Control system residual life prediction method and system based on double time scales, and electronic equipment

Abstract

The invention provides a control system residual life prediction method and system based on double time scales and electronic equipment. The residual life prediction method comprises the following steps: constructing a system state space model influenced by a degradation state and a degradation model influenced by the system state; updating a system state in the system state space model, a degradation state in the degradation model and unknown parameters in the degradation model in real time according to system state observation data; jointly estimating a system state in the system state space model and a degradation state in the degradation model; unknown parameters in the degradation model are estimated; according to the estimation result of the system state, the estimation result of the degradation state and the estimation result of unknown parameters in the degradation model, the residual life of the control system is predicted through a Monte Carlo simulation method; the method has the advantages that interaction of the system state and the degradation state is considered, and the residual life prediction result of the control system is more accurate and effective; the method is suitable for the technical field of control system residual life prediction.

Description

Technical Field

[0001] The present application relates to the technical field of remaining life prediction of control systems, and in particular to a method, system and electronic equipment for predicting remaining life of control systems based on dual time scales. Background Art

[0002] With the continuous advancement of industrial automation, the structure and functionality of control systems are becoming increasingly complex. Their ability to efficiently and safely complete their assigned tasks is crucial to the entire production process. During operation, control systems are affected by factors such as material aging, the operating environment, and loads, and their performance inevitably degrades. Severe degradation can lead to control system failure, resulting in serious consequences. Therefore, predicting the remaining useful life (RUL) of control systems has become a research hotspot in the field of prognostic and health management (PHM).

[0003] Current research on control system residual life prediction focuses on closed-loop control systems that consider actuator degradation. The main idea is that actuator degradation causes a continuous decline in control system performance until the system fails to meet performance requirements and cannot complete its assigned tasks, at which point the control system fails. Therefore, the focus is on modeling actuator degradation and assuming that control system failure occurs when actuator degradation reaches a certain threshold. This approach uses actuator failure as a proxy for control system failure. This use of actuator failure as a proxy for control system failure can lead to two problems: First, the actuator degradation threshold is set too conservatively. Due to the control system's inherent feedback control, the system may still meet performance requirements when actuator degradation reaches the failure threshold, meaning the system has not failed. Second, the actuator degradation threshold is set too high, causing the control system to fail before the actuator degradation reaches the threshold. Therefore, using the failure of key components such as actuators as a proxy for control system failure can reduce the accuracy of control system residual life prediction.

[0004] In recent years, some experts and scholars have proposed predicting the remaining useful life (RUL) of control systems from a control theory perspective. These studies have considered the impact of degradation on control system performance and proposed methods for predicting the RUL of control systems based on control system stability and dynamic performance. However, these studies on degradation modeling and RUL prediction of control systems model the dynamic and degradation processes of the control system on the same time scale. In practice, control system states typically change rapidly, while control system degradation processes are much slower than these state changes. This poses new challenges to control system degradation modeling and RUL prediction. From the perspective of control system dynamics theory, a control system with degradation evolution can be viewed as a hierarchical dynamical system consisting of a fast-varying, observable subsystem coupled to a slow-varying subsystem. Therefore, how to model degradation and predict the RUL of such control systems has become a key issue that needs to be addressed in the field of PHM. Summary of the Invention

[0005] In order to solve one of the above technical defects, the present application provides a control system remaining life prediction method, system and electronic equipment based on dual time scales.

[0006] According to a first aspect of the present application, a method for predicting the remaining life of a control system based on a dual time scale is provided, comprising: constructing a system state space model affected by a degradation state and a degradation model affected by the system state;

[0007] Update the system state in the system state space model, the degradation state in the degradation model, and the unknown parameters in the degradation model in real time according to the system state observation data;

[0008] The system state in the system state space model and the degradation state in the degradation model are jointly estimated based on the dual-time-scale Kalman filter algorithm;

[0009] Estimate the unknown parameters in the constructed degradation model;

[0010] According to the estimation results of the system state, the estimation results of the degradation state and the estimation results of the unknown parameters in the degradation model, the remaining service life of the control system is predicted by the Monte Carlo simulation method.

[0011] According to a second aspect of the present application, a control system remaining life prediction system based on dual time scales is provided, comprising: a module for implementing the control system remaining life prediction method based on dual time scales as described in any one of the above.

[0012] According to a third aspect of the present application, an electronic device is provided, including:

[0013] Memory;

[0014] processor; and

[0015] computer programs;

[0016] The computer program is stored in the memory and is configured to be executed by the processor to implement the control system remaining life prediction method based on dual time scales as described in any one of the above.

[0017] This application constructs a system state space model and degradation model with dual time scales to describe the degradation evolution process of the control system under the interaction of the system state and the degradation state. The dynamic model of the control system is established as a system state space model related to the degradation state, and the natural degradation of the control system is established as a degradation model affected by the system state. It solves the problem of inaccurate RUL prediction results caused by modeling the dynamic process and degradation process of the control system as the same time scale in the prior art. The system state and degradation state are jointly estimated, and the unknown parameters in the model are estimated, so that the system state space model and degradation model can be updated. Finally, the remaining life of the control system is predicted by the Monte Carlo simulation method, and the prediction results are more accurate and effective.

