Electric vehicle wireless charging system LPV-Hammerstein model identification method based on alternating least square iteration strategy

Abstract

The invention relates to an electric vehicle wireless charging system LPV-Hammerstein model identification method based on an alternating least square iteration strategy, and belongs to the technical field of power electronic system modeling and parameter identification. The method comprises the following steps: firstly, constructing an LPV-Hammerstein model structure based on a WPT system circuit topology and a working mechanism, and then collecting discrete data of a system input control signal U, an output DC voltage Vo and a scheduling variable Req; then, alternately fixing other parameters by adopting an alternate least square iterative algorithm, and converting a to-be-estimated parameter problem into a linear least square sub-problem to be solved; and when a convergence condition is satisfied, a final LPV-Hammerstein model parameter estimation result is obtained. According to the method, the common nonlinear and parameter change coupling characteristics in the wireless charging system of the electric vehicle can be effectively processed, a systematized and efficient way is provided for obtaining a high-precision system dynamic model, and the limitation that the system cannot be accurately described by a traditional linear model or a simple nonlinear model is overcome.

Description

Technical Field

[0001] The present invention belongs to the technical field of power electronic system modeling and parameter identification, and relates to an LPV-Hammerstein model identification method for an electric vehicle wireless charging system based on an alternating least squares iterative strategy. Background Art

[0002] As a convenient, safe, and flexible energy transmission method, wireless charging (WPT) technology for electric vehicles has developed rapidly in recent years, especially in the field of dynamic wireless charging (DWC), showing great application prospects. However, the dynamic characteristics of actual WPT systems are complex, and their performance is easily affected by a variety of time-varying factors, such as the change in mutual inductance M caused by the relative position change between the transmitting and receiving coils, the fluctuation of load demand, and the equivalent load resistance R caused by the rectification process. eq With the output voltage V o and the current envelope |I s |The power supply system fluctuates in real time with changes in the operating point. Furthermore, the control strategy of the front-end inverter introduces significant static input nonlinearities. These nonlinearities, often coupled with parameter variations, pose significant challenges to the accurate modeling, state estimation, and high-performance control of WPT systems.

[0003] An accurate system dynamic model is the basis for achieving efficient, robust and safe operation of the WPT system. At present, the modeling methods of WPT systems mainly include mechanism modeling and data-driven modeling. Mechanism modeling is based on physical laws, such as circuit theory and electromagnetic field theory, and can provide clear physical meaning. However, in scenarios where parameters are rapidly changing, such as dynamic wireless charging of electric vehicles, key physical parameters (such as mutual inductance M, equivalent load resistance R) are often difficult to accurately predict. eq ) is difficult to accurately measure or track in real time. This causes mechanistic models based on static or quasi-static parameter assumptions to deviate significantly from the actual system state under dynamic conditions, resulting in model mismatch and affecting model effectiveness. Data-driven modeling directly utilizes the system's input and output data to build models, eliminating the need for precise physical parameters. This approach offers potential advantages for systems with uncertain parameters and time-varying systems. However, its effectiveness is highly dependent on whether the selected model structure can accurately capture the complex characteristics of the system.

[0004] Based on the in-depth analysis of the WPT system mechanism, especially the static nonlinearity of the inverter output (e.g., approximately Function form) and the equivalent resistance R introduced by the rectifier load eq The time-varying characteristics of R eq With V o and|I s| changes), the WPT system is considered to exhibit an LPV-Hammerstein model structure. This model structure decomposes the system into a static nonlinear link (corresponding to the inverter nonlinearity) and a linear parameter variation (LPV) dynamic subsystem (whose parameters depend on the measurable dispatch variable R eq ) in series, providing a structured framework that can capture both nonlinear behavior and reflect the changes in system dynamics with external scheduling variables. In this model architecture, the LPV component can be understood as a functional extension or evolution of the classic Hammerstein model, replacing the linear time-invariant (LTI) dynamic system with an LPV system whose parameters change with scheduling variables, thereby more accurately approximating and characterizing the actual operating conditions under the influence of parameter dynamics. This model clearly separates the effects of nonlinearity and time-varying dynamics, laying a theoretical foundation for system performance analysis, state estimation, and model-based prediction and optimization control strategy design.

