardware, while reducing the computing power of related devices. Moreover, the electronic computing unit constructs the above equivalent system based on the externally input information. Once the operation error occurs, the performance of the equivalent system obtained is far from the performance of the real unknown system. Re-establishing the equivalent system model will inevitably increase the difficulty. Secondly, the disadvantage of the gradient correction method is that the searched solution is often a local optimal solution that falls near the starting value, rather than the best solution of the whole domain. The reason is that the gradient correction method is a single-direction search method, which makes it possible to find The solution easily falls into the local extremum.

The problem to be solved by the present invention is to provide a method by which a user can quickly establish an optimal equivalent system model for an unknown system.

In order to solve the above problems, the technical means provided by the present invention discloses a system equivalent model establishing method combining the Votra system, which is used to establish an equivalent system model of a target system model, and the method first provides a neural network system. The model combines a Volterra system model with a feedforward neural network model to simultaneously input a digital input signal into a neural network system model and a target system model to obtain a neural network system output signal. And a target system output signal, based on the neural network system output signal and the target system output signal, using a differential evolution rule to calculate a type of neural network system coefficient, and importing a neural network system coefficient to the neural network The system model is such that the neural network system output signal approaches the target system output signal to make the neural network system model equivalent to the target system model.

In order to solve the above problems, the technical means provided by the present invention discloses a computer program product. After reading the computer program product, a computer system executes a system equivalent model establishing method combining the Votra system, and the method flow includes: A neural network system model is provided, which is a Votra system model, and a digital input signal is simultaneously input into a neural network system model and a target system model to obtain a neural network system output signal and a target system output signal. According to the output signal of the neural network system and the output signal of the target system, a differential evolution rule is used to calculate a class of neural network system coefficients, and a neural network system coefficient is introduced into the neural network system model to make the neural network. The road system output signal approaches the target system output signal to make the neural network system model equivalent to the target system model.

The invention is characterized by:

First, this method has excellent system coefficient search ability and fast convergence, so that the designed neural network system model will be completely equivalent or quite close to the performance of the unknown target system model. Satisfy or as close as possible to the operational needs of the unknown target system model, thus significantly reducing the time cost of establishing an equivalent system model.

Secondly, this method can also break away from the situation that the local optimal solution generated by data conversion during the construction of the model helps to shorten the time required for the electronic operator to construct the above equivalent system model.

Third, this method does not require complicated mathematical derivation and lengthy numerical operations, so it does not generate a large amount of data, and does not increase the burden of software and hardware of a computer or other similar electronic computing device to maintain a certain degree of related equipment. The performance of the operation.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS The preferred embodiments of the present invention will be described in detail below with reference to the drawings.

1 is a schematic flowchart of a method according to an embodiment of the present invention, FIG. 3 is a schematic diagram of a neural network construction system according to an embodiment of the present invention, and FIG. 4 is a schematic diagram of a feed-like neural network model according to an embodiment of the present invention. Architecture diagram. This method mainly constructs a neural network system model by the following processes. The neural network system model is stored and executed in an electronic device to establish an equivalent system model of a target system model. Moreover, the present invention discloses a computer program product, and a computer system executes the above-described system equivalent model establishing method in combination with the Votra system after reading the computer program product. It is known from Fig. 1 that the steps of the design method of the neural network system model are as follows:

First, a neural network system model 130 is provided, which is composed of a Wotra system model 131 and a feedforward neural network model 132 (step S110). This Votra system model 131 can be expressed by the following equation:

Where x is the input signal of (Equation 1), y is the output signal of (Equation 1), h [ k ] is the primary system coefficient of (Equation 1), and N is the past input of (Equation 1), h [ k ₁ , k ₂ ] is the quadratic system coefficient of (Formula 1). For the convenience of the following description, (Formula 1) can be expressed as:

y [ n ]= h [0]+ h [1] x [ n ]+ h [2] x [ n -1]+...+ h [ N ] x [ n - N +1]+ h [0,0 ] x ² [ n ]+ h [0,1] x [ n ] x [ n -1]+...+ h [0, N -1] x [ n ] x [ n - N +1]+...+ h [ N -1, N -1] x ² [ n - N +1] (Equation 2)

Among them, the total number of coefficients of the Votra system model 131 is:

L represents the total number of coefficients of the Votra system model. Thereafter, in order to facilitate the integration of the Votra system model 131 with the feedforward neural network model 132, the order is:

X =[ x ₁ , x ₂ ,..., x _L ]=[1, x [ n ], x [ n -1],..., x [ n - N +1], x ² [ n ], x [ n ] x [ n -1],... x [ n ] x [ n - N +1],..., x ² [ n - N +1]] (Equation 4)

Where X = [ x ₁ , x ₂ , ..., x _L ] is the input signal (or input vector) of the feedforward neural network model 132.

