Intermittent fault diagnosis and residual service life prediction method of hybrid system
By combining extended Kalman filtering and a dual stochastic process model with a multi-stage expectation-maximization algorithm, the accuracy problem of intermittent fault prediction in hybrid systems is solved, enabling accurate diagnosis and lifetime prediction of intermittently faulty components.
Patent Information
- Application Number
- CN202511662577.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-11-13
- Publication Date
- 2026-02-10
AI Technical Summary
Existing technologies cannot fully account for the randomness of faults in intermittent fault prediction of hybrid systems, resulting in low prediction accuracy.
The extended Kalman filter algorithm is used for fault diagnosis. A dual stochastic process model is constructed to describe the degradation and occurrence of intermittent faults. The multi-stage expectation-maximization algorithm is used to estimate unknown parameters. An event-triggered collaborative failure process is proposed to derive the probability density distribution function of the remaining service life of intermittently faulty components.
It improves the prediction accuracy of intermittent faults in hybrid systems. By using a dual stochastic process model and a multi-stage expectation-maximization algorithm, it achieves effective diagnosis of intermittently faulty components and accurate prediction of their remaining service life.
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Figure CN121503254A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of fault diagnosis and remaining useful life prediction, and particularly to a method for intermittent fault diagnosis and remaining useful life prediction of a hybrid system. BACKGROUND
[0002] A hybrid system is composed of continuous dynamics and discrete dynamics, and the state change of the system includes both continuous state change and discrete state jump. In many industrial applications, such as power systems, power electronic devices, electric vehicles, etc., such hybrid characteristics are ubiquitous. These systems are usually composed of different types of components, mainly divided into continuous components and discrete components. The state change of the continuous component is continuous, for example, the change of the switch in the analog circuit or the pressure regulation in the hydraulic control system; while the discrete component has discrete state change, such as the opening and closing of the switch.
[0003] The health monitoring of a hybrid system not only needs to estimate the continuous dynamics and the discrete dynamics simultaneously, but also needs to take into account the influence of the interaction between the continuous dynamics and the discrete dynamics. Therefore, compared with continuous systems, the fault diagnosis and prediction of hybrid systems are more difficult. Since the 1990s, the health monitoring (including fault diagnosis and remaining life prediction) of hybrid systems has gradually attracted widespread attention from scholars at home and abroad. After decades of development, the related field has made many important theoretical and application achievements. However, for the intermittent fault prediction problem of hybrid systems, most of the literature adopts the method of deterministic model. This kind of method cannot fully consider the randomness of intermittent faults in the degradation process and the occurrence process, and thus leads to low prediction accuracy. Therefore, how to use the stochastic process model to predict the remaining useful life of the hybrid system under intermittent fault is a problem to be solved. SUMMARY
[0004] In order to overcome the defects in the prior art, the present application provides a method for intermittent fault diagnosis and remaining useful life prediction of a hybrid system, which solves the problem of remaining useful life prediction of a hybrid system under intermittent fault.
[0005] To achieve the above purpose, the present application adopts the following technical scheme, comprising: A method for intermittent fault diagnosis and remaining useful life prediction of a hybrid system, comprising the following steps: S1, performing fault diagnosis on the hybrid system based on an extended Kalman filter algorithm; S2, constructing a double stochastic process model to describe the degradation process and the fault occurrence process of the intermittent fault component; S3, estimating the unknown parameters of the double stochastic process model by using a multi-stage expectation maximization algorithm; S4 proposes the concept of event-triggered collaborative failure process and derives the probability density distribution function of the remaining useful life of intermittently faulty components based on the failure mechanism of this process.
[0006] Preferably, step S1 specifically includes the following steps: S11, Establish the state-space equations of the hybrid system; the hybrid system contains several continuous and discrete elements; the mathematical model of the hybrid system is expressed as: ; In the formula, Represents the state vector. Represents the model parameter vector. Indicates the output vector. Represents the input vector. and These represent the process noise vector and the measurement noise vector, respectively. Indicates system mode, Indicates the first The state of a discrete component , This indicates the number of discrete components in a hybrid system. and Representing the patterns respectively The state transition equations and output equations are as follows: express The first derivative; S12, Construct the extended Kalman filter, which is expressed as: ; In the formula, Indicates the number of time steps Prior state estimation, and Indicates time The system parameter vector and input quantities, This represents the Jacobian matrix formed by the first-order partial derivatives of the state transition function with respect to the state. Indicates time The prior estimation error covariance matrix, and Let these represent the system process noise covariance and the observation noise covariance, respectively. Indicates time Prior observation estimates, This represents the Jacobian matrix formed by the first-order partial derivatives of the observation function with respect to the state. Represents the Kalman gain matrix. Indicates time The system observations, and Indicates time The posterior state estimate and the posterior estimate error covariance matrix, Represents the identity matrix; S13, by comparing the prior observation estimates obtained in S12 With measured value By understanding the magnitude relationship between them, we can obtain the residual vector: ; In the formula, Represents the residual vector. Indicates the number of time steps The first time One residual; When the system is fault-free, each residual is below the fault threshold; when a component in the system fails, at least one residual exceeds the fault threshold; by comparing the residuals with the residual thresholds, fault detection can be performed on the hybrid system. S14, In order to identify the amplitude, occurrence time, and disappearance time of each fault of the intermittent faulty component, the amplitude time history curve of the faulty component is... Provide a parameterized description: ; In the formula, The nominal value of the parameter indicating the faulty component. , and They represent the first The magnitude, occurrence time, and disappearance time of the fault. Represents the unit step function; By combining the system state and faulty component parameters, the augmented state vector is obtained as follows: ; S15 utilizes an enhanced extended Kalman filter for fault identification, introducing an enhancement factor to strengthen the posterior state error covariance, as shown below: ; In the formula, This represents the augmented posterior state error covariance. Indicates the enhanced threshold. This indicates an enhancing factor.
