An Improved Method for Parameter Identification in the BOUC-WEN Model Combining Sampling Rule Particle Filter and EKF

Abstract

This invention discloses a parameter identification method for the BOUC-WEN model combining an improved sampling rule particle filter and an EKF, belonging to the field of parameter identification technology. It addresses the problem that existing methods lack an effective mechanism to balance the relationship between global exploration and local convergence, leading to poor robustness in practical applications. The method includes establishing the state-space equation for the parameters to be identified in the BOUC-WEN model, generating an initial particle set for the particle filter, using the particle filter for parameter identification, constructing a new particle set required by the particle filter, performing calculations for the next time step, and obtaining accurate identification values ​​of the BOUC-WEN model parameters based on the improved particle filter identification results. This invention constructs an initial particle set covering a wide area through order-of-magnitude partitioning sampling and combines it with an improved resampling strategy with local optimum discrimination, solving the problems of large parameter magnitude differences and particle degradation. It achieves rapid and high-precision identification of unknown parameters in the Bouc-Wen model without the need for precise initial values.

Description

Technical Field

[0001] This invention belongs to the field of parameter identification technology, specifically relating to an improved method for parameter identification of the BOUC-WEN model combining a sampling rule particle filter and an EKF. Background Technology

[0002] Hysteresis phenomena are widespread in engineering systems such as mechanical, civil, and electrical engineering, as well as in interdisciplinary fields such as biology and psychology. A key characteristic is the formation of input-output hysteresis curves even under quasi-static excitation. In structural dynamics, hysteresis characteristics are frequently used to characterize various nonlinear dynamic behaviors. To effectively describe and simulate this complex hysteresis behavior, the Bouc-Wen model was proposed and widely applied. This model defines the relationship between hysteresis force and displacement / velocity through a set of nonlinear differential equations. It boasts advantages such as flexible mathematical expression and the ability to fit various hysteresis curves with different shapes by adjusting parameters (e.g., hardening / softening parameters, hysteresis shape parameters), making it one of the core tools for simulating this type of nonlinear hysteresis phenomenon. Therefore, accurate identification of the Bouc-Wen model parameters is a crucial foundation for constructing reliable nonlinear system models and achieving structural state assessment and fault diagnosis.

[0003] For parameter identification in the Bouc-Wen model, existing techniques are mainly divided into stochastic optimization methods and deterministic estimation methods. While stochastic optimization methods (such as genetic algorithms and particle swarm optimization) have strong global search capabilities, they generally suffer from low computational efficiency and slow convergence speed. On the other hand, deterministic methods (such as least squares methods and extended Kalman filter EKF) converge rapidly, but they heavily rely on the selection of initial parameter values ​​and are prone to getting trapped in local optima, leading to identification failure.

[0004] Furthermore, most existing parameter identification methods require strong prior assumptions, typically demanding that the initial values ​​of the parameters to be identified be close to their true values, or that the parameter range be set within a very narrow interval. However, in practical engineering applications, the physical parameters of the system are often difficult to know in advance, making it hard to meet the above-mentioned strict prior conditions; especially when the parameters are completely unknown, existing methods lack an effective mechanism to balance the relationship between global exploration and local convergence, and also fail to fully consider the implicit, high-dimensional, and strongly nonlinear characteristics of the Bouc-Wen model itself. This results in poor robustness of existing identification methods in practical applications, unstable identification results, and insufficient accuracy. To address these problems, we propose an improved parameter identification method for the Bouc-Wen model that combines a sampling rule particle filter with an EKF. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of existing technologies by providing an improved method for identifying parameters of the BOUC-WEN model that combines a sampling rule particle filter and an EKF. This method solves the problem that existing methods lack an effective mechanism to balance the relationship between global exploration and local convergence, and also fail to fully consider the implicit, high-dimensional, and strongly nonlinear characteristics of the Bouc-Wen model itself, resulting in poor robustness in practical applications.

[0006] This invention is implemented as follows: an improved method for identifying parameters of the BOUC-WEN model jointly using a sampling rule particle filter and an EKF, comprising:

[0007] S10, Establish the state-space equation for the identification of the parameters to be identified in the BOUC-WEN model;

[0008] S20, based on the system excitation signal and displacement response signal, set the number of particles and the upper and lower bounds of the parameters to be identified for the particle filter, establish an improved initial value sampling method, and generate the initial particle set for the particle filter.

[0009] S30 uses a particle filter to identify parameters and calculates the state estimate, observation, and weight coefficient of each particle for the next time step.

[0010] S40, based on the improved resampling strategy, resamples the initial particle set, determines whether it is trapped in a local optimum region, and constructs the new particle set required by the particle filter;

[0011] S50, based on the obtained new particle set, repeat steps S30-S40 to perform the calculation for the next time step, until all excitation signals and displacement response signals are calculated;

[0012] S60, based on the improved particle filter identification result, use the identification result as the initial value of EKF to obtain the accurate identification value of the BOUC-WEN model parameters.

