CN118333129A - Identification model training method, nonlinear system identification method and system - Google Patents

Abstract

The present invention belongs to the technical field of nonlinear system identification, and provides an identification model training method, a nonlinear system identification method and a system. A plurality of different neural network models are used to extract features of input data and output data to obtain different intermediate features; an alternating direction multiplier method is used to optimize parameters; a stochastic gradient descent algorithm based on a sliding data window is used to obtain the variation of each layer of the neural network model, and the parameters of each layer of the neural network model are updated; input features are extracted using a plurality of different models, and the effect is better than that of the original single model, and the fitting effect of the nonlinear system is better. In addition, the stochastic gradient descent algorithm based on the sliding data window enhances the utilization rate of data, improves the convergence speed and accuracy of the algorithm, and at the same time, only one model direction is followed when optimizing the model parameters, which enhances the training effect of the model and shows good results in the identification task of the nonlinear system.

Description

Identification model training method, nonlinear system identification method and system

Technical Field

The present invention belongs to the technical field of nonlinear system identification, and in particular relates to an identification model training method, a nonlinear system identification method and a system.

Background technique

In the automation of industrial production processes, it is often necessary to measure and control the liquid levels of certain equipment and containers, and adjust the balance of input and output materials in the containers to ensure proper material matching in each link of the production process. The cascade water tank system is a relatively common industrial field liquid level system, which consists of two water tanks, a reservoir and a water pump. The basic principle is that the water pump pumps the water in the pool to the higher water tank, and then the water flows from the higher water tank to the lower water tank through an opening, and finally flows to the reservoir.

System identification is a classic topic widely used in automatic control. It is the basic theory for establishing the mathematical model of the target system and plays an irreplaceable role in modern engineering. At present, the system objects to be identified are generally nonlinear systems, such as the identification of cascade water tank systems. The main goal of system identification is to infer an actual automatic system or to establish a dynamic model from observed data to accurately predict future data. Multi-innovation theory is a branch of system identification. Its basic idea is to extend the length of innovation and make full use of useful information from data, that is, to introduce past data multiple times in training. Deep learning has been a very popular field in recent years. It is based on the previous neural network and adds a more complex and deep network, which can be used to fit most nonlinear problems. Deep networks have been applied in many fields and have achieved great success, such as computer vision, speech recognition and natural language processing. Stochastic gradient-based optimization methods have core practical significance in many fields of science and engineering. In deep learning, stochastic gradient descent has been proven to be an effective parameter search optimization method in countless practices.

The inventors have found that when identifying nonlinear systems such as cascade water tank systems, by adding a more complex and deep network on the basis of the neural network, it can be used to fit most nonlinear problems; however, the current nonlinear system identification model based on the neural network model still has many difficult-to-handle nonlinear problems, the fitting effect is poor, and the utilization rate of data during the training process needs to be improved, the convergence speed and accuracy are not high, and the training effect and effect identification are poor.

Summary of the invention

In order to solve the above problems, the present invention proposes an identification model training method, a nonlinear system identification method and a system. The present invention uses a variety of different models to extract input features, which has better performance than the original single model and better fitting effect on nonlinear systems. The stochastic gradient descent algorithm based on the sliding data window enhances the utilization of data and improves the convergence speed and accuracy of the algorithm. The parameter optimization strategy based on the principle of the alternating direction multiplier method enhances the training effect of the model.

In order to achieve the above object, the present invention is implemented through the following technical solutions:

In a first aspect, the present invention provides a recognition model training method, comprising:

Obtain input and output data of nonlinear systems;

Input data and output data are input into preset multi-layer neural network models for training to obtain recognition models; during training, multiple different neural network models are used to extract features of input data and output data to obtain different intermediate features; the alternating direction multiplier method is used for parameter optimization. In each round of parameter optimization, the parameters of other neural network models are fixed, and only the parameters of one neural network model are adjusted, and all neural network models are updated in sequence;

According to the pre-constructed loss function, the output of the network is compared with the actual output of the nonlinear system to obtain the error; based on the stochastic gradient descent algorithm of the sliding data window, the change of each layer of the neural network model is obtained, and the parameters of each layer of the neural network model are updated.