[0005] However, while research has been conducted on the accurate parameter identification of this type of LPV-Hammerstein model in practical, noisy WPT systems, it has not received widespread and in-depth attention. Research on related identification methods is relatively limited, and their maturity and practicality still need to be further improved. There are inherent challenges in tackling the identification of such complex models. For example, the identification algorithm needs to effectively handle the coupling relationship between static nonlinear parameters and LPV dynamic parameters and resolve the scale ambiguity between parameters. Furthermore, overparameterization methods are sometimes considered, but overparameterized models (those with far more parameters than theoretically required) are often accompanied by increased parameter variance and the risk of overfitting in traditional system identification. Existing identification methods for certain complex models (e.g., models with a large number of parameters), especially those relying on low-rank decomposition techniques such as singular value decomposition (SVD), are limited in their effectiveness in terms of low-rank approximation when faced with noise interference inherent in the actual system or when there is a slight mismatch between the model structure and the real system (especially its unmodeled dynamics or subtle nonlinearities). This makes it difficult to accurately capture the complete dynamics of the system, resulting in a significant decrease in the accuracy of the identified model and affecting its application in dynamic control and performance optimization.

[0006] Therefore, how to develop a new LPV-Hammerstein model identification method that can effectively deal with the noise interference and model mismatch that are common in actual systems, overcome the limitations of existing methods (such as over-parameterization methods relying on low-rank decomposition) in identifying complex models, and achieve high-precision and robust parameter estimation of the LPV-Hammerstein model of the WPT system is crucial to improving the control performance of the dynamic wireless charging system. Summary of the Invention

[0007] In view of this, the purpose of the present invention is to provide an LPV-Hammerstein model identification method for an electric vehicle wireless charging system based on an alternating least squares iterative strategy, aiming to solve the problem that the coupling effects of static input nonlinearity and parameter time-varying characteristics that are prevalent in dynamic wireless charging systems are difficult to accurately model and identify, overcome the limitations of traditional modeling methods (such as mechanism models that are sensitive to time-varying parameters and simple data-driven models that are difficult to capture complex coupling characteristics), and overcome the challenges that existing complex model identification methods (such as methods that partially rely on low-rank approximation) may face in the presence of noise and model mismatch, thereby achieving a high-precision and robust description of the dynamic characteristics of the system.

[0008] In order to achieve the above object, the present invention provides the following technical solutions:

[0009] An LPV-Hammerstein model identification method for an electric vehicle wireless charging system based on an alternating least squares iterative strategy comprises the following steps:

[0010] S1. Construct the LPV-Hammerstein model structure based on the WPT system circuit topology and working mechanism;

[0011] S2, acquisition system input control signal U, output DC voltage V o and scheduling variable R eq discrete data;

[0012] S3. Initialize the parameters to be identified θ = (a, b, c);

[0013] S4, using the alternating least squares iterative algorithm, alternately fixing other parameters, and transforming the problem of the parameter to be estimated into a linear least squares subproblem for solution;

[0014] S5. Check whether the convergence criterion is met or the maximum number of iterations is reached. If so, output the estimated result; otherwise, return to S4 to continue iteration.

[0015] Furthermore, in step S1, the LPV-Hammerstein model structure is established as follows:

[0016] The inverter control characteristics of the WPT system are described as a static input nonlinear link, and its equivalent fundamental wave input is related to the control signal U, which can be expressed as:

[0017]

[0018] Where c = [c1, c2] is the parameter to be identified; U(t) represents the control signal at time t;

[0019] The dynamic response of the WPT system is described as a linear parameter change dynamic link, where the parameter A of the LPV dynamic model is i and B j is the scheduling variable R eq The affine function of , that is:

[0020] A i (R eq (t))=a i,1 +a i,2 R eq (t)

[0021] B j (R eq (t))=b j,1 +b j,2 R eq (t)

[0022] Where a i,1 ,a i,2 ,b j,1 ,b j,2 is the linear parameter to be identified;

[0023] The final discrete-time LPV-Hammerstein model structure is:

[0024]

[0025] The parameter vector to be identified is θ=(a,b,c), where a=[a i,k ],b=[b j,k ],c=[c1,c2];V o (t) represents the system output DC voltage; model order n a and n b The selection is made based on the actual system characteristics and identification requirements; e(t) represents zero-mean white noise or modeling error.

