Motor system simulation method under data exception condition
By using a nonlinear state-space model and a variational Bayesian inference framework, the problems of data anomalies and non-Gaussian noise in motor systems are solved, enabling high-precision system identification under complex operating conditions, which is applicable to motor control and health monitoring.
Patent Information
- Application Number
- CN202511163054.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-08-19
- Publication Date
- 2025-11-28
AI Technical Summary
Existing technologies suffer from reduced robustness of state observers when faced with abnormal data interference and non-Gaussian noise in motor systems, leading to deviations in parameter estimation results and making it difficult to accurately reconstruct the dynamic process of the system under complex operating conditions.
A nonlinear state-space model is adopted, and the non-Gaussian noise is modeled using a variational Bayesian inference framework and a skewed t-distribution. Hierarchical modeling is achieved through auxiliary variables to identify the probability distribution of unknown parameters and improve the Bayesian processing method to handle data anomalies.
It achieves high-precision system identification under conditions of outliers and missing measurements, which is significantly better than the traditional method under the Gaussian assumption. It is suitable for motor control and health monitoring in highly dynamic and multi-interference industrial scenarios.
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Figure CN121031337A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The application relates to a motor system simulation method under data abnormality, and belongs to the technical field of motor system modeling. BACKGROUND
[0002] As a core tool for modern motor system dynamic analysis and control design, the state space model has been widely used in simulation, state observation and high-performance control of various electromechanical systems such as permanent magnet synchronous motor (PMSM) and induction motor (IM). By converting the high-order differential equation of the system into a first-order matrix differential equation form, the internal dynamic characteristics of the system are described by state variables (such as current, speed, rotor flux, etc.), which significantly improves the mathematical expression clarity of the multivariable coupled system and the flexibility of the control algorithm design. The classical method such as Kalman filter (KF) and its extended form (EKF, UKF) is often based on the state space model to realize the real-time estimation of key state quantities such as motor speed and torque, and relies on least squares, maximum likelihood and other parameter identification algorithms to calibrate the physical parameters such as resistance, inductance and inertia in the model online or offline.
[0003] However, the existing technology has significant limitations in dealing with two typical challenges in actual engineering scenarios:
[0004] Data abnormality interference: abnormal data (abnormal values and missing measurement values) caused by sensor failure, communication packet loss, electromagnetic interference or transient overload during motor operation will destroy the convergence of the state observer and make the parameter estimation process deviate from the true system dynamics;
[0005] Non-Gaussian noise pollution: traditional methods usually assume that system noise follows Gaussian distribution, but the disturbance (such as power electronic switching harmonic, mechanical vibration impact, load mutation) of actual motor system often exhibits strong non-Gaussian characteristics such as impulse noise and heavy-tailed distribution, which leads to a sharp decline in the robustness of estimators based on Gaussian assumption (such as standard Kalman filter), and the parameter estimation results of the model deviate significantly.
[0006] The above problems directly restrict the accurate restoration of the real dynamic process of the system by the state space model under complex working conditions, therefore, developing a state space modeling and parameter estimation method that is robust to data abnormality and non-Gaussian noise has become a key research direction to improve the operation reliability of motor systems in real industrial environments. SUMMARY
[0007] In view of the problem that the parameter estimation of the motor system model under nonlinear state space model is not accurate under data abnormality and non-Gaussian disturbance noise, the application provides a motor system simulation method under data abnormality.
[0008] The motor system simulation method under data abnormality provided by the application comprises:
[0009] S1, establishing a nonlinear state space model of a motor system, wherein a control quantity output by a motor system controller and a state quantity of the motor system constitute a state variable, and a measurement value of a sensor on a load is an output variable;
[0010] S2, in an inference framework, each component of measurement noise in the nonlinear state space model is subject to an independent single-variable skewed distribution, modeling of non-Gaussian noise is achieved, layered modeling of noise is achieved by using auxiliary variables, and a probability distribution of unknown parameters in the nonlinear state space model is determined;
[0011] S3, identifying unknown parameters in the nonlinear state space model based on a variational Bayesian inference framework and the probability distribution of the unknown parameters, and obtaining a posterior distribution of the unknown parameters;
[0012] S4, simulating the motor system by using the nonlinear state space model in which the unknown parameters are identified.
