Magnetic control shape memory alloy actuator neural network hysteresis modeling method under complex physical field coupling

Abstract

The invention provides a magnetic control shape memory alloy actuator neural network hysteresis modeling method under complex physical field coupling, and belongs to the technical field of control. According to the method, firstly, a multi-field coupling NARMAX model is constructed to describe hysteresis nonlinearity of a magnetic control shape memory alloy actuator under complex physical field coupling; an unknown nonlinear function of a multi-field coupling NARMAX model is constructed by using a long short-term memory neural network, and a multi-field coupling hysteresis model capable of updating model parameters online and adapting to dynamic hysteresis characteristics under complex physical field coupling is established. According to the hysteresis modeling method fusing the multi-physical field information, the problem that most of existing hysteresis models only describe the hysteresis behavior of a magnetic control shape memory alloy actuator and neglect the influence of a complex physical field coupling effect on the hysteresis behavior can be solved; and a theoretical basis and technical support are provided for design optimization of a magnetic control shape memory alloy actuator control system.

Description

Technical Field

[0001] The invention belongs to the field of control technology. Background Art

[0002] With the rapid development of science and technology, traditional mechanical processing and manufacturing methods can no longer meet people's needs. The precision manufacturing industry has begun to develop rapidly, and people have put forward new requirements for high-precision and high-resolution positioning technology. Actuators with magnetically controlled shape memory alloy materials as core components have become a hot research topic in various countries in the field of high-precision manufacturing in recent years due to their micro-nanoscale precision positioning capabilities. However, magnetically controlled shape memory alloy materials have hysteresis nonlinear characteristics that are significantly different from traditional smart materials. At the same time, hysteresis nonlinearity is also affected by the amplitude-frequency characteristics of the input signal, external force, and temperature. Therefore, modeling the hysteresis nonlinearity of magnetically controlled shape memory alloy actuators under complex physical field coupling is an extremely challenging task and is attracting more and more attention.

[0003] Currently, models describing hysteresis nonlinearity are primarily categorized into physical property-based modeling, hysteresis-based modeling, and other types of modeling approaches. Physical property-based modeling approaches focus on modeling based on the physical properties of the object under investigation and incorporate the mechanisms of hysteresis. These approaches can more intuitively reflect the physical properties of the system and reveal the relationship between hysteresis and system parameters. However, because physical modeling approaches often involve many difficult-to-measure parameters and involve complex computational processes, they suffer from low accuracy and limited practicality. Hysteresis-based models construct mathematical models based on the hysteresis exhibited by the object under investigation and describe hysteresis nonlinearity through the superposition of basic hysteresis operators. Common operator-based hysteresis models include the Preisach model, the PI model, and the KP model. Furthermore, the NARMAX model is a nonlinear black-box model that exhibits excellent descriptive capabilities for complex nonlinear systems. To enable the NARMAX model to better describe the hysteresis nonlinearity of multivalued mappings, introducing exogenous variable functions is an effective approach. However, the hysteresis characteristics of magnetically controlled shape memory alloy actuators are susceptible to multiple factors, including the input signal's amplitude-frequency characteristics, temperature, and load. Existing modeling methods cannot fully account for the effects of multi-physics coupling on hysteresis. The core challenge of current research is to establish a high-precision hysteresis model that can fully characterize the hysteretic nonlinearity of magnetically controlled shape memory alloy actuators under the influence of multi-physics coupling. Summary of the Invention

[0004] This paper aims to construct a multi-field coupled NARMAX model that integrates multi-field information to describe the multi-field coupled hysteresis nonlinearity of magnetically controlled shape memory alloy actuators. This model not only improves the NARMAX model's ability to depict multi-valued mapping hysteresis when complex physical field coupling occurs, but also effectively overcomes the shortcomings of the traditional KP model in capturing hysteresis characteristics and adapting to complex coupling effects, providing a new approach to hysteresis modeling for magnetically controlled shape memory alloy actuators.

[0005] The steps of the present invention are:

[0006] Step 1: Use the NARMAX model to describe the multi-value mapping hysteresis of the magnetically controlled shape memory alloy actuator. Furthermore, temperature and load are used as model inputs to establish a multi-field coupled NARMAX model that includes multi-physics coupling information to reflect the influence of these physical field factors on the hysteresis behavior of the magnetically controlled shape memory alloy actuator.