[0026] Furthermore, in step S2, the measured data for model parameter identification are obtained, including the system input control signal U(t) and the system output DC voltage V at each sampling time t. o (t) and the corresponding scheduling variable R eq (t), where the collected data forms a data set containing N sets of data points The data record length N is set based on the premise of ensuring recognition accuracy;

[0027] The input control signal U(t) includes the phase shift angle of the inverter in phase shift control;

[0028] The scheduling variable is selected as the equivalent resistance R eq(t), since it is difficult to directly measure the load change in a real environment, the scheduling variable R eq (t) According to the measured system output DC voltage V o (t) and the AC current envelope flowing through the rectifier bridge |I s (t)|Approximately calculated:

[0029]

[0030] Furthermore, in step S3, before starting the alternating least squares iteration process, an initial estimate is set for the parameter vector θ to be identified of the LPV-Hammerstein model. The parameters include parameter vectors a and b describing the dynamic link of LPV, and parameter vector c describing the static nonlinear link;

[0031] The initial value setting methods include: (1) making a rough estimate based on prior knowledge and the physical characteristics of the system; (2) setting it to a small random value close to zero.

[0032] Furthermore, in step S4, the parameter identification problem of the LPV-Hammerstein model is transformed into a nonlinear optimization problem, the goal of which is to minimize the sum of squared errors between the model's predicted output and the actual output:

[0033]

[0034] in, represents the cost function value at the kth iteration; t represents a discrete time point; t0 represents the starting time point of the data window; N represents the length of the data window or the number of samples used for parameter identification; V o (t) represents the actual output voltage of the wireless charging system at time t, that is, the actual measured value; Represents the model parameter vector obtained using the kth iteration The predicted value of the output voltage at time t.

[0035] The alternating least squares iterative algorithm is used to solve this nonlinear problem. The alternating least squares iterative algorithm fixes some parameters iteratively and decomposes the original nonlinear problem into linear least squares sub-problems about the remaining parameters for solution.

[0036] Furthermore, in the kth iteration, the algorithm uses the updated parameter estimates from the previous or current round to perform the following solution steps in sequence:

[0037] S41, estimated parameter a: fix the parameter obtained in the previous iteration and The estimated value of constructs the corresponding regression matrix Φ1, based on Calculate the partial residual vector Among them, the column vector of the regression matrix Φ1 is expressed as:

[0038] [V o (t-1),R eq (t)V o (t-1),…,V o (tn a ),R eq (t)V o (tn a )] T

[0039] Partial residual vector Expressed as:

[0040]

[0041] Where V o For the output vector [V o (t0),…,V o (t0+N-1)] T , For about The regression matrix of

[0042] By solving the linear least squares problem with respect to parameter a Get new parameter estimates:

[0043]

[0044] if If it is not reversible, use pseudo-inverse to solve it;

[0045] S42, estimated parameter c: fixed parameter obtained in the current iteration and the parameters obtained in the previous iteration The estimated value of the model equation is rearranged so that it depends linearly on the parameter c, and the corresponding regression matrix is ​​constructed. and based on Calculate the partial residual vector Among them, the regression matrix The column vector of is represented as:

[0046]

[0047] Partial residual vector Expressed as:

[0048]

[0049] Solve the linear least squares problem with respect to parameter c Get preliminary parameter estimates

[0050]

[0051] The initial estimate obtained Normalization is performed to eliminate the scale ambiguity between the static nonlinear link parameters and the LPV dynamic link parameters. The normalized parameter c is expressed as

[0052] S43: Estimated parameter b: Fixed the parameter obtained in the current iteration and normalized Construct the corresponding regression matrix and based on Calculate the partial residual vector Among them, the regression matrix The column vector of is represented as:

[0053]

[0054] Where,

[0055] Partial residual vector Expressed as:

[0056]

[0057] Solve the linear least squares problem with respect to parameter b Get new parameter estimates

[0058]

[0059] This gives the updated parameters for this round

[0060] Further, in step S42, for the preliminary estimated value Normalization is performed to obtain parameter estimates The methods include:

[0061] (1) Fix the L2 norm of parameter c to 1 and calculate the initial parameter estimate The Euclidean norm of And the preliminary parameter estimates Divide by its norm to get the normalized parameter estimate

[0062]

[0063] if If it is zero, it means that the identification process is abnormal;

[0064] (2) The first element c1 of the fixed parameter c is 1. If the first basis function of the static nonlinear link The corresponding parameter c1 is not zero in the actual system, so the initial estimate is selected The first element is fixed to 1, and a scale factor is calculated. Right now The first element of Divide by the scale factor to get the normalized parameter estimate

[0065]

[0066] if If it is zero or close to zero, this method is not used for processing.