[0018] Other features and advantages of the present application will be described in the following description, and in part will become apparent from the description, or will be understood by practicing the present application. The purpose and other advantages of the present application can be realized and obtained by the contents indicated in the written description and the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] The drawings described herein are used to provide a further understanding of the present application and constitute a part of the present application. The illustrative embodiments of the present application and their descriptions are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0020] Figure 1 A flow chart of the control system remaining life prediction method based on dual time scales provided in this application;

[0021] Figure 2 for Figure 1 Schematic diagram of the process of joint estimation in ;

[0022] Figure 3 This is the control structure of the stabilization loop control system on the inertial platform in the embodiment of the present application;

[0023] Figure 4 is the system state trajectory affected by the degradation state in the embodiment of the present application;

[0024] Figure 5is the average effect curve of the system state in different degradation times in the embodiment of the present application;

[0025] Figure 6 is a degradation state trajectory affected by the system state in the embodiment of the present application;

[0026] Figure 7 This is a diagram showing the system state and degradation state estimation results based on the DTSKF algorithm in an embodiment of the present application;

[0027] Figure 8 This is a diagram of unknown parameter estimation results in an embodiment of the present application;

[0028] Figure 9 This is a graph showing the RUL prediction results for the 110th sampling in the embodiments and comparative examples of the present application;

[0029] Figure 10 This is a graph showing the RUL prediction results for the 130th sampling in the Examples and Comparative Examples of the present application;

[0030] Figure 11 This is a graph showing the RUL prediction results of the 150th sampling in the examples and comparative examples of the present application;

[0031] Figure 12 This is a graph showing the RUL prediction results for the 170th sampling in the Examples and Comparative Examples of the present application;

[0032] Figure 13 Graph showing the MSE results of RUL prediction in the Examples and Comparative Examples of the present application;

[0033] Figure 14 Schematic diagram of the functional structure of the control system remaining life prediction system based on dual time scales provided in this application;

[0034] Figure 15 for Figure 14 Schematic diagram of the functional structure of the model building module;

[0035] Figure 16 for Figure 14 Schematic diagram of the functional structure of the joint estimation module;

[0036] Figure 17 for Figure 14 Schematic diagram of the functional structure of the remaining life prediction module;

[0037] In the picture:

[0038] 10 is a model construction module, 101 is a system state space model construction unit, 102 is a degradation model construction unit, 1021 is a preliminary construction unit, 1022 is a nonlinear drift function determination unit, 1023 is a reconstruction unit, and 1024 is an expansion unit; 20 is an unknown parameter real-time update module; 30 is a joint estimation module, 301 is an initialization unit, 302 is a state estimation unit, 3021 is a system state sampling estimation unit, 3022 is a first judgment unit, 3023 is a degradation state sampling estimation unit, 3024 is a second judgment unit, 3025 is a state estimation end unit, and 3026 is a loop unit; 40 is an unknown parameter estimation module; 50 is a remaining life prediction module, 501 is a first preset unit, 502 is a simulation trajectory generation unit, 503 is a second preset unit, 504 is a remaining life calculation unit, and 505 is a RUL prediction unit. DETAILED DESCRIPTION

[0039] In order to make the technical solutions and advantages of the embodiments of the present application more clearly understood, the exemplary embodiments of the present application are further described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present application, and are not an exhaustive list of all the embodiments. It should be noted that the embodiments and features in the embodiments of the present application can be combined with each other unless they conflict.

[0040] To address the above issues, an embodiment of the present application provides a control system remaining life prediction method based on a dual time scale, including:

[0041] Construct a system state space model affected by degradation state and a degradation model affected by system state;

[0042] Update the system state in the system state space model, the degradation state in the degradation model, and the unknown parameters in the degradation model in real time according to the system state observation data;

[0043] The system state in the system state space model and the degradation state in the degradation model are jointly estimated based on the dual-time-scale Kalman filter algorithm;

[0044] Estimate the unknown parameters in the constructed degradation model;

[0045] According to the estimation results of the system state, the estimation results of the degradation state and the estimation results of the unknown parameters in the degradation model, the remaining service life of the control system is predicted by the Monte Carlo simulation method.

[0046] This application constructs a system state space model and degradation model with dual time scales to describe the degradation evolution process of the control system under the interaction of the system state and the degradation state. The dynamic model of the control system is established as a system state space model related to the degradation state, and the natural degradation of the control system is established as a degradation model affected by the system state. It solves the problem of inaccurate RUL prediction results caused by modeling the dynamic process and degradation process of the control system as the same time scale in the prior art. The system state and degradation state are jointly estimated, and the unknown parameters in the model are estimated, so that the system state space model and degradation model can be updated. Finally, the remaining life of the control system is predicted by the Monte Carlo simulation method, and the prediction results are more accurate and effective.

[0047] In this application, T is used to represent the time scale of the degradation process, and t is used to represent the time scale of the system state change. Since the degradation process of the control system is much slower than the system state change, T>>t.

[0048] Furthermore, the constructing of the system state space model affected by the degradation state specifically includes:

[0049] Determine the system input formula

[0050]

[0051] Where, e(t i ) represents t i The system output residual at time t i The deviation between the expected output and the actual output of the system at time , Indicates t i The expected output of the system at time y't i Indicates t i The actual system output at time Indicates t0 to t i The sum of the system output residuals at time j = 0, 1, ..., i, K P , K I and K D Represent the proportional coefficient, integral coefficient and differential coefficient respectively;

[0052] Construct a system state space model affected by degradation state based on the system input formula:

[0053]

[0054] Where, Respectively represent t i time, t i-1 The system status at any moment, R represents a real number, n represents the number of system states, n represents the number of system states, Q represents the variance of process noise, R' represents the variance of the measurement noise, Indicates that the control system is in T k The initial degenerate state of the moment, They represent the controlled system at T k The system state matrix, input matrix and output matrix affected by the degradation state at the moment.

[0055] In this application, a system state space model affected by degradation state is constructed. Since linear systems are the basis of complex systems, taking a single-input and single-output linear system as an example, its degradation process may affect the structure of the system and may also change the system parameters, which can be specifically reflected through the system state space model.