In a second aspect, the present invention provides a nonlinear system identification method, comprising:

Obtain input and output data of nonlinear systems;

Obtain identification results based on input data, output data, and a preset identification model;

Among them, the identification model includes multiple layers of different neural network models for training to obtain the identification model; during training, multiple different neural network models are used to extract features of input data and output data to obtain different intermediate features; the alternating direction multiplier method is used for parameter optimization, and in each round of parameter optimization, the parameters of other neural network models are fixed, and only the parameters of one of the neural network models are adjusted, and all the neural network models are updated in turn; according to a pre-constructed loss function, the output of the network is compared with the true output of the nonlinear system to obtain the error; based on the stochastic gradient descent algorithm of the sliding data window, the change amount of each layer of the neural network model is obtained, and the parameters of each layer of the neural network model are updated.

Furthermore, the nonlinear system is a cascade water tank system characterized by a nonlinear autoregressive model, and the cascade water tank system includes two water tanks and a water pump; the two water tanks have different heights, the input data is the water level of the lower water tank, and the input data is the water pump voltage.

Furthermore, different intermediate features are merged as input to the feature processing network; the merged intermediate features are subjected to multi-layer nonlinear transformation using the feature processing network to obtain the final model output.

Furthermore, the loss function of the h -th feature extraction network in each round of parameter iteration is as follows:

;

;

;

Among them, β is a hyperparameter that controls the degree to which the model is affected by the overall network output; represents the intermediate features obtained by input processing, represents the corresponding real output of the system, i is a constant; Indicated in The model output under the action of ; n represents the number of training data.

Furthermore, the loss function is reconstructed as follows:

;

Where W and b represent the network's learnable parameter weight and bias, respectively; p represents the innovation length, and j is a constant;

The error between the model output and the true output for:

.

In a third aspect, the present invention further provides a nonlinear system identification system, comprising:

The data acquisition module is configured to: obtain input data and output data of the nonlinear system;

The identification module is configured to: obtain an identification result according to the input data and the output data and a preset identification model;

Among them, the identification model includes multiple layers of different neural network models for training to obtain the identification model; during training, multiple different neural network models are used to extract features of input data and output data to obtain different intermediate features; the alternating direction multiplier method is used for parameter optimization, and in each round of parameter optimization, the parameters of other neural network models are fixed, and only the parameters of one of the neural network models are adjusted, and all the neural network models are updated in turn; according to a pre-constructed loss function, the output of the network is compared with the true output of the nonlinear system to obtain the error; based on the stochastic gradient descent algorithm of the sliding data window, the change amount of each layer of the neural network model is obtained, and the parameters of each layer of the neural network model are updated.

In a fourth aspect, the present invention further provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the nonlinear system identification method described in the first aspect.

In a fifth aspect, the present invention further provides an electronic device comprising a memory, a processor, and a computer program stored in the memory and capable of running on the processor, wherein when the processor executes the program, the steps of the nonlinear system identification method described in the first aspect are implemented.

In a sixth aspect, the present invention further provides a computer program product, wherein the computer program product comprises a computer program, and when the computer program is executed by a processor, the steps of the nonlinear system identification method described in the first aspect are implemented.

Compared with the prior art, the present invention has the following beneficial effects:

The present invention uses a plurality of different neural network models to extract features from input data and output data during model training to obtain different intermediate features; uses an alternating direction multiplier method to perform parameter optimization, and in each round of parameter optimization, fixes the parameters of other neural network models, only adjusts the parameters of one of the neural network models, and updates all the neural network models in sequence; compares the output of the network with the true output of the nonlinear system according to a pre-constructed loss function to obtain an error; uses a random gradient descent algorithm based on a sliding data window to obtain the variation of each layer of the neural network model, and updates the parameters of each layer of the neural network model; uses a plurality of different models to extract input features to obtain more diversified information, which is more excellent than the original single model effect and has a better fitting effect on the nonlinear system. In addition, the random gradient descent algorithm based on the sliding data window introduces past information in the parameter training process, enhances the utilization rate of data, and improves the convergence speed and accuracy of the algorithm. At the same time, a parameter optimization strategy based on the principle of the alternating direction multiplier method is proposed. When optimizing the model parameters, only one model direction is used, instead of all model parameters participating in the training at the same time in the past, so as to enhance the training effect of the model and show better results in the identification task of the nonlinear system.

BRIEF DESCRIPTION OF THE DRAWINGS

The drawings in the specification that constitute a part of this embodiment are used to provide a further understanding of this embodiment. The schematic embodiments of this embodiment and their descriptions are used to explain this embodiment and do not constitute improper limitations on this embodiment.

