A method for modeling asymmetric rate-dependent hysteresis based on play operator

Abstract

The present invention discloses an asymmetric rate-dependent hysteresis modeling method based on the play operator, comprising the following steps: S1, collecting the input voltage and output displacement of piezoelectric ceramics; S2, combining the play operator and the Elman neural network to establish an asymmetric hysteresis model; S3, introducing rate-dependent terms into the asymmetric hysteresis model; S4, updating the weights by the gradient descent method, and establishing the final model of asymmetric rate-dependent hysteresis. By using the play operator as the input of the Elman neural network, the input layer of the neural network is expanded. At the same time, the high-precision approximation capability of the Elman neural network is utilized to make the model parameter identification more convenient, and the Elman neural network has a classic training algorithm.

Description

Technical Field

[0001] The present invention relates to the technical field of signal processing, and in particular to an asymmetric rate-dependent hysteresis modeling method based on a play operator. Background Art

[0002] As the demand for positioning accuracy in important fields such as biomedicine, aerospace, and ultra-precision machining increases, traditional mechanical transmission positioning devices such as lever mechanisms, sliding or rolling guides, etc., cannot meet the requirements of precision positioning due to the large friction and gaps inside. In the exploration of micro-nano positioning devices, people have turned their attention to smart materials. Piezoelectric ceramics, as the driving element of the micro-displacement platform, are a kind of smart material that can convert mechanical energy and electrical energy into each other. They are familiar to the public because of their good mechanical properties and piezoelectric properties. In addition, piezoelectric ceramics also have a series of advantages such as fast response speed, strong load-bearing capacity, high positioning accuracy, and heat and moisture resistance. This has led more and more researchers to try to apply piezoelectric ceramic drivers to micro-positioning systems in order to achieve micro-nano positioning accuracy.

[0003] However, while piezoelectric ceramic actuators bring convenience in micro-nano positioning research, they also bring some disadvantages. Hysteresis nonlinearity is one of the main disadvantages of piezoelectric ceramics in micro-positioning applications. The complexity of hysteresis nonlinearity is manifested in: (1) multi-mapping: the output displacement of the piezoelectric ceramic actuator is different at the same input voltage value in the rising and falling segments of the input signal; (2) memory: the current output of the hysteresis is not only related to the current input value, but also to the historical extreme value of the input signal. The nonlinear relationship between the driving voltage and the output displacement seriously affects the positioning accuracy of the piezoelectric micro-motion stage and may even cause system instability, which limits the application of piezoelectric ceramic actuators in micro-positioning systems to a certain extent. In addition, hysteresis nonlinearity also shows obvious frequency correlation, that is, when the frequency of the input signal gradually increases, the width of the hysteresis loop increases and the height decreases. Therefore, in order to achieve precise positioning control of piezoelectric actuators, it is often necessary to establish a mathematical model that can accurately describe hysteresis nonlinearity in view of the inherent hysteresis nonlinearity of piezoelectric ceramics.

[0004] Due to the high-precision approximation ability, fast parallel computing ability and strong fault tolerance of neural networks, they are widely used in the identification of nonlinear systems. For the existing dynamic modeling methods of piezoelectric actuators using neural networks, RBF neural networks are mostly used. When using RBF neural networks to model piezoelectric hysteresis, not only is there a lack of research on the system's adaptability to time-varying characteristics, but the existing hysteresis modeling methods based on RBF neural networks also lack research on asymmetric hysteresis models and hysteresis characteristic modeling of frequency-related items. Summary of the invention

[0005] In view of the above technical problems, the present invention proposes a method for modeling asymmetric rate-dependent hysteresis based on the play operator, establishes an elman neural network structure, uses the play operator of the generalized PI model as the input layer input of the elman neural network, and introduces the frequency-related part in the weight of the elman neural network, so as to reduce the modeling error of the asymmetric rate-dependent hysteresis characteristics and improve the frequency generalization ability of the hysteresis model. By utilizing the high-precision approximation ability of the elman neural network, the modeling of asymmetric rate-dependent hysteresis based on the play operator and the elman neural network is realized, which can accurately describe the hysteresis curve of the piezoelectric actuator and has good frequency generalization ability, and is easy to implement in engineering.