[0056] Furthermore, the construction of the degradation model affected by the system state specifically includes:

[0057] Preliminary construction of degradation model:

[0058]

[0059] Where, They represent the control system at T k Time, T k-1 The initial degenerate state of the moment, represents the nonlinear drift function, Degradation time ΔT k Average effect function of system state change, ΔT = T k -T k-1 , i∈(k-1)·p+1~k·p, represents the maximum integer that does not exceed ΔT / Δt, that is, p represents the number of system states within the degradation time ΔT, γ represents the parameter vector, θ=(α,γ,λ,ξ), α represents the inherent characteristics of the same type of system, α is an unknown constant, λ represents the individual difference between systems, λ is a random variable parameter, ξ represents the unknown parameter vector, σW(ΔT)~N(0,σ 2 ΔT), W(ΔT)=B(T k )-B(T k-1 ), σ represents the diffusion coefficient, B(T k )、B(T k-1 ) represent the k Time, T k-1 Stochastic dynamics of moment-degradation processes;

[0060] Let λ and {B(T k ),Tk ≥0} are independent and identically distributed, and The nonlinear drift function is obtained:

[0061]

[0062] Where, h(T k-1 ξ) represents T k-1 A function of the unknown parameter vector ξ at each moment, λ Tk-1 Indicates T k-1 Parameters of random variables at time t;

[0063] The initially constructed degradation model is reconstructed according to the nonlinear drift function, and the reconstructed degradation model is obtained as follows:

[0064]

[0065] Where, Indicates T k The random variable parameters at time , Indicates T k The random term at time λ, The initial distribution of λ is Right now Subject to the mean μ λ , the variance is The normal distribution of Indicates T k The reconstructed observation equation at time t, Indicates T k The measurement noise at the moment, denote the variance of the random term of the measurement noise and random effect parameter, respectively;

[0066] The random variable parameter Expanding to the implicit degradation state, the constructed degradation model is:

[0067]

[0068] Where, Represents T k Time, T k-1 The vector of degradation states and random effect parameters at time , Indicates T k The observation equation at time t,

[0069] Influenced by internal and external environmental factors, the degradation process of a control system is random. Among random process models, the Wiener process, also known as Brownian motion, has been widely used to model system degradation due to its excellent mathematical properties and physical interpretability. Therefore, the natural degradation of control systems is modeled as a nonlinear Wiener process. Furthermore, changes in the system state can accelerate or delay the degradation of a control system; that is, changes in the system state can affect the degradation rate of the control system. Therefore, to accurately predict the remaining life of a control system, it is necessary to incorporate the impact of system state changes on degradation into the degradation model, that is, to establish a functional relationship between the system state and the degradation rate.

[0070] Furthermore, because the degradation process of a control system is much slower than the change in system state, that is, the system state will change continuously multiple times within a unit degradation time. Therefore, the degradation rate of a control system within a unit degradation time is not the result of the system state at a single moment in time, but rather the result of the combined effect of system state changes over that period of time. In this application, the impact of the system state on the degradation rate is reflected by the average effect of system state changes within a unit degradation time.

[0071] Furthermore, the method of jointly estimating the system state in the system state space model and the implicit degradation state in the degradation model according to the dual-time-scale Kalman filter algorithm specifically includes:

[0072] Initialize the system state and degrade the state;

[0073] Perform state estimation, including:

[0074] Sampling and estimating the system state at the current sampling moment;

[0075] Determine whether the current sampling moment is a degradation state sampling moment. If so, sample and estimate the degradation state at the current sampling moment, and then determine whether the sampling is completed.

[0076] Otherwise, directly determine whether the sampling is completed. If so, end the state estimation; otherwise, perform state estimation at the next sampling moment.

[0077] In this application, because the system state changes much faster than the degraded state, the system state and the degraded state have different time-varying characteristics. To avoid excessive computational costs and the impact of drastic fluctuations in the system state on the accuracy of the control system's degraded state and parameter estimation results, a dual-time-scale Kalman filter algorithm is used to jointly estimate the system state and the degraded state.

[0078] Furthermore, estimating the system state at the current sampling moment includes the following steps:

[0079] Preset the expectation and covariance matrices of the system state:

[0080] The expected system state is:

[0081] Where, Indicates the current sampling time t i System status at any moment The estimated value of represents the time from t0 to t i All system observation data between time,

[0082] The covariance matrix of the system state is:

[0083] Preset the expectation and covariance matrices for the one-step prediction system state:

[0084] The expectation of predicting the system state in one step is:

[0085] Where, Indicates t i-1 The estimated value of the system state at time represents the time from t0 to t i-1 All system observation data between time,

[0086] The covariance matrix of the one-step prediction system state is:

[0087]

[0088] Perform temporal updates on the expectation and covariance matrices of the one-step predicted system state:

[0089] The expectations for updating the system status are:

[0090] The covariance matrix of the updated system state is:

[0091] Compute the expectation and covariance matrices of the system state:

[0092] The expected calculation formula of the system state is:

[0093] Where,

[0094] The calculation formula of the covariance matrix of the system state is:

[0095] Where I represents the identity matrix.

[0096] Furthermore, estimating the degradation state at the current sampling moment includes the following steps:

[0097] Preset the expectation and covariance matrices of the degenerate state:

[0098] The expectation of the degenerate state is:

[0099] Where,

[0100] The covariance matrix of the degenerate state is:

[0101] Where,

[0102] Preset the expectation and covariance matrices for the one-step forecast degradation state:

[0103] The expectation of one-step prediction of the degraded state is:

[0104] The covariance matrix of the one-step prediction degradation state is:

[0105] According to the degradation time ΔT k Expectations of internal system states Calculate degradation time ΔT k Average effect function of internal system state change

[0106] The degradation time ΔT is calculated using the RTS smoothing algorithm. k The expectation of the average effect function of the internal system state change

[0107] Where, ΔT k =T k -T k-1 , i∈(k-1)·p+1~k·p;

