Fault Detection Observer Design Method Based on Simulated Annealing Algorithm

Abstract

The present invention relates to a fault detection observer design method based on a simulated annealing algorithm. The method comprises: establishing an MJSs model and an FDO model; improving the event triggering mechanism of the MJSs model and setting a dynamic event triggering mechanism; setting an evaluation function value and a threshold value for the FDO model, and setting an H∞ / H‑index; designing several Lyapunov functions to obtain a target nonlinear matrix inequality, and introducing a simulated annealing algorithm into the target nonlinear matrix inequality, solving the dynamic event triggering mechanism, the evaluation function value and the threshold value, and the H∞ / H‑index to obtain dynamic event triggering mechanism parameters and FDO parameters; designing a fault detection observer based on the dynamic event triggering mechanism parameters and the FDO parameters. Since the simulated annealing algorithm is introduced to solve the coupling term problem in the nonlinear matrix inequality, the conservatism is completely removed, so that the obtained fault detection observer has the global optimal anti-disturbance robustness and fault sensitivity performance.

Description

Technical Field

[0001] The present invention relates to the technical field of fault detection, and in particular to a fault detection observer design method based on a simulated annealing algorithm. Background Art

[0002] In recent years, the study of Markov Jump Systems (MJSs) has gradually attracted attention. In practical engineering applications, structural changes of the system are usually inevitable due to factors such as component failure or external interference, and MJS is very effective in simulating these situations. At present, MJS has been widely used in various fields such as circuit systems and unmanned vehicle systems.

[0003] In contemporary industrial processes, equipment may fail over time due to aging or other factors, bringing the risk of significant property losses or safety issues. Therefore, it is imperative to develop methods for timely fault detection, which has led to an increasing focus on the design of Fault Detection Observers (FDOs). The main goal of FDOs is to identify anomalies and deviations from expected behavior and improve overall system performance. Typically, FDOs do this by comparing the residual signal with a predefined evaluation function, enabling it to detect system failures and issue warnings as promptly as possible.

[0004] However, traditional fault detection observers suffer from poor observation effects and low sensitivity to faults. Summary of the invention

[0005] Based on this, in order to solve the above technical problems, a fault detection observer design method based on simulated annealing algorithm is provided, which can optimize the anti-disturbance robustness and fault sensitivity performance.

[0006] A fault detection observer design method based on a simulated annealing algorithm, the method comprising:

[0007] Establish the Markov jump system MJSs model and the fault detection observer FDO model;

[0008] The event triggering mechanism of the MJSs model is improved, the time point of data transmission is dynamically adjusted through the auxiliary dynamic variables in the Markov jump system, and a dynamic event triggering mechanism is set;

[0009] Setting an evaluation function value and a threshold for the FDO model, and setting an H∞ / H-index;

[0010] Design several Lyapunov functions to obtain the target nonlinear matrix inequality, introduce the simulated annealing algorithm into the target nonlinear matrix inequality, solve it based on the dynamic event trigger mechanism, the evaluation function value and the threshold, and the H∞ / H-index, and obtain the dynamic event trigger mechanism parameters and FDO parameters;

[0011] A fault detection observer is designed based on the dynamic event triggering mechanism parameters and the FDO parameters.

[0012] In one embodiment, the state space expression and transition probability matrix of the MJSs model are:

[0013]

[0014] π ij =Prob{r(k+1)=j|r(k)=i}

[0015] Where x(k) is the system state, y(k) is the measured output, ω(k) is the external disturbance, f(k) is the fault signal, and A r(k) , B r(k) , C r(k) and D r(k) is a known matrix, π ij represents the transfer probability matrix, has dimension for each r(k)=i, j represents the system mode at time k+1, and has the same value range as i.

[0016] In one embodiment, the FDO model is:

[0017]

[0018] in, r(k) are the state, output, and residual signal of FDO, respectively. i , L i , D i , γ are both known matrices.

[0019] In one embodiment, under the dynamic event triggering mechanism, the time determination condition for data transmission is:

[0020]

[0021] Where f(k,m(k))=e T (k)Ψ i e(k)-δ i m(k)y T (k)Ψ iy(k), i is the mode related to the system, μ(k) and m(k) are two auxiliary dynamic variables set to dynamically adjust the trigger threshold; λ, κ, ρ and ∈ are preset positive scalars, k s represents the time when the event trigger mechanism is triggered for the sth time, e(k) = y(k) - y(k s ), represents the k moment and k s The difference in output signals is measured at all times.