[0006] The technical solution adopted by the present invention to solve the above problems is: a method for modeling asymmetric rate-related hysteresis based on a play operator, comprising the following steps:

[0007] S1. Collecting piezoelectric ceramic input voltage and output displacement

[0008] The method for acquiring the output displacement of the piezoelectric ceramic is to amplify the input voltage through a power amplifier circuit and load it to both ends of the piezoelectric ceramic to drive the piezoelectric ceramic to generate displacement, and collect the position of the piezoelectric ceramic through a laser displacement sensor;

[0009] S2, combining the play operator and the Elman neural network to establish an asymmetric hysteresis model;

[0010] S3, introducing rate-dependent terms into the asymmetric hysteresis model, and establishing an asymmetric rate-dependent hysteresis model;

[0011] S4, the gradient descent method is used to update the weights and establish the final model of asymmetric rate-dependent hysteresis.

[0012] Preferably, the piezoelectric ceramic is a piezoelectric ceramic with hysteresis characteristics.

[0013] Preferably, in step S2, the play operator is output by the PI model, and the output play operator is defined as:

[0014]

[0015]

[0016] Among them, t i =tT <t≤t i+1 ,0≤i≤N-1, N is the input voltage at the same time, N play operators are generated, v(t) is the control input, is the output of the play operator, r iis the input threshold of the play operator, t is the sampling time, T is the sampling period, for any input v(t)∈C m [0,t E ], so that the function in each subinterval [t i ,t i+1 ] is monotonous, C m [0,t E ] represents piecewise monotone continuous function space, 0 = t 0 <t 1 <… <t N =t E It is C m [0,t E ] is a division.

[0017] Preferably, the input threshold r of the play operator i Settings:

[0018]

[0019] Among them, max{|v(t)|, v(t)∈C m [0,t E ]} is the maximum value under the input conditions.

[0020] Preferably, the method for establishing the asymmetric hysteresis model in step S2 is:

[0021] S2-1. Introduce the envelope function H(v(t)):

[0022] H(v(t))=a 1 v 3 (t)+a 2 v(t)

[0023] Among them, H(v(t)) is a non-decreasing continuous function,

[0024] S2-2, according to the obtained play operator In the construction of the Elman neural network structure, the play operator and the envelope function H(v(t)) are used as the input space of the Elman neural network.

[0025] Under this condition, the calculation expressions of the function signal and error signal of the Elman neural network are described as:

[0026] The input and output of the input layer nodes of the Elman neural network are:

[0027]

[0028]

[0029] i=0,1,…,N-1

[0030] In the formula, I 0 is the input layer’s input, O 0 is the output of the input layer, N is the number of play operators under the input voltage at the same time, then the number of input layer nodes is N+2,

[0031] The input and output of the hidden layer of the Elman neural network are:

[0032]

[0033]

[0034] In the formula, I 1 is the input of the hidden layer, O 1 is the output of the hidden layer, is the synaptic weight connecting the feedback node of the background unit to the hidden layer neurons; is the synaptic weight connecting the external input point to the hidden layer neurons; q is the number of nodes of the hidden layer neurons,

[0035] The activation function for the hidden layer neurons is: positive and negative symmetric sigmoid function - hyperbolic tangent function:

[0036]

[0037] The input and output of the feedback layer node in the background unit are:

[0038]

[0039]

[0040] In the formula, I' 0 is the input of the feedback layer, O' 0 is the output of the feedback layer, and q is the number of nodes in the feedback layer, that is, the number of nodes in the hidden layer.

[0041] The output of the output neuron of the Elman neural network is:

[0042]

[0043] In the formula, I 2 is the input of the output layer, O 2 is the output of the output layer, q is the number of neurons in the hidden layer,

[0044] S2-3, finally combining the asymmetric hysteresis model of the Paly operator and the Elman neural network:

[0045]

[0046]

[0047] i=0,1,…,N-1

[0048]

[0049]

[0050] Preferably, in step S3, the method of introducing rate-related terms to establish an asymmetric rate-related hysteresis model is:

[0051] The derivative of the input voltage dv(t) / dt is introduced at the weight from the hidden layer to the output layer of the Elman neural network.