[0007] The multi-field coupled NARMAX model expression is:

[0008]

[0009] Among them, k is the discrete moment of the system, N is the unknown nonlinear function, y m represents the output value of the NARMAX model, h represents the exogenous variable of the NARMAX model, l and t represent the load and temperature of the system respectively, v and y represent the input and output values ​​of the system respectively, n v 、n h 、n l 、n t and n y Represents the memory delay of v, h, l, t and y respectively, a=n v +n h +n l +n t +n y +2 is the total system delay, and the exogenous variable h is represented by the KP model. The KP model function expression is as follows:

[0010]

[0011] Among them, h(k) is the hysteresis output; k p [v,ξ p ] is the KP hysteresis operator; ξ p is the previous extreme value output by the hysteresis operator; p is the integration area of ​​the Preisach plane; μ(p) is the density function of the Preisach plane; 0 and β are the boundary values ​​of the Preisach plane; β is the maximum input of the system; (p1, p2) represents a pair of thresholds of the KP operator in the Preisach plane.

[0012] For convenience, the multi-field coupled NARMAX model is rewritten into a polynomial form as follows:

[0013]

[0014] Where θ is the polynomial coefficient, is the matrix term composed of coefficients, is the autoregressive sliding average term; q is the model order, and n = (a + q)! / a!q!-1 is the total number of terms.

[0015] Step 2: Use the long short-term memory neural network (LSTMNN) to construct the unknown nonlinear function of the multi-field coupled NARMAX model, so that the established model can update parameters online and accurately describe the dynamic hysteresis characteristics under complex physical field coupling.

[0016] The expression of LSTMNN is as follows:

[0017]

[0018] F r (k)=Φ(W Fr σ r (k)+Γ Fr g r (k-1)+δ Fr ) (6)

[0019] Ω r (k)=Φ(W Ωr σ r (k)+Γ Ωr g r (k-1)+δ Ωr ) (7)

[0020]

[0021] Among them, η i and O(k) represent the input and output of LSTMNN, η i represents the i-th term in the autoregressive sliding average term η, O(k) is y m (k), LSTM units act as hidden neurons. F r and Ω r Represent the cell state, input gate, forget gate and output gate of the rth LSTM unit respectively. In (5)-(10), the historical hidden state g is used r (k-1), and the current input σ r (k) to calculate the hidden state gr (k). Φ represents the sigmoid activation function, and tanh represents the hyperbolic tangent function. The number of neurons in the input layer and hidden layer are c and f, respectively.

[0022] It is a vector composed of LSTMNN weights and biases. LSTMNN updates the parameters of W through the optimization algorithm.

[0023] Considering the computational complexity and modeling accuracy, q is selected as 3 in step 1, and n is v 、n h 、n l 、n t and n y Select 2, 2, 0, 0 and 1 respectively.

[0024] Taking into account the computational complexity and modeling accuracy, the number of neurons in the input layer of the neural network in step 2 is selected as 119, the number of neurons in the hidden layer is selected as 11, the number of neurons in the output layer is selected as 1, and the initial weights are set to random values ​​between 0 and 1.

[0025] The objective function of the optimization algorithm is defined as follows:

[0026]

[0027] Update the parameters through the gradient descent algorithm as shown below:

[0028]

[0029] in, is the learning rate.

[0030] Compared with the prior art, the present invention has the following beneficial effects: The neural network hysteresis modeling method for magnetic shape memory alloy actuators under complex physical field coupling provided by the present invention provides a new idea and method for hysteresis modeling of magnetic shape memory alloy actuators, and has the following three significant advantages: First, a multi-field coupling NARMAX model is constructed. By taking physical field information such as temperature and load as model input, the influence of multi-physical field coupling on the hysteresis behavior of magnetic shape memory alloy actuators is effectively reflected, overcoming the defect that the existing modeling method cannot fully consider the effect of multi-physical field coupling, and improving the model's ability to characterize multi-value mapping hysteresis under complex physical field coupling. Second, the unknown nonlinear function of the multi-field coupling NARMAX model is constructed using LSTMNN. Thanks to the powerful advantages of LSTMNN in processing time series data, it can effectively capture the correlation and time dynamic characteristics in long sequences, better memorize historical information, and thus provide strong support for the model to accurately describe the dynamic hysteresis characteristics of magnetic shape memory alloy actuators when facing dynamic changes under complex physical field coupling. Third, it effectively makes up for the shortcomings of the traditional KP model. This method introduces temperature and load into a NARMAX model with the KP model as an exogenous variable function. This overcomes the shortcomings of the traditional KP model in capturing hysteresis characteristics and adapting to complex coupling effects, thereby establishing a more accurate and adaptable multi-field coupled hysteresis model. This method provides a solid theoretical basis and technical support for the design and optimization of magnetically controlled shape memory alloy actuator control systems, better meeting the demand for high-precision hysteresis modeling in practical engineering applications, and promoting the further development of magnetically controlled shape memory alloy actuators in fields such as precision manufacturing. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 This is a principle block diagram of the complex physical field coupled hysteresis modeling method based on LSTMNN of the present invention;