[0022] In one embodiment, the evaluation function value is: The thresholds are:

[0023] Among them, k0 represents the initial evaluation time, t is the evaluation step length, r e (k) = r(k) - f(k), Represents r e The transpose of (k).

[0024] In one embodiment, the method further comprises:

[0025] Assuming zero initial conditions, the Markov jump system is stochastically stable and satisfies: Then the Markov jump system has H ∞ The index γ>0; ω(k) represents the external disturbance, ω T (k) represents the transpose of ω(k).

[0026] In one embodiment, the method further comprises:

[0027] Assuming zero initial conditions, the Markov jump system is stochastically stable and satisfies: Then the Markov jump system has H - Indicator β<0; f(k) indicates a fault signal, f T (k) represents the transpose of f(k).

[0028] In one embodiment, the target nonlinear matrix inequality is:

[0029]

[0030]

[0031]

[0032]

[0033] in, All are matrices; P 1i ,P 2i is a positive definite symmetric matrix, m,s,κ,∈,ρ,τ1<1; v>1 is a preset positive scalar,

[0034] In one embodiment, the simulated annealing algorithm construction process includes:

[0035] Converting the target nonlinear matrix inequality into a set of linear matrix inequalities to determine the target function;

[0036] Substituting the initial value into the linear matrix inequality to calculate the initial value of the objective function;

[0037] Initialize the simulated annealing algorithm parameters and perform iterative calculations until the maximum number of iterations is met, and then construct a simulated annealing algorithm.

[0038] In one embodiment, the objective function is ι(γ,β);

[0039] When initializing the simulated annealing algorithm parameters and performing iterative calculations, ι(γ,β) is minimized; where γ is H ∞ Index parameter, β is H - Indicator parameters.

[0040] The above-mentioned fault detection observer design method based on the simulated annealing algorithm can save resources by setting a dynamic event trigger mechanism; by setting the H∞ / H-indicator to quantify the standard, it can ensure that the designed fault detection observer has both robustness against disturbances and sensitivity to faults; since the simulated annealing algorithm is introduced to solve the coupling term problem in the nonlinear matrix inequality, the conservatism is completely removed, so that the obtained fault detection observer has the global optimal robustness against disturbances and sensitivity to faults. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 It is the fault detection structure diagram of MJSs;

[0042] Figure 2 is a flow chart of a fault detection observer design method based on a simulated annealing algorithm in one embodiment;

[0043] Figure 3 A schematic diagram of the objective function value for each iteration of the simulated annealing algorithm;

[0044] Figure 4 It is a schematic diagram of the state change trajectory of the Markov jump system;

[0045] Figure 5 This is a diagram showing the performance of FDO. DETAILED DESCRIPTION

[0046] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0047] The fault detection observer design method based on the simulated annealing algorithm provided in the embodiment of the present application can be used for fault detection. In this embodiment, the fault detection structure of the Markov jump system MJSs is as follows: Figure 1 As shown, the fault detection observer FDO can be connected to the network to realize fault detection.

[0048] In one embodiment, Figure 2 As shown, a fault detection observer design method based on a simulated annealing algorithm is provided, comprising the following steps:

[0049] Step 202: Establish a Markov jump system MJSs model and establish a fault detection observer FDO model.

[0050] First, MJSs modeling and FDO modeling can be carried out. Specifically, the state space expression of MJSs is established and the transition probability matrix of the jump between modes is given.

[0051] In one embodiment, the state space expression and transition probability matrix of the MJSs model are:

[0052]

[0053] π ij =Prob{r(k+1)=j|r(k)=i}

[0054] Where x(k) is the system state, y(k) is the measured output, ω(k) is the external disturbance, f(k) is the fault signal, and A r(k) , B r(k) , C r(k) and D r(k) is a known matrix, π ij represents the transfer probability matrix, has dimension for each r(k)=i, j represents the system mode at time k+1, and has the same value range as i.

[0055] The purpose of FDO modeling is to generate residual signals in the presence of fault signals. The FDO model is:

[0056]

[0057] in, They are the state, output, and residual signal of FDO, A i , L i , D i , γ are both known matrices.

[0058] Step 204, improve the event triggering mechanism of the MJSs model, dynamically adjust the time point of data transmission through the auxiliary dynamic variables in the Markov jump system, and set the dynamic event triggering mechanism.

[0059] By improving the traditional event trigger mechanism, the time point of data transmission in the Markov jump system can be adjusted through two auxiliary dynamic variables related to the system state. The purpose of introducing the dynamic event trigger mechanism is to improve the utilization rate of network communication resources.