[0007] Preferably, step S2 specifically includes the following steps: S21. Based on the amplitude, occurrence time, and disappearance time of each fault obtained from fault identification, a joint intermittent fault degradation feature is constructed to describe the severity of each fault, as shown below: ; In the formula, Indicates the first The combined intermittent fault degradation characteristic value of the sub-fault; S22 describes the degradation process of intermittently failing components through both internal degradation processes and external shocks. The specific steps are as follows: S221, the degradation process of intermittently faulty components is represented as follows: ; In the formula, This indicates an internal degradation process. Indicates instantaneous external impact. The first character represents the first element that follows a gamma distribution. External impact amount during the occurrence of the secondary failure. and The shape parameter representing the gamma distribution. Indicates the end time The number of failures Represents the Dirac function, express The amount of degradation at any given time; S222, using a Wiener process with mode-dependent drift coefficients, describes the internal degradation process as follows: ; In the formula, This represents the initial internal degradation amount that follows a normal distribution. These represent the initial mean and variance of internal degradation, respectively. Representation pattern The drift coefficient below, This represents the nonlinear equation used to describe the nonlinear degradation process. Indicates the time of the first occurrence of the intermittent fault. Indicates the diffusion coefficient. To represent the standard Brownian motion process, Represents the integral variable. Indicates model parameters; S23 describes the occurrence process of intermittent faults using a non-homogeneous Poisson process with fault occurrence rates exhibiting pattern dependence and internal degradation dependence. This fault occurrence rate is expressed as: ; In the formula, Represents pattern dependency factor, Indicates internal degradation dependency factor. express Failure rate at any given time; S24. Based on the two stochastic processes described in S22 and S23, a dual stochastic process model is constructed to simultaneously describe the degradation and occurrence processes of intermittent faults. Its expression is as follows: ; In the formula, Indicates the time interval Internal occurrence The probability of secondary failures; They represent the cutoff times respectively. , The number of times the fault occurred.
[0008] Preferably, in step S3, a multi-stage expectation-maximization algorithm is designed to estimate the unknown parameters of the double stochastic process model, as follows: S31, utilizing A historical degradation dataset is constructed by combining historical intermittent fault degradation feature datasets of several similar components, as shown below: ; In the formula, Indicates the first A dataset of historical intermittent fault degradation features of similar components. , and These represent the first faults obtained through fault identification. The first of the same type of components The fault occurrence time, combined intermittent fault degradation characteristic value, and total number of faults for each fault; S32, in the multi-stage expectation-maximization algorithm... During the phase, the time interval Divided into equal parts The random integral is obtained by integrating each part numerically and summing the results. The approximation value is represented as follows: ; In the formula, Indicates the first Time interval in the phase The first Numerical integration results for each part, , Indicates time The amount of internal degradation, Indicates time interval The first One dividing point, Indicates the time interval between adjacent dividing points; S33, based on the statistical properties of Wiener processes, gamma distributions, and non-homogeneous Poisson processes, in the multi-stage expectation-maximization algorithm... In this stage, the log-likelihood function of the unknown parameters of the double stochastic process model is expressed as: ; In the formula, ; ; ; ; In the formula, This represents the set of unknown parameters in a double stochastic process model. This represents the difference in internal degradation between two adjacent dividing points. Represents the complete gamma function. , ; Indicative functions are represented as follows: ; In the formula, This indicates the first result obtained through fault identification. The first of the same type of components The time of occurrence of this fault. express The pattern of time, Indicates a specific pattern; S34, the Expectation-Maximization algorithm consists of two main steps: the E-step (expectation step) and the M-step (maximization step). By alternately executing these two steps in each iteration, the model parameters are continuously optimized until convergence to a local optimum. In the E-step, given the current parameter estimates, the posterior distribution of the latent variables is calculated, thereby constructing the expected value of the complete data. In the M-step, the model parameter estimates are updated by maximizing the expected log-likelihood function obtained in the E-step. S35, after completing the first... After applying the expectation-maximization algorithm for this stage, the estimated result for this stage is... Compared with the estimation results of the previous stage The comparison is performed, and if the difference in their log-likelihood functions is less than a pre-set termination value, that is... If the algorithm converges, the result obtained at this stage is considered the final estimate. .