FIG1 is an overall flow chart of model parameter optimization in Example 1 of the present invention;

FIG2 is a graph showing the variation of the MLP model training error when the number of samples is 500 according to Example 1 of the present invention;

FIG3 is a graph showing the variation of the MLP model test error when the number of samples is 500 according to Example 1 of the present invention;

FIG4 is a graph showing the test error variation of the TCN model according to Example 1 of the present invention;

FIG5 is a graph showing the test error variation of the RNN model of Example 1 of the present invention;

FIG6 is a box plot of the error distribution of the new model and other single models when the number of samples is 1000 in Example 1 of the present invention;

FIG7 is a box plot of the error distribution of the new model and other single models when the number of samples is 8000 in Example 1 of the present invention.

Detailed ways

The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

It should be noted that the following detailed descriptions are exemplary and are intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present application belongs.

Embodiment 1:

This embodiment provides a recognition model training method, including:

Obtain input and output data of nonlinear systems;

Input data and output data are input into preset multi-layer neural network models for training to obtain recognition models; during training, multiple different neural network models are used to extract features of input data and output data to obtain different intermediate features; the alternating direction multiplier method is used for parameter optimization. In each round of parameter optimization, the parameters of other neural network models are fixed, and only the parameters of one neural network model are adjusted, and all neural network models are updated in sequence;

According to the pre-constructed loss function, the output of the network is compared with the actual output of the nonlinear system to obtain the error; based on the stochastic gradient descent algorithm of the sliding data window, the change in the parameters of each layer of the neural network model is obtained, and the parameters of each layer of the neural network model are updated.

By using a variety of different models to extract input features, we can obtain more diversified information, which performs better than the original single model and has a better fitting effect on nonlinear systems. In addition, the stochastic gradient descent algorithm based on the sliding data window introduces past information in the parameter training process, which enhances the utilization of data and improves the convergence speed and accuracy of the algorithm. At the same time, a parameter optimization strategy based on the principle of alternating direction multiplier method is proposed. When optimizing model parameters, only one model direction is used instead of all model parameters participating in the training at the same time as before, which enhances the training effect of the model and shows good results in the identification task of nonlinear systems.

Based on the identification model training method, this embodiment also provides a nonlinear system identification method, as shown in FIG1 , the specific steps include:

S1. Data acquisition and preprocessing of nonlinear systems;

Optionally, the nonlinear system adopts a cascade water tank system, which is a liquid level control system including two water tanks. The input and output of the cascade water tank system are the water pump voltage and the water level of the low water tank, respectively. A general nonlinear model, i.e., a nonlinear autoregressive model with exogenous inputs (NARX), can be used to characterize the cascade water tank system:

in, represents the mapping of the nonlinear autoregressive model; y ( k ) represents the system output, i.e., the water level of the low water tank, is a positive integer representing the sampling time sequence, u ( k ) is the external input of the model, i.e., the pump voltage; lu and ly represent the maximum lag time between input and output respectively; take N inputs u (1), u (2), ..., u ( k )..., u ( N ), input them into the model in sequence, and obtain N outputs y (1), y (2), ..., y ( k )..., y ( N ) with corresponding time sequence, and obtain a data set ( U , Y ) with N samples, where U contains N inputs. , Y contains the system output corresponding to the timing ; Divide the data set into a training data set and a test data set, and normalize and standardize the training data set and the test data set respectively.

S2. Combining multiple networks into an identification model to fit the collected training data, that is, using the neural network as the mapping g () of the nonlinear autoregressive model in step S1 to construct the relationship between the pump voltage and the low water tank water level in the cascade water tank system. The steps for building the identification model are as follows:

S2.1. Select appropriate m neural network models f for feature extraction. These models can be convolutional networks (CNN) and long short-term memory networks (LSTM). The input is processed by different networks, and different features are extracted from each network. The output of a network with L layers can be expressed as:

in, represents the output of the feature extraction network; represents the input of the network; W and b are the learnable parameter weight and bias of the network respectively; L represents the number of layers of the network; Represents a nonlinear transformation function, which can be in the form of RELU or related variants.

S2.2. Different intermediate features Merge as input to the feature processing network .

S2.3, the feature processing network combines these abstract features Perform multiple layers of nonlinear transformation to obtain the final model output , the whole model can be expressed as:

Among them, Fd is the feature processing network, which processes _the intermediate features to obtain the final output.