Please refer to FIG. 4 , which is a schematic diagram of the structure of the feed-forward neural network model 132 of the present invention. The feed-forward neural network model 132 includes an input layer structure 1321 , a hidden layer structure 1322 , and an output layer structure 1323 . . The number of neurons in the input layer 1321 comprising a structure that is the total number of the coefficients L, this is also the vector length L (equation 4) of the input signal. The number of neurons in the hidden layer structure 1322 is assumed to be M , and the number of neurons in the output layer structure 1323 is one.

Where X (ie, X = [ x ₁ , x ₂ ,..., x _L ], a positive integer of i = 1 to L ) is the input vector of the feedforward neural network model 132, and each of the hidden layer structures 1322 Yuan can be expressed as:

Wherein, w _ Representative xh _ij input layer structure 1321 i-th neural structures 1322 j th right neurons coupling weight value elements and the hidden layer, w _ hy _j representative of the hidden layer structure 1322 j-th neuron of the output layer structure 1323 The weight value of the neuron-linked, where i = 1, 2, ..., L and j = 1, 2, ..., M , y _model (described later) is the output representing the feedback-like neural network The output signal of the layer structure 1323. Further, net _ h _j , θ_ h _j , and h _j are the internal state, the threshold, and the output signal of the j- th neuron of the hidden layer structure 1322, respectively, and (Equation 6) is a nonlinear excitation function. The neurons of the output layer structure 1323 can be represented as:

y _model = f ( net _ y )= net _ y (Equation 8)

Where net _ y and θ_ y are the internal states and thresholds of the neurons representing the output layer structure 1323, respectively, and y _model is the output signal of the feedforward neural network model 132 (ie, the subsequent neural network system output) Signal), the output signal should be as close as possible to the output signal of the target system model (ie, the target system output signal stated later). Therefore, through the teachings of the foregoing formulas, the total number of tunable parameters within the feedback-like neural network is:

P = L × M + M + M +1= M ( L +2) +1 (Equation 9)

Where P is the total number of tunable parameters of the feedforward neural network model 132. In order to enable the neural network system model to further cite the differential evolution algorithm, the feedforward neural network model 132 is combined with the Votra system model 131, and the formation vector of the required system prediction coefficient is revealed. (Equation 10):

W =[ w ₁ , w ₂ ,..., w _P ]=[ w _ xh ₁₁ ,..., w _ xh _{1 M} , w _ xh ₂₁ ,..., w _ xh _{2 M} ,...,, w _ xh _{L 1} ,..., w _ xh _LM , θ_ h ₁ ,..., θ_ h _M , w _ hy ₁ ,..., w _ hy _M , θ_ y ] (Equation 10)

Where W=[w _i1 , w _i2 ,...,w _iP ] is the estimated coefficient of each system of the different values of the neural network system model.

A digital input signal is simultaneously input into the neural network system model 130 and the target system model 140 to obtain a type of neural network system output signal and a target system output signal (step S120). As described above, the same digital input signal x is simultaneously input to the neural network system model 130 and the target system model 140 to obtain the respective neural network system output signals y _model and the target system output signal y of the two modes.

In addition, in order to facilitate the use in the differential evolution algorithm, the coefficients of the neural network system model 130 are first constructed into a plurality of system prediction coefficient vectors, and the coefficient vector of each system is represented by (Equation 10), the vector The length is shown in (Equation 9).

Then, based on the neural network system output signal and the target system output signal, a differential evolution rule is used to calculate a type of neural network system coefficient (step S130). In this step, the calculation module 110 first calculates the error value e of the target system output signal y and the neural network system output signal y _model , where e [ n ]= y [ n ]- y _model [ n ], and It is imported into the calculus module 120 running the differential evolution rule, and the calculus module 120 finds a set of system prediction coefficients after the introduction of the neural network system model 130, so that the neural network system outputs the signal y _model and the target. The error value e between the system output signals y is minimized.