[0009] Preferably, in step S34, the multi-stage expectation-maximization algorithm... The specific steps for updating unknown parameters in stages are as follows: S341, in step E, uses a particle smoother for calculation. , , and The expectation, that is , , and ; The particle smoother consists of two steps: forward filtering and backward smoothing; assuming the number of particles is... In forward filtering, the first Particles The update steps are as follows: ; ; In the formula, ; .
[0010] In backward smoothing, the particle state remains unchanged, and only the particle weights are updated; the expression for updating the particle weights is as follows: ; In the formula, ; Based on the above formula , , and It is calculated using the following formula: ; ; ; ; Therefore, the expected log-likelihood function Represented as: ; In the formula, ; ; ; ; In the formula, Indicates the first Phase 1 The next iteration The estimated value, and Indicates based on calculate and The value of .
[0011] S342, in the M-step, by maximizing the expected log-likelihood function get The expression is as follows: .
[0012] Preferably, step S4 specifically includes the following steps: S41, the failure of an intermittently faulty component satisfies the following two conditions: a fault occurs, and the combined intermittent fault degradation characteristic value of the fault exceeds the failure threshold; the failure process of an intermittently faulty component is defined as an event-triggered coordinated failure process, and its failure time is expressed as: ; In the formula, This indicates the pre-set failure threshold. This represents a very short time interval during which a failure will occur only once. Indicates the earliest time when the condition is met; S42, intermittently faulty components at time... The reliability function is expressed as at time... The reliability function is the product of the probability that no joint intermittent failure degradation eigenvalue exceeds the failure threshold, expressed as follows: ; In the formula, The probability that a fault occurs and the combined intermittent fault degradation characteristic value exceeds the failure threshold is expressed as follows: ; In the formula, ; ; ; In the formula, , , and These represent the number of intermittently faulty components in service. The amount of internal degradation and the time of failure at the time of the failure; S43, to Differentiation yields: ; In the formula, ; joint and The reliability function is expressed as follows: ; In the formula, , ; S44, Definition and At time respectively The failure time and remaining service life of in-service intermittently faulty components; The probability density distribution function is derived from The negative derivative is obtained as follows: ; The probability density distribution function can be based on The result is represented as follows: .
[0013] The present invention also provides a readable storage medium having a computer program stored thereon, which, when executed, implements the method for intermittent fault diagnosis and remaining useful life prediction of a hybrid system.
[0014] The present invention also provides an electronic device, which includes a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the intermittent fault diagnosis and remaining service life prediction method for a hybrid system.
[0015] The present invention also provides a computer program product comprising a computer program / instruction that, when executed by a processor, implements the intermittent fault diagnosis and remaining useful life prediction method for a hybrid system.
[0016] The advantages of this invention are: (1) This invention introduces a double stochastic process model to describe the degradation and occurrence process of intermittent faults, wherein the non-homogeneous Poisson process model is used to characterize the fault occurrence process and the Wiener process model is used to describe the fault degradation process.
[0017] (2) This invention proposes a multi-stage expectation maximization algorithm for estimating unknown parameters of a double stochastic process model.
[0018] (3) This invention proposes an event-triggered collaborative failure process to describe the failure mechanism of intermittently faulty components, and derives the probability density distribution function of the failure time of intermittently faulty components based on this process. Attached Figure Description
[0019] Figure 1 This is a flowchart of the method of the present invention.
[0020] Figure 2 This is a circuit diagram of a hybrid circuit system in an example of the present invention.
[0021] Figure 3 This is the residual response in an example of the present invention.
[0022] Figure 4 This is the fault identification result in an example of the present invention.
[0023] Figure 5 This refers to the combined intermittent fault degradation features extracted in the examples of this invention.
[0024] Figure 6 This is a prediction diagram of the remaining service life of the hybrid circuit system in an example of the present invention. Detailed Implementation
[0025] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0026] Depend on Figure 1 As shown, a method for intermittent fault diagnosis and remaining service life prediction of a hybrid system includes the following steps: S1, Fault diagnosis of hybrid systems based on extended Kalman filter algorithm; S2, Construct a double stochastic process model to describe the degradation process and failure occurrence process of intermittently faulty components; S3, using the multi-stage expectation-maximization algorithm to estimate the unknown parameters of the double stochastic process model; S4 proposes the concept of event-triggered collaborative failure process and derives the probability density distribution function of the remaining useful life of intermittently faulty components based on the failure mechanism of this process.