[0108] Since T>>t, in practical applications, as an example: when ΔT=4, Δt=1, Then when k=3, the corresponding i∈(k-1)·p+1~k·p, that is, i∈9~12. In other words, when the number of system states p within the degradation time ΔT is 4, the corresponding system states within time T3 are

[0109] Perform temporal updates on the expectation and covariance matrices of the one-step-forecast degraded state:

[0110] The expectation of updating the degraded state is:

[0111] Where,

[0112] The covariance matrix of the updated degraded state is:

[0113] Compute the expectation and covariance matrices of the degenerate state:

[0114] The expectation of the degenerate state is:

[0115] Where,

[0116] The covariance matrix of the degenerate state is:

[0117] In this application, because the system state changes much faster than the degradation state, the degradation state of the control system remains virtually unchanged on the time scale t. In this case, the system state space model can be considered a linear steady-state system. A Kalman filter (KF) algorithm is used to jointly estimate the system state and degradation state on both time scales, facilitating subsequent accurate service life prediction.

[0118] Due to the degradation model Degradation time ΔT k The average effect function of the system state change within the degradation time ΔT k System observation data should be used Further calculation of expectation i=(k-1)·p+1,...,k·p.

[0119] Specifically, the RTS smoothing algorithm is used to calculate the degradation time ΔT k Average effect function of internal system state change Specifically include:

[0120] make

[0121] The backward iterative process is:

[0122]

[0123]

[0124] in,

[0125] Furthermore, estimating the unknown parameters in the constructed degradation model specifically includes:

[0126] The unknown parameters in the constructed degradation model are constructed as an unknown parameter set, which is:

[0127]

[0128] Where, represents the expectation of the degraded state at time T0, that is, the initialized degraded state, Represents the covariance matrix of the degraded state at time T0;

[0129] The unknown parameters in the unknown parameter set are estimated using the EM algorithm, specifically including:

[0130] When T k When new system degradation data is obtained at any time and the estimated result of the current system state is available, the T k The unknown parameter set at the moment is iterated, and the iteration formula is:

[0131]

[0132] Where, Indicates T k The estimated result of the unknown parameter set obtained at the l+1th iteration;

[0133] Make a first estimate, including:

[0134] The RTS smoothing algorithm is used to calculate the conditional expectation, which includes:

[0135] Preset

[0136] The backward iterative process is:

[0137]

[0138] Where,

[0139] The conditional expectation can be obtained: and

[0140] According to Bayesian theory, the conditional expectation of the lth iteration is:

[0141]

[0142] Where:

[0143]

[0144]

[0145] Conduct a second estimate, including:

[0146] Estimate model parameters:

[0147] Substituting (Equation 26) to (Equation 28) into (Equation 29) yields:

[0148] (33);

[0149] Divide into three parts Maximize and get the unknown parameter vector The estimated values ​​include:

[0150]

[0151] Estimate the unknown parameters in (Equation 34), (Equation 35), and (Equation 36) respectively;

[0152] The first estimation and the second estimation are iteratively performed until a convergence condition is satisfied.

[0153] Specifically, the convergence condition means that the estimated result of the unknown parameters at the current moment is almost unchanged compared with the estimated result of the unknown parameters at the previous moment. In practical applications, it can be δ is a very small number close to zero.

[0154] In this application, the cut-off T k The unknown parameters are estimated by the system state data and degradation state data at the moment. Due to the existence of implicit variables The EM algorithm can be used to solve the problem of estimating the parameters of implicit variables in the unknown parameter set.

[0155] Specifically, the unknown parameters included in equation (34) are: The unknown parameters included in formula (35) are: The unknown parameters included in equation (36) are: Then, the unknown parameters in equations (34), (35), and (36) are estimated respectively, specifically including:

[0156] 1. For formula (34), find and Taking the partial derivative of and setting it to zero, we can get:

[0157]

[0158] 2. For formula (35), find the vectors The partial derivatives of each element in , Equation (35) can be further expanded as:

[0159]

[0160] In formula (35-1), assuming that γ, α, and ξ are fixed, calculate σ 2 and The partial derivative of and set it to zero, specifically expressed as:

[0161]

[0162]

[0163] Substituting Equations (35-2) and (35-3) into Equation (35-1), we can obtain the local log-likelihood function of γ, α, and ξ. Then, we can estimate γ by maximizing the local likelihood function using the optimization function (fminsearch) commonly used in MATLAB software. (l+1) , α (l+1) and ξ (l+1) .

[0164] 3. For formula (36), find Taking the partial derivative of and setting it to zero, we can get:

[0165]

[0166] This application is divided into three parts, and the three parts are maximized separately to estimate the parameters, which is obtained by directly maximizing formula (33). In contrast, the maximization and It can reduce the number of unknown parameters and make calculation and implementation easier.

[0167] Furthermore, the remaining life of the control system is predicted by a Monte Carlo simulation method based on the estimated results of the system state, the estimated results of the degradation state, and the estimated results of the unknown parameters in the degradation model, specifically including:

[0168] System status Degenerate state

[0169] The preset Monte Carlo simulation trajectory is H;

[0170] Expected system state Expectations of a degraded state As t i and T kThe system state value and degradation state value at each moment are simulated through the system state space model and degradation model to generate H simulation trajectories;

[0171] Preset e max is the residual threshold, and the failure time of the hth simulation trajectory is preset to t' h , h=1,2,...,H; the RUL of H simulation trajectories is calculated separately using the remaining life calculation formula, which is:

[0172]

[0173] Where, Indicates t i Control the RUL of the h-th simulation trajectory of the system at all times, for The minimum value of Indicates that at t i Before time t, all RULs of the hth simulation trajectory of the control system meet the following conditions: the system deviation e(t) is less than e max 、System in The system output residual at the moment is greater than or equal to e max ; From formula (37), we can see that when the failure time t' of the hth simulation trajectory h Satisfy |e(t' h )|≥e max When e(t' h ) indicates t' h The system output residual at time t is saved i ;

[0174] t i The RUL of the hth simulation trajectory at time is

[0175] t i The RUL prediction results of all simulation trajectories of the time control system are: This set is plotted as a curve. The probability distribution of .