[0032] Figure 2 Schematic diagram of the experimental device of the magnetically controlled shape memory alloy actuator of the present invention;

[0033] Figure 3 This is a connection diagram of the magnetically controlled shape memory alloy actuator experimental device of the present invention;

[0034] Figure 4 This is a comparison diagram of the actuator output curve and the model output curve under the mixed wave input signal at 22°C of the present invention;

[0035] Figure 5 is an error diagram of the actuator output curve and the model output curve under the mixed wave input signal at 22°C of the present invention;

[0036] Figure 6This is a comparison diagram of the actuator output curve and the model output curve under the mixed wave input signal at 26°C of the present invention;

[0037] Figure 7 is an error diagram of the actuator output curve and the model output curve under the mixed wave input signal at 26°C of the present invention;

[0038] Figure 8 This is a comparison diagram of the actuator output curve and the model output curve under the mixed wave input signal at 30°C of the present invention;

[0039] Figure 9 This is an error diagram of the actuator output curve and the model output curve under the mixed wave input signal at 30°C of the present invention;

[0040] Figure 10 This is a comparison diagram of the actuator output curve and the model output curve under the mixed wave input signal at 100g of the present invention;

[0041] Figure 11 is an error diagram of the actuator output curve and the model output curve under the mixed wave input signal at 100g of the present invention;

[0042] Figure 12 This is a comparison diagram of the actuator output curve and the model output curve under the mixed wave input signal at 200g of the present invention;

[0043] Figure 13 is an error diagram of the actuator output curve and the model output curve under the mixed wave input signal at 200g of the present invention;

[0044] Figure 14 This is a comparison diagram of the actuator output curve and the model output curve under the mixed wave input signal at 300g of the present invention;

[0045] Figure 15 is an error diagram of the actuator output curve and the model output curve under the mixed wave input signal at 300g of the present invention; DETAILED DESCRIPTION

[0046] The technical solution of the present invention is explained and illustrated in the following by means of specific embodiments.

[0047] Step 1: Use the NARMAX model to describe the multi-value mapping hysteresis of the magnetically controlled shape memory alloy actuator. Furthermore, physical field information such as temperature and load is used as model input to establish a multi-field coupled NARMAX model that includes multi-field coupling information to reflect the impact of these physical fields on the system's hysteretic behavior.

[0048] The multi-field coupled NARMAX model expression is:

[0049]

[0050] Among them, k is the discrete moment of the system, N is the unknown nonlinear function, y m represents the output value of the NARMAX model, h represents the exogenous variable of the NARMAX model, l and t represent the load and temperature of the system respectively, v and y represent the input and output values ​​of the system respectively, n v 、n h 、n l 、n t and n y Represents the memory delay of v, h, l, t and y respectively, a=n v +n h +n l +n t +n y +2 is the total system delay, and the exogenous variable h is represented by the KP model. The KP model function expression is as follows:

[0051]

[0052] Among them, h(k) is the hysteresis output; k p [v,ξ p ] is the KP hysteresis operator; ξ p is the previous extreme value output by the hysteresis operator; p is the integration area of ​​the Preisach plane; μ(p) is the density function of the Preisach plane; 0 and β are the boundary values ​​of the Preisach plane; β is the maximum input of the system; (p1, p2) represents a pair of thresholds of the KP operator in the Preisach plane.