[0013] The application has the beneficial effects that, based on a variational Bayesian inference framework, the application introduces a skewed t distribution to model non-Gaussian noise, and layered modeling is achieved by using auxiliary variables, and the equation is improved to solve the problem of data missing. The application formulates a Bayesian process for identifying LP-NSSMs, solves the problem of jointly estimating parameters with uncertainty, hidden states and other potential variables under a VB framework, and comprehensively processes data anomaly problems such as outliers and missing measurement values. Simulation experiments show that, under the condition of a high proportion of outliers and missing measurement values, the method can still achieve high-precision system identification, which is significantly better than traditional system identification methods under the assumption of Gaussian distribution. The application is suitable for direct current motor control and health monitoring systems in high-dynamic and multi-interference industrial scenes. BRIEF DESCRIPTION OF DRAWINGS
[0014] Figure 1 is a direct current motor motion system;
[0015] Figure 2 is experimental data;
[0016] Figure 3 is an outlier identification situation;
[0017] Figure 4 is a comparison between the method of the application and the real output;
[0018] Figure 5 is the parameter change process in each iteration;
[0019] Figure 6 is the RMSE and R2 value in each iteration. DETAILED DESCRIPTION
[0020] The technical solutions in the embodiments of the present application will be described clearly and completely below in combination with the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the protection scope of the present application.
[0021] It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict.
[0022] The present application will be further described below in combination with the drawings and specific embodiments, but not as a limitation of the present application.
[0023] The motor system simulation method in the data abnormality case of the present embodiment includes:
[0024] Step 1, establishing a nonlinear state space model of the motor system, wherein the state variables are composed of the control variables output by the motor system controller and the state variables of the motor system, the measured values of the load by the sensor are the output variables, and the nonlinear state space model is:
[0025]
[0026] wherein, is a time index, represents a state variable, each time state variable includes a hidden state variable of the motor system state variable and a control variable output by the motor system controller, the motor system state variable includes a speed vector and a position vector, and the two are vertically spliced into a hidden state variable, represents an output variable, represents a deterministic nonlinear function, represents a system matrix, represents an observation matrix, represents a state noise, represents a measurement noise, , , , , .
[0027] Step 2, in the reasoning framework, each component of the measurement noise in the nonlinear state space model is subject to an independent single-variable skewed distribution, realizing modeling of non-Gaussian noise, and realizing hierarchical modeling of noise by using auxiliary variables to determine the probability distribution of unknown parameters in the nonlinear state space model;
[0028] This step uses a skewed distribution instead of the traditional Gaussian distribution to better capture asymmetric noise in real-world motor systems, such as asymmetric interference caused by power electronic switches. Allowing each noise component to independently follow a univariate skewed distribution maintains model flexibility while avoiding the computational complexity issues associated with high-dimensional skewed distributions. Skewness is achieved using auxiliary variables. Layered modeling of the distribution decouples the various characteristics of the distribution.
[0029] Step 3: Identify the unknown parameters in the nonlinear state-space model based on the variational Bayesian inference framework and the probability distribution of the unknown parameters, and obtain the posterior distribution of the unknown parameters. Step 3 uses variational Bayesian to efficiently jointly estimate all unknowns, output the posterior distribution, quantify the estimation uncertainty, and robustly handle non-Gaussian interference noise.
[0030] Step 4: Simulate the motor system using a nonlinear state-space model with identified unknown parameters.
[0031] In this embodiment, within a probabilistic framework, a statistical characterization of the state variables and output variables of a nonlinear state-space model is established, and the probability distribution of the unknown parameters is determined. Step 2 specifically includes:
[0032] Step 21: Assume the noise is being measured. Independent of state noise, and Each component follows an independent univariate skewness. distributed:
[0033]
[0034] in, Represents the first parameter vector Quantity, and The first parameter matrix represents the first parameter matrix. Element. Univariate skewness distributed From position parameters diffusion parameters Shape parameters and degrees of freedom Parameterization. Introducing auxiliary variables. and Then the above independent univariate skewness The noise model can be represented hierarchically as follows:
[0035]
[0036]
[0037]
[0038] where is a Gaussian distribution with mean and covariance ; is a semi-Gaussian distribution (0, +∞) with mean and covariance ; is a Gamma distribution with parameters .