[0013] Preferably, establishing the state-space equation for identifying the parameters to be identified in the BOUC-WEN model includes:

[0014] S101, Establish the equations of motion for the single-degree-of-freedom BOUC-WEN model, which are expressed as follows:

[0015] (1)

[0016] (2)

[0017] In the formula: m represents mass, c represents damping, k represents stiffness, u represents excitation, z represents nonlinear restoring force, and y represents displacement. Indicates speed, Indicates acceleration. The first derivative of the nonlinear restoring force z with respect to time, α, , ν represents the parameters of the nonlinear restoring force system;

[0018] S102, Process variables based on the BOUC-WEN model , , Construct the state vector of the state-space equation with the parameters to be identified, where the state vector of the state-space equation is represented as:

[0019] (3)

[0020] In the formula, This represents the state vector of the state-space equation at time s; ~ express Elements 1-10 in the model are also process variables in the BOUC-WEN model. , , The values ​​of the parameters to be identified at time s, where the parameters to be identified are m, c, k, α, and . , 、ν;

[0021] S103, Establish the state-space equation for parameter identification, where the state-space equation is expressed as follows:

[0022] (4)

[0023] The output equation is as follows:

[0024] (5)

[0025] In the formula, This represents the state vector of the state-space equation at time s+1; ~ express Elements 1-10 in the model are also process variables in the BOUC-WEN model. , , and the value of the parameter to be identified at time s+1; Indicates time interval, Indicates process noise; This represents the stimulus at time s; This represents the output of the state-space equation at time s, which is also the displacement response of the BOUC-WEN model.

[0026] Preferably, the step of establishing the improved initial value sampling method and generating the initial particle set for the particle filter includes:

[0027] S201, Set the number of particles in the particle filter. The number of particles N in the particle filter can be between 10⁴ and 10⁸.

[0028] S202, determine the upper and lower bounds of the identification interval for the parameter k to be identified based on the system excitation signal and displacement response signal, wherein the upper and lower bounds of the identification interval are expressed as:

[0029] (6)

[0030] (7)

[0031] (8)

[0032] S203, determine other parameters to be identified: m, c, α, , The upper and lower bounds of ν are within their respective ranges;

[0033] S204, based on the upper and lower bounds of each parameter to be identified, divide the range of values ​​of the upper and lower bounds into j sub-intervals, such that the upper bounds of adjacent sub-intervals differ by an order of magnitude.

[0034] S205, uniformly sample each sub-interval of each parameter to be identified, and obtain N / j parameter samples in each sub-interval, for a total of N parameter samples in j sub-intervals;

[0035] S206, randomly combine the N parameter samples of all parameters to be identified, and each combination constitutes a particle, for a total of N parameter particles to be estimated;

[0036] S207, process variables of the BOUC-WEN model , , The initial value is set to 0, and the process variable and the parameter particles to be estimated form the initial particle set of the particle filter.

[0037] Preferably, the parameter identification using a particle filter includes:

[0038] S301, taking the particles of the particle filter as state vectors in the state-space equation, and estimating the state vector for the next time step using the Runge-Kutta method based on the state vector at time s, where the state vector for the next time step is expressed as:

[0039] i=1,…,N (9)

[0040] In the formula: Let represent the i-th state vector at time s+1. Representing the state-space equations, Let represent the i-th state vector at time s. This represents the stimulus at time s. represents the time value at time s, and w represents the process noise;

[0041] S302, Calculate the weight coefficient of each state vector at time s+1 based on the displacement signal. Among them, the weighting coefficient The calculation formula is expressed as follows:

[0042] (10)

[0043] (11)

[0044] in, Let represent the relative likelihood probability of the i-th state vector. This represents the displacement signal value at time s+1. The output equation represents the state-space equation. This represents the exponentiation operator.

[0045] Preferably, the new particle set required to construct the particle filter includes:

[0046] S401, based on particle weight coefficients Uniform sampling Particles , where λ is the number of parameters to be identified;

[0047] S402, will particles The parameters to be estimated in the calculation are magnified sequentially by 5-100 times to calculate the particles. The output fluctuation factor is used to determine the particle. Whether the particle gets trapped in a local optimum depends on the particle's behavior. If there is a point in the output fluctuation factor that is less than a given threshold, then the particle is determined to belong to a point in the local optimal solution region and the particle is deleted.

[0048] (12)

[0049] In the formula, Represents particles The output volatility factor, The output equation represents the state-space equation;

[0050] Among them, the parameters to be identified are If there are 2, then 2 can be calculated. indivual Value; take the minimum threshold. =10 -1 -10 -5 When 2 indivual If any of the particles is less than a given threshold, the particle belongs to a local optimum region. Delete the particle and resample new particles according to their weights to replenish it.

[0051] S403, with Based on individual particles, each particle is perturbed to generate... A new set of particles is needed to construct the particle filter, namely:

[0052] (13)

[0053] in Yes The first parameter to be identified in the vector multiplied by the coefficient of variation ( <1); Yes The first parameter to be identified in the vector is multiplied by And so on. The fundamental particles and The new particles form a new set of N particles for the next calculation. .