[0053] For convenience, the multi-field coupled NARMAX model is rewritten into a polynomial form as follows:

[0054]

[0055] Where θ is the polynomial coefficient, is the matrix term composed of coefficients, q is the model order, n=(a+q)! / a!q!-1 is the total number of terms, is the autoregressive sliding average term. Considering the computational complexity and modeling accuracy, q is selected as 3, n v 、n h 、n l 、n t and n y Select 2, 2, 0, 0 and 1 respectively.

[0056] Step 2: Use LSTMNN to construct the unknown nonlinear function of the multi-field coupled NARMAX model, so that the established model can update parameters online and accurately describe the dynamic hysteresis characteristics under complex physical field coupling.

[0057] The expression of LSTMNN is as follows:

[0058]

[0059] F r (k)=Φ(W Fr σ r (k)+Γ Fr g r (k-1)+δ Fr ) (19)

[0060] Ω r (k)=Φ(W Ωr σ r (k)+Γ Ωr g r (k-1)+δ Ωr ) (20)

[0061]

[0062]

[0063] Among them, η i and O(k) represent the input and output of LSTMNN, O(k) is y m (k), η i represents the i-th term in the autoregressive sliding average term η, and the LSTM unit acts as a hidden neuron. F r and Ω r Represent the cell state, input gate, forget gate and output gate of the rth LSTM unit respectively. In (5)-(10), the historical hidden state g is used r (k-1), and the current input σ r (k) to calculate the hidden state g r (k). Φ represents the sigmoid activation function, and tanh represents the hyperbolic tangent function. The number of neurons in the input layer and hidden layer are c and f, respectively.

[0064] is a vector of LSTMNN weights and biases. Figure 1 This is a block diagram of the principle behind the LSTMNN-based complex physical field coupled hysteresis modeling method. Taking into account both computational complexity and modeling accuracy, the neural network's input layer uses 119 neurons, the hidden layer uses 11 neurons, and the output layer uses 1 neuron. Initial weights are set to random values ​​between 0 and 1, and the optimization algorithm uses gradient descent.

[0065] In order to optimize the model parameters, the objective function is defined as follows:

[0066]

[0067] Update the parameters through the gradient descent algorithm as shown below:

[0068]

[0069] in, is the learning rate.

[0070] The following specific examples verify the beneficial effects of the above method.

[0071] Figure 2 and Figure 3 The experimental platform for a magnetically controlled shape memory alloy actuator and a schematic diagram of the equipment connections are shown. The experimental system includes a computer, a data acquisition card, a programmable DC power supply, a magnetically controlled shape memory alloy actuator, a displacement sensor, and a temperature sensor. The computer communicates with other experimental equipment via the data acquisition card, which is responsible for data acquisition and analysis. MATLAB software on the computer generates a drive signal, which is converted to an analog signal by the data acquisition card and then sent to the programmable DC power supply. The programmable DC power supply outputs an adjustable current based on the drive signal, which serves as the excitation signal for the magnetically controlled shape memory alloy actuator. Under current excitation, the magnetically controlled shape memory alloy actuator generates an output displacement. The displacement sensor acquires this signal and feeds it back to the computer via the data acquisition card. MATLAB software analyzes and processes the real-time displacement response data. Furthermore, a temperature sensor collects the real-time operating temperature of the magnetically controlled shape memory alloy actuator to ensure its safe and stable operation.

[0072] In order to verify the effectiveness of the proposed modeling method, a series of experiments were carried out under different temperature and load conditions. The experimental results are shown in Figure 2. Figure 4-Figure 15 shown. Figure 4-Figure 9 The modeling results at different temperatures (22°C, 26°C, and 30°C) are presented. Under mixed wave signal input, the proposed model has good modeling accuracy and can effectively describe the impact of different temperatures on the hysteresis output. Figure 10-15 The modeling results are presented for loads of 100g, 200g, and 300g under mixed wave signal input. The experimental results demonstrate that the proposed model accurately fits the load-dependent hysteresis characteristics of the magnetically controlled shape memory alloy actuator, indicating that the proposed model is highly adaptable and can accommodate changes in hysteresis nonlinearity under the influence of different loads.