Please also refer to FIG. 2 for a flow chart of the steps of the differential evolution method of the present invention.

The calculus module 120 randomly generates a plurality of system prediction coefficient vectors to form a group (step S210), wherein each system prediction coefficient vector has a plurality of system prediction coefficients, as described above, each system prediction coefficient vector is determined by The coefficients of the neural network system model 130 are composed of:

W =[ w ₁ , w ₂ ,..., w _P ]=[ w_xh ₁₁ ,..., w_xh _{1 M} , w_xh ₂₁ ,..., w_xh _{2 M} ,...,, w_xh _{L 1} ,..., w_xh _LM , θ_ h ₁ , ..., θ_ h _M , w_hy ₁ ,..., w_hy _M , θ_ y ] (Equation 10)

Where P = L × M + M + M +1 = M ( L + 2) +1. However, in order to avoid excessive divergence during particle operation, the calculus module can pre-set a search boundary [ w _l , w _u ] of the particle displacement as the boundary value of the particle displacement, but not limited thereto. This boundary value is pre-designed by the designer or not, depending on the needs of the designer.

The calculus module 120 calculates one of the value functions of each coefficient vector (step S220). As described above, in order to satisfy the requirement that the output signal y _{model of the} neural network system is close to the output signal y of the target system, a relation function of a value function is defined, and the value function of each coefficient vector is calculated by using the relationship. The relationship of this value function is expressed as follows:

Where H is the maximum number of sampling points of n (ie, the largest integer value of time n ), and e is the error value. When the value function is smaller, it means that the design meets the requirements.

The calculus module 120 selects a target coefficient vector from all the value functions, and takes the value function of the target coefficient vector as the target value function of the group (step S230). The target coefficient vector refers to the coefficient vector with the best value function in the ethnic group, that is, the system prediction coefficient contained in the coefficient vector, so that the output signal y _{model of the} neural network system is closest to the target system output signal y , with a view to A neural network system model 130 that is closest to the target system model 140 is established.

The calculus module 120 determines whether a termination condition has been reached (step S240). Here, the termination condition includes two: one has reached the number of iterations for this group, and the number of iterations refers to the maximum number of executables of the differential evolution algorithm, or the number of times the population can be evolved. The number of iterations needs to be preset. The other is that the target value function has converged to a minimum or reaches a target value, which needs to be preset.

When the termination condition is not established, the evolution of the ethnic group is performed (step S260). This evolutionary process has three operational steps of mutation, mating, and selection.

First, the way the mutation evolves is as follows, here (Formula 12):

V = W _α + f _s ‧ ( W _β - W _γ ) (Equation 12)

Where V = [ v ₁ , v ₂ ..., v _P ] is called a mutatric vector, and the vectors W _α , W _β and W _γ are three system prediction coefficient vectors arbitrarily selected from the above-mentioned groups. f _s [0, 2] is called a mutation constant factor and is a parameter that determines the size of a mutation.

When the calculus module 120 obtains the mutation vector V , it enters the mating evolution step of the differential evolution calculus. In this mating step, it is assumed that W = [ w ₁ , w ₂ , ..., w _P ] is a target vector in the population. Then, the target vector is exchanged with the element in the vector in the mutation vector V obtained in the above mutation process, and the vector T = [ t ₁ , t ₂ ..., t _P ] obtained after the mating is called a test vector. (trial vector). The process of the exchange condition is as follows: First, the calculus module 120 generates a set of P numbers between r _i A random random number [ r ₁ , r ₂ ,..., r _P ] between [0,1], and then obtain the values of P m _i according to the following formula:

Where CR (0, 1) is a crossover rate, and is usually set to 0.5. The test vector W is further generated by the following equation:

When m _i =1, the calculus module 120 takes the element of the target vector as the element of the test vector; when m _i =0, the element of the mutation vector is used as the element of the test vector, thus completing the mating process. Therefore, the test vector is the result of the mating of the elements of the mutation vector and the target vector.

When the test vector W is determined by the calculus module 120, the selection evolution step is entered. According to this (Equation 11), the value function of the coefficient vector of the above test vector and the target vector is calculated and compared at the same time.

When the calculus module 120 determines that the value function obtained by the test vector is smaller than the value function of the target vector, the target vector is removed from the next generation evolution (mutation, mating, and selection evolution) to test the vector complement; otherwise, the target The vector continues to be retained and the resulting test vector is removed.