[0054] Preferably, obtaining accurate identification values ​​for the BOUC-WEN model parameters includes:

[0055] S601, Based on the particle filter identification results of the obtained parameters to be identified, establish the initial state vector and initial state covariance of the EKF algorithm at time s=1;

[0056] S602, based on the state vector and covariance matrix at time s, estimate the prior state vector and prior covariance matrix for the next time step using the Runge-Kutta method;

[0057] (14)

[0058] (15)

[0059] (16)

[0060] (17)

[0061] In the formula: Let represent the prior state vector at time s+1. Representing the state-space equations, Let represent the posterior state vector at time s. This represents the stimulus at time s. Let s represent the time value at time s, and w represent the process noise. Let represent the covariance matrix at time s;

[0062] S603, Calculate the posterior state vector at time s+1. and posterior covariance matrix ;

[0063] (18)

[0064] (19)

[0065] (20)

[0066] (twenty one)

[0067] In the formula: This represents the displacement signal value at time s+1. The output equation represents the state-space equation. Indicate the output equation The noise matrix, Represents the identity matrix;

[0068] S604. Repeat steps S602-S603 to calculate the next time step until all excitation signals and displacement response signals are calculated. Obtain the posterior state vector of the last step as the final BOUC-WEN model parameter identification result, that is, the accurate identification value of the BOUC-WEN model parameters.

[0069] Compared with the prior art, the embodiments of this application have the following main advantages:

[0070] This invention constructs an initial sample set covering different order-of-magnitude ranges by dividing the estimation interval of each parameter to be identified into several sub-intervals according to the order of magnitude, and then randomly combining samples uniformly within each sub-interval. Based on this, the iterative update process of the particle filter algorithm is combined to estimate the unknown parameters in the Bouc-Wen model, thereby effectively solving the problem of convergence difficulties in traditional sampling methods due to large differences in parameter order of magnitude, and improving the accuracy and computational efficiency of parameter identification. Furthermore, this invention enhances particle diversity by introducing random perturbations to generate new particles and performs local optimum discrimination on resampled particles. Specifically, by amplifying or reducing the parameters and calculating the output fluctuation factor, particles trapped in local optima are discarded and resampled, thus constructing a parameter identification framework that effectively avoids local optima. Based on this, a parameter estimation model based on the particle filter algorithm is established to estimate the state values ​​of the parameters to be identified at different times, thereby enabling rapid and accurate identification of the unknown parameters of the system model. Attached Figure Description

[0071] Figure 1 This is a schematic diagram illustrating the implementation process of the BOUC-WEN model parameter identification method combining the improved sampling rule particle filter and EKF provided by this invention.

[0072] Figure 2 The excitation signal time history diagram in Embodiment 2 of the present invention is shown.

[0073] Figure 3 The displacement time history diagram of Embodiment 2 of the present invention is shown.

[0074] Figure 4 The diagram illustrates the calculation process of the target parameters for the improved particle filter in Embodiment 2 of the present invention.

[0075] Figure 5 The diagram shows the calculation process of the EKF parameters to be identified in Embodiment 2 of the present invention. Detailed Implementation

[0076] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs; the terminology used herein in the specification of the application is for the purpose of describing particular embodiments only and is not intended to be limiting of the application; the terms "comprising" and "having," and any variations thereof, in the specification, claims, and foregoing drawings of this application are intended to cover non-exclusive inclusion. The terms "first," "second," etc., in the specification, claims, or foregoing drawings of this application are used to distinguish different objects, not to describe a particular order.

[0077] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0078] Most existing parameter identification methods require strong prior assumptions, typically demanding that the initial values ​​of the parameters to be identified be close to their true values, or that the parameter range be set within a very narrow interval. However, in practical engineering applications, the physical parameters of the system are often difficult to know in advance, making it hard to meet the above-mentioned strict prior conditions; especially when the parameters are completely unknown, existing methods lack an effective mechanism to balance the relationship between global exploration and local convergence, and also fail to fully consider the implicit, high-dimensional, and strongly nonlinear characteristics of the Bouc-Wen model itself. This results in poor robustness of existing identification methods in practical applications, unstable identification results, and insufficient accuracy. To address these problems, we propose an improved parameter identification method for the Bouc-Wen model that combines a sampling rule particle filter with an EKF. The method first establishes the state-space equation for the parameters to be identified in the BOUC-WEN model, establishes an improved initial value sampling method and generates an initial particle set for the particle filter, uses the particle filter for parameter identification, constructs a new particle set required by the particle filter, performs calculations for the next time step, and uses the identification result of the improved particle filter as the initial value of the EKF to obtain the accurate identification value of the BOUC-WEN model parameters. This invention constructs an initial particle set covering a wide area through order-of-magnitude partitioning sampling, and combines it with an improved resampling strategy with local optimum discrimination, solving the problems of large parameter magnitude differences and particle degradation, and achieving rapid and high-precision identification of unknown parameters in the Bouc-Wen model without precise initial values. Specifically, this invention constructs an initial sample set covering different order-of-magnitude ranges by dividing the estimation interval of each parameter to be identified into several sub-intervals according to the order of magnitude, and then randomly combining samples uniformly within each sub-interval. Based on this, the iterative update process of the particle filter algorithm is combined to estimate the unknown parameters in the Bouc-Wen model, thereby effectively solving the problem of convergence difficulties in traditional sampling methods due to large differences in parameter order of magnitude, and improving the accuracy and computational efficiency of parameter identification. Furthermore, this invention enhances particle diversity by introducing random perturbations to generate new particles and performs local optimum discrimination on resampled particles. Specifically, by amplifying or reducing the parameters and calculating the output fluctuation factor, particles trapped in local optima are discarded and resampled, thus constructing a parameter identification framework that effectively avoids local optima. Based on this, a parameter estimation model based on the particle filter algorithm is established to estimate the state values ​​of the parameters to be identified at different times, thereby enabling rapid and accurate identification of the unknown parameters of the system model.