[0039] Step 22, assuming that the state noise is Gaussian white noise, which obeys a Gaussian distribution with mean 0 and covariance :
[0040]
[0041] Step 23, using the state vector to represent the state variable at time , i.e., the state vector , then the joint probability density function of is:
[0042]
[0043] where is the probability density function of the initial state , which is a Gaussian distribution with mean and covariance ;
[0044] Step 24, using the output vector to represent the output variable at time , i.e., , and letting , then the joint probability density function of is:
[0045]
[0046] Step 25, the probability distributions of the system matrix , the observation matrix , are respectively:
[0047]
[0048]
[0049]
[0050]
[0051]
[0052]
[0053]
[0054]
[0055]
[0056]
[0057] Among them, the system matrix Each element Follow the mean covariance is Gaussian distribution; Indicates a Gaussian distribution;
[0058] Precision parameters Each element in Obtain the parameter as gamma distribution, Indicates the gamma distribution;
[0059] Observation matrix Each element Follow the mean covariance is Gaussian distribution;
[0060] Precision parameters Each element Obtain the parameter as The gamma distribution;
[0061] Precision parameters Each row of elements Obtain the parameter as The gamma distribution;
[0062] diffusion parameters Each diagonal element Obtain the parameter as The inverse gamma distribution, Indicates the inverse gamma distribution;
[0063] Shape parameters Each diagonal element in It follows a pattern with a mean of 0 and a covariance of . Gaussian distribution;
[0064] Auxiliary variables Each row of elements Obtain the parameter as The half-Gaussian distribution;
[0065] auxiliary variables each diagonal element in subject to a gamma distribution with parameters ;
[0066] degrees of freedom each row element in subject to a gamma distribution with parameters .
[0067] denotes a semi-Gaussian distribution; denotes the dimension of the state variable; denotes the dimension of the observation matrix; denotes the output dimension of the deterministic nonlinear function; , , is a hyperparameter; denotes the covariance of the observation matrix elements; denotes the variance of the shape parameter prior distribution.
[0068] Step 3 of the embodiment is based on a variational Bayesian inference framework to identify unknown parameters in the nonlinear state-space model according to the existing motor system controller output control quantity and motor system state quantity, and obtain the approximate posterior distribution of the unknown parameters.
[0069] First, the mathematical description of the model identification problem is established, and the specific process is as follows:
[0070] The mathematical description of the model identification problem of the present application can be expressed as: given the measurement output , auxiliary variables and are introduced, and the unknown parameters in the system matrix and the observation matrix , the state vector and the parameter are jointly estimated based on the Bayesian framework.
[0071] Fourth step: obtain the approximate posterior distribution of the unknown parameters using the mean field theory, and the specific process is as follows:
[0072] All unknown parameters can be marked as , and . Based on the mean field theory, the joint probability density function of all unknown parameters can be approximated as:
[0073]
[0074] where is the approximate posterior distribution of ; is the system matrix The approximate posterior distribution of ; the other terms in the above formula are the approximate posterior distributions of the corresponding parameters.
[0075] The KL divergence is used to measure the distance between the approximate posterior distribution and the true posterior distribution. By minimizing this distance, the formula for calculating the log-posterior distribution with any unknown parameters can be obtained. The first in The unknown parameters are ,but The log-posterior distribution can be calculated as follows:
[0076] Formula 1
[0077] in, This indicates the function within the angle brackets is evaluated using a notation. Dividing variables The expected value of all other variables except for the constant term;
[0078] The representation of `const` differs when evaluating various variables; it is used differently depending on the variable being evaluated. Irrelevant constant terms. These terms may take different forms when different variables are updated, but they have no effect on the current variable in the optimization objective (variational lower bound), so they can be uniformly regarded as constant terms and ignored.