When the mutation, mating, and selection processes are completed, the process returns to step S220 to repeat steps S220, S230, S240, and S260 until the termination condition is established.

When the termination condition is established, that is, the population has reached an iteration number, or the target value function has converged to a minimum or reaches a target value.

The calculus module 120 outputs the target coefficient vector to which the target value function belongs (step S250). At this time, the target value function of the target coefficient vector must have converged to a minimum, and the system predictor coefficient included in the target coefficient vector is a neural network. Road system factor.

Finally, the calculus module 120 introduces the obtained neural network system coefficients into the neural network system model 130 to adjust the neural network system model 130 so that the neural network system output signal y _model approaches the target system output signal. y (step S140), so that the neural network system model 130 operates as equivalent as possible to the target system model 140, thereby completing the modeling process of the equivalent system model of the entire target system model.

In the above, it is merely described that the present invention is an embodiment or an embodiment of the technical means for solving the problem, and is not intended to limit the scope of implementation of the present invention. That is, the equivalent changes and modifications made in accordance with the scope of the patent application of the present invention or the scope of the invention are covered by the scope of the invention.

110. . . Computing module

120. . . Calculus module

130. . . Neural network system model

131. . . Votra system model

132. . . Feedforward neural network model

1321. . . Input layer structure

1322. . . Hidden layer structure

1323. . . Output layer structure

140. . . Target system model

1 is a flow chart of a method for establishing a system equivalent model of the Votera system according to the present invention;

2 is a flow chart of the operation of the differential evolution method of the present invention;

3 is a structural diagram of an equivalent model establishing system according to an embodiment of the present invention;

FIG. 4 is a structural diagram of a feed-like neural network model before the embodiment of the present invention.

Step S110 to step S140

Claims (10)