[0176] In this application, when |e(t' h )|<e max When |e(t' h )|<e max The situation is not handled.

[0177] In this application, once new system observation data and degradation state data are available, the control system RUL prediction will be updated; the output residual is used as the basis for the control system RUL prediction, considering that the control system has a certain tolerance for degradation, e(t'h The threshold must be greater than the upper limit of normal fluctuations to prevent misjudgment. This solves the problem in existing technologies where it is difficult to determine a reasonable and accurate failure threshold during the system state and degradation process of the control system, and the output residual can change rapidly before and after the control system fails.

[0178] In practical applications, the stabilization loop control system on the inertial platform is used as an example to explain in detail, wherein the control structure of the stabilization loop control system on the inertial platform is as follows: Figure 3 shown. Figure 3 In the control system, the detection link is composed of sensitive components on the platform, such as gyroscopes, accelerometers, etc.; the frame angle sensor and position compensation controller together form the controller; the actuator is the torque motor that directly acts on the controlled object platform of the system output. Figure 3 As shown in the figure, the control principle is as follows: the control system's sensitive components convert the detection signal into a physical quantity equivalent to the reference posture, feed it back to the input, and compare it with the given reference posture. The deviation passes through the platform frame angle sensor and position compensation controller, driving the torque motor to directly act on the controlled object platform at the system output. The platform then rotates at a fixed speed.

[0179] According to formula (2), the system state space model is constructed:

[0180]

[0181] Where x1(t), x2(t) and x3(t) represent the armature current, frame angular velocity and angle of the motor at time t, respectively, and u m (t) represents the control voltage at time t, K m Indicates the motor torque coefficient, K e Represents the back electromotive force coefficient, J m and J L Represent the rotor inertia moment and load inertia moment, R m and L m They represent the resistance and inductance of the armature winding, ω(t) and v(t) represent the white noise in the motor shaft and gyroscope output shaft at time t, respectively.

[0182] During the operation of the control system, the performance of the actuator will decrease over time. This performance degradation can be reflected by some parameters of the actuator. We choose the motor torque coefficient K m is used as a degradation variable to characterize the degradation of the actuator.

[0183] According to formula (6), the degradation process of the actuator can be expressed as:

[0184]

[0185] Where z T represents the degraded state of the actuator at time T, represents the initial degraded state of the actuator, represents the drift function affected by the motor load, i.e. the armature current, σ B represents the diffusion coefficient, σ B Represents Brownian motion; this assumption that links the working stress of the motor with the load it bears is in line with reality. At the same time, the fact that the greater the load, the faster the degradation rate is also in line with objective laws.

[0186] Assume that the degradation drift function is:

[0187]

[0188] Where α represents the degradation rate coefficient, The degradation rate of the motor is proportional to the sum of the squares of the armature current per unit degradation time. Substituting it into equation (40) yields the degradation model:

[0189]

[0190] To facilitate numerical calculation, we discretize the system state space model (39) and the system degradation model (42), which are specifically expressed as:

[0191] t i =t i-1 +Δt formula (43);

[0192] T k =T k-1 +ΔT formula (44);

[0193]

[0194]

[0195] Where, Δt=0.001s is the sampling interval of the system state, ΔT=10 3 *Δt is the sampling interval of degradation state, T I is the integration time constant, T D is the differential time constant, v is both the process noise of the state quantity x3 and the observation noise of the output quantity y, so the additional measurement error is no longer considered in Equation (45). The process noise υ, w, v, ε and diffusion motion are all independent Gaussian random variables with a mean of 0 and variances of Q1, Q2, Q3, υ~N(0,Q1), w~N(0,Q2), v~N(0,Q3),

[0196] The system state space model, degradation model parameters and initial state settings are shown in Table 1. When the RUL prediction method provided in this application is used to predict the RUL of the control system, the total number of Monte Carlo simulation trajectories is H = 1000. The failure threshold is set to e max =0.28rad.

[0197] Table 1 Model parameters and initial state settings

[0198]

[0199] Based on equations (43)-(54), the system state and degradation state trajectories can be generated. Since the system state changes much faster than the degradation state, that is, the system state changes very frequently during the entire life cycle of the motor, for the sake of clarity, only a few complete cycles of system state curves are given here, such as Figure 4-6 As shown, Figure 4 is the system state trajectory affected by the degradation state. Figure 5 is the average effect curve of the system state at different degradation times; Figure 6 is the degradation trajectory curve affected by the system state.

[0200] Depend on Figure 5 It can be seen that by using the average effect mechanism to transform the fast-changing system state to the slow time scale of the control system degradation state, it is possible to effectively avoid the drastic fluctuations in the system state affecting the degradation state and parameter estimation results. In addition, when the control system degrades to failure (the 179th sampling point), the average effect change of the system state will intensify, which is normal because the control system is already unstable at this time.

[0201] The method provided in this application provides the following one-step prediction results for the system state and degradation state: Figure 7 As shown in the figure, and compared with the actual system state and degradation path, it can be seen that the predicted path matches the actual degradation path well, which illustrates the effectiveness of the proposed DTSKF algorithm.

[0202] The parameter updating process in the degradation model is as follows: Figure 8 As shown in Figure 2, it is clear that as the system degradation observation data gradually increases, all parameters converge to their true values. This verifies the correctness of the proposed parameter estimation method.