[0079] Output vector and The joint probability density function is:
[0080] Based on Formula 1, combined with , The joint probability density functions are obtained respectively. , , , , , , , , , , posterior distribution , , , , , , , , , , And obtain the covariance matrix and mean of the corresponding posterior distribution;
[0081] If the convergence condition is satisfied for the two adjacent iterations, output the current 、 、 、 、 、 、 、 、 、 、 the covariance matrix and the mean vector of the current 、 、 、 、 、 、 、 、 、 、 the mean vector is marked as , and the next iteration is performed using Formula One.
[0082] The stopping condition of the embodiment can be set to reach a set upper limit of the number of iterations, or the relative change of the current parameter estimation with respect to the parameter estimation obtained in the previous iteration is less than an arbitrarily small constant.
[0083] The key of the variational method is to assume that the variational distribution can be decomposed into several approximate posterior distributions, which greatly simplifies the optimization problem. And by iteratively optimizing each approximate posterior distribution, the KL divergence is minimized. The specific iteration steps usually involve:
[0084] When updating , other parameters are fixed to obtain the probability distribution of other parameters, and Formula One is used for calculation. When calculating, the updated parameters are used to adopt the probability distribution of the updated parameters, and the parameters that have not been updated are used to adopt the results of the last iteration.
[0085] The embodiment is a joint estimation, and each parameter is estimated simultaneously and iteratively. The variational Bayesian simultaneously solves the problems of state estimation and parameter identification under the influence of unknown time delay, state estimation and time delay estimation under the influence of non-Gaussian noise.
[0086] Formula One is the calculation formula of the logarithmic posterior distribution of any unknown parameter. It can be derived that the posterior distribution of the system matrix is:
[0087]
[0088] wherein,
[0089] The covariance matrix of the system matrix is:
[0090]
[0091] System matrix The mean vector of
[0092]
[0093] denotes the mathematical expectation with respect to the function inside the angle brackets with respect to the variables contained therein, denotes the element in the row of ; and is the element in the row of the system matrix ; and denotes the element in the row of the precision parameter ; and denotes the prior mean vector of the ith row vector of the system matrix ; and
[0094] The posterior distribution of the observation matrix is:
[0095]
[0096] The covariance matrix of the observation matrix is:
[0097]
[0098] The mean vector of the observation matrix is:
[0099]
[0100] wherein is the element in the row of , and is the element in the row of the precision parameter ; and is the element in the row of the observation matrix ; and denotes the prior mean vector of the ith row vector of the observation matrix .
[0101] The posterior distribution of the parameter is:
[0102]
[0103] where:
[0104]
[0105]
[0106] denotes the prior mean of the element of the system matrix A, is the shape parameter of the gamma distribution, is the rate parameter of the gamma distribution; The posterior distribution of
[0107] is:
[0108]
[0109] where:
[0110]
[0111]
[0112] denotes the prior mean of the element of the observation matrix B, is the shape parameter of the gamma distribution, is the rate parameter of the gamma distribution; The posterior distribution of
[0113] is:
[0114] . where:
[0115]
[0116]
[0117]
[0118] is the shape parameter of the gamma distribution, is the rate parameter of the gamma distribution, denotes the element of the row of is the element of the row of the system matrix ;
[0119] the posterior distribution of
[0120]
[0121] where
[0122]
[0123]
[0124] is the inverse gamma distribution with shape parameter is the inverse gamma distribution with rate parameter is the element in the th row of is the element in the th row of
[0125] the posterior distribution of
[0126]
[0127] where
[0128] the covariance matrix of
[0129]
[0130] the mean vector of
[0131]
[0132] where denotes the element in the th row of denotes the element in the th row of
[0133] the posterior distribution of
[0134]
[0135] where
[0136] the covariance matrix of
[0137]
[0138] the mean vector of is
[0139]
[0140] the posterior distribution of is
[0141]
[0142] where
[0143] the covariance matrix of is
[0144]
[0145] the mean vector of is
[0146]
[0147] the posterior distribution of is
[0148]
[0149] where
[0150] the covariance matrix of is
[0151]
[0152] the mean vector of is
[0153] .
