Piezoelectric ceramic actuator creep prediction method based on ABSO-GRU

Abstract

The application discloses a piezoelectric ceramic actuator creep prediction method based on ABSO-GRU. The method comprises the following steps: (1) collecting piezoelectric ceramic actuator creep variable time series data under different input voltage conditions to construct a data set, and dividing the data set into a training set and a test set; (2) setting the time step of the GRU network to 10, taking the historical creep variable, the initial input voltage value and the input voltage transformation value as the input, and using the adaptive bumblebee swarm optimization algorithm (ABSO) to optimize the hyperparameters of the gated recurrent unit neural network (GRU) model on the randomly selected training set, so that the creep data characteristics and the network topology structure are matched; (3) based on the historical data, the optimal hyperparameter combination obtained by the ABSO algorithm is used to construct a GRU creep prediction model to realize real-time prediction of the piezoelectric ceramic actuator creep variable. The method can effectively predict the creep trend of the piezoelectric ceramic actuator, and solves the problem that the GRU creep prediction network hyperparameters cannot determine the optimal value, thereby reducing the prediction accuracy.

Description

TECHNICAL FIELD

[0001] The application relates to a piezoelectric ceramic actuator, in particular to a piezoelectric ceramic actuator creep prediction method based on ABSO-GRU. BACKGROUND

[0002] In the fields of satellite laser communication and space astronomical observation, in order to achieve the accuracy of seconds or even milliseconds, large optoelectronic tracking systems widely adopt compound axis control technology, which is the most effective control structure to achieve large-range and high-precision tracking indexes. Compound axis control is a form of two-dimensional associated control system, and a control system with a fast steering mirror (FSM) as an actuator is a precision tracking system of the compound axis system, and the precision that can be achieved by the system is mainly determined by the fast steering mirror actuator. The fast steering mirror mechanism usually adopts a voice coil motor (VCM) and a piezoelectric actuator (PZT) as a driver. Compared with the former, the latter has the advantages of high resonant frequency and large displacement resolution, however, the inherent creep nonlinearity will adversely affect the positioning accuracy. The piezoelectric creep characteristic is that when a piezoelectric actuator is applied with a certain fixed voltage, the displacement generated will not be immediately stable, but will change slowly in the subsequent period of time. The displacement in the subsequent period of time is the piezoelectric creep, and the micro mechanism is that the crystal domains will affect each other when turning, and a certain hysteresis is generated. The piezoelectric creep amount is greatly affected by the piezoelectric actuator material and the external environment, and the values of L0, gamma and t0 in the model will change due to the input voltage increment, the initial input voltage, the voltage change direction and the different piezoelectric actuator materials, so the model has a certain effect on the modeling of the piezoelectric creep characteristic under the determined condition, but it is not universal, therefore, at present, there is still a lack of a high-precision and real-time piezoelectric ceramic actuator creep prediction method. SUMMARY

[0003] In view of the above application background, the application provides a piezoelectric ceramic actuator creep prediction method based on ABSO-GRU, which comprises the following steps:

[0004] 1) Collecting piezoelectric ceramic actuator creep amount time series data under different input voltage conditions to construct a data set, and dividing the data set into a training set and a test set;

[0005] 2) The time step of the GRU network model is set to 10, and the historical creep variable, the initial input voltage value, and the input voltage transformation value are used as inputs. On the randomly selected training set, the ABSO optimization algorithm (Zhang Q, Gao Y, Li Q, et al. Adaptive compound control based on generalized Bouc-Wen inverse hysteresis modeling in piezoelectric actuators [J]. Review of Scientific Instruments, 2021, 92(11): 115004) is used to optimize the GRU model hyperparameters, so that the creep data characteristics match the network topology structure;

[0006] 3) Based on the historical data, the optimal hyperparameter combination obtained by the ABSO optimization algorithm is used to construct the GRU creep prediction model to predict the creep variable of the piezoelectric ceramic actuator in real time.

[0007] Specifically, in step 1:

[0008] The specific process of constructing the data set is as follows: set different initial driving voltages and voltage step changes of the piezoelectric ceramic actuator, and collect the corresponding creep variables. The time length of each group of input and output time series data is 1s, and the sampling rate is 100Hz. The first 0.8s of each group of data is used to form the training set, and the last 0.2s of data is used to form the test set.

[0009] Specifically, in step 2:

[0010] 1) The time step of the GRU network model is 10, and the input features are: historical creep variable, initial input voltage value, and input voltage transformation value;

[0011] 2) The specific process of using the ABSO optimization algorithm to optimize the GRU model hyperparameters is as follows: initialize the iteration number of the adaptive Bumblebee Swarm Optimization algorithm, the population size NP, the acceleration constants c1 and c2, the maximum inertia weight ω max , the minimum inertia weight ω min , the constant λ, the initial step step(1), the antenna distance attenuation factor c, the initial value of the attenuation factor eta(1), and the position range of each bumblebee. The BSO-GRU model is trained on the randomly selected training set, and the root mean square error of the predicted output creep variable and the actual collected creep variable is used as the objective function of each individual. Through continuous iteration and updating, the GRU network model hyperparameters are optimized.