[0079] Example 1

[0080] This invention provides an improved method for identifying parameters of the BOUC-WEN model by combining a sampling rule particle filter and an EKF. Figure 1This diagram illustrates the implementation flow of the BOUC-WEN model parameter identification method combining the improved sampling rule particle filter and EKF. The BOUC-WEN model parameter identification method specifically includes:

[0081] S10, Establish the state-space equation for the identification of the parameters to be identified in the BOUC-WEN model;

[0082] S20, based on the system excitation signal and displacement response signal, set the number of particles and the upper and lower bounds of the parameters to be identified for the particle filter, establish an improved initial value sampling method, and generate the initial particle set for the particle filter.

[0083] S30 uses a particle filter to identify parameters and calculates the state estimate, observation, and weight coefficient of each particle for the next time step.

[0084] S40, based on the improved resampling strategy, resamples the initial particle set, determines whether it is trapped in a local optimum region, and constructs the new particle set required by the particle filter;

[0085] S50, based on the obtained new particle set, repeat steps S30-S40 to perform the calculation for the next time step, until all excitation signals and displacement response signals are calculated;

[0086] S60, based on the improved particle filter identification result, use the identification result as the initial value of EKF to obtain the accurate identification value of the BOUC-WEN model parameters.

[0087] This invention constructs an initial sample set covering different order-of-magnitude ranges by dividing the estimation interval of each parameter to be identified into several sub-intervals according to the order of magnitude, and then randomly combining samples uniformly within each sub-interval. Based on this, the iterative update process of the particle filter algorithm is combined to estimate the unknown parameters in the Bouc-Wen model, thereby effectively solving the problem of convergence difficulties in traditional sampling methods due to large differences in parameter order of magnitude, and improving the accuracy and computational efficiency of parameter identification. Furthermore, this invention enhances particle diversity by introducing random perturbations to generate new particles and performs local optimum discrimination on resampled particles. Specifically, by amplifying or reducing the parameters and calculating the output fluctuation factor, particles trapped in local optima are discarded and resampled, thus constructing a parameter identification framework that effectively avoids local optima. Based on this, a parameter estimation model based on the particle filter algorithm is established to estimate the state values ​​of the parameters to be identified at different times, thereby enabling rapid and accurate identification of the unknown parameters of the system model.

[0088] This invention provides a method for establishing the state-space equation for identifying parameters in a BOUC-WEN model. The method specifically includes:

[0089] S101, Establish the equations of motion for the single-degree-of-freedom BOUC-WEN model, which are expressed as follows:

[0090] (1)

[0091] (2)

[0092] In the formula: m represents mass, c represents damping, k represents stiffness, u represents excitation, z represents nonlinear restoring force, and y represents displacement. Indicates speed, Indicates acceleration. The first derivative of the nonlinear restoring force z with respect to time, α, , ν represents the parameters of the nonlinear restoring force system;

[0093] S102, Process variables based on the BOUC-WEN model , , Construct the state vector of the state-space equation with the parameters to be identified, where the state vector of the state-space equation is represented as:

[0094] (3)

[0095] In the formula, This represents the state vector of the state-space equation at time s; ~ express Elements 1-10 in the model are also process variables in the BOUC-WEN model. , , The values ​​of the parameters to be identified at time s, where the parameters to be identified are m, c, k, α, and . , 、ν;

[0096] S103, Establish the state-space equation for parameter identification, where the state-space equation is expressed as follows:

[0097] (4)

[0098] The output equation is as follows:

[0099] (5)

[0100] In the formula, This represents the state vector of the state-space equation at time s+1; ~ express Elements 1-10 in the model are also process variables in the BOUC-WEN model. , , and the value of the parameter to be identified at time s+1; Indicates time interval, Indicates process noise; This represents the stimulus at time s; This represents the output of the state-space equation at time s, which is also the displacement response of the BOUC-WEN model.

[0101] This invention provides a method for establishing an improved initial value sampling method and generating an initial particle set for a particle filter. Specifically, this method includes:

[0102] S201, Set the number of particles in the particle filter. The number of particles N in the particle filter can be between 10⁴ and 10⁸.