[0060] Specifically, in one embodiment, under the dynamic event triggering mechanism, the time determination condition for data transmission is:

[0061]

[0062] Where f(k,m(k))=e T (k)Ψ i e(k)-δ i m(k)y T (k)Ψ i y(k), i is the mode related to the system, μ(k) and m(k) are two auxiliary dynamic variables set to dynamically adjust the trigger threshold; λ, κ, ρ and ∈ are preset positive scalars, k s represents the time when the event trigger mechanism is triggered for the sth time, e(k) = y(k) - y(k s ), represents the k moment and k s The difference in output signals is measured at all times.

[0063] Step 206: Setting the evaluation function value and threshold for the FDO model, and setting the H∞ / H-index.

[0064] By comparing the set evaluation function value with the threshold, the time point when the fault signal occurs can be determined.

[0065] In one embodiment, the evaluation The thresholds are:

[0066] Among them, k0 represents the initial evaluation time, t is the evaluation step length, r e (k) = r(k) - f(k), Represents r e The transpose of (k).

[0067] Through the designed evaluation function value and threshold, the fault detection process can be implemented using decision logic, where the decision logic can be expressed as:

[0068] The significance of setting the H∞ index is to quantify the robustness of the designed FDO to external disturbances, and the significance of setting the H-index is to quantify the sensitivity of the designed FDO to internal faults.

[0069] In one embodiment, the H∞ indicator is defined as follows: Under the assumption of zero initial conditions, if the MJSs are stochastically stable and satisfy: It is believed that MJSs have H ∞ The index γ>0; ω(k) represents the external disturbance, ω T (k) represents the transpose of ω(k).

[0070] In one embodiment, H - The indicator is defined as: Under the assumption of zero initial conditions, if MJSs are stochastically stable and satisfy: It is considered that MJSs have H-index β<0; f(k) represents the fault signal, f T (k) represents the transpose of f(k).

[0071] Step 208, design several Lyapunov functions to obtain the target nonlinear matrix inequality, and introduce the simulated annealing algorithm into the target nonlinear matrix inequality, solve it based on the dynamic event trigger mechanism, the evaluation function value and the threshold, and the H∞ / H-index, and obtain the dynamic event trigger mechanism parameters and FDO parameters.

[0072] By designing multiple Lyapunov functions, a set of target nonlinear matrix inequalities that can meet the design objectives can be obtained.

[0073] In one embodiment, the target nonlinear matrix inequality is:

[0074]

[0075]

[0076]

[0077]

[0078] in, All are matrices; P 1i ,P 2i is a positive definite symmetric matrix, m,s,κ,∈,ρ,τ1<1; ν>1 is a preset positive scalar,

[0079] However, these conditions involve coupling terms, which cause the inequality to be nonlinear, making it impossible to solve it directly using a convex algorithm. Although these problems can be solved by introducing a relaxation matrix and manually setting parameters, these practices will lead to increased conservatism and bring challenges in balancing system performance and network resource utilization. Therefore, the simulated annealing algorithm SAA can be introduced to solve the problem, thereby obtaining the dynamic event triggering mechanism parameters and FDO parameters with global optimal robustness to external disturbances and sensitivity to internal faults.

[0080] Specifically, the design of FDO can be expressed as a minimization problem:

[0081]

[0082] stl 1i ,…,l ni >0,τ1,τ2>0,δ i >0,κ>0,λ>0

[0083] in, The objective parameter to be optimized is represented by the H∞ index, which represents the robustness of FDO to external disturbances, and the goal is to minimize its value to reduce the impact of external disturbances on the residual. The H-index represents the sensitivity of FDO to internal faults, and the goal is to maximize its value. Therefore, the ultimate goal is to achieve the minimum possible value.

[0084] Therefore, the minimization problem can be handled by constructing a simulated annealing algorithm SAA.

[0085] In one embodiment, the simulated annealing algorithm construction process includes: converting the target nonlinear matrix inequality into a set of linear matrix inequalities to determine the objective function; substituting the initial value into the linear matrix inequality to calculate the initial value of the objective function; initializing the simulated annealing algorithm parameters and performing iterative calculations until the maximum number of iterations is met, thereby constructing a simulated annealing algorithm.

[0086] Specifically, the simulated annealing algorithm construction process may include parameter initialization, SAA initialization, SAA main program execution, SAA termination criteria, and finally the FDO is designed.