[0027] Step S1 includes the following specific steps: S11, Establish the state-space equations for the hybrid system. A hybrid system contains several continuous and discrete elements. The states of continuous elements are continuous, such as capacitors and inductors in an analog circuit system. Discrete elements have only two states (i.e., open and closed), such as hydraulic valves in a hydraulic system and circuit breakers in an electrical system. The mathematical model of a hybrid system can be expressed as: (1) In the formula, Represents the state vector. Represents the model parameter vector. Indicates the output vector. Represents the input vector. and These represent the process noise vector and the measurement noise vector, respectively. Indicates system mode, Indicates the first The state of a discrete component , This indicates the number of discrete components in a hybrid system. and Representing the patterns respectively The state transition equations and output equations are as follows: express The first derivative.
[0028] In this embodiment, the hybrid system in step S11 is represented by a hybrid circuit system. The circuit diagram of this hybrid circuit system is shown below. Figure 2 As shown, it contains two capacitors. and 4 resistors , , and 2 switches and 2 voltage sources and and two voltage sensors and The mathematical model of a hybrid circuit system is expressed as follows: ; In the formula, , , , , , , , and They represent , , and The efficiency factor.
[0029] S12, construct the extended Kalman filter. The extended Kalman filter is represented as: (2) In the formula, Indicates the number of time steps Prior state estimation, and Indicates time The system parameter vector and input quantities, This represents the Jacobian matrix formed by the first-order partial derivatives of the state transition function with respect to the state. Indicates time The prior estimation error covariance matrix, and Let these represent the system process noise covariance and the observation noise covariance, respectively. Indicates time Prior observation estimates, This represents the Jacobian matrix formed by the first-order partial derivatives of the observation function with respect to the state. Represents the Kalman gain matrix. Indicates time The system observations, and Indicates time The posterior state estimate and the posterior estimate error covariance matrix, Represents the identity matrix. S13, by comparing the magnitudes of the prior observation estimates obtained in S12 with the measured values, the residual vector can be obtained, as shown below: (3) In the formula, Represents the residual vector. Indicates the number of time steps The first time One residual, This represents the total number of residuals.
[0030] When the system is fault-free, every calculated residual will be below the fault threshold. However, when a component in the system fails, at least one residual will exceed the fault threshold. By comparing the residuals with the residual threshold, fault detection can be performed on hybrid systems.
[0031] S14. In order to identify the amplitude, occurrence time, and disappearance time of each fault in the intermittently faulty component, it is necessary to obtain the amplitude time history curve of the faulty component. Provide a parameterized description: (4) In the formula, The nominal value of the parameter indicating the faulty component. , and They represent the first The magnitude, occurrence time, and disappearance time of the fault. This represents the unit step function.
[0032] By combining the system state and the parameters of the faulty component, the augmented state vector can be obtained as follows: . This represents the transpose (lateral quantity) of the state vector at time step k. The fault parameter value represents the time step k.
[0033] S15 utilizes an enhanced extended Kalman filter for fault identification, characterized by the introduction of an auxiliary factor to enhance the posterior state error covariance, as shown below: (5) In the formula, This represents the augmented posterior state error covariance. Indicates the enhanced threshold. This indicates an enhancing factor.
[0034] Step S2 includes the following specific steps: S21, based on the amplitude of each fault obtained from fault identification. Time of occurrence and the moment of disappearance A joint intermittent fault degradation feature is constructed to describe the severity of each fault, as shown below: (6) In the formula, Indicates the first The combined intermittent fault degradation characteristic value of the secondary fault.
[0035] S22 describes the degradation process of intermittently failing components through both internal degradation processes and external impacts. The specific steps are as follows: S221, the degradation process of intermittently faulty components is represented as follows: (7) In the formula, This indicates an internal degradation process. Indicates instantaneous external impact. The first character represents the first element that follows a gamma distribution. External impact amount during the occurrence of the secondary failure. and The shape parameter representing the gamma distribution. Indicates the end time The number of times the fault occurred Represents the Dirac function, Indicates time The amount of degradation.
[0036] S222 describes the internal degradation process using a Wiener process with mode-dependent drift coefficients, as follows: (8) In the formula, This represents the initial internal degradation amount that follows a normal distribution. Representation pattern The drift coefficient below, This represents the nonlinear equation used to describe the nonlinear degradation process. Indicates the time of the first occurrence of the intermittent fault. Indicates the diffusion coefficient. This represents the standard Brownian motion process.
[0037] S23 describes the occurrence of intermittent faults using a non-homogeneous Poisson process with fault occurrence rates exhibiting pattern dependence and internal degradation dependence. This fault occurrence rate is expressed as: (9) In the formula, Represents pattern dependency factor, Indicates internal degradation dependency factor. Indicates time The failure rate.