[0052]

[0053] At this time, an asymmetric rate-dependent hysteresis model with rate-dependent terms is introduced:

[0054]

[0055]

[0056] i=0,1,…,N-1

[0057]

[0058]

[0059] Preferably, in step S4, the method for establishing the final model of asymmetric rate-related hysteresis is:

[0060] S4-1. Initialize the weight parameters of the Elman neural network

[0061] The elman neural network uses the hyperbolic tangent activation function The weight from the input layer to the hidden layer of the Elman neural network is The weights of the background unit feedback layer to the hidden layer Using Xavier's weight initialization method,

[0062] The weight from the input layer to the hidden layer Independent and identically distributed, its input layer input Independent and identically distributed, that is, random variables and If they are independent and their means are all 0, then:

[0063]

[0064] so,

[0065] When , the output variance from the input layer to the hidden layer is equal to the input The variance of is consistent, then the weights are randomly initialized When , the weights are sampled from a Gaussian distribution of N(0,1 / (N+2)), where N+2 is the number of neurons in the input layer.

[0066] Similarly, we can get the random initialization weights from the feedback layer of the background unit to the hidden layer When , the weights are sampled from a Gaussian distribution of N(0,1 / q), where q is the number of neurons in the background unit feedback layer, that is, the number of neurons in the hidden layer.

[0067] S4-2, using the BP learning method, the synaptic weights of the network are iteratively modified, and a momentum term is added to make the search converge quickly to the global minimum. The cost function of the system is defined as:

[0068]

[0069] The identification error is

[0070] e m (t) = y out (t)-y m (t)

[0071] Among them, y out (t) is the ideal output,

[0072] Synaptic weight learning algorithm from input layer to hidden layer neurons:

[0073]

[0074]

[0075] Among them, the local gradient of neuron j is for:

[0076]

[0077] In the formula,

[0078]

[0079] The synaptic weight learning algorithm from the feedback layer to the hidden layer neurons in the background unit:

[0080]

[0081]

[0082] Prominent weight learning algorithm for neurons from hidden layer to output layer:

[0083]

[0084]

[0085] Since the frequency-related part is added from the hidden layer to the output layer, the weight adjustment from the hidden layer to the output layer is divided into two parts, which are:

[0086]

[0087]

[0088]

[0089]

[0090] Therefore, in the weight learning algorithm from the hidden layer to the output layer:

[0091]

[0092]

[0093] Where η is the learning efficiency; α is the momentum factor; j = 1, 2, …, q;

[0094] S4-3, when the Elman neural network is trained and learned, its input end receives all input vectors, calculates the output results, and compares them with the target vector, thereby generating a series of error vectors. In each iteration, the approximate error gradient of each weight is determined by back propagation, and the back propagation training function uses the gradient to update the weight until the network output reaches the expected output. The expected output here is selected as the output displacement of the piezoelectric ceramic device obtained in S1, so as to obtain the weight parameters of each layer and establish the final model of asymmetric rate-dependent hysteresis based on the play operator and the Elman neural network.

[0095] Beneficial effects of the present invention

[0096] By using the play operator as the input of the Elman neural network, the input layer of the Elman neural network is expanded. At the same time, the high-precision approximation of nonlinear functions by the Elman neural network makes the identification of model parameters more convenient, and the Elman neural network already has a classic training algorithm.

[0097] The asymmetric characteristics of hysteresis are modeled and rate-dependent terms are introduced to effectively reduce the modeling error of asymmetric rate-dependent hysteresis characteristics. The method has good frequency generalization ability and is easy to implement in engineering. BRIEF DESCRIPTION OF THE DRAWINGS

[0098] Figure 1 Shown is a schematic block diagram of the asymmetric rate-dependent hysteresis modeling process based on the play operator and the Elman neural network.

[0099] Figure 2 Shown is the schematic diagram of the experimental setup for the hysteresis characteristics of a piezoelectric actuator.

[0100] Figure 3 Shown is the structure diagram of the asymmetric rate-dependent hysteresis model based on the play operator and the Elman neural network.