[0087] Among them, in the process of parameter initialization, the upper and lower bounds of the initial parameters can select random values ​​within the set range as the initial solution, and then the nonlinear matrix inequality can be transformed into a set of linear matrix inequalities; ι(γ,β) is used as the objective function, and the objective function should be as small as possible; the initial value is substituted into the linear matrix inequality to calculate the initial value of the objective function.

[0088] SAA initialization can mainly initialize algorithm parameters, including initial temperature, final temperature and annealing rate.

[0089] During the execution of the SAA main program, starting from the determined initial temperature, values ​​within the specified range can be randomly selected according to the current temperature, and these values ​​are input into the linear matrix inequality as a new set to optimize the parameters. If their replacement results in a smaller value of the objective function ι(γ,β), the recorded value is updated; if their replacement results in a non-positive definite matrix in the linear matrix inequality or causes the linear matrix inequality to be unable to be solved, a very large value is manually assigned to the objective function to ensure that the result is not used. After each program run, cooling is performed according to the predefined annealing rate, and then the next temperature iteration is performed.

[0090] When the program temperature reaches the specified initial temperature or the program completes the set maximum number of iterations, the loop is terminated and the recorded value is output as the final value of . The obtained final value and the value of are used to design an FDO with H∞ / H-mixed performance indicators.

[0091] Step 210 : designing a fault detection observer based on the dynamic event triggering mechanism parameters and the FDO parameters.

[0092] A fault detection observer design method based on a simulated annealing algorithm provided in the present application can save resources by setting a dynamic event trigger mechanism; by setting an H∞ / H-index to quantify the standard, it can ensure that the designed fault detection observer has both robustness against disturbances and sensitivity to faults; since a simulated annealing algorithm is introduced to solve the coupling term problem in a nonlinear matrix inequality, conservatism is completely eliminated, so that the obtained fault detection observer has global optimal robustness against disturbances and sensitivity to faults.

[0093] It should be understood that, although the various steps in the above-mentioned flow chart are displayed in sequence according to the indication of the arrows, these steps are not necessarily executed in sequence according to the order indicated by the arrows. Unless there is a clear explanation in this article, the execution of these steps is not strictly limited in order, and these steps can be executed in other orders. Moreover, at least a part of the steps in the above-mentioned flow chart may include a plurality of sub-steps or a plurality of stages, and these sub-steps or stages are not necessarily executed at the same time, but can be executed at different times, and the execution order of these sub-steps or stages is not necessarily to be carried out in sequence, but can be executed in turn or alternately with other steps or at least a part of the sub-steps or stages of other steps.

[0094] In one embodiment, an experiment is conducted on the provided fault detection observer design method based on simulated annealing algorithm. The experimental process and result analysis are as follows:

[0095] In the experimental part, a vertical take-off and landing aircraft power system is used to verify the effectiveness of the proposed FDO design method. Different wind speeds will cause transitions between different subsystem modes, and the external disturbance is set to ω(k) = 0.5e -k cos(πk), the fault signal is set to:

[0096]

[0097] like Figure 3 , Figure 4 As shown, Figure 3 The iterative process of SAA and the dynamic evolution of the optimal value of the objective function are demonstrated; Figure 4 The change trajectory of the system state is displayed, demonstrating the obvious adverse impact on the system state when the fault signal occurs.

[0098] like Figure 5 As shown, Figure 5 The performance of the FDO designed by this method is demonstrated. It can be seen that the FDO is able to detect the fault signal within 1 unit time after the fault signal occurs, which clearly proves the robustness of the FDO proposed in this study to external interference and its sensitivity to fault signals.

[0099] In one embodiment, a computer device is provided, comprising a processor, a memory, a network interface, a display screen and an input device connected through a system bus. The processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The network interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, a fault detection observer design method based on a simulated annealing algorithm is implemented. The display screen of the computer device can be a liquid crystal display screen or an electronic ink display screen, and the input device of the computer device can be a touch layer covered on the display screen, or a key, trackball or touchpad set on the computer device housing, or an external keyboard, touchpad or mouse, etc.

[0100] Among them, the simulation software that can be installed on the computer device is MATLAB2020a, and the operating system is Windows. When implementing the fault detection observer design method based on simulated annealing algorithm in this application, the simulation software used is MATLAB2020a, and the operating system is Windows.

[0101] Those skilled in the art will understand that the structure of the computer device is merely a block diagram of a partial structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components, or combine certain components, or have a different arrangement of components.

[0102] In one embodiment, a computer device is provided, including a memory and a processor. The memory stores a computer program, and the processor implements the steps of a fault detection observer design method based on a simulated annealing algorithm when executing the computer program.