[0012] 3) The GRU network model to be optimized is: the number of neuron nodes of the first layer GRU, the number of neuron nodes of the second layer GRU, the learning rate of the GRU and the maximum iteration number of the prediction model.

[0013] The ABSO-GRU piezoelectric ceramic actuator creep prediction model is established, the next time creep variable of the piezoelectric ceramic actuator can be predicted in high precision and real time, and the nonlinear creep is inhibited in the piezoelectric ceramic actuator control process, so that the positioning precision is improved. BRIEF DESCRIPTION OF DRAWINGS

[0014] Figure 1 It is a piezoelectric ceramic actuator creep prediction structure diagram.

[0015] Figure 2 It is a piezoelectric ceramic actuator data acquisition system block diagram.

[0016] Figure 3 It is a GRU unit structure.

[0017] Figure 4 It is a 0-30V input voltage range creep curve.

[0018] Figure 5 It is a GRU network creep prediction curve. DETAILED DESCRIPTION

[0019] The present application will be further described below in combination with specific embodiments, the illustrative embodiments of the present application and the description are used to explain the present application, but are not as a limitation of the present application.

[0020] An actual control system is built for data acquisition. The piezoelectric ceramic actuator control system is composed of an SGS micro-displacement sensor, an SGS signal conditioning module, a main control module, a piezoelectric ceramic actuator driving module and a piezoelectric ceramic actuator, wherein the main control module adopts a semi-physical real-time simulation platform. The main control module generates a piezoelectric ceramic actuator driving signal, which is sent to the driving module to control the piezoelectric ceramic actuator, and the SGS signal conditioning module feeds back the detected actual displacement to the main control module. The data acquisition system block diagram is shown in Figure 2

[0021] ​The piezoelectric ceramic actuator input voltage range is 0-100V, corresponding to the output displacement of 0-30pm. The piezoelectric ceramic actuator creep time series data under different input voltage conditions is collected, the creep time under each condition is 1s, and the sampling rate is 100Hz. The driving voltage input mode is as follows: 0V is respectively stepped to 1V, 2V, …, 100V, 1V is respectively stepped to 2V, 3V, …, 100V, 2V is respectively stepped to 3V, 4V, …, 100V, and so on; 100V is respectively stepped to 99V, 98V, …, 0V, 99V is respectively stepped to 98V, 97V, …, 0V, 98V is respectively stepped to 97V, 96V, …, 0V, and so on. The corresponding piezoelectric ceramic actuator output displacement data is collected, a total of 10100 groups of time-creep variable data, and each group of data is 100.

[0022] The adaptive firefly optimization algorithm is used to identify model parameters a, b, g, p0, p1, q1, q 0, . The iteration number of the adaptive firefly optimization algorithm is 300, the population number NP = 120, the acceleration constant c1 = 2.8, c2 = 1.3, the maximum weight ω max = 0.9, the minimum weight ω min = 0.4, λ = 0.95, the initial step step(1) = 2, c = 2, the initial value of the decay factor eta(1) = 0.95, the neuron node number range of the first layer GRU is set to [1, 100], the neuron node number range of the second layer GRU is set to [1, 100], the learning rate range of the GRU is set to [0.01, 0.15], and the maximum iteration number range of the prediction model is set to [40, 100]. The core problem of the optimization algorithm is to select the objective function:

[0023]

[0024] Wherein, n is the sample number, y i represents the true value, represents the predicted value.

[0025] The GRU is a variant of the traditional recurrent neural network. The GRU neural network uses update gate and reset gate to determine the output of the gated recurrent unit, which can save the information in the long sequence and will not be cleared or removed because it is not related to prediction. The structure of the GRU unit is shown in Figure 3 .

[0026] Figure 3In the formula, φ(·) is a tanh activation function, and σ(·) is a sigmoid activation function. The σ(·) function is used to make the output of the gate tend to 0 or 1.

[0027] The reset gate is used to determine the forgetting degree of the candidate state at the current moment to the network state at the previous moment, and the expression is shown in formula (2):

[0028] r t =σ(ω r ·[a t-1 ,x t ]) (2)

[0029] In the formula, at-1 is the hidden state at the previous moment, xt is the network input at the current moment, and rt represents the output of the reset gate.