[0101] Figure 4 The figure shows the comparison curve between the platform hysteresis output and the model output under 40HZ sine wave drive. DETAILED DESCRIPTION

[0102] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0103] The present invention provides an asymmetric rate-dependent hysteresis modeling method based on the play operator, such as Figure 1 As shown, the following steps are included:

[0104] S1. Collecting piezoelectric ceramic input voltage and output displacement

[0105] Specifically, input voltage signal, test the response curve of piezoelectric driver, collect hysteresis data of piezoelectric driver, and obtain the output displacement generated by piezoelectric ceramic actuator:

[0106] Among them, piezoelectric ceramics with hysteresis characteristics were selected as the research object.

[0107] Understandable, such as Figure 2 As shown, the piezoelectric ceramic includes a signal generator, a power amplifier, a laser displacement sensor and a data acquisition and analysis device. The signal generator generates an input signal and stores it in the data acquisition and analysis device. The data acquisition and analysis device receives and saves the input signal generated by the signal generator and the displacement signal output by the displacement sensor, performs data processing, and draws a hysteresis characteristic curve. The power amplifier circuit can amplify the low-voltage drive signal to tens of volts or even hundreds of volts, load it to both ends of the piezoelectric ceramic, and drive the piezoelectric ceramic to generate displacement. The laser displacement sensor collects the displacement of the piezoelectric ceramic, converts it into a voltage signal, and stores it in the data acquisition and analysis device.

[0108] In this embodiment, in order to better characterize the hysteresis characteristics, the driving voltage of the piezoelectric ceramic driver selects a triangular wave signal as the simulation input, and a 40HZ sinusoidal voltage is used as the input signal. The input signal is Test the response curve of the piezoelectric driver and collect the output displacement signal y of the piezoelectric driver out40 , and obtain the hysteresis curve at 40HZ frequency. At the same time, the derivative of the piezoelectric drive input voltage dv(t) / dt is collected.

[0109] S2. Combining the play operator and the Elman neural network to establish an asymmetric hysteresis model

[0110] Specifically, based on the play operator in the piezoelectric ceramic Prandtl-Ishlinskii (PI) hysteresis model, an asymmetric hysteresis model structure under the Elman neural network structure is established, such as Figure 3 As shown, the specific steps include:

[0111] The acquisition of the play operator is based on the PI model to obtain the output of the play operator. m [0,t E ] represents piecewise monotone continuous function space. 0 = t 0 <t 1 <… <t N =t E It is C m [0,t E ] is a partition, for any input V(t)∈C m [0,t E ], so that the function in each subinterval [t i ,t i+1 ] is monotonic. Then the output of the play operator is defined as:

[0112]

[0113]

[0114] Among them, t i =tT <t≤t i+1 ,0≤i≤N-1, N is the input voltage at the same time, N play operators are generated. v(t) is the control input, is the output of the play operator, r i is the input threshold of the play operator, t is the sampling time, and T is the sampling period. i Select as:

[0115]

[0116] Among them, max{|v(t)|, v(t)∈C m [0,t E ]} is the maximum value under the input conditions.

[0117] Furthermore, the method of establishing an asymmetric hysteresis model is

[0118] S2-1 Based on the obtained play operator and the Elman neural network, an asymmetric hysteresis model structure is established:

[0119] It can be understood that due to the nature of the play operator, the hysteresis loop of the hysteresis model is symmetric, and for the asymmetric hysteresis model, the envelope function H(v(t)) is introduced:

[0120] H(v(t))=a 1 v 3 (t)+a 2 v(t)

[0121] Among them, H(v(t)) is a non-decreasing continuous function.

[0122] According to the obtained play operator In the construction of the Elman neural network structure, the play operator and the envelope function H(v(t)) are used as the input space of the Elman neural network. Under this condition, the calculation expressions of the function signal and the error signal of the Elman neural network are described as follows:

[0123] The input and output of the input layer nodes of the Elman neural network are:

[0124]

[0125] i=0,1,…,N-1

[0126] In the formula, I 0 is the input layer’s input, O 0 is the output of the input layer, and N is the number of play operators under the input voltage at the same time. Then the number of input layer nodes is N+2.

[0127] The input and output of the hidden layer of the Elman neural network are:

[0128]

[0129]

[0130] In the formula, I 1 is the input of the hidden layer, O 1 is the output of the hidden layer, is the synaptic weight connecting the feedback node of the background unit to the hidden layer neurons; is the synaptic weight connecting the external input point to the hidden layer neurons; q is the number of nodes of the hidden layer neurons.