[0038] S24. Based on the two stochastic processes described in S22 and S23, a dual stochastic process model is constructed to simultaneously describe the degradation and occurrence processes of intermittent faults. Its expression is as follows: (10) In the formula, Indicates the time interval Internal occurrence The probability of a secondary failure.
[0039] Step S3 includes the following specific steps: S31, utilizing A historical degradation dataset is constructed from a combined historical intermittent fault degradation feature dataset of several similar components, and is represented as follows: (11) In the formula, Indicates the first A dataset of historical intermittent fault degradation features of similar components. , and These represent the first faults obtained through fault identification. The first of the same type of components The fault occurrence time, combined intermittent fault degradation characteristic value, and total number of faults for each fault.
[0040] S32, in the multi-stage expectation-maximization algorithm... During the phase, the time interval Divided into equal parts The process involves several parts. By integrating each part numerically and summing the results, the stochastic integral is obtained. The approximation value is represented as follows: (12) In the formula, Indicates the first Time interval in the phase The first Numerical integration results for each part, , Indicates time The amount of internal degradation, Indicates time interval The first One dividing point, This indicates the time interval between adjacent dividing points.
[0041] S33, based on the statistical properties of Wiener processes, gamma distributions, and non-homogeneous Poisson processes, in the multi-stage expectation-maximization algorithm... In this stage, the log-likelihood function of the unknown parameters of the double stochastic process model can be expressed as: (13) In the formula, (14) (15) (16) (17) This represents the set of unknown parameters in a double stochastic process model. This represents the difference in internal degradation between two adjacent dividing points. Represents the complete gamma function. , ; Indicative functions are represented as follows: (18) S34, the Expectation-Maximization (EM) algorithm consists of two main steps: the E-step (expectation step) and the M-step (maximization step). These two steps are executed alternately in each iteration to continuously optimize the model's parameters until convergence to a local optimum. In the E-step, given the current parameter estimates, the posterior distribution of the latent variables (or missing data) is calculated, thus constructing the expected value for the complete data. In the M-step, the model's parameter estimates are updated by maximizing the expected log-likelihood function obtained in the E-step. Therefore, the multi-stage Expectation-Maximization algorithm... The specific steps for updating unknown parameters in stages are as follows: S341, in step E, uses a particle smoother for calculation. , , and The expectation, that is , , and .
[0042] The particle smoother consists of two steps: forward filtering and backward smoothing. Assume the number of particles is... In forward filtering, the first Particles The update steps are as follows: (19) (20) In the formula, ; ; In backward smoothing, the particle state remains unchanged; only the particle weights are updated. The expression for updating the particle weights is as follows: (twenty one) In the formula, .
[0043] Based on the above formula , , and It can be calculated using the following formula: (twenty two) (twenty three) (twenty four) (25) Therefore, the expected log-likelihood function can be expressed as: (26) In the formula, (27) (28) (29) (30) Indicates the first Phase 1 The next iteration The estimated value, and Indicates based on calculate and The value of .
[0044] S342, in step M, can be obtained by maximizing equation (26). The expression is as follows: (31) S35, after completing the first... After applying the expectation-maximization algorithm for this stage, the estimated result for this stage is... Compared with the estimation results of the previous stage The comparison is performed, and if the difference in their log-likelihood functions is less than a pre-set termination value, that is... If the algorithm converges, the result obtained at this stage is considered the final estimate. .
[0045] Step S4 includes the following specific steps: S41, the failure of an intermittently faulty component requires the following two conditions to be met: (1) a fault occurs; (2) the combined intermittent fault degradation characteristic value of the fault exceeds the failure threshold. Therefore, the failure process of an intermittently faulty component can be defined as an event-triggered coordinated failure process, and its failure time can be expressed as: (32) In the formula, This indicates the pre-set failure threshold. This represents a very short time interval during which a failure will occur only once.
[0046] S42, intermittently faulty components at time... The reliability function can be expressed as time... The reliability function is the product of the probability that no joint intermittent failure degradation eigenvalue exceeds the failure threshold, expressed as follows: (33) In the formula, The probability that a fault occurs and the combined intermittent fault degradation characteristic value exceeds the failure threshold can be expressed as follows: (34) In the formula, (35) (36) (37) In the formula, , , and These represent the number of intermittently faulty components in service. The amount of internal degradation and the time of failure at the time of the failure.
[0047] S43, differentiating equation (33) yields: (38) In the formula, .
[0048] Combining equations (33) and (38), the reliability function can be expressed as follows: (39) In the formula, , .