[0067] Furthermore, in step S5, it is determined whether the parameter estimation results in the iterative process meet the preset convergence criteria including the first convergence criterion and the second convergence criterion. When any convergence criterion is met or the maximum number of iterations is reached, the algorithm terminates and the parameter estimation value obtained in the last iteration is converted to Output as the final LPV-Hammerstein model parameter identification result, otherwise update the number of iterations k←k+1 and enter the next round of iteration;

[0068] Among them, the judgment method of the first convergence criterion is:

[0069] Calculate the parameter vector obtained from two consecutive iterations When the relative change is less than the preset threshold ∈1, it is determined to be converged. The convergence condition is expressed as:

[0070]

[0071] The second convergence criterion is determined as follows:

[0072] Calculate the cost function of the model prediction error obtained from two consecutive iterations If the relative change is less than the preset threshold ∈2, it is considered to be converged. The convergence condition is expressed as:

[0073]

[0074] Where δ is a positive number to avoid the denominator being zero.

[0075] The beneficial effects of the present invention are:

[0076] By combining WPT system mechanism analysis with a data-driven approach, this paper constructs and identifies an LPV-Hammerstein model structure suitable for accurately characterizing the system's static input nonlinearity and time-varying parameter coupling characteristics. This effectively addresses the difficulty of traditional modeling methods in accurately describing the complex dynamic behavior of dynamic wireless charging systems, such as mechanism models that rely solely on static parameters or simple data-driven models that struggle to capture complex coupling characteristics. The identification method proposed in this paper can effectively handle the nonlinearity and parameter variation coupling characteristics that are prevalent in electric vehicle wireless charging systems, providing a systematic and efficient approach to obtaining high-precision system dynamic models. This overcomes the limitations of traditional linear models or simple nonlinear models that cannot accurately describe such systems, laying a solid foundation for subsequent model-based controller design and performance optimization.

[0077] Secondly, the present invention adopts an alternating least squares (ALS) iterative algorithm to decompose the nonlinear identification problem of the LPV-Hammerstein model parameters into easy-to-solve linear least squares sub-problems, and realizes parameter estimation through iterative optimization, providing a systematic, efficient and easy-to-implement parameter identification approach. The algorithm introduces normalization processing of the static nonlinear link parameters in the iterative process, effectively eliminating the inherent parameter scale ambiguity of the model, improving the uniqueness and robustness of the parameter estimation results, and avoiding the impact of scale uncertainty on the model application. The high-precision LPV-Hammerstein model identified can more accurately reflect the behavior of the WPT system at different operating points and dynamic processes, laying a solid foundation for subsequent model-based advanced control strategies (such as predictive control, adaptive control), system state estimation and performance optimization, thereby significantly improving the efficiency, stability and safety of the electric vehicle wireless charging system.

[0078] Other advantages, objects, and features of the present invention will be described in part in the following description and, in part, will be apparent to those skilled in the art upon examination of the following description or may be learned from practice of the present invention. The objects and other advantages of the present invention may be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0079] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below with reference to the accompanying drawings, in which:

[0080] Figure 1 This is a block diagram showing the overall logical flow of an LPV-Hammerstein model identification method for an electric vehicle wireless charging system based on an alternating least squares iterative strategy according to an embodiment of the present invention;

[0081] Figure 2A schematic diagram of a single-input single-output SS topology wireless power transmission system according to an embodiment of the present invention;

[0082] Figure 3 Schematic diagram of an equivalent circuit of a wireless power transmission system according to an embodiment of the present invention. DETAILED DESCRIPTION

[0083] The following describes the embodiments of the present invention by means of specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic illustrations of the basic concept of the present invention, and the following embodiments and features in the embodiments can be combined with each other without conflict.