[0131] The activation function for the hidden layer neurons is: positive and negative symmetric sigmoid function - hyperbolic tangent function:

[0132]

[0133] The input and output of the feedback layer node in the background unit are:

[0134]

[0135]

[0136] In the formula, I' 0 is the input of the feedback layer, O' 0 is the output of the feedback layer, and q is the number of nodes in the feedback layer, that is, the number of nodes in the hidden layer.

[0137] The output of the network output neuron is:

[0138]

[0139] In the formula, I 2 is the input of the output layer, O 2 is the output of the output layer, and q is the number of neurons in the hidden layer.

[0140] Finally, the asymmetric hysteresis model combining the play operator and the Elman neural network is:

[0141]

[0142]

[0143] i=0,1,…,N-1

[0144]

[0145]

[0146] It can be understood that the extended input of the input end is the envelope function H(v) and the play operator. According to the above formula, an asymmetric hysteresis model combining the play operator with the Elman neural network is established.

[0147] In this embodiment, the number of operators N is selected as N=20, wherein the number of input layer nodes is 22, and the number of hidden layer nodes and the number of feedback layer nodes are both q=11.

[0148] S3. Based on step S2, a rate-dependent term is introduced into the established asymmetric hysteresis model to establish an asymmetric rate-dependent hysteresis model:

[0149] Step S3 specifically introduces rate-related conditions. Since the piezoelectric drive exhibits rate-related characteristics, in order to accurately describe the rate-related hysteresis characteristics of the piezoelectric drive, while reducing the modeling error of the asymmetric hysteresis model and improving the frequency generalization capability, the asymmetric hysteresis modeling structure based on the Paly operator and the Elman neural network constructed in step S2 is introduced with rate-related terms, that is, the derivative dv(t) / dt of the input voltage is introduced at the weight from the hidden layer to the output layer of the Elman neural network.

[0150]

[0151] At this time, an asymmetric rate-dependent hysteresis model with rate-dependent terms is introduced based on S2:

[0152]

[0153]

[0154] i=0,1,…,N-1

[0155]

[0156]

[0157] On the basis of step S2, the derivative of the input voltage dv(t) / dt is introduced at the weight of the output layer to establish an asymmetric rate-dependent hysteresis model.

[0158] S4, use the gradient descent method to update the weights of each layer of the Elman neural network and establish the final model of asymmetric rate-dependent hysteresis:

[0159] S4-1 initializes the weight parameters of the Elman neural network.

[0160] From step S2, we can see that the Elman neural network uses the hyperbolic tangent activation function The weight from the input layer to the hidden layer of the Elman neural network is The weights of the background unit feedback layer to the hidden layer Xavier's weight initialization method is used.

[0161] The weight from the input layer to the hidden layer Independent and identically distributed, its input layer input Independent and identically distributed, that is, random variables and If they are independent and their means are all 0, then:

[0162]

[0163] so,

[0164] When , the output variance from the input layer to the hidden layer is equal to the input The variance of is consistent. Then when the weights are randomly initialized When , the weights are sampled from a Gaussian distribution of N(0,1 / (N+2)), where N+2 is the number of neurons in the input layer. The weights are initialized to a Gaussian distribution of N(0,1 / 22).

[0165] Similarly, we can get the random initialization weights from the feedback layer of the background unit to the hidden layer When , the weights are sampled from a Gaussian distribution of N(0,1 / q), where q is the number of neurons in the background unit feedback layer, i.e., the number of neurons in the hidden layer. The weights are initialized to a Gaussian distribution of N(0,1 / 11).

[0166] S4-2. Specifically, the BP learning method is used to iteratively modify the synaptic weights of the network, and a momentum term is added to make the search converge quickly to the global minimum. The cost function of the system is defined as:

[0167]

[0168] The identification error is

[0169] e m (t) = y out (t)-y m (t) where y out (t) is the ideal output.