S3. Select the loss function J according to the properties of the input and output data, and use the theory of multiple innovations and the alternating direction method of multipliers (ADMM) to improve the loss function J and improve the fitting effect of the model on the actual data. That is, select an evaluation function to detect whether the proposed neural network can effectively reflect the relationship between the preset input and output. The specific steps are as follows:

S3.1. System identification usually involves regression prediction tasks, and its data is usually positive. Therefore, the loss function J of the evaluation model uses the mean square error (MSE):

in, is the network model output under the action of the kth data u ( k ) input in the data set; y ( k ) represents the corresponding real output of the system; N represents the total number of samples.

S3.2. In the parameter optimization iteration of the model, batch processing is adopted. In each round of parameter optimization, n training data are randomly selected for training, where the network input , Represents the input randomly extracted from the data set U , processed by the model, and the output is obtained ,in, Indicated in The model output under the action of , so the loss function in each round of parameter iteration can be written as:

S3.3. Using the parameter optimization idea of ADMM, the parameters of each network are optimized separately during parameter iteration. That is, in each round of parameter optimization, the parameters of other models are fixed, and only the parameters of one of the models are adjusted. All models are updated in sequence to enhance the integrity of the network.

S3.4. In each feature extraction model f , introduce the model's own loss function:

in, It is for input The intermediate features obtained by processing are used to suppress the excessive liberalization of the parameter space and make the model more stable. Under the above conditions, the loss function of the hth feature extraction network in each round of parameter iteration is as follows:

Among them, β is a configurable hyperparameter between 0 and 1, which controls the degree to which the model is affected by the overall network output. The loss function of the output _network Fd remains consistent with the original formula.

S4. Combining the multi-innovation theory, on the basis of the original batch stochastic gradient algorithm, the data used in each round of training is expanded to obtain a gradient descent algorithm based on a moving data window, which is applied to the training of the model to optimize the entire network structure and obtain the best model. That is, the network parameters are obtained through the optimization algorithm to restore the model of the cascade water tank system.

S4.1. According to the data set obtained in step S1, divide it into a training set and a test set, and use the samples in the training set to train the parameters.

S4.2. The parameters of the network model are initialized randomly. The weight W and bias b of each layer are randomly selected from a Gaussian distribution with a mean of 0 and a variance of 0.25.

S4.3, use the random search method to find the best hyperparameters. Specifically, set the batch size, optimizer learning rate, and β in step S3.4 to a reasonable range, randomly select a combination of the three values within these ranges for partial training, and select the most appropriate set of values as the subsequent parameters based on the training results;

Expand the input and output data with a batch size of innovation length p , introduce the data used in the previous rounds into this training, increase the data used in each round of training, and on this basis, reconstruct the loss function in step S3 as follows:

Among them, n represents the number of training data, that is, the batch size; p represents the length of the new information.

S4.4. Input the training data into the network and get the network output According to the reconstructed loss function, the network output is compared with the real output of the system to obtain the new error E. According to the stochastic gradient descent algorithm, the change of each layer parameter is obtained. Through reverse propagation, the optimization path of each layer parameter is obtained, and the parameters of each layer are updated. At the tth iteration, the parameter optimization algorithm of w can be expressed as:

in, represents the step size at the tth iteration; n represents the amount of training data; p represents the information length; Indicates the model output corresponding to the pn inputs involved in the calculation; is the error between the model output and the true output. Since the sliding window data is added, it is expressed as:

S4.5. All training data are put into the training for a specified number of times. In each round of parameter training, the loss function is reconstructed according to the principle of ADMM, and the parameters of each model are updated in turn, which can be expressed as:

Where w _h represents the parameters of the h -th model; w _d represents the parameters of the feature processing network F _d ; E _h ( p, t ) represents the error between the h -th model output and the true output at time t :

The training data is subjected to a specified number of reciprocating optimization calculations, and the best performing model parameters are saved, that is, the model with the closest mapping relationship to the original system. The test data is input into the saved model to obtain the predicted output of the model. The MSE is used to measure the gap between the predicted input of the model and the actual output of the system. If the error meets the requirements, the system is identified. If the error does not meet the requirements, the model is trained continuously until the requirements are met, thereby achieving the approximation of the cascade water tank system and achieving the purpose of controlling the water level of the water tank by the water pump voltage.