[0084] Among them, the accompanying drawings are only for illustrative purposes and represent only schematic diagrams rather than actual pictures, and should not be understood as limiting the present invention. In order to better illustrate the embodiments of the present invention, some parts of the accompanying drawings may be omitted, enlarged or reduced, and do not represent the dimensions of actual products. For those skilled in the art, it is understandable that some well-known structures and their descriptions may be omitted in the accompanying drawings.

[0085] The same or similar numbers in the drawings of the embodiments of the present invention correspond to the same or similar parts; in the description of the present invention, it should be understood that if there are terms such as "upper", "lower", "left", "right", "front", "back", etc. indicating directions or positional relationships, they are based on the directions or positional relationships shown in the drawings. They are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific direction, be constructed and operate in a specific direction. Therefore, the terms describing the positional relationship in the drawings are only used for illustrative purposes and cannot be understood as limiting the present invention. For ordinary technicians in this field, the specific meanings of the above terms can be understood according to specific circumstances.

[0086] See also Figures 1 to 3 , which is an LPV-Hammerstein model identification method for electric vehicle wireless charging system based on alternating least squares iterative strategy.

[0087] This embodiment provides a specific implementation process of an LPV-Hammerstein model identification method for an electric vehicle wireless charging system based on an alternating least squares iterative strategy. Specifically, Figure 1 As shown, it includes the following steps:

[0088] Step S1: Based on the WPT system circuit topology and working mechanism, construct the LPV-Hammerstein model structure, including static input nonlinear links and parameter-dependent scheduling variables R eq LPV dynamic link

[0089] This step aims to determine the mathematical model structure suitable for describing the dynamic characteristics of the electric vehicle wireless charging system. For the WPT system, especially the typical series-series (SS) compensation topology, its equivalent circuit is as follows: Figure 2 Based on circuit principles, including Kirchhoff's laws, and using methods such as First Harmonic Approximation (FHA), the dynamic characteristics of the main modules such as the inverter, resonant network, coupling mechanism, rectifier and load are deeply analyzed.

[0090] The analysis shows that the dynamic behavior of the WPT system can be described by an LPV-Hammerstein model structure consisting of a static input nonlinear link and a series linear parameter variation (LPV) dynamic link, as shown in Figure 3 As shown. Among them, the static input nonlinear link originates from the inverter control characteristics, and its equivalent fundamental wave input is related to the control signal U and can be expressed as Where c = [c1, c2] is the parameter to be identified. The linear parameter variation (LPV) dynamic link describes the dynamic response of the system, and its parameters depend on the scheduling variable R that reflects the change of the system operating point. eq Parameter A of the LPV dynamic model i and B j is the scheduling variable R eq Affine function of i (R eq (t))=a i,1 +a i,2 R eq (t) and B j (R eq (t))=b j,1 +b j, 2R eq (t), where a i,1 ,a i,2 ,b j,1 ,b j,2 is the linear parameter to be identified. The final discrete-time LPV-Hammerstein model structure is:

[0091]

[0092] The parameter vector to be identified is θ=(a,b,c), where a=[a i,k ],b=[bj,k ], c=[c1,c2], model order n a and n b The selection is made based on the actual system characteristics and identification requirements; e(t) represents zero-mean white noise or modeling error.

[0093] Step S2: Acquisition system input control signal U, output DC voltage V o and scheduling variable R eq Discrete data

[0094] This step aims to obtain measured data for model parameter identification. When the WPT system is operating normally or undergoing special identification experiments, a series of discrete time data are collected at a certain sampling frequency, including the system input control signal U(t) (such as the phase shift angle of the inverter in phase shift control), the system output DC voltage V o (t) and the corresponding scheduling variable R eq (t). The scheduling variable R eq (t) can be obtained by sensor measurement or based on the measured V o (t) and the AC current envelope flowing through the rectifier bridge |I s (t)|, according to the formula Calculated; or when the load resistance R is known o In the case of V o (t) is calculated. The collected data forms a data set containing N groups of data points The data record length N should be long enough to ensure the recognition accuracy.