[0170] Synaptic weight learning algorithm from input layer to hidden layer neurons:

[0171]

[0172]

[0173] Among them, the local gradient of neuron j is for:

[0174]

[0175] In the formula,

[0176]

[0177] The synaptic weight learning algorithm from the feedback layer to the hidden layer neurons in the background unit:

[0178]

[0179]

[0180] Prominent weight learning algorithm for neurons from hidden layer to output layer:

[0181]

[0182]

[0183] Since the frequency-related part is added from the hidden layer to the output layer, the weight adjustment from the hidden layer to the output layer is divided into two parts, which are:

[0184]

[0185]

[0186]

[0187]

[0188] Therefore, in the weight learning algorithm from the hidden layer to the output layer:

[0189]

[0190]

[0191] Where η is the learning efficiency; α is the momentum factor; j = 1, 2,…, q.

[0192] S4-3, when the Elman neural network is trained and learned, its input end receives all input vectors, calculates the output results, and compares them with the target vector, thereby generating a series of error vectors. In each iteration, the approximate error gradient of each weight is determined by back propagation, and the back propagation training function uses the gradient to update the weight until the network output reaches the expected output, thereby obtaining the weight parameters of each layer and establishing the final model based on the asymmetric rate-dependent hysteresis of the play operator and the Elman neural network.

[0193] In the present invention, out (t) is the actual output displacement of the piezoelectric actuator.

[0194] Furthermore, in combination with the above technical solution, a modeling analysis and verification of an asymmetric rate-related hysteresis characteristic based on the play operator provided in this embodiment is performed. The output displacement is obtained by the piezoelectric actuator under the condition of 40HZ input voltage. The sampling frequency during input is 20000HZ. The input voltage data and output displacement under the condition of 40HZ input voltage are used as training data for Elman neural network modeling to approximate the hysteresis curve.

[0195] In order to verify the rate correlation, the input voltage with a frequency of 40HZ is discretized and input into the established asymmetric rate-dependent hysteresis model, and the simulated displacement data output at 40HZ is obtained and compared with the input and output data of the piezoelectric ceramic actuator at 40HZ. Figure 4 , where the solid line is the real hysteresis image and the dotted line is the output curve of the asymmetric rate-dependent hysteresis model obtained by this method. Figure 4 It can be seen that the simulation curve of the asymmetric rate-dependent hysteresis model is basically consistent with the experimental hysteresis curve of the piezoelectric displacement stage. The root mean square error of the output displacement of the simulation model is 0.071μm, and the relative error is 1.1%, indicating that the constructed asymmetric rate-dependent model can accurately describe the asymmetric rate-dependent hysteresis characteristics of the piezoelectric ceramic micropositioning stage.

Claims

1. A method for modeling asymmetric rate-dependent hysteresis based on a play operator, characterized in that: The following steps are involved: S1. Collecting piezoelectric ceramic input voltage and output displacement The method for acquiring the output displacement of the piezoelectric ceramic is to amplify the input voltage through a power amplifier circuit and load it to both ends of the piezoelectric ceramic to drive the piezoelectric ceramic to generate displacement, and collect the position of the piezoelectric ceramic through a laser displacement sensor; S2, combining the play operator and the Elman neural network to establish an asymmetric hysteresis model; The play operator is output by the PI model, and the output play operator is defined as: Among them, t i =tT<t≤t i+1 , 0≤i≤N-1, N is the input voltage at the same time, N play operators are generated, v(t) is the control input, is the output of the play operator, ri is the input threshold of the play operator, t is the sampling time, T is the sampling period, for any input v(t)∈C m [0, t E ], so that the function in each subinterval [t i , t i+1 ] is monotonous, C m [0, t E ] represents piecewise monotone continuous function space, 0 = t0 <t1<…<t N =t E It is C m [0, t E ] a division; The input threshold r of the play operator i Settings: Among them, max{|v(t)|, v(t)∈C m [0,t E ]} is the maximum value under the input conditions; The method for establishing the asymmetric hysteresis model is: S2-1. Introduce the envelope function H(v(t)): H(v(t))=a1v 3 (t)+a2v(t) Among them, H(v(t)) is a non-decreasing continuous function, S2-2. According to the obtained play operator In the construction of the Elman neural network structure, the play operator and the envelope function H(v(t)) are used as the input space of the Elman neural network. Under this condition, the calculation expressions of the function signal and error signal of the Elman neural network are described as: The input and output of the input layer nodes of the Elman neural network are: In the formula, I 0 is the input layer’s input, O 0 is the output of the input layer, N is the number of play operators under the input voltage at the same time, then the number of input layer nodes is N+2, The input and output of the hidden layer of the Elman neural network are: In the formula, I 1 is the input of the hidden layer, O 1 is the output of the hidden layer, is the synaptic weight connecting the feedback node of the background unit to the hidden layer neurons; is the synaptic weight connecting the external input point to the hidden layer neurons; q is the number of nodes of the hidden layer neurons, The activation function for the hidden layer neurons is: positive and negative symmetric sigmoid function - hyperbolic tangent function: The input and output of the feedback layer node in the background unit are: In the formula, I′ 0 is the input of the feedback layer, O′ 0 is the output of the feedback layer, q is the number of nodes in the feedback layer, that is, the number of nodes in the hidden layer; The output of the output neuron of the Elman neural network is: In the formula, I 2 is the input of the output layer, O 2 is the output of the output layer, q is the number of neurons in the hidden layer, S2-3, finally combining the play operator with the asymmetric hysteresis model of the Elman neural network: S3, introducing rate-dependent terms into the asymmetric hysteresis model, and establishing an asymmetric rate-dependent hysteresis model; S4, the gradient descent method is used to update the weights and establish the final model of asymmetric rate-dependent hysteresis.