[0203] Once new degradation observation data is obtained, the model parameters can be updated in real time to achieve online RUL prediction of the system. The prior art takes into account the impact of the system state on the degradation process, but does not take into account the different time scales of the system state and the degradation state, that is, the degradation of the system and the system state are on the same time scale. In this case, the motor fails very quickly (tens of seconds). This is obviously inconsistent with reality. In order to illustrate the accuracy of the proposed model and RUL prediction method, and to prove the accuracy of the control system remaining life prediction method based on dual time scales provided by this application, this application also provides comparative examples 1 and 2.

[0204] Specifically:

[0205] The degradation model provided in the embodiment is M1;

[0206] Comparative Example 1: Only the mutual influence between the system state and the degradation state is considered, without considering the degradation model of different time scales of the system state change and the degradation state as M2;

[0207] Comparative Example 2: The degradation model of the nonlinear Wiener process without considering the influence of the system state is M3.

[0208] In order to facilitate comparative analysis, the 110th, 130th, 150th and 170th sampling moments are taken as examples, corresponding to Figure 9 、 Figure 10 、 Figure 11 、 Figure 12 , respectively, using the degradation models provided in Example, Comparative Example 1, and Comparative Example 2 to perform RUL prediction. The RUL prediction results are as follows: Figure 9-12 shown.

[0209] from Figure 9-12 As can be seen from the table, M1 has obvious advantages over the three degradation models. Specifically, the average RUL of the system predicted by M3 is closer to the actual average RUL of the system than M2 and M3. In addition, the dispersion range of the prediction results of M1 is narrower than that of M2 and M3. This is consistent with the expected results, because M3 takes into account the mutual influence between the system state and the degradation state, as well as the different time scales of the fast-changing system state and the slow-changing degradation state. In this way, the uncertainty in the RUL estimation can be naturally reduced. Figure 8 From the RUL at different prediction times, we can see that as the prediction time is delayed, the range of the predicted RUL becomes narrower and narrower. This shows that as the degradation observation data increases, the RUL predicted by the method proposed in this application becomes more and more accurate.

[0210] In order to further compare the performance of the three models in predicting RUL, the mean square error (MSE) of the three models in predicting RUL is calculated respectively. MSE can directly evaluate the fitting effect of the data. Since the RUL of the system is obtained by numerical integration approximation, here The MSE curves of the three models at different observation points are as follows: Figure 13 shown.

[0211] Figure 13 Only the results of the last 80 observation points (i.e., from the 91st sampling point to the 170th sampling point) are plotted. This is because after the 90th observation point, the parameter estimation results are relatively stable. This conclusion can be seen from Figure 8 In addition, the MSE curves of all methods are relatively close. This is mainly because the generated degradation data looks relatively simple, without strong nonlinearity and measurement uncertainty. To be precise, in most cases, the MSE obtained by M1 is smaller than that of M2 and M3 models. Finally, although the degradation path contains some fluctuations, the MSE in the embodiment of the present application can still decrease rapidly and eventually approach zero as the observed data increases, which means that when the observed data varies in a moderate range, the probability density function (PDF) of the predicted RUL is robust, stable and accurate.

[0212] The present application also provides a control system remaining life prediction system based on dual time scales, comprising: a module for implementing any of the control system remaining life prediction methods based on dual time scales described above.

[0213] Specifically, the control system remaining life prediction system based on dual time scales includes:

[0214] A model building module 10 is used to build a system state space model affected by the degradation state and a degradation model affected by the system state;

[0215] An unknown parameter real-time updating module 20 is used to update the system state in the system state space model, the degradation state in the degradation model, and the unknown parameters in the degradation model in real time according to the system state observation data;

[0216] a joint estimation module 30 for jointly estimating the system state in the system state space model and the degradation state in the degradation model according to a dual-time-scale Kalman filter algorithm;

[0217] The unknown parameter estimation module 40 is used to estimate the unknown parameters in the constructed degradation model;

[0218] The remaining life prediction module 50 is used to predict the remaining life of the control system through a Monte Carlo simulation method based on the estimation results of the system state, the estimation results of the degradation state and the estimation results of the unknown parameters in the degradation model.

[0219] More specifically, the model building module 10 includes: a system state space model building unit 101 and a degradation model building unit 102;

[0220] The degradation model building unit 102 includes:

[0221] A preliminary construction unit 1021 is used to preliminarily construct a degradation model;

[0222] The nonlinear drift function determining unit 1022 is used to set λ and {B(T k ),T k ≥0} are independent and identically distributed, and Obtain nonlinear drift function;

[0223] The reconstruction unit 1023 is used to reconstruct the initially constructed degradation model according to the nonlinear drift function to obtain a reconstructed degradation model;

[0224] Extension unit 1024, used to convert random variable parameters Expand to implicit degradation state and obtain the constructed degradation model;

[0225] More specifically, the joint estimation module 30 includes:

[0226] Initialization unit 301, used to initialize the system state and degradation state;

[0227] A state estimation unit 302, configured to perform state estimation;

[0228] The system state sampling and estimation unit 3021 is used to sample and estimate the system state at the current sampling moment;

[0229] The first judging unit 3022 is configured to judge whether the current sampling moment is a degraded state sampling moment;

[0230] The degradation state sampling and estimation unit 3023 is configured to sample and estimate the degradation state at the current sampling moment when the current sampling moment is the degradation state sampling moment;

[0231] The second judgment unit 3024 is configured to judge whether sampling is completed when the current sampling moment is not the degradation state sampling moment or after sampling and estimating the degradation state at the current sampling moment;

[0232] The state estimation ending unit 3025 is used to end the state estimation when the sampling is completed;

[0233] The loop unit 3026 is used to return to the system state sampling estimation unit 3021 to perform state estimation at the next sampling moment when the sampling is not completed.