[0103] S202, determine the upper and lower bounds of the identification interval for the parameter k to be identified based on the system excitation signal and displacement response signal, wherein the upper and lower bounds of the identification interval are expressed as:

[0104] (6)

[0105] (7)

[0106] (8)

[0107] S203, determine other parameters to be identified: m, c, α, , The upper and lower bounds of ν are defined, and the upper and lower bounds should include the exact values ​​of the parameter to be identified.

[0108] S204. Based on the upper and lower bounds of each parameter to be identified, the range of values ​​of the upper and lower bounds is divided into j sub-intervals, such that the upper bounds of adjacent sub-intervals differ by an order of magnitude, i.e., 10 times.

[0109] S205, uniformly sample each sub-interval of each parameter to be identified, and obtain N / j parameter samples in each sub-interval, for a total of N parameter samples in j sub-intervals;

[0110] S206, randomly combine the N parameter samples of all parameters to be identified, and each combination constitutes a particle, for a total of N parameter particles to be estimated;

[0111] S207, process variables of the BOUC-WEN model , , The initial value is set to 0, and the process variable and the parameter particles to be estimated form the initial particle set of the particle filter.

[0112] In this embodiment of the invention, when establishing an improved initial value sampling method and generating the initial particle set of the particle filter, the proposed improved initial value sampling method effectively overcomes the shortcomings of traditional uniform random sampling, which concentrates particle distribution on a certain order of magnitude and is difficult to cover the true order of magnitude of parameters when the parameter order of magnitude differs greatly. This ensures that the initial particle set has a reasonable distribution density across different order of magnitudes. Furthermore, generating the initial particle set of the particle filter does not rely on initial values ​​close to the true value, allowing the parameters to be identified to be searched within a wider range, significantly enhancing the algorithm's adaptability to insufficient prior information about parameters. Simultaneously, through the sub-interval uniform sampling and random combination strategy, efficient coverage of the parameter space is achieved while ensuring particle diversity, providing a higher-quality initial sample foundation for subsequent particle filter iterations. This effectively improves the convergence speed and global search capability of parameter identification, avoiding premature convergence or local optimum traps caused by improper initial sampling.

[0113] This invention provides a method for parameter identification using a particle filter, which specifically includes:

[0114] S301, taking the particles of the particle filter as state vectors in the state-space equation, and estimating the state vector for the next time step using the Runge-Kutta method based on the state vector at time s, where the state vector for the next time step is expressed as:

[0115] i=1,…,N (9)

[0116] In the formula: Let represent the i-th state vector at time s+1. Representing the state-space equations, Let represent the i-th state vector at time s. This represents the stimulus at time s. represents the time value at time s, and w represents the process noise;

[0117] S302, Calculate the weight coefficient of each state vector at time s+1 based on the displacement signal. Among them, the weighting coefficient The calculation formula is expressed as follows:

[0118] (10)

[0119] (11)

[0120] in, Let represent the relative likelihood probability of the i-th state vector. This represents the displacement signal value at time s+1. The output equation represents the state-space equation. This represents the exponentiation operator.

[0121] In this embodiment of the invention, the method of parameter identification using a particle filter, by treating particles as state vectors in the state-space equation and employing the Runge-Kutta method for recursive state estimation, effectively adapts to the implicit and strongly nonlinear dynamic characteristics of the BOUC-WEN model, achieving accurate tracking of the state evolution of complex nonlinear systems. By calculating the relative likelihood probability of each state vector using displacement signals and updating the weight coefficients, the goodness of fit of each particle to the observed data can be objectively quantified, providing a reliable basis for subsequent resampling. Simultaneously, combined with an improved resampling strategy, high-weight particles are selected as the basis through uniform sampling, and a parameter amplification perturbation mechanism is introduced to calculate the output fluctuation factor to accurately identify and eliminate locally optimal particles. New particles are then added based on their weights, and new particles are generated by adding mutation perturbations to the basic particles to expand particle diversity, thus constructing a particle update mechanism that combines selection pressure and exploration capabilities. This method effectively suppresses the particle degradation and diversity loss problems common in standard particle filtering, significantly enhances the algorithm's ability to escape local optima traps, and ensures stable and efficient parameter identification within a wide range of parameter search spaces.

[0122] The new particle set required to construct the particle filter includes:

[0123] S401, based on particle weight coefficients Uniform sampling Particles , where λ is the number of parameters to be identified;

[0124] S402, will particles The parameters to be estimated in the calculation are magnified sequentially by 5-100 times to calculate the particles. The output fluctuation factor is used to determine the particle. Whether the particle gets trapped in a local optimum depends on the particle's behavior. If there is a point in the output fluctuation factor that is less than a given threshold, then the particle is determined to belong to a point in the local optimal solution region and the particle is deleted.