[0049] S44, Definition and At time respectively The failure time and remaining service life of the in-service intermittently failing components. Then, The probability density distribution function can be derived from The negative derivative is obtained as follows: (40) The probability density distribution function can be obtained from equation (40), and is expressed as follows: (41) In this embodiment, to verify the effectiveness of the proposed intermittent fault diagnosis and remaining useful life prediction method for hybrid systems, experimental verification was conducted, and the experimental results are as follows: The experiment changed the actuator effective factors To inject faults, the designed double-stochastic process model is as follows: , , , , , , , , , , , , , , Each mode lasts for 50 seconds, and the mode changes in the following order: To obtain sufficient failure data to verify the effectiveness of the proposed method, four independent sets of degradation data were generated based on the designed double-stochastic process model. The first three sets were used as degradation data for historical intermittently faulty components, and the fourth set was used as degradation data for in-service intermittently faulty components. The fault detection results are as follows: Figure 3As shown, the dashed line represents the threshold, set to 0.005. From Figure 3 It can be observed that the times for the first fault detection in the four independent runs were 213.37 seconds, 58.57 seconds, 146.48 seconds, and 236.02 seconds, respectively. After the fault was detected, the state vector was augmented as follows: Fault identification was performed using an enhanced extended Kalman filter, and the identification results are as follows: Figure 4 As shown, the dashed lines represent the identification results, and the solid lines represent the design values. Based on the occurrence time, disappearance time, and amplitude of each fault obtained from the fault identification results, the degradation characteristics of the joint intermittent fault can be calculated, as shown in the figure. Figure 5 As shown, the asterisks and circles represent the designed and calculated joint intermittent fault degradation characteristic values, respectively. The location parameters of the double stochastic process model are estimated using a multi-stage expectation-maximization algorithm and a dataset of joint intermittent fault degradation characteristics from historical components. The estimation results are as follows: , , , , , , , , , , , , , , Based on the estimation results, the remaining service life of in-service intermittently failing components can be predicted. The prediction results are as follows: Figure 6 As shown, the red solid line represents the probability density curve, the black dotted line represents the actual remaining useful life, and the blue dashed line represents the average predicted remaining useful life. The calculation formula is... .
[0050] In this embodiment, the nominal parameter values of the hybrid circuit system are shown in Table 1 below: Table 1 .
[0051] Example 2 An electronic device includes a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the intermittent fault diagnosis and remaining service life prediction method for a hybrid system according to Embodiment 1 above.
[0052] The electronic device in this application embodiment may be the mobile device itself, or a standalone device independent of it. The standalone device may communicate with the mobile device to receive the collected input signals from it and send the selected target decision behavior to it.
[0053] An electronic device includes one or more processors and memory. The processor may be a central processing unit (CPU) or other processing unit with data processing capabilities and / or instruction execution capabilities, and may control other components in the electronic device to perform desired functions. The memory may include one or more computer program products, which may include various forms of computer-readable storage media, such as volatile memory and / or non-volatile memory. The volatile memory may, for example, include random access memory (RAM) and / or cache memory. The non-volatile memory may, for example, include read-only memory (ROM), hard disk, flash memory, etc. One or more computer program instructions may be stored on the computer-readable storage medium, and the processor may execute the program instructions to implement the decision-making behavior and decision-making methods of the various embodiments of this application described above, and / or other desired functions.
[0054] Electronic devices may also include input devices and output devices.
[0055] Example 3 In addition to the methods and devices described above, embodiments of this application may also be computer program products, which include computer program instructions that, when executed by a processor, cause the processor to perform the steps in the decision-making behavior method according to various embodiments of this application as described in Embodiment 1 above.
[0056] The computer program product can be written in any combination of one or more programming languages to perform the operations of the embodiments of this application. The programming languages include object-oriented programming languages such as Java and C++, as well as conventional procedural programming languages such as C or similar languages. The program code can be executed entirely on the user's computing device, partially on the user's computing device, as a standalone software package, partially on the user's computing device and partially on a remote computing device, or entirely on a remote computing device or server.
[0057] Example 4 Embodiments of this application may also be computer-readable storage media storing computer program instructions thereon, which, when executed by a processor, cause the processor to perform the steps in the decision-making behavior decision-making method according to various embodiments of this application described in Embodiment 1 above.
[0058] The computer-readable storage medium may be any combination of one or more readable media. A readable medium may be a readable signal medium or a readable storage medium. A readable storage medium may, for example, include, but is not limited to, electrical, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatuses, or devices, or any combination thereof. More specific examples of readable storage media (a non-exhaustive list) include: electrical connections having one or more wires, portable disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof.
[0059] The above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.
Claims
1. A method for intermittent fault diagnosis and remaining service life prediction of a hybrid system, characterized in that, Includes the following steps: S1, Fault diagnosis of hybrid systems based on extended Kalman filter algorithm; S2, Construct a double stochastic process model to describe the degradation process and failure occurrence process of intermittently faulty components; S3, using the multi-stage expectation-maximization algorithm to estimate the unknown parameters of the double stochastic process model; S4 proposes the concept of event-triggered collaborative failure process and derives the probability density distribution function of the remaining useful life of intermittently faulty components based on the failure mechanism of this process.