[0154] state vector the log-posterior distribution of is
[0155]
[0156] where, is obtained according to Formula I the corresponding constant term;
[0157] intermediate variable , intermediate variable ;
[0158] denotes the hidden variable, denotes the posterior covariance matrix of the observation matrix B, denotes the covariance matrix of the system matrix A;
[0159] construct an augmented state space model with deterministic parameters having the same form of the log-posterior distribution
[0160]
[0161]
[0162] wherein: , , , is an augmented form of the system matrix A, state noise , observation matrix , measurement noise ;
[0163]
[0164]
[0165]
[0166] wherein, , is an identity matrix, is a zero vector, is a zero matrix, denotes the concatenation of the input parameters in the vertical direction, and denote the Cholesky decomposition of and respectively, is the Cholesky decomposition of ;
[0167] For the augmented state space model, the state vector is estimated by using particle filtering and particle smoothing, and the covariance matrix is taken as the uncertainty measure of the state estimation, to obtain the state vector .
[0168] Embodiment:
[0169] This embodiment adopts a direct current motor motion system to verify the effectiveness of the present application. The experimental device diagram of the system is shown in Figure 1 . The main components include: (1) a direct current motor equipped with an incremental encoder, which realizes position control by using a PD controller; (2) a star type high-precision low-friction ball screw transmission positioning unit; (3) a load. The dynamic characteristics of the direct current motor motion system can be described by the following nonlinear system:
[0170]
[0171]
[0172] wherein and represent Gaussian noise with variance and , respectively. The input signal is generated from Gaussian white noise with data length , the true model parameters are set as and . For this example, the system matrix and nonlinear function of the nonlinear state space model can be represented as , , and . In the preliminary test, the simulated data of the system contains 5% randomly missing outputs and 5% outliers uniformly distributed in the interval [-4, -3] and [3, 4]. Figure 2 The generated experimental observation data is shown, where the blue broken line is the system output disturbed by noise; the red circles mark the injected outlier positions, and the red plus signs represent the abnormal moments identified by the MATLAB built-in outlier detection function (isoutlier). As can be seen from the figure, the MATLAB algorithm can accurately locate the abnormal points in most cases, but there are also some missed detection and misjudgment. Figure 3 Further, the performance of the proposed variational Bayesian nonlinear state space model (VBNSSM) in anomaly detection is shown. The blue curve in the figure is the anomaly index of the model output. It can be observed that all outliers correspond to significant peaks, indicating that the model effectively identifies and describes the abnormal interference in the observation in the Bayesian inference process. Compared with traditional methods, the proposed method can adaptively adjust the observation accuracy and significantly suppress the disturbance of outliers on system modeling. Figure 4 The prediction effect comparison of the model in cross-validation is shown. The black curve is the true output, the red curve is the model prediction result, and the blue dashed line represents the observation value containing abnormal and missing disturbances. It can be seen that even if there are a large number of missing and outlier disturbances in the observation data, the proposed method can still accurately restore the true dynamic process of the system, which reflects its good robustness to non-Gaussian noise and data anomalies. Figure 5 shows the parameter convergence process, and the initial values of parameters a, b, and c are all 0.5, which converge to the true value around the twentieth iteration, indicating that the proposed algorithm can effectively estimate the parameters of the nonlinear state space model. Figure 6The state estimation error is shown, with a high initial root mean square error (RMSE) of about 1.5, indicating a large initial state estimation error. It rapidly decreases within 10 iterations and stabilizes at about 0.25 after 20 iterations, indicating that the algorithm can quickly optimize state estimation. The initial R2 is about 0.4, indicating that the initial estimate has a low correlation with the true state. It rapidly rises to 1.0 within 10 iterations and remains stable in subsequent iterations, indicating that the estimated state is highly consistent with the true state. In summary, the proposed algorithm performs well in handling nonlinear state space models, can efficiently estimate parameters and states, and is suitable for data with noise and outliers.