[0095] Step S3: Initialize the model parameters to be identified θ = (a, b, c)

[0096] This step is intended to provide a starting point for the subsequent iterative optimization algorithm. Before starting the alternating least squares (ALS) iteration process, set the initial estimate of the parameter vector θ to be identified for the LPV-Hammerstein model. The parameters include parameter vectors a and b that describe the dynamic link of the LPV, and parameter vector c that describes the static nonlinear link. The initial value can be roughly estimated based on prior knowledge and the physical characteristics of the system, or set to a small random value close to zero, for example, and Set to zero vector, Set to a non-zero vector with L2 norm of 1 to enable normalization.

[0097] Step S4: Use the alternating least squares (ALS) iterative algorithm to alternately fix other parameters and transform the problem of estimated parameters into a linear least squares subproblem for solution

[0098] This step is the core algorithm implementation of the parameter identification of the present invention. The parameter identification problem of the LPV-Hammerstein model is transformed into a nonlinear optimization problem, the goal of which is to minimize the sum of squares of the error between the model's predicted output and the actual output. in, represents the cost function value at the kth iteration; t represents a discrete time point; t0 represents the starting time point of the data window; N represents the length of the data window or the number of samples used for parameter identification; V o (t) represents the actual output voltage of the wireless charging system at time t, that is, the actual measured value; Represents the model parameter vector obtained using the kth iteration The predicted value of the output voltage at time t.

[0099] This nonlinear problem is solved using an iterative algorithm based on alternating least squares (ALS). The ALS algorithm iteratively fixes some parameters and decomposes the original nonlinear problem into linear least squares subproblems concerning the remaining parameters. In the kth iteration, the algorithm uses the updated parameter estimates from the previous or current round and performs the following solution steps in sequence:

[0100] Step 4.1: Estimate parameter a: Fix the parameter obtained in the previous iteration and Construct the corresponding regression matrix φ1 (whose column vector is [V o (t-1),R eq (t)V o (t-1),…,V o (tn a ),R eq (t)V o (tn a )] T ) and based on Calculate the partial residual vector Where V o For the output vector [V o (t0),…,V o (t0+N-1)] T , For about By solving the linear least squares problem about parameter a Get new parameter estimates:

[0101]

[0102] if If it is not reversible, use pseudo-inverse to solve it.

[0103] Step 4.2: Estimate parameter c: Fix the parameter obtained in the current iteration and the parameters obtained in the previous iteration The estimated value of . Rearrange the model equation so that it depends linearly on the parameter c. Construct the corresponding regression matrix (The column vector is and based on Calculate the partial residual vector Solve the linear least squares problem with respect to parameter c Get preliminary parameter estimates:

[0104]

[0105] Step 4.3: Estimate parameter b: Fix the parameter obtained in the current iteration and normalized Construct the corresponding regression matrix (The column vector is in and based on Calculate the partial residual vector Solve the linear least squares problem with respect to parameter b Get new parameter estimates:

[0106]

[0107] Step S5: Normalize the parameter c during iteration to eliminate parameter scale ambiguity

[0108] This step aims to deal with the scale ambiguity between the static nonlinear link parameters and the LPV dynamic link parameters in the model to improve the uniqueness of the identification results. The preliminary estimate of the static nonlinear parameters is obtained in step 4.2. After that, it is normalized. Since the gain of the static nonlinear link can offset the gain of the LPV dynamic link (that is, for any non-zero constants α, αb and Describing the same system input-output relationship), there is scale ambiguity. To eliminate parameter scale ambiguity, the present invention provides two optional normalization methods:

[0109] Method 1: Fix the L2 norm of parameter c to 1. Calculate the initial parameter estimate The Euclidean norm of And the preliminary parameter estimates Divide by its norm to obtain the normalized parameter estimate

[0110]

[0111] if If it is zero, it means that an abnormality occurs in the identification process.

[0112] Method 2: Fix the first element c1 of parameter c to 1. If the first basis function of the static nonlinear link (i.e. ) The corresponding parameter c1 will not be zero in the actual system, so you can choose to set the initial estimate The first element of is fixed to 1. Specifically, a scale factor is calculated (Right now ), and then taking the initial estimate Divide by the scale factor to get the normalized parameter estimate

[0113]

[0114] if If it is zero or very close to zero, this method should not be used. In this case, method 1 or other appropriate normalization methods should be selected. Select one of the normalization methods to obtain the normalized The parameter b used in step 4.3 is estimated.

[0115] Step S6: Check whether the convergence criterion is met or the maximum number of iterations is reached. If so, output the result. Otherwise, return to S4 to continue iteration.