In order to verify the effectiveness of the network model and the optimization algorithm in this embodiment, this embodiment uses the identification model in the task of system identification. Optionally, the fitted NARX system is:

Among them, u [ k ] is selected from a randomly generated standard Gaussian distribution. In this embodiment, u [ k ] is used as input to predict the output y [ k ]. The backtracking step length used is 5, that is, the first 5 input data are used as the input of the model to predict the output of the 6th data at the next moment. The model used in this experiment is composed of a multilayer perceptron (MLP) and a temporal convolution network (TCN). TCN is a variant of a convolutional neural network that can be used for sequence signals. This experiment uses the above network to fit the above-mentioned nonlinear function. The data set is randomly generated by the system, that is, the system output is obtained by randomly generating input, and the generated training set samples are used to optimize the parameters of the model. Then, the fitting effect of the model is tested through the test data set, and the mean square error is used to judge the performance of the model. In the experiment, this embodiment first tested the effect of the stochastic gradient algorithm based on the sliding data window. This embodiment tested the descent effect of the algorithm by using different innovation lengths p . p = 1 represents the use of the original gradient descent algorithm. When the number of samples is 500, the MLP model is modeled, and the changes in the training loss and the test loss are shown in Figures 2 and 3. The optimal test error is shown in Table 1:

Table 1 Test results of improved gradient descent algorithm

It can be seen that under different sample numbers, the optimization algorithm based on the sliding data window performs better, and the tests on other models also show the same results. Figures 4 and 5 are the test errors of the recurrent neural network (RNN) and TCN. As the length of the new information increases, the convergence speed is obviously faster and the test results are relatively better.

When testing the performance of the proposed new model, the input and output data of the above system are collected. Under the same conditions, the single model MLP, TCN and the proposed new model are modeled respectively, and their optimal test errors are compared. The optimizer is set to Adam, the learning rate is 0.01, the number of training times is 10, and the best result is taken. Under the same running time, the test error of the new network model is shown in Table 2:

Table 2 Modeling test results of different network models

It can be seen that the model in this embodiment performs better. Even if the performance is slightly insufficient under certain sample numbers, its convergence speed is still faster than other single models. In addition, according to the distribution of data, this embodiment obtains a box plot of the test error, as shown in Figures 6 and 7. The results of this embodiment are obviously better than the original single model.

Embodiment 2:

This embodiment provides a nonlinear system identification method, including:

Obtain input and output data of nonlinear systems;

Obtain identification results based on input data, output data, and a preset identification model;

Among them, the identification model includes multiple layers of different neural network models for training to obtain the identification model; during training, multiple different neural network models are used to extract features of input data and output data to obtain different intermediate features; the alternating direction multiplier method is used for parameter optimization, and in each round of parameter optimization, the parameters of other neural network models are fixed, and only the parameters of one of the neural network models are adjusted, and all the neural network models are updated in turn; according to a pre-constructed loss function, the output of the network is compared with the true output of the nonlinear system to obtain the error; based on the stochastic gradient descent algorithm of the sliding data window, the change amount of each layer of the neural network model is obtained, and the parameters of each layer of the neural network model are updated.

The identification model training method in the method is the same as the identification model training method in Example 1, and will not be repeated here.

Embodiment 3:

This embodiment provides a nonlinear system identification system, including:

The data acquisition module is configured to: obtain input data and output data of the nonlinear system;

The identification module is configured to: obtain an identification result according to the input data and the output data and a preset identification model;

Among them, the identification model includes multiple layers of different neural network models for training to obtain the identification model; during training, multiple different neural network models are used to extract features of input data and output data to obtain different intermediate features; the alternating direction multiplier method is used for parameter optimization, and in each round of parameter optimization, the parameters of other neural network models are fixed, and only the parameters of one of the neural network models are adjusted, and all the neural network models are updated in turn; according to a pre-constructed loss function, the output of the network is compared with the true output of the nonlinear system to obtain the error; based on the stochastic gradient descent algorithm of the sliding data window, the change amount of each layer of the neural network model is obtained, and the parameters of each layer of the neural network model are updated.

The working method of the system is the same as the nonlinear system identification method of Example 1, and will not be repeated here.

Embodiment 4:

This embodiment provides a computer-readable storage medium on which a computer program is stored. When the program is executed by a processor, the steps of the nonlinear system identification method described in Embodiment 1 are implemented.

Embodiment 5:

This embodiment provides an electronic device, including a memory, a processor, and a computer program stored in the memory and capable of running on the processor. When the processor executes the program, the steps of the nonlinear system identification method described in Example 1 are implemented.

Embodiment 6:

This embodiment provides a computer program product, which includes a computer program. When the computer program is executed by a processor, the steps of the nonlinear system identification method described in Embodiment 1 are implemented.