[0103] In one embodiment, a computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the steps of a fault detection observer design method based on a simulated annealing algorithm are implemented.

[0104] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, storage, database or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM) or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. As an illustration and not limitation, RAM is available in many forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link (Synchlink) DRAM (SLDRAM), memory bus (Rambus) direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM).

[0105] The technical features of the above embodiments may be arbitrarily combined. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0106] The above-mentioned embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the patent of the present application shall be subject to the attached claims.

Claims

1. A fault detection observer design method based on simulated annealing algorithm, characterized in that: The method comprises: Establish the Markov jump system MJSs model and the fault detection observer FDO model; The event triggering mechanism of the MJSs model is improved, the time point of data transmission is dynamically adjusted through the auxiliary dynamic variables in the Markov jump system, and a dynamic event triggering mechanism is set; Setting an evaluation function value and a threshold for the FDO model, and setting an H∞ / H-index; Several Lyapunov functions are designed to obtain the target nonlinear matrix inequality, and the simulated annealing algorithm is introduced into the target nonlinear matrix inequality. Based on the dynamic event trigger mechanism, the evaluation function value and the threshold and the H∞ / H-index, the dynamic event trigger mechanism parameters and the FDO parameters are obtained. The target nonlinear matrix inequality is: in, A i , D i , L i All are matrices; P 1i ,P 2i is a positive definite symmetric matrix, The simulated annealing algorithm construction process includes: converting the target nonlinear matrix inequality into a set of linear matrix inequalities to determine the target function; bringing the initial value into the linear matrix inequality to calculate the initial value of the target function; initializing the simulated annealing algorithm parameters and performing iterative calculations until the maximum number of iterations is met, thereby constructing a simulated annealing algorithm; The objective function is ι(γ, β); when the simulated annealing algorithm parameters are initialized and iterative calculations are performed, ι(γ, β) is minimized; wherein γ is the H∞ index parameter and β is the H-index parameter; A fault detection observer is designed based on the dynamic event triggering mechanism parameters and the FDO parameters.

2. The fault detection observer design method based on simulated annealing algorithm according to claim 1 is characterized in that: The state space expression and transition probability matrix of the MJSs model are: π ij =Prob{s(k+1)=j|s(k)=i} Among them, x(k) is the system state at time k, y(k) is the measured output, ω(k) is the external disturbance, f(k) is the fault signal, and A s(k) , B s(k) , C s(k) and D s(k) is a known matrix, π ij represents the transfer probability matrix, has dimension for each s(k)=i, j represents the system mode at time k+1, and has the same value range as i.

3. The fault detection observer design method based on simulated annealing algorithm according to claim 2 is characterized in that: The FDO model is: in, r(k) are the state, output, and residual signal of FDO, respectively. i , L i , D i are all known matrices.

4. The fault detection observer design method based on simulated annealing algorithm according to claim 3 is characterized in that: Under the dynamic event triggering mechanism, the time determination conditions for data transmission are: Where f(k,m(k))=e T (k)Ψ i e(k)-δ i m(k)y T (k)Ψ i y(k), i is the mode related to the system, μ(k) and m(k) are two auxiliary dynamic variables set to dynamically adjust the trigger threshold; λ, k, ρ and ∈ are preset positive scalars, δ i is a preset scalar associated with mode i; Ψ i represents the positive definite matrix associated with mode i, k s With k s+1 represents the time when the event trigger mechanism is triggered for the sth time and the s+1th time respectively, e(k)=y(k)-y(k s ), represents the k moment and k s The difference in output signals is measured at all times.

5. The fault detection observer design method based on simulated annealing algorithm according to claim 4 is characterized in that: The evaluation function value is: The thresholds are: Among them, k0 represents the initial evaluation time, t is the evaluation step length, r e (k) = r(k) - f(k), Represents r e The transpose of (k).

6. The fault detection observer design method based on simulated annealing algorithm according to claim 5, characterized in that: The method further comprises: Assuming zero initial conditions, the Markov jump system is stochastically stable and satisfies: Then the Markov jump system has the H∞ index γ>0; ω(k) represents the external disturbance, ω T (k) represents the transpose of ω(k).

7. The fault detection observer design method based on simulated annealing algorithm according to claim 6, characterized in that: The method further comprises: Assuming zero initial conditions, the Markov jump system is stochastically stable and satisfies: Then the Markov jump system has an H-index β<0; f(k) represents the fault signal, f T (k) represents the transpose of f(k).

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