[0234] Specifically, the remaining life prediction module 50 includes:

[0235] The first preset unit 501 is used to set the system status Degenerate state The preset Monte Carlo simulation trajectory is H;

[0236] The simulation trajectory generating unit 502 is used to generate the expected value of the system state. Expectations of a degraded state As t i and T k The system state value and degradation state value at each moment are simulated through the system state space model and degradation model to generate H simulation trajectories;

[0237] The second preset unit 503 is used to preset e max is the residual threshold, and the failure time of the hth simulation trajectory is preset to t' h , h=1,2,...,H;

[0238] The remaining life calculation unit 504 is used to calculate the RUL of the H simulation trajectories respectively using the remaining life calculation formula. The remaining life calculation formula is:

[0239]

[0240] Where, Indicates t i Control the RUL of the h-th simulation trajectory of the system at all times, for The minimum value of Indicates that at t i Before time t, all RULs of the hth simulation trajectory of the control system meet the following conditions: the system deviation e(t) is less than e max , the system is The system output residual at the moment is greater than or equal to e max ;

[0241] The RUL prediction unit 505 is used to predict the failure time t' of the hth simulation trajectory. h Satisfy |e(t' h )|≥e max When e(t' h ) indicates t' h The system output residual at time t is saved i ;

[0242] t i The RUL of the hth simulation trajectory at time is

[0243] t i The RUL prediction results of all simulation trajectories of the time control system are:

[0244] The present application also provides an electronic device, comprising:

[0245] Memory;

[0246] processor; and

[0247] computer programs;

[0248] The computer program is stored in the memory and is configured to be executed by the processor to implement the control system remaining life prediction method based on dual time scales as described in any one of the above.

[0249] Those skilled in the art will appreciate that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code. The scheme in the embodiment of the present application can be implemented in various computer languages, for example, C language, VHDL language, Verilog language, object-oriented programming language Java, and directly interpreted scripting language JavaScript, etc.

[0250] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the steps in the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0251] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0252] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0253] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be understood to indicate or imply relative importance or implicitly specify the number of the technical features indicated. Thus, a feature specified as "first" or "second" may explicitly or implicitly include one or more of the features. Throughout the description of this application, "plurality" means at least two, such as two, three, etc., unless otherwise specifically defined.

[0254] Although the preferred embodiments of the present application have been described, those skilled in the art may make additional changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present application.

[0255] Obviously, those skilled in the art may make various changes and modifications to this application without departing from the spirit and scope of this application. Thus, if these modifications and variations of this application fall within the scope of the claims of this application and their equivalents, this application is intended to include these modifications and variations.

Claims

1. A control system remaining life prediction method based on dual time scales, characterized in that: include: Construct a system state space model affected by degradation state and a degradation model affected by system state; Update the system state in the system state space model, the degradation state in the degradation model, and the unknown parameters in the degradation model in real time according to the system state observation data; The system state in the system state space model and the degradation state in the degradation model are jointly estimated based on the dual-time-scale Kalman filter algorithm; Estimate the unknown parameters in the constructed degradation model; According to the estimation results of the system state, the estimation results of the degradation state and the estimation results of the unknown parameters in the degradation model, the remaining service life of the control system is predicted by the Monte Carlo simulation method.

2. The method for predicting the remaining life of a control system based on dual time scales according to claim 1, characterized in that: The constructing of the system state space model affected by the degradation state specifically includes: Determine the system input formula Where, e(t i ) represents t i The system output residual at time t i The deviation between the expected output and the actual output of the system at time , Indicates t i The expected output of the system at time Indicates t i The actual system output at time Indicates t0 to t i The sum of the system output residuals at time j = 0, 1, ..., i, K P , K I and K D Represent the proportional coefficient, integral coefficient and differential coefficient respectively; Construct a system state space model affected by degradation state based on the system input formula: Where, Respectively represent t i time, t i-1 The system status at any moment, R represents a real number, n represents the number of system states, n represents the number of system states, Q represents the variance of process noise, R' represents the variance of the measurement noise, Indicates that the control system is in T k The initial degenerate state of the moment, They represent the controlled system at T k The system state matrix, input matrix and output matrix affected by the degradation state at the moment.

3. The method for predicting the remaining life of a control system based on dual time scales according to claim 2, characterized in that: The construction of the degradation model affected by the system state specifically includes: Preliminary construction of degradation model: Where, They represent the control system at T k Time, T k-1 The initial degenerate state of the moment, represents the nonlinear drift function, Degradation time ΔT k Average effect function of system state change, ΔT = T k -T k-1 , i∈(k-1)·p+1~k·p, represents the maximum integer that does not exceed ΔT / Δt, that is, p represents the number of system states within the degradation time ΔT, γ represents the parameter vector, θ=(α,γ,λ,ξ), α represents the inherent characteristics of the same type of system, α is an unknown constant, λ represents the individual difference between systems, λ is a random variable parameter, ξ represents the unknown parameter vector, σW(ΔT)~N(0,σ 2 ΔT), W(ΔT)=B(T k )-B(T k-1 ), σ represents the diffusion coefficient, B(T k )、B(T k-1 ) represent the k Time, T k-1 Stochastic dynamics of moment-degradation processes; Let λ and {B(T k ),T k ≥0} are independent and identically distributed, and The nonlinear drift function is obtained: Where, h(T k-1 ξ) represents T k-1 A function of the unknown parameter vector ξ at each moment, Indicates T k-1 Parameters of random variables at time t; The initially constructed degradation model is reconstructed according to the nonlinear drift function, and the reconstructed degradation model is obtained as follows: Where, Indicates T k The random variable parameters at time , Indicates T k The random term at time λ, The initial distribution of λ is Right now Subject to the mean μ λ , the variance is The normal distribution of Indicates T k The reconstructed observation equation at time t, Indicates T k The measurement noise at the moment, denote the variance of the random term of the measurement noise and random effect parameter, respectively; The random variable parameter Expanding to the implicit degradation state, the constructed degradation model is: Where, Represents T k Time, T k-1 The vector of degradation states and random effect parameters at time , Indicates T k The observation equation at time t, 4. The method for predicting the remaining life of a control system based on dual time scales according to claim 3 is characterized in that: The method of jointly estimating the system state in the system state space model and the implicit degradation state in the degradation model according to the dual-time-scale Kalman filter algorithm specifically includes: Initialize the system state and degrade the state; Perform state estimation, including: Sampling and estimating the system state at the current sampling moment; Determine whether the current sampling moment is a degradation state sampling moment. If so, sample and estimate the degradation state at the current sampling moment, and then determine whether the sampling is completed. Otherwise, directly determine whether the sampling is completed. If so, end the state estimation; otherwise, perform state estimation at the next sampling moment.