[0125] (12)

[0126] In the formula, Represents particles The output volatility factor, The output equation represents the state-space equation;

[0127] Among them, the parameters to be identified are If there are 2, then 2 can be calculated. indivual Value; take the minimum threshold. =10 -1 -10 -5 When 2 indivual If any of the particles is less than a given threshold, the particle belongs to a local optimum region. Delete the particle and resample new particles according to their weights to replenish it.

[0128] S403, with Based on individual particles, each particle is perturbed to generate... A new set of particles is needed to construct the particle filter, namely:

[0129] (13)

[0130] in Yes The first parameter to be identified in the vector multiplied by the coefficient of variation ( <1); Yes The first parameter to be identified in the vector is multiplied by And so on. The fundamental particles and The new particles form a new set of N particles for the next calculation. .

[0131] This invention provides a method for obtaining accurate identification values ​​of BOUC-WEN model parameters. The method specifically includes:

[0132] S601, Based on the particle filter identification results of the obtained parameters to be identified, establish the initial state vector and initial state covariance of the EKF algorithm at time s=1;

[0133] S602, based on the state vector and covariance matrix at time s, estimate the prior state vector and prior covariance matrix for the next time step using the Runge-Kutta method;

[0134] (14)

[0135] (15)

[0136] (16)

[0137] (17)

[0138] In the formula: Let represent the prior state vector at time s+1. Representing the state-space equations, Let represent the posterior state vector at time s. This represents the stimulus at time s. Let s represent the time value at time s, and w represent the process noise. Let represent the covariance matrix at time s;

[0139] S603, Calculate the posterior state vector at time s+1. and posterior covariance matrix ;

[0140] (18)

[0141] (19)

[0142] (20)

[0143] (twenty one)

[0144] In the formula: This represents the displacement signal value at time s+1. The output equation represents the state-space equation. Indicate the output equation The noise matrix, Represents the identity matrix;

[0145] S604. Repeat steps S602-S603 to calculate the next time step until all excitation signals and displacement response signals are calculated. Obtain the posterior state vector of the last step as the final BOUC-WEN model parameter identification result, that is, the accurate identification value of the BOUC-WEN model parameters.

[0146] In this embodiment of the invention, by using the coarse identification result of the improved particle filter as the initial state vector and covariance matrix of the EKF algorithm, the inherent defects of traditional EKF, such as heavy reliance on precise initial values ​​and easy divergence or getting trapped in local optima within a wide parameter space, are effectively overcome. This achieves the complementary advantages of global exploration and local fine convergence. In the recursive estimation process, the Runge-Kutta method is used for nonlinear state prediction, ensuring the computational accuracy of the strong nonlinear dynamic characteristics of the BOUC-WEN model. At the same time, the Kalman gain mechanism is combined to perform observational correction on the prior estimate. The estimation uncertainty is quantified in real time by updating the covariance matrix, so that the parameter identification result gradually converges to the true value and achieves a high estimation accuracy. This method makes full use of the quadratic convergence characteristic of EKF in the local region. Based on the high-quality initial values ​​provided by the particle filter, it further improves the accuracy and stability of parameter identification. The final posterior state vector is the parameter identification result of the BOUC-WEN model that takes into account both global optima and local accuracy, significantly enhancing the engineering applicability of the algorithm in scenarios where the parameters are completely unknown or prior information is scarce.

[0147] Example 2

[0148] To verify the effectiveness of the BOUC-WEN model parameter identification method combining the improved sampling rule particle filter and EKF, the performance of the present invention in identifying single-degree-of-freedom Bouc-Wen model parameters was tested using publicly available examples. This was to verify whether the method can effectively identify Bouc-Wen model parameters when the parameter estimation range is wide and no initial values ​​close to the true values ​​are provided.

[0149] In testing the performance of this invention in identifying parameters of a single-degree-of-freedom Bouc-Wen model using publicly available examples, the model parameters shown in Table 1 were selected based on the published benchmark examples for numerical analysis. A multi-sinusoidal excitation with a frequency band of 5-150Hz was used as input, with a root mean square value of 50N and a sampling frequency of 750Hz. Each excitation cycle contained 8192 sampling points. To simulate a real measurement environment, a root mean square amplitude of 3.5 × 10⁻⁶ was added to the displacement response. -5 Band-limited Gaussian noise (frequency band 0-375Hz) of mm / s (standard deviation 5%). Three-cycle excitation and displacement data (a total of 24576 sampling points) were used as the known excitation for the Bouc-Wen model. Figure 2 The excitation signal time history diagram in Embodiment 2 of the present invention is shown. The displacement is solved by substituting the excitation signal and the parameters in Table 1 into formulas (1) to (2). Figure 3 The displacement time history diagram of Embodiment 2 of the present invention is shown.

[0150] Table 1. Values ​​of the parameters to be identified in the benchmark example

[0151]

[0152] To verify the effectiveness of the method (i.e., the BOUC-WEN model parameter identification method combining the improved sampling rule particle filter and EKF) in cases with a wide parameter estimation range and no precise initial values, an improved particle filter was used for preliminary parameter identification. Based on the order of magnitude of the excitation and displacement data, the estimation interval for stiffness k was set to

[10] . 3 10 7 The upper and lower bounds of the remaining parameters to be estimated are shown in Table 2.