2. The asymmetric rate-dependent hysteresis modeling method based on the play operator according to claim 1 is characterized in that: The piezoelectric ceramic is selected from piezoelectric ceramics with hysteresis characteristics.

3. The asymmetric rate-dependent hysteresis modeling method based on the play operator according to claim 2 is characterized in that: In step S3, the method of introducing rate-related terms to establish an asymmetric rate-related hysteresis model is: The derivative of the input voltage dv(t) / dt is introduced at the weight from the hidden layer to the output layer of the Elman neural network. At this time, an asymmetric rate-dependent hysteresis model with rate-dependent terms is introduced:

4. The asymmetric rate-dependent hysteresis modeling method based on the play operator according to claim 3 is characterized in that: In step S4, the method for establishing the final model of asymmetric rate-related hysteresis is: S4-1. Initialize the weight parameters of the Elman neural network The elman neural network uses the hyperbolic tangent activation function The weight from the input layer to the hidden layer of the Elman neural network is The weights of the background unit feedback layer to the hidden layer Using Xavier's weight initialization method, The weight from the input layer to the hidden layer Independent and identically distributed, its input layer input Independent and identically distributed, that is, random variables and If they are independent and their means are all 0, then: so, When , the output variance from the input layer to the hidden layer is equal to the input The variance of is consistent, then the weights are randomly initialized When , the weights are sampled from a Gaussian distribution of N(0, 1 / (N+2)), where N+2 is the number of neurons in the input layer. Similarly, we can get the random initialization weights from the feedback layer of the background unit to the hidden layer When , the weights are sampled from a Gaussian distribution of N(0, 1 / q), where q is the number of neurons in the background unit feedback layer, that is, the number of neurons in the hidden layer; S4-2, using the BP learning method, the synaptic weights of the network are iteratively modified, and a momentum term is added to make the search converge quickly to the global minimum. The cost function of the system is defined as: The identification error is e m (t)=y out (t)-y m (t) Among them, y out (t) is the ideal output, Synaptic weight learning algorithm from input layer to hidden layer neurons: Among them, the local gradient of neuron j is for: In the formula, The synaptic weight learning algorithm from the feedback layer to the hidden layer neurons in the background unit: Prominent weight learning algorithm for neurons from hidden layer to output layer: Since the frequency-related part is added from the hidden layer to the output layer, the weight adjustment from the hidden layer to the output layer is divided into two parts, which are: Therefore, in the weight learning algorithm from the hidden layer to the output layer: Where η is the learning efficiency; α is the momentum factor; j = 1, 2, …, q; S4-3, when the Elman neural network is trained and learned, its input end receives all input vectors, calculates the output results, and compares them with the target vector, thereby generating a series of error vectors. In each iteration process, the approximate error gradient of each weight is determined according to back propagation, and the back propagation training function uses the gradient to update the weight until the Elman neural network output reaches the expected output. The expected output here is selected as the output displacement of the piezoelectric ceramic device obtained in S1, so as to obtain the weight parameters of each layer and establish the final model of asymmetric rate-dependent hysteresis based on the play operator and the Elman neural network.

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