[0116] This step is to control the termination of the iterative algorithm. After completing one iteration in step S4 (i.e., steps 4.1-4.3 and step S5), check whether the parameter estimation results meet the preset convergence criteria or whether the set maximum number of iterations K has been reached. max The step S6 specifically includes two ways to judge convergence: one is to calculate the parameter vector obtained by two consecutive iterations When the relative change is less than the preset threshold ∈1, it is determined to be convergent. For example, the calculation is:

[0117]

[0118] Where δ is a small positive number (e.g. 10 -9 ) to avoid division by zero. The second is to calculate the cost function of the model prediction error obtained from two consecutive iterations If the relative change is less than the preset threshold ∈2, it is considered to be converged, for example:

[0119]

[0120] At the same time, set a maximum number of iterations K max If any convergence criterion is met or K is reached max , the algorithm terminates and the parameter estimate obtained in the last iteration is The final LPV-Hammerstein model parameter identification result is output. Otherwise, the number of iterations is updated k←k+1, and the process returns to step S4 to start the next iteration.

[0121] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not limiting. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solutions, which should all be included in the scope of the claims of the present invention.

Claims

1. A LPV-Hammerstein model identification method for an electric vehicle wireless charging system based on an alternating least squares iterative strategy, characterized by: The method comprises the following steps: S1. Construct the LPV-Hammerstein model structure based on the WPT system circuit topology and working mechanism; S2, acquisition system input control signal U, output DC voltage V o and scheduling variable R eq discrete data; S3. Initialize the parameters to be identified θ = (a, b, c); S4, using the alternating least squares iterative algorithm, alternately fixing other parameters, and transforming the problem of the parameter to be estimated into a linear least squares subproblem for solution; S5. Check whether the convergence criterion is met or the maximum number of iterations is reached. If so, output the estimated result; otherwise, return to S4 to continue iteration.

2. The LPV-Hammerstein model identification method for an electric vehicle wireless charging system based on an alternating least squares iterative strategy according to claim 1 is characterized by: In step S1, the process of establishing the LPV-Hammerstein model structure is as follows: The inverter control characteristics of the WPT system are described as a static input nonlinear link, and its equivalent fundamental wave input is related to the control signal U, which can be expressed as: Where c = [c1, c2] is the parameter to be identified; U(t) represents the control signal at time t; The dynamic response of the WPT system is described as a linear parameter change dynamic link, where the parameter A of the LPV dynamic model is i and B j is the scheduling variable R eq The affine function of , that is: A i (R eq (t))=a i,1 +a i,2 R eq (t) B j (R eq (t))=b j,1 +b j,2 R eq (t) Where a i,1 ,a i,2 ,b j,1 ,b j,2 is the linear parameter to be identified; The final discrete-time LPV-Hammerstein model structure is: The parameter vector to be identified is θ=(a,b,c), where a=[a i,k ],b=[b j,k ],c=[c1,c2];V o (t) represents the system output DC voltage; model order n a and n b The selection is made based on the actual system characteristics and identification requirements; e(t) represents zero-mean white noise or modeling error.

3. The LPV-Hammerstein model identification method for an electric vehicle wireless charging system based on an alternating least squares iterative strategy according to claim 2, characterized in that: In step S2, the measured data for model parameter identification are obtained, including the system input control signal U(t) and the system output DC voltage V at each sampling time t. o (t) and the corresponding scheduling variable R eq (t), where the collected data forms a data set containing N sets of data points The data record length N is set based on the premise of ensuring recognition accuracy.

4. The LPV-Hammerstein model identification method for an electric vehicle wireless charging system based on an alternating least squares iterative strategy according to claim 2, characterized in that: In step S3, before starting the alternating least squares iterative process, an initial estimate is set for the parameter vector θ to be identified of the LPV-Hammerstein model. The parameters include parameter vectors a and b describing the dynamic link of LPV, and parameter vector c describing the static nonlinear link; The initial value setting methods include: (1) making a rough estimate based on prior knowledge and the physical characteristics of the system; (2) setting it to a small random value close to zero.