[0153] Table 2. Upper and lower bounds of the parameters to be identified.

[0154]

[0155] The particle number N is set to 150,000, and the iteration steps are 2,000. Based on the recognition results of the improved particle filter, the EKF is used for fine parameter estimation. Then, the PF result is used as the initial state value of the EKF. Relevant calculation parameters are set, and the final value of the parameter to be identified is obtained. The identified parameter is close to the accurate value. The recognition results are shown in Table 3. Figures 4-5 As shown, where, Figure 4 The diagram illustrates the calculation process of the parameters to be identified in the improved particle filter in Embodiment 2 of the present invention, that is, the evolution trajectory of each parameter to be identified with time step / iteration step (Samples) during the identification process of the improved particle filter parameters. Figure 4 Each subgraph corresponds to a parameter (mass m, damping c, stiffness k, nonlinear parameter α, ...). , And v), the horizontal axis is the number of iterations, and the vertical axis is the parameter estimate. Figure 4 This reflects the process of parameters gradually converging from a wide-range dispersed state to the neighborhood of the true value. The figure visually demonstrates the effectiveness of the proposed improved initial sampling strategy and improved resampling strategy in avoiding local optima and achieving wide-range global search. Figure 5 The diagram illustrates the calculation process of the EKF's target parameters in Embodiment 2 of the present invention. Figure 5 Each subgraph corresponds to a parameter (mass m, damping c, stiffness k, nonlinear parameter α, ...). , And v), the horizontal axis represents the number of iterations, and the vertical axis represents the parameter estimates. Figure 5 It includes an EKF initialization diagram, indicating that... Figure 4 The process of setting the final convergence value as the initial state vector and initial covariance matrix is ​​also demonstrated; the iterative mechanism of nonlinear state prediction using the Runge-Kutta method and posterior correction using Kalman gain fusion of observation information is also shown; finally, the fine convergence trajectory curves of each parameter to be identified in the EKF iteration process are presented, and... Figure 4The comparison shows that parameter fluctuations are significantly reduced, convergence speed is accelerated, and the system eventually stabilizes at the exact true value. From Figure 5 As can be seen, with iteration, the parameters gradually converge to near their true values, demonstrating strong robustness and stability in the convergence process. This indicates that the proposed method can effectively avoid local optima and achieve global convergence over a wide parameter range. Example verification results show that the present invention can accurately identify the parameters of the Bouc-Wen model under conditions of a wide parameter range and no precise initial values.

[0156] Table 3 Final recognition results of the parameters to be identified

[0157]

[0158] In summary, this invention provides an improved sampling rule-based particle filter and EKF combined method for BOUC-WEN model parameter identification. This invention divides the estimation interval of each parameter to be identified into several sub-intervals according to order of magnitude, and then randomly combines samples uniformly within each sub-interval to construct an initial sample set covering different order of magnitude ranges. Based on this, the iterative update process of the particle filter algorithm is combined to estimate the unknown parameters in the Bouc-Wen model, thus effectively solving the problem of convergence difficulties in traditional sampling methods due to large differences in parameter order of magnitude, improving the accuracy and computational efficiency of parameter identification. Furthermore, this invention enhances particle diversity by introducing random perturbations to generate new particles and performs local optimum discrimination on resampled particles. Specifically, by amplifying or reducing parameters and calculating the output fluctuation factor, particles trapped in local optima are discarded and resampled, thus constructing a parameter identification framework that effectively avoids local optima. Based on this, a parameter estimation model based on the particle filter algorithm is established to estimate the state values ​​of the parameters to be identified at different times, thereby enabling rapid and accurate identification of the unknown parameters of the system model.

[0159] It should be noted that, for the sake of simplicity, the foregoing embodiments are all described as a series of actions. However, those skilled in the art should understand that the present invention is not limited to the described order of actions, as some steps may be performed in other orders or simultaneously according to the present invention. Furthermore, those skilled in the art should also understand that the embodiments described in the specification are preferred embodiments, and the actions and modules involved are not necessarily essential to the present invention.

[0160] It should be understood that the disclosed apparatus can be implemented in other ways, given the several embodiments provided in this application. For example, the apparatus embodiments described above are merely illustrative; the division of units described above is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or communication connections shown or discussed may be through some interfaces; the indirect coupling or communication connections between devices or units may be telecommunications or other forms.

[0161] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit the scope of protection of the invention. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on these embodiments, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art can still combine, add, delete, or otherwise adjust the features of the various embodiments of the present invention according to the circumstances without conflict or creative effort, thereby obtaining different technical solutions that do not fundamentally depart from the concept of the present invention. These technical solutions also fall within the scope of protection of the present invention.