[0073] Experimental results show that the proposed model can accurately describe the hysteresis nonlinearity of magnetic shape memory alloy actuators under complex physical field coupling. On the one hand, because the hysteresis characteristics of magnetic shape memory alloy actuators are usually time-related, and LSTMNN has a stronger ability to process time series data, it can effectively capture the correlation and time dynamic characteristics in long sequences, and can better remember historical information, thereby providing more accurate predictions for future outputs. On the other hand, by using physical field information such as temperature and load as input variables of the model, it effectively reflects the changing pattern of the hysteresis characteristics of magnetic shape memory alloy actuators under the action of multi-physical field coupling, overcoming the limitation of traditional modeling methods that cannot fully consider the influence of multi-physical field coupling, thereby improving the accuracy and reliability of the model's description of hysteresis characteristics under complex physical field coupling.

Claims

1. A neural network hysteresis modeling method for magnetically controlled shape memory alloy actuators under complex physical field coupling, characterized in that: The steps of this method are as follows: Step 1: Use the NARMAX model to describe the multi-value mapping hysteresis of the magnetically controlled shape memory alloy actuator. Take temperature and load as model inputs to establish a multi-field coupling NARMAX model containing multi-physics field coupling information. The expression of the multi-field coupling NARMAX model is: Where k is the discrete moment of the system; N is the unknown nonlinear function; y m represents the output value of the NARMAX model; h represents the exogenous variable of the NARMAX model; l and t represent the load and temperature of the system respectively; v and y represent the input and output values ​​of the system respectively; n v 、n h 、n l 、n t and n y They represent the delay of system input v, exogenous variable h, load l, temperature t and system output y respectively; a=n v +n h +n l +n t +n y +2 is the total system delay; The exogenous variable h is represented by the KP model, and the function expression is as follows: Where h(k) is the hysteresis output; k p [v,ξ p ] is the KP hysteresis operator; ξ p is the previous extreme value of the hysteresis operator output; p is the integration area of ​​the Preisach plane; μ(p) is the density function of the Preisach plane; 0 and β are the boundary values ​​of the Preisach plane; β is the maximum input of the system; (p1, p2) represents a pair of thresholds of the KP operator in the Preisach plane; Then, the multi-field coupled NARMAX model is rewritten into a polynomial form as follows: Where θ is the polynomial coefficient, is the matrix term composed of coefficients, is the autoregressive sliding average term; q is the model order, and n = (a + q)! / a! q! -1 is the total number of terms; Step 2: Use the long short-term memory neural network to construct the unknown nonlinear function of the multi-field coupled NARMAX model, so that the established model can update parameters online and accurately describe the dynamic hysteresis characteristics under complex physical field coupling; The expression of the long short-term memory neural network is as follows: F r (k)=Φ(W Fr s r (k)+C Fr g r (k-1)+δ Fr ) (6) Oh r (k)=Φ(W Ωr s r (k)+C Ωr g r (k-1)+δ Ωr ) (7) Among them, η i and O(k) are the input and output of the long short-term memory neural network, η i represents the i-th term in the autoregressive sliding average term η, O(k) is y m (k), LSTM units act as hidden neurons; F r and Ω r Represent the cell state, input gate, forget gate and output gate of the rth LSTM unit respectively; in formula (5)-(10), the historical hidden state g is used r (k-1), and the current input σ r (k) to calculate the hidden state g r (k); Φ represents the sigmoid activation function, tanh represents the hyperbolic tangent function; the number of neurons in the input layer and the number of neurons in the hidden layer are c and f respectively; is a vector consisting of the weights and biases of the long short-term memory neural network; the long short-term memory neural network updates the parameters of W through an optimization algorithm.

2. A neural network hysteresis modeling method for magnetically controlled shape memory alloy actuators under complex physical field coupling, characterized in that: In step 1, q is selected as 3, n v 、n h 、n l 、n t and n y Select 2, 2, 0, 0 and 1 respectively.

3. A neural network hysteresis modeling method for magnetically controlled shape memory alloy actuators under complex physical field coupling, characterized in that: In step 2, the number of neurons c in the input layer of the long short-term memory neural network is selected as 119, the number of neurons f in the hidden layer is selected as 11, the number of neurons in the output layer is 1, and the initial weights are set to random values ​​between 0 and 1.

4. A neural network hysteresis modeling method for magnetically controlled shape memory alloy actuators under complex physical field coupling, characterized in that: The objective function of the LSTM neural network optimization algorithm in step 2 is defined as follows: The parameters are updated by the gradient descent algorithm as shown below: in, is the learning rate.

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