A system equivalent model establishing method for combining a Votra system for establishing an equivalent system model of a target system model, the method comprising: providing a neural network system model, which is composed of a Votra system model and a former a feed-like neural network model is formed; a digital input signal is simultaneously input into the neural network system model and the target system model to obtain a neural network system output signal and a target system output signal; according to the neural network The road system output signal and the target system output signal are conditional, a differential evolution rule is used to calculate a type of neural network system coefficient; and the neural network system coefficient is introduced into the neural network system model to make the nerve The network system output signal approximates the target system output signal such that the neural network system model is equivalent to the target system model. The system equivalent model establishing method of the Votra system is described in the first claim of the patent scope, wherein the Votra system model is as follows: Where x is the input signal of the Votra system model, y is the output signal of the Votra system model, h [ k ] is the primary system coefficient of the Votra system model, and N is the Votra system model. In the past, the input term, h [ k ₁ , k ₂ ] is the quadratic system coefficient of the Votra system model; wherein the total coefficients of the Votra system model are: Where L is the total number of coefficients of the Votra system model, and let X = [ x ₁ , x ₂ ,..., x _L ]=[1, x [ n ], x [ n -1],..., x [ n - N +1], x ² [ n ], x [ n ] x [ n -1],... x [ n ] x [ n - N +1],..., x ² [ n - N +1]] The feedforward neural network model includes an input layer structure, a hidden layer structure and an output layer structure, wherein the neuron structure of the hidden layer structure is as follows: Wherein, the L is the number of neurons included in the input layer structure, and the X = [ x ₁ , x ₂ , . . . , x _L ] is an input signal of the feedforward neural network model, w _ xh _ij representative of the input layer structure of the i-th neuron and j-th weights of neurons connected to the hidden layer structure weighting value, w _ hy _j representing the hidden layer structure of the j-th neuron connected to neural layer structure of the output element weight value, i = 1,2, ..., N , j = 1,2, ..., M ,, net j is the j-th neuron internal state _ h, θ_ h _j is the j-th neuron threshold , h _j is the output signal of the jth neuron; and the neuron structure of the output layer structure is as follows: Where y _{model is} the output signal of the feedforward neural network model, net _ y is the internal state of the output neuron of one of the output layer structures, and θ_ y is the threshold of the output neuron of the output layer structure . The method for establishing a system equivalent model of the Votra system according to the second aspect of the patent application scope, wherein a differential evolution algorithm is used to calculate a type of nerve according to the output signal of the system and the output signal of the neural network system. The step of the network system coefficient includes at least: randomly generating a plurality of system prediction coefficient vectors to form a group, wherein each system prediction coefficient vector has a plurality of system prediction coefficients; and calculating the system prediction coefficient vector An individual value function, and according to the value function, selects a target value function representing one of the ethnic groups; and determines whether a termination condition is reached, and if the determination is yes, the target coefficient vector to which the target value function belongs is The included system prediction coefficient is used as the coefficient of the neural network system. If it is judged as no, the population is evolved. The system equivalent model establishing method of the Votra system is described in claim 3, wherein the estimated coefficient vector of each system is: W = [ w ₁ , w ₂ ,..., w _P ]=[ w _ Xh ₁₁ ,..., w _ xh _{1 M} , w _ xh ₂₁ ,..., w _ xh _{2 M} ,...,, w _ xh _{L 1} ,..., w _ xh _LM , θ_ h ₁ ,...,θ_ h _M , w _ hy ₁ ,..., w _ hy _M , θ_ y ], where W=[w _i1 , w _i2 , . . . , w _iP ] is the estimated coefficient of each of the system of the neural network system model. The method for establishing a system equivalent model of the Votra system, as described in claim 3, wherein the group undergoes an evolution process comprising the following steps: performing a mutation evolution on the group, arbitrarily from the neural network system model The plurality of system prediction coefficient vectors are selected to form a group, and a mutation vector is calculated according to the system prediction coefficient vectors; a mating evolution is performed on the group, and one target vector in the system of the prediction coefficients of the systems is set. And exchanging the mutation vector according to an exchange condition to obtain a trial vector; and performing a selection evolution on the population, calculating and selecting the target value function according to the test vector and the target vector Taking the target value function as the coefficient of the neural network system of the group. A method for establishing a system equivalent model of a Votra system as described in claim 5, wherein the target value function is defined as Where H is the number of points sampled and e is the error value. The method for establishing a system equivalent model of the Votra system according to Item 6 of the patent application scope, wherein in the mutation evolution step, the mutation vector is obtained by a construction operation, and the construction is V = W _α + f _s ‧ ( W _β - W _γ ), where V = [ v ₁ , v ₂ ..., v _L ] is the mutation vector, and W _α , W _β and W _γ are any selected ones of the group System prediction coefficient vector, f _s [0, 2] is called a mutation constant factor and is a parameter that determines the size of the mutation. The method for establishing a system equivalent model of the Votra system according to the seventh aspect of the patent application, wherein the mating evolution step is such that the W = [ w ₁ , w ₂ , ..., w _P ] is the systems A target vector in the estimated coefficient vector, which is exchanged with the element in the vector obtained by the mutation evolution, and the obtained coefficient vector is the test vector T = [ t ₁ , t ₂ ... , t _P ], the exchange condition is as follows: generate a group of P between r _i A random random number [ r ₁ , r ₂ ,..., r _P ] between [0,1], and then obtain the values of P m _i according to the following formula: Where CR (0, 1) is the crossover rate, which is set to 0.5, and the test vector W is as follows: A computer program product, after reading a computer program product, a computer system performs a system equivalent model establishing method combining a Votra system to establish an equivalent system model of a target system model, the method comprising: providing a class A neural network system model consisting of a Votra system model and a feedforward neural network model; a digital input signal is simultaneously input into the neural network system model and the target system model to obtain a class The neural network system outputs a signal and a target system output signal; according to the output signal of the neural network system and the output signal of the target system, a differential evolution rule is used to calculate a type of neural network system coefficient; and the neural network is introduced The network system coefficients are applied to the neural network system model such that the neural network system output signals approximate the target system output signals such that the neural network system model is equivalent to the target system model. For example, in the computer program product of claim 9, wherein the step of calculating a type of neural network system coefficient by using a differential evolution rule is at least included according to the output signal of the neural network system and the output signal of the target system. : randomly generating a plurality of system prediction coefficient vectors to form a group, wherein each system prediction coefficient vector has a plurality of system prediction coefficients; calculating individual value functions of the system prediction coefficient vectors, and according to the a value function, which selects a target value function representing one of the ethnic groups; and determines whether a termination condition is reached, and if the determination is yes, the target coefficient vector to which the target value function belongs, which includes the system prediction coefficient, is used as the class The neural network system coefficient, if judged as no, evolves the group.