2. The method for intermittent fault diagnosis and remaining service life prediction of a hybrid system according to claim 1, characterized in that, Step S1 specifically includes the following steps: S11, Establish the state-space equations of the hybrid system; the hybrid system contains several continuous and discrete elements; the mathematical model of the hybrid system is expressed as: In the formula, Represents the state vector. Represents the model parameter vector. Indicates the output vector. Represents the input vector. and These represent the process noise vector and the measurement noise vector, respectively. Indicates system mode, Indicates the first The state of a discrete component , This indicates the number of discrete components in a hybrid system. and Representing the patterns respectively The state transition equations and output equations are as follows: express The first derivative; S12, Construct the extended Kalman filter, which is expressed as: In the formula, Indicates the number of time steps Prior state estimation, and Indicates time The system parameter vector and input quantities, This represents the Jacobian matrix formed by the first-order partial derivatives of the state transition function with respect to the state. Indicates time The prior estimation error covariance matrix, and Let these represent the system process noise covariance and the observation noise covariance, respectively. Indicates time Prior observation estimates, This represents the Jacobian matrix formed by the first-order partial derivatives of the observation function with respect to the state. Represents the Kalman gain matrix. Indicates time The system observations, and Indicates time The posterior state estimate and the posterior estimate error covariance matrix, Represents the identity matrix; S13, by comparing the prior observation estimates obtained in S12 With measured value To obtain the residual vector, we can determine the magnitude relationship between them. In the formula, Represents the residual vector. Indicates the number of time steps The first time One residual; When the system is fault-free, each residual is below the fault threshold; when a component of the system fails, at least one residual exceeds the fault threshold. Fault detection in hybrid systems is achieved by comparing residuals with residual thresholds. S14, In order to identify the amplitude, occurrence time, and disappearance time of each fault of the intermittent faulty component, the amplitude time history curve of the faulty component is... Provide a parameterized description: In the formula, The nominal value of the parameter indicating the faulty component. , and They represent the first The magnitude, occurrence time, and disappearance time of the fault. Represents the unit step function; By combining the system state and faulty component parameters, the augmented state vector is obtained as follows: ; S15 utilizes an enhanced extended Kalman filter for fault identification, introducing an enhancement factor to strengthen the posterior state error covariance, as shown below: In the formula, This represents the augmented posterior state error covariance. Indicates the enhanced threshold. This indicates an enhancing factor.
3. The method for intermittent fault diagnosis and remaining service life prediction of a hybrid system according to claim 2, characterized in that, Step S2 specifically includes the following steps: S21. Based on the amplitude, occurrence time, and disappearance time of each fault obtained from fault identification, a joint intermittent fault degradation feature is constructed to describe the severity of each fault, as shown below: In the formula, Indicates the first The combined intermittent fault degradation characteristic value of the sub-fault; S22 describes the degradation process of intermittently failing components through both internal degradation processes and external shocks. The specific steps are as follows: S221, the degradation process of intermittently faulty components is represented as follows: In the formula, This indicates an internal degradation process. Indicates instantaneous external impact. The first character represents the first element that follows a gamma distribution. External impact amount during the occurrence of the secondary failure. and The shape parameter representing the gamma distribution. Indicates the end time The number of failures Represents the Dirac function, express The amount of degradation at any given time; S222, using a Wiener process with mode-dependent drift coefficients, describes the internal degradation process as follows: In the formula, This represents the initial internal degradation amount that follows a normal distribution. These represent the initial mean and variance of internal degradation, respectively. Representation pattern The drift coefficient below, This represents the nonlinear equation used to describe the nonlinear degradation process. Indicates the time of the first occurrence of the intermittent fault. Indicates the diffusion coefficient. To represent the standard Brownian motion process, Represents the integral variable. Indicates model parameters; S23 describes the occurrence process of intermittent faults using a non-homogeneous Poisson process with fault occurrence rates exhibiting pattern dependence and internal degradation dependence. This fault occurrence rate is expressed as: In the formula, Represents pattern dependency factor, Indicates internal degradation dependency factor. express Failure rate at any given time; S24. Based on the two stochastic processes described in S22 and S23, a dual stochastic process model is constructed to simultaneously describe the degradation and occurrence processes of intermittent faults. Its expression is as follows: In the formula, Indicates the time interval Internal occurrence The probability of secondary failures; They represent the cutoff times respectively. , The number of times the fault occurred.