5. The LPV-Hammerstein model identification method for an electric vehicle wireless charging system based on an alternating least squares iterative strategy according to claim 4 is characterized by: In step S4, the parameter identification problem of the LPV-Hammerstein model is transformed into a nonlinear optimization problem. The goal is to minimize the sum of squared errors between the model's predicted output and the actual output. The cost function is defined as the sum of the squares of the residuals: in, represents the cost function value at the kth iteration; t represents a discrete time point; t0 represents the starting time point of the data window; N represents the length of the data window or the number of samples used for parameter identification; V o (t) represents the actual output voltage of the wireless charging system at time t, that is, the actual measured value; Represents the model parameter vector obtained using the kth iteration The predicted value of the output voltage at time t; The alternating least squares iterative algorithm is used to solve this nonlinear problem. The alternating least squares iterative algorithm fixes some parameters iteratively and decomposes the original nonlinear problem into linear least squares sub-problems about the remaining parameters for solution.

6. The LPV-Hammerstein model identification method for an electric vehicle wireless charging system based on an alternating least squares iterative strategy according to claim 5, characterized in that: In the kth iteration, the algorithm uses the updated parameter estimates from the previous or current round and performs the following solution steps in sequence: S41, estimated parameter a: fix the parameter obtained in the previous iteration and The estimated value of constructs the corresponding regression matrix Φ1, based on Calculate the partial residual vector Among them, the column vector of the regression matrix Φ1 is expressed as: Partial residual vector Expressed as: Where V o is the output vector For about The regression matrix of By solving the linear least squares problem with respect to parameter a Get new parameter estimates: if If it is not reversible, use pseudo-inverse to solve it; S42, estimated parameter c: fixed parameter obtained in the current iteration and the parameters obtained in the previous iteration The estimated value of the model equation is rearranged so that it depends linearly on the parameter c, and the corresponding regression matrix is ​​constructed. and based on Calculate the partial residual vector Among them, the regression matrix The column vector of is represented as: Partial residual vector Expressed as: Solve the linear least squares problem with respect to parameter c Get preliminary parameter estimates The initial estimate obtained Normalization is performed to eliminate the scale ambiguity between the static nonlinear link parameters and the LPV dynamic link parameters. The normalized parameter c is expressed as S43: Estimated parameter b: Fixed the parameter obtained in the current iteration and normalized Construct the corresponding regression matrix and based on Calculate the partial residual vector Among them, the regression matrix The column vector of is represented as: Where, Partial residual vector Expressed as: Solve the linear least squares problem with respect to parameter b Get new parameter estimates This gives the updated parameters for this round 7. The LPV-Hammerstein model identification method for an electric vehicle wireless charging system based on an alternating least squares iterative strategy according to claim 6, characterized in that: In step S42, the initial estimated value Normalization is performed to obtain parameter estimates The methods include: (1) Fix the L2 norm of parameter c to 1 and calculate the initial parameter estimate The Euclidean norm of And the preliminary parameter estimates Divide by its norm to get the normalized parameter estimate if If it is zero, it means that the identification process is abnormal; (2) The first element c1 of the fixed parameter c is 1. If the first basis function of the static nonlinear link The corresponding parameter c1 is not zero in the actual system, so the initial estimate is selected The first element is fixed to 1, and a scale factor is calculated. Right now The first element of Divide by the scale factor to get the normalized parameter estimate if If it is zero or close to zero, this method is not used for processing.

8. The LPV-Hammerstein model identification method for an electric vehicle wireless charging system based on an alternating least squares iterative strategy according to claim 6, characterized in that: In step S5, it is determined whether the parameter estimation results in the iterative process meet the preset convergence criteria, including the first convergence criterion and the second convergence criterion. When any convergence criterion is met or the maximum number of iterations is reached, the algorithm terminates and the parameter estimation value obtained in the last iteration is used as the new parameter. Output as the final LPV-Hammerstein model parameter identification result, otherwise update the number of iterations k←k+1 and enter the next round of iteration; Among them, the judgment method of the first convergence criterion is: Calculate the parameter vector obtained from two consecutive iterations When the relative change is less than the preset threshold ∈1, it is determined to be converged. The convergence condition is expressed as: The second convergence criterion is determined as follows: Calculate the cost function of the model prediction error obtained from two consecutive iterations If the relative change is less than the preset threshold ∈2, it is considered to be converged. The convergence condition is expressed as: Where δ is a positive number to avoid the denominator being zero.

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