Claims

1. An improved method for parameter identification of the BOUC-WEN model combining a sampling rule particle filter and an EKF, characterized in that, The method includes: S10, Establish the state-space equation for the identification of the parameters to be identified in the BOUC-WEN model; S20, based on the system excitation signal and displacement response signal, set the number of particles and the upper and lower bounds of the parameters to be identified for the particle filter, establish an improved initial value sampling method, and generate the initial particle set for the particle filter. S30 uses a particle filter to identify parameters and calculates the state estimate, observation, and weight coefficient of each particle for the next time step. S40, based on the improved resampling strategy, resamples the initial particle set, determines whether it is trapped in a local optimum region, and constructs the new particle set required by the particle filter; S50, based on the obtained new particle set, repeat steps S30-S40 to perform the calculation for the next time step, until all excitation signals and displacement response signals are calculated; S60, based on the improved particle filter identification result, use the identification result as the initial value of EKF to obtain the accurate identification value of the BOUC-WEN model parameters.

2. The method for parameter identification of the BOUC-WEN model combined with the improved sampling rule particle filter and EKF as described in claim 1, characterized in that: The state-space equation for identifying the parameters to be identified in the BOUC-WEN model includes: S101, Establish the equations of motion for the single-degree-of-freedom BOUC-WEN model, which are expressed as follows: （1） （2） In the formula: m represents mass, c represents damping, k represents stiffness, u represents excitation, z represents nonlinear restoring force, and y represents displacement. Indicates speed, Indicates acceleration. The first derivative of the nonlinear restoring force z with respect to time, α, , ν represents the parameters of the nonlinear restoring force system; S102, Process variables based on the BOUC-WEN model , , Construct the state vector of the state-space equation with the parameters to be identified, where the state vector of the state-space equation is represented as: （3） In the formula, This represents the state vector of the state-space equation at time s; ~ express Elements 1-10 in the model are also process variables in the BOUC-WEN model. , , The values ​​of the parameters to be identified at time s, where the parameters to be identified are m, c, k, α, and . , 、ν; S103, Establish the state-space equation for parameter identification.

3. The method for parameter identification of the BOUC-WEN model combined with the improved sampling rule particle filter and EKF as described in claim 1, characterized in that: The establishment of the improved initial value sampling method and the generation of the initial particle set for the particle filter include: S201, Set the number of particles in the particle filter. The number of particles N in the particle filter can be between 10⁴ and 10⁸. S202, determine the upper and lower bounds of the identification interval of the parameter k to be identified based on the system excitation signal and displacement response signal; S203, determine other parameters to be identified: m, c, α, , The upper and lower bounds of ν are within their respective ranges; S204, based on the upper and lower bounds of each parameter to be identified, divide the range of values ​​of the upper and lower bounds into j sub-intervals, such that the upper bounds of adjacent sub-intervals differ by an order of magnitude. S205, uniformly sample each sub-interval of each parameter to be identified, and obtain N / j parameter samples in each sub-interval, for a total of N parameter samples in j sub-intervals; S206, randomly combine the N parameter samples of all parameters to be identified, and each combination constitutes a particle, for a total of N parameter particles to be estimated; S207, process variables of the BOUC-WEN model , , The initial value is set to 0, and the process variable and the parameter particles to be estimated form the initial particle set of the particle filter.

4. The BOUC-WEN model parameter identification method combining the improved sampling rule particle filter and EKF as described in claim 3, characterized in that: The parameter identification using a particle filter includes: S301, the particles of the particle filter are used as state vectors in the state space equation. Based on the state vector at time s, the state vector of the next time step is estimated using the Runge-Kutta method. S302, Calculate the weight coefficient of each state vector at time s+1 based on the displacement signal. .

5. The BOUC-WEN model parameter identification method combining the improved sampling rule particle filter and EKF as described in claim 4, characterized in that: The new particle set required to construct the particle filter includes: S401, based on particle weight coefficients Uniform sampling Particles , where λ is the number of parameters to be identified; S402, will particles The parameters to be estimated in the calculation are magnified sequentially by 5-100 times to calculate the particles. The output fluctuation factor is used to determine the particle. Whether the particle gets trapped in a local optimum depends on whether it is in a local optimum. If there is a point in the output fluctuation factor that is less than a given threshold, then the particle is determined to belong to a point in the local optimal solution region and the particle is deleted. S403, with Based on individual particles, each particle is perturbed to generate... A new particle, the new set of particles needed to construct the particle filter.

6. The method for parameter identification of the BOUC-WEN model combined with the improved sampling rule particle filter and EKF as described in claim 5, characterized in that: Obtain accurate identification values ​​for the BOUC-WEN model parameters, including: S601, Based on the particle filter identification results of the obtained parameters to be identified, establish the initial state vector and initial state covariance of the EKF algorithm at time s=1; S602, based on the state vector and covariance matrix at time s, use the Runge-Kutta method to estimate the prior state vector and prior covariance matrix for the next time step; S603, Calculate the posterior state vector at time s+1. and posterior covariance matrix ; S604. Repeat steps S602-S603 to calculate the next time step until all excitation signals and displacement response signals are calculated. Obtain the posterior state vector of the last step as the final BOUC-WEN model parameter identification result, that is, the accurate identification value of the BOUC-WEN model parameters.

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