4. The method for intermittent fault diagnosis and remaining service life prediction of a hybrid system according to claim 3, characterized in that, In step S3, a multi-stage expectation-maximization algorithm is designed to estimate the unknown parameters of the double stochastic process model, as follows: S31, utilizing A historical degradation dataset is constructed by combining historical intermittent fault degradation feature datasets of several similar components, as shown below: In the formula, Indicates the first A dataset of historical intermittent fault degradation features of similar components. , and These represent the first faults obtained through fault identification. The first of the same type of components The fault occurrence time, combined intermittent fault degradation characteristic value, and total number of faults; S32, in the multi-stage expectation-maximization algorithm... During the phase, the time interval Divided into equal parts The random integral is obtained by integrating each part numerically and summing the results. The approximation value is represented as follows: In the formula, Indicates the first Time interval in the phase The first Numerical integration results for each part, , Indicates time The amount of internal degradation, Indicates time interval The first One dividing point, Indicates the time interval between adjacent dividing points; S33, based on the statistical properties of Wiener processes, gamma distributions, and non-homogeneous Poisson processes, in the multi-stage expectation-maximization algorithm... In this stage, the log-likelihood function of the unknown parameters of the double stochastic process model is expressed as: In the formula, In the formula, This represents the set of unknown parameters in a double stochastic process model. This represents the difference in internal degradation between two adjacent dividing points. Represents the complete gamma function. , Indicative functions are represented as follows: In the formula, This indicates the first result obtained through fault identification. The first of the same type of components The time of occurrence of this fault. express The pattern of time, Indicates a specific pattern; S34, the Expectation-Maximization algorithm consists of two main steps: the E-step (expectation step) and the M-step (maximization step). By alternately executing these two steps in each iteration, the model parameters are continuously optimized until convergence to a local optimum. In the E-step, given the current parameter estimates, the posterior distribution of the latent variables is calculated, thereby constructing the expected value of the complete data. In the M-step, the model parameter estimates are updated by maximizing the expected log-likelihood function obtained in the E-step. S35, after completing the first... After applying the expectation-maximization algorithm for this stage, the estimated result for this stage is... Compared with the estimation results of the previous stage The comparison is performed, and if the difference in their log-likelihood functions is less than a pre-set termination value, that is... If the algorithm converges, the result obtained at this stage is considered the final estimate. .
5. The method for intermittent fault diagnosis and remaining service life prediction of a hybrid system according to claim 4, characterized in that, In step S34, the multi-stage expectation-maximization algorithm... The specific steps for updating unknown parameters in stages are as follows: S341, in step E, uses a particle smoother for calculation. , , and The expectation, that is , , and ; The particle smoother consists of two steps: forward filtering and backward smoothing; assuming the number of particles is... In forward filtering, the first Particles The update steps are as follows: In the formula, In backward smoothing, the particle state remains unchanged, and only the particle weights are updated; the expression for updating the particle weights is as follows: In the formula, ; Based on the above formula , , and It is calculated using the following formula: Therefore, the expected log-likelihood function Represented as: In the formula, In the formula, Indicates the first Phase 1 The next iteration The estimated value, and Indicates based on calculate and value S342, in the M-step, by maximizing the expected log-likelihood function get The expression is as follows: 。 6. A method for intermittent fault diagnosis and remaining service life prediction of a hybrid system according to claim 4 or 5, characterized in that, Step S4 specifically includes the following steps: S41, the failure of an intermittently faulty component satisfies the following two conditions: a fault occurs, and the combined intermittent fault degradation characteristic value of the fault exceeds the failure threshold; the failure process of an intermittently faulty component is defined as an event-triggered coordinated failure process, and its failure time is expressed as: In the formula, This indicates the pre-set failure threshold. This represents a very short time interval during which a failure will occur only once. Indicates the earliest time when the condition is met; S42, intermittent faulty element at time The reliability function is expressed as time... The reliability function is the product of the probability that no joint intermittent failure degradation eigenvalue exceeds the failure threshold, expressed as follows: In the formula, The probability that a fault occurs and the combined intermittent fault degradation characteristic value exceeds the failure threshold is expressed as follows: In the formula, In the formula, , , and These represent the number of intermittently faulty components in service. The amount of internal degradation and the time of failure at the time of the failure; S43, to Differentiation yields: In the formula, ; joint and The reliability function is expressed as follows: In the formula, , ; S44, Definition and At time respectively The failure time and remaining service life of in-service intermittently faulty components; The probability density distribution function is derived from The negative derivative is obtained as follows: The probability density distribution function can be based on The result is represented as follows: 。 7. A readable storage medium, characterized in that, It stores a computer program, which, when executed, implements the intermittent fault diagnosis and remaining service life prediction method for a hybrid system as described in any one of claims 1 to 6.
8. An electronic device, characterized in that, It includes a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the intermittent fault diagnosis and remaining service life prediction method for a hybrid system according to any one of claims 1 to 6.
9. A computer program product, characterized in that, It includes a computer program / instruction that, when executed by a processor, implements the intermittent fault diagnosis and remaining useful life prediction method for a hybrid system as described in any one of claims 1 to 6.