The above description is only a preferred embodiment of the present embodiment and is not intended to limit the present embodiment. For those skilled in the art, the present embodiment may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present embodiment shall be included in the protection scope of the present embodiment.

Claims (10)

1. The identification model training method is characterized by comprising the following steps of:

Acquiring input data and output data of a nonlinear system;

Inputting the input data and the output data into a preset multi-layer different neural network model for training to obtain an identification model; during training, a plurality of different neural network models are utilized to extract characteristics of input data and output data, so that different intermediate characteristics are obtained; parameter optimization is carried out by using an alternate direction multiplier method, parameters of other neural network models are fixed in the optimization process of each round of parameters, only the parameters of one neural network model are adjusted, and all the neural network models are updated in sequence;

Comparing the output of the network with the real output of the nonlinear system according to a pre-constructed loss function to obtain an error; and obtaining the variable quantity of each layer of neural network model based on a random gradient descent algorithm of the sliding data window, and updating the parameters of each layer of neural network model.

2. The nonlinear system identification method is characterized by comprising the following steps:

Acquiring input data and output data of a nonlinear system;

Obtaining an identification result according to the input data, the output data and a preset identification model;

The identification model comprises a plurality of layers of different neural network models for training to obtain the identification model; during training, a plurality of different neural network models are utilized to extract characteristics of input data and output data, so that different intermediate characteristics are obtained; parameter optimization is carried out by using an alternate direction multiplier method, parameters of other neural network models are fixed in the optimization process of each round of parameters, only the parameters of one neural network model are adjusted, and all the neural network models are updated in sequence; comparing the output of the network with the real output of the nonlinear system according to a pre-constructed loss function to obtain an error; and obtaining the variable quantity of each layer of neural network model based on a random gradient descent algorithm of the sliding data window, and updating the parameters of each layer of neural network model.

3. The nonlinear system identification method of claim 2, wherein the nonlinear system is a cascade water tank system characterized by a nonlinear autoregressive model, the cascade water tank system comprising two water tanks and a water pump; the two water tanks are different in height, the input data is the water level of the lower water tank, and the input data is the water pump voltage.

4. The nonlinear system identification method as claimed in claim 2, wherein different intermediate features are combined as inputs to the feature processing network; and carrying out multi-layer nonlinear transformation on the combined intermediate features by utilizing a feature processing network to obtain a final model output.

5. The nonlinear system identification method in accordance with claim 2, wherein the loss function of the h feature extraction network at each round of parameter iteration is as follows:

；

；

；

wherein beta is a super parameter, and the control model is influenced by the output of the whole network; Representing intermediate features resulting from the processing of the input, Representing the corresponding real output of the system, wherein i is a constant; is shown in Outputting the model under action; n represents the number of training data.

6. The nonlinear system identification method in accordance with claim 5, wherein reconstructing the loss function is as follows:

；

wherein W and b represent the learnable parameter weight and bias of the network, respectively; p represents the length of the innovation; j is a constant;

Error of model output and true output The method comprises the following steps:

。

7. a nonlinear system identification system, comprising:

a data acquisition module configured to: acquiring input data and output data of a nonlinear system;

An identification module configured to: obtaining an identification result according to the input data, the output data and a preset identification model;

The identification model comprises a plurality of layers of different neural network models for training to obtain the identification model; during training, a plurality of different neural network models are utilized to extract characteristics of input data and output data, so that different intermediate characteristics are obtained; parameter optimization is carried out by using an alternate direction multiplier method, parameters of other neural network models are fixed in the optimization process of each round of parameters, only the parameters of one neural network model are adjusted, and all the neural network models are updated in sequence; comparing the output of the network with the real output of the nonlinear system according to a pre-constructed loss function to obtain an error; and obtaining the variable quantity of each layer of neural network model based on a random gradient descent algorithm of the sliding data window, and updating the parameters of each layer of neural network model.

8. A computer readable storage medium, on which a computer program is stored, characterized in that the program, when being executed by a processor, implements the steps of the nonlinear system recognition method in accordance with any one of claims 2-6.

9. An electronic device comprising a memory, a processor and a computer program stored on the memory and capable of running on the processor, characterized in that the processor implements the steps of the nonlinear system identification method in accordance with any one of claims 2-6 when the program is executed by the processor.

10. A computer program product, characterized in that the computer program product comprises a computer program which, when being executed by a processor, implements the steps of the nonlinear system recognition method in accordance with any one of claims 2-6.