[0030] The smaller the value of the reset gate, the greater the forgetting degree of the state information at the previous moment. The output of the reset gate and the current input are subjected to a tanh activation function to obtain the candidate hidden state, as shown in formula (3):

[0031]

[0032] In the formula, at-1 is the hidden state at the previous moment, xt is the network input at the current moment, and rt represents the output of the reset gate, which represents the candidate hidden state.

[0033] The update gate is used to determine the retention degree of the output state at the current moment to the state at the previous moment, and the expression is as follows:

[0034] z t =σ(ω z ·[a t-1 ,x t ]) (4)

[0035] In the formula, at-1 is the hidden state at the previous moment, xt is the network input at the current moment, and zt represents the output of the update gate.

[0036] The greater the value of the update gate, the greater the retention degree of the state information at the previous moment. The update gate is a control gate of the final output of the GRU unit. According to formula (4), the output of the update gate and the candidate hidden state are updated to obtain the output of the network at the current moment, as shown in formula (5):

[0037]

[0038] In the formula, at-1 is the hidden state at the previous moment, and zt represents the output of the update gate, which represents the candidate hidden state.

[0039] As can be seen from formula (2) to formula (5), the GRU does not forget the information of the previous moment with time, but retains the relevant information and passes it to the next GRU unit, and the gradient disappearance is avoided by directly adding a linear dependence between the current moment state and the previous moment state of the network.

[0040] The creep amount of the piezoceramic actuator at any moment is not only related to the current moment, but also related to the historical creep amount. The initial input voltage, voltage transformation value and historical creep amount of the piezoceramic actuator are selected as input features. The time step of the GRU network is set to 10, and the historical creep amount, initial input voltage and voltage transformation value of the previous 10 moments are used to predict the piezoceramic actuator creep amount at the next moment. The initial input voltage and voltage step transformation value are normalized to [-1, 1].

[0041] The hardware platform for training the model is CPU: Intel i7-12700k, and the software uses Python 3.6 and Pytorch 1.1 deep learning framework to build the network.

[0042] The activation function of the full connection layer is set to Linear function, which is used for neural network regression result output. The trained network output is compared with the actual value by statistical evaluation index, and the performance of the trained network is evaluated. The Adam adaptive learning rate method is used to update the model parameters. Essentially, the Adam method is a parameter optimization method with momentum term, and its learning rate is determined by the gradient matrix estimation. The parameter update is stable and not easy to fall into local optimum.

[0043] The input voltage signal is set to 0-30V, the creep time is 1s, the sampling rate is 100Hz, and the creep-time curve is as shown in Figure 4 The measured piezoceramic actuator creep amount data from 0.79s to 0.99s is input into the model in turn, and the piezoceramic actuator creep amount from 0.8s to 1s is obtained. The above neural network creep prediction curve is as shown in Figure 5 The root mean square error of the prediction is shown in Table 1.

[0044] Table 1 GRU network prediction accuracy

[0045]

Claims

1. A ABSO-GRU-based piezoceramic actuator creep prediction method, characterized by The method comprises the following steps: 1) collecting time series data of piezoelectric ceramic actuator creep under different input voltage conditions to construct a data set, and dividing the data set into a training set and a test set; 2) setting the time step of the GRU network model to 10, taking the historical creep, the initial input voltage value and the input voltage transformation value as the input, and using the ABSO optimization algorithm to optimize the hyperparameters of the GRU network model on the randomly selected training set, so that the creep data features match the network topology structure; 3) based on the historical data, the optimal hyperparameter combination obtained by the ABSO optimization algorithm is used to construct a GRU creep prediction model to predict the piezoelectric ceramic actuator creep in real time; The specific process of constructing the data set in step 1) is as follows: different initial driving voltages and voltage step changes of the piezoelectric ceramic actuator are set, and the corresponding creep is collected; the time length of each input-output time series data is 1s, and the sampling rate is 100Hz; the first 0.8s data of each group of data is used to form the training set, and the last 0.2s data is used to form the test set; The specific process of optimizing the GRU model hyperparameters by ABSO in step 2) is as follows: initializing the iteration number of the adaptive artificial bee optimization algorithm, the population number NP, the acceleration constants c1 and c2, the maximum inertia weight ω max , the minimum inertia weight ω min , the constant λ, the initial step step(1), the antenna distance attenuation factor c, the initial attenuation factor eta(1), and the position range of each artificial bee; training the ABSO-GRU model on the randomly selected training set to predict the root mean square error of the predicted output creep variable and the actually collected creep variable as the objective function of each individual, and optimizing the GRU network hyperparameters through continuous iteration and updating; The hyperparameters of the GRU network model in step 2) are as follows: the number of neuron nodes of the first layer GRU, the number of neuron nodes of the second layer GRU, the learning rate of the GRU and the maximum number of iterations of the prediction model.

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