[0173] While the application has been described herein with reference to particular embodiments thereof, it is to be understood that the application is not limited to the examples discussed, which can vary. It is therefore understood that numerous modifications can be made to the illustrative embodiments and that other arrangements can be devised without departing from the spirit and scope of the present application as defined by the appended claims. It is intended that the scope of the application disclosed by the words of the claims issued from this application be determined by the appropriate consideration of flaws of equivalents under 35 U.S.C. § 112(6) and 35 U.S.C. § 101. It is intended that the phrase "consisting of have the inclusion disjunctive "or" interpreted using a give and take analysis in light of the overall disclosure. It is intended that the phrase "consisting of have the inclusion disjunctive "or" interpreted using a give and take analysis in light of the overall disclosure. It is intended that the phrase "consisting of have the inclusion disjunctive "or" interpreted using a give and take analysis in light of the overall disclosure. It is intended that the phrase "consisting of have the inclusion disjunctive "or" interpreted using a give and take analysis in light of the overall disclosure. It is intended that the phrase "consisting of have the inclusion disjunctive "or" interpreted using a give and take analysis in light of the overall disclosure. It is intended that the phrase "consisting of have the inclusion disjunctive "or" interpreted using a give and take analysis in light of the overall disclosure. It is intended that the phrase "consisting of have the inclusion disjunctive "or" interpreted using a give and take analysis in light of the overall disclosure.
Claims
1. A method of motor system simulation in the presence of data anomalies, characterized by, The simulation method comprises: S1, establishing a nonlinear state space model of the motor system, wherein the control quantity output by the motor system controller and the state quantity of the motor system constitute state variables, and the measurement value of the sensor to the load is an output variable; S2, each component of the measurement noise in the nonlinear state space model is subject to an independent single variable skew under the inference framework The distribution is achieved to model the non-Gaussian noise, and the auxiliary variable is used to achieve the hierarchical modeling of the noise, and the probability distribution of the unknown parameters in the nonlinear state space model is determined. S3, identifying unknown parameters in the nonlinear state space model based on a variational Bayesian inference framework and a probability distribution of the unknown parameters, to obtain a posterior distribution of the unknown parameters; S4, simulating the motor system by using the nonlinear state space model in which the unknown parameters are identified.
2. The data abnormality-conditional motor system simulation method according to claim 1, characterized by, The nonlinear state space model is: wherein, is a time index, denotes state variables, each time instant state variable comprising hidden state variables of motor system state quantities and control quantities of motor system controller outputs, denotes output variables, denotes a deterministic nonlinear function, denotes a system matrix, denotes an observation matrix, denotes state noise, denotes measurement noise.
3. The data abnormality-conditional motor system simulation method according to claim 2, characterized by, Unknown parameters include system matrix , observation matrix , and state vector , represent state variables at time The joint probability density function is: wherein, is a Gaussian distribution with probability density function of initial state , mean , and covariance Output vector , Indicates the output variable at the time, The joint probability density function of System matrix , observation matrix , The probability distributions of the system matrix where each element of the system matrix obeys a Gaussian distribution with mean and covariance ; denotes a Gaussian distribution. precision parameter each element in the precision parameter is a gamma distribution with denotes a gamma distribution; Observation matrix each element of obeys a Gaussian distribution with mean and covariance precision parameter each element of compliance parameter is a gamma distribution; Precision parameters Each row of elements Obtain the parameter as The gamma distribution; diffusion parameters each diagonal element of the inverse gamma distribution with parameters denotes the inverse gamma distribution; shape parameters each of the diagonal elements in subject to a Gaussian distribution with mean 0 and covariance auxiliary variables each row element in subject to parameters being half-gaussian distribution; auxiliary variables each diagonal element in subject to a parameter gamma distribution; Degrees of freedom each row element in Gamma distribution with parameters subject to represents a half-Gaussian distribution; represents the dimension of the state variable; represents the dimension of the observation matrix; represents the output dimension of the deterministic nonlinear function; , , is a hyperparameter; represents the covariance of the observation matrix elements; represents the variance of the shape parameter prior distribution.