5. The method for predicting the remaining life of a control system based on dual time scales according to claim 4, characterized in that: The estimating of the system state at the current sampling moment comprises the following steps: Preset the expectation and covariance matrices of the system state: The expected system state is: Where, Indicates the current sampling time t i System status at any moment The estimated value of represents the time from t0 to t i All system observation data between time, The covariance matrix of the system state is: Preset the expectation and covariance matrices for the one-step prediction system state: The expectation of predicting the system state in one step is: Where, Indicates t i-1 The estimated value of the system state at time represents the time from t0 to t i-1 All system observation data between time, The covariance matrix of the one-step prediction system state is: Perform temporal updates on the expectation and covariance matrices of the one-step predicted system state: The expectations for updating the system status are: The covariance matrix of the updated system state is: Compute the expectation and covariance matrices of the system state: The expected calculation formula of the system state is: Where, The calculation formula of the covariance matrix of the system state is: Where I represents the identity matrix.

6. The method for predicting the remaining life of a control system based on dual time scales according to claim 5, characterized in that: The estimating of the degradation state at the current sampling moment comprises the following steps: Preset the expectation and covariance matrices of the degenerate state: The expectation of the degenerate state is: Where, The covariance matrix of the degenerate state is: Where, Preset the expectation and covariance matrices for the one-step forecast degradation state: The expectation of one-step prediction of the degraded state is: The covariance matrix of the one-step prediction degradation state is: According to the degradation time ΔT k Expectations of internal system states Calculate degradation time ΔT k Average effect function of internal system state change The degradation time ΔT is calculated using the RTS smoothing algorithm. k The expectation of the average effect function of the internal system state change Where, ΔT k =T k -T k-1 , i∈(k-1)·p+1~k·p; Perform temporal updates on the expectation and covariance matrices of the one-step-forecast degraded state: The expectation of updating the degraded state is: Where, The covariance matrix of the updated degraded state is: Compute the expectation and covariance matrices of the degenerate state: The expectation of the degenerate state is: Where, The covariance matrix of the degenerate state is:

7. The method for predicting the remaining life of a control system based on dual time scales according to claim 6, characterized in that: The estimating of unknown parameters in the constructed degradation model specifically includes: The unknown parameters in the constructed degradation model are constructed as an unknown parameter set, which is: Where, represents the expectation of the degraded state at time T0, that is, the initialized degraded state, Represents the covariance matrix of the degraded state at time T0; The unknown parameters in the unknown parameter set are estimated using the EM algorithm, specifically including: When T k When new system degradation data is obtained at any time and the estimated result of the current system state is available, the T k The unknown parameter set at the moment is iterated, and the iteration formula is: Where, Indicates T k The estimated result of the unknown parameter set obtained at the l+1th iteration; Make a first estimate, including: The RTS smoothing algorithm is used to calculate the conditional expectation, which includes: Preset The backward iterative process is: Where, The conditional expectation can be obtained: and According to Bayesian theory, the conditional expectation of the lth iteration is: Where: Conduct a second estimate, including: Estimate model parameters: Substituting (Equation 26) to (Equation 28) into (Equation 29) yields: Divide into three parts Maximize and get the unknown parameter vector The estimated values ​​include: Estimate the unknown parameters in (Equation 34), (Equation 35), and (Equation 36) respectively; The first estimation and the second estimation are iteratively performed until a convergence condition is satisfied.

8. The method for predicting the remaining life of a control system based on dual time scales according to claim 4, characterized in that: The method of predicting the remaining life of the control system by using a Monte Carlo simulation method based on the estimated results of the system state, the estimated results of the degradation state, and the estimated results of the unknown parameters in the degradation model specifically includes: System status Degenerate state The preset Monte Carlo simulation trajectory is H; Expected system state Expectations of a degraded state As t i and T k The system state value and degradation state value at each moment are simulated through the system state space model and degradation model to generate H simulation trajectories; Preset e max is the residual threshold, and the failure time of the hth simulation trajectory is preset to t' h , h=1,2,...,H; the RUL of H simulation trajectories is calculated separately using the remaining life calculation formula, which is: Where, Indicates t i Control the RUL of the h-th simulation trajectory of the system at all times, for The minimum value of Indicates that at t i Before time t, all RULs of the hth simulation trajectory of the control system meet the following conditions: the system deviation e(t) is less than e max 、System in The system output residual at the moment is greater than or equal to e max ; From formula (37), we can see that when the failure time t' of the hth simulation trajectory h Satisfy |e(t' h )|≥e max When e(t' h ) indicates t' h The system output residual at time t is saved i ; t i The RUL of the hth simulation trajectory at time is t i The RUL prediction results of all simulation trajectories of the time control system are:

9. The control system remaining life prediction system based on dual time scale is characterized by: include: A module for implementing the control system remaining service life prediction method based on dual time scales as claimed in any one of claims 1 to 8.

10. An electronic device, characterized in that: include: Memory; processor; as well as computer programs; The computer program is stored in the memory and is configured to be executed by the processor to implement the control system remaining service life prediction method based on dual time scales according to any one of claims 1 to 8.

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