4. The data abnormality-conditional motor system simulation method according to claim 2, characterized by S3 Comprises: S31, mark the mean vector of the parameters obtained in the last iteration as , the th unknown parameter in the middle as , the log posterior distribution of is: Formula One in, This indicates the function within the angle brackets is evaluated using a notation. Dividing variables The expected value of all other variables except for the constant term; Output vector And The joint probability density function of and is: S32, based on formula one, combined with 、 the joint probability density function respectively 、 、 、 、 、 、 、 、 、 、 the posterior distribution 、 、 、 、 、 、 、 、 、 、 , and get the covariance matrix and mean of the corresponding posterior distribution; S33, judging whether the convergence condition is met, if not, turning to S31 for next iteration, if yes, outputting the current 、 、 、 、 、 、 、 、 、 、 covariance matrix and mean vector.
5. The data abnormality-conditional motor system simulation method according to claim 2, characterized by, System matrix The posterior distribution of the parameters is Gaussian: Wherein, System matrix The covariance matrix of the system is: System matrix The mean vector of the system matrix is: denotes the mathematical expectation with respect to the variables contained in the function within the pointed brackets, the element of the i-th row of the matrix ; the element of the i-th row of the system matrix ; denotes the precision parameter ; the element of the i-th row of the precision matrix , denotes the prior mean vector of the i-th row vector of the system matrix ; Observation matrix The posterior distribution of the parameters is: Observation matrix The covariance matrix of the observation matrix is: Observation matrix The mean vector of the observation matrix wherein is the element of the row of the matrix is a precision parameter is the element of the row of the observation matrix is the element of the row of the observation matrix denotes the row vector of the observation matrix prior mean vector.
6. The data abnormality-conditional motor system simulation method according to claim 2, characterized by, Parameters The posterior distribution of the parameters is: Wherein: In system matrix A The prior mean, for Shape parameters of the gamma distribution for Velocity parameters of the gamma distribution; The posterior distribution is: Wherein: In the observation matrix B The prior mean; for Shape parameters of the gamma distribution for Velocity parameters of the gamma distribution; The posterior distribution is: . Wherein: is a shape parameter of the gamma distribution, is a rate parameter of the gamma distribution, denotes the element of the first row of the matrix is an element of the first row of the system matrix ; The posterior distribution is: Wherein: is a shape parameter of the inverse gamma distribution, is a shape parameter of the inverse gamma distribution, is a rate parameter of the inverse gamma distribution; is a rate parameter of the inverse gamma distribution; is the first row element of the matrix is the first row element of the observation matrix is the first row element of the observation matrix The posterior distribution is: Wherein: The covariance matrix of the is: The mean vector of the is: wherein represents the first row element of represents the first row element of The posterior distribution is: Wherein: The covariance matrix of the is: The mean vector of the is: The posterior distribution is: Wherein: The covariance matrix is: The mean vector of the is: The posterior distribution is: An augmented state space model of deterministic parameters with the same form of log posterior distribution is constructed: The covariance matrix of the is: The mean vector is: 。 7. The data abnormality-conditional motor system simulation method according to claim 2, characterized by, State vector The log posterior distribution of the state vector x is: wherein is the value obtained according to equation one corresponding constant term; intermediate variable , intermediate variable ; represents the hidden variable, represents the posterior covariance matrix of the observation matrix B, represents the covariance matrix of the system matrix A; The computer program is executed by the processor to realize the steps of the motor system simulation method under the data abnormal condition according to any one of claims 1 to 7. wherein: , , , is an augmented form of the system matrix A, the state noise , the observation matrix , the measurement noise . wherein , is the identity matrix, is the zero vector, is the zero matrix, denotes the concatenation of the input parameters in the vertical direction, and denote the Cholesky decomposition of and respectively, is the Cholesky decomposition of ; For the augmented state space model, the state vector is estimated using particle filtering and particle smoothing, and the covariance matrix is taken as a measure of uncertainty of the state estimate, resulting in the state vector .
8. A storage device readable by a computer, the storage device storing a computer program, characterized in that, The processor executes the computer program to realize the steps of the motor system simulation method under the data abnormal condition according to any one of claims 1 to 7.
9. An apparatus for simulating a motor system under data abnormality, comprising a storage device, a processor, and a computer program stored in the storage device and executable on the processor, wherein, The computer program is executed by the processor to realize the steps of the motor system simulation method under the data abnormal condition according to any one of claims 1 to 7.
10. A computer program product comprising a computer program, characterized in that,