An evaluation method, device and application of collective fault detection

Abstract

The present invention provides an evaluation method, device and application for set membership fault detection, which belongs to the technical field of fault diagnosability. The performance of the fault detection system is evaluated according to the minimum detectable fault index of the fault detection system. The minimum detectable fault index is the fault amplitude when the fault residual feasible set and the fault-free residual feasible set of the system to be detected are just separated. The method includes obtaining the residual system equations of the fault-free state and the fault-fault state of the system to be detected in combination with the observer equation used for the system to be detected; using a geometric body to characterize the measurement noise range, combining set membership operation to obtain the residual feasible set characterization of the fault-free state and the fault-fault state of the system to be detected; and determining the minimum detectable fault index of the system to be detected. The present invention can guide the design optimization of the observer, as well as the design of the control system and the correction of the system model parameters, so as to make the control system more stable.

Description

Technical Field

[0001] The present invention belongs to the technical field of fault diagnosability, and in particular relates to an evaluation method, device and application of collective fault detection. Background Art

[0002] In fault diagnosis technology, the accuracy of fault diagnosis will be affected by the existence of factors such as noise, model uncertainty, and unknown input. In model-based fault diagnosis methods, according to different noise assumptions, they can be divided into statistical theory framework methods and set membership theory framework methods. The former assumes that system uncertainty has probabilistic characteristics such as mean and probability density; the latter assumes that system uncertainty is unknown but bounded and can be characterized using set membership methods.

[0003] Process disturbances are complex, and the probabilistic characteristics of uncertainties such as noise are difficult to accurately capture. Therefore, modeling them as bounded signals is more appropriate. Numerous fault detection methods have been proposed under bounded uncertainty. These methods typically consider disturbance robustness and fault sensitivity during the design process to ensure that the observer meets a certain minimum design performance. However, in practical applications, the actual performance achieved by the designed fault diagnosis algorithms is often difficult to accurately analyze. As key parameters in engineering applications, performance evaluation metrics for fault detection methods are crucial. References (Wang Weiliang, Geng Yanfeng, Sun Jian, et al., Sensor Fault Detection and Minimum Detectable Fault Analysis for Dynamic Pointing Rotary Steering Systems [J]. Journal of the International Society of Automation, 2022, 127: 108-119) propose a fault diagnosis performance analysis method, but this method only analyzes fault detection performance in steady-state conditions. In practical applications, faults often trigger fault alarms during dynamic processes, without waiting for the system to enter steady-state conditions. Therefore, conventional fault diagnosability analysis methods under steady-state conditions are relatively conservative. Studying fault diagnosability in dynamic processes can help more accurately analyze the performance of fault diagnosis systems. However, there is no diagnostic analysis method for faults in dynamic processes in the currently published literature. Therefore, from the perspective of engineering application theory research, how to select a better fault detection method and further guide the design and optimization of the fault detection method is a technical problem that needs to be solved urgently. Summary of the Invention

[0004] In view of the problem that the actual effect of fault detection methods in the prior art is difficult to evaluate, the present invention proposes an evaluation method, device and application of set membership fault detection, which can effectively guide observer design and fault detection performance evaluation under the set membership theory framework method.

[0005] A first aspect of the present invention provides a performance evaluation method for a set-membership fault detection method. The method evaluates the performance of a fault detection system based on a minimum detectable fault index of the fault detection system. The minimum detectable fault index is the fault amplitude at which a feasible set of residual errors with faults and a feasible set of residual errors without faults of the system to be detected are exactly separated. The performance evaluation method includes:

[0006] S101. For the system to be detected, in combination with the observer equation used, obtain the residual system equations of the system to be detected in a non-fault state and a fault state;

[0007] S102, using a geometric representation of the measurement noise range, combined with set membership operation to obtain a residual feasible set representation of the fault-free state and the faulty state of the system to be detected;

[0008] S103 , determining a minimum detectable fault index of the system to be detected, wherein the minimum detectable fault index is a fault amplitude when the residual feasible sets of the fault state and the non-fault state of the system to be detected are just separated at the sampling time.

[0009] Furthermore, in step S101, the system to be detected is a linear discrete time-invariant system containing a fault, and the linear discrete time-invariant system containing a fault is:

[0010]

[0011] in, 、 、 、 、 They are System state vector, system input vector, system output vector, measurement noise vector, sensor fault vector, for The system state vector at time t, is the system matrix, is the input matrix, is the output matrix, is the noise distribution matrix; is the fault distribution matrix;

[0012] The observer equation is:

[0013]

[0014] in, 、 They are The observed value of the system state vector and the observed value of the output vector at time t, for The observed value of the system state vector at time t, is the observer parameter matrix;

[0015] The state estimation error is:

[0016] The residual is:

[0017] The residual system equation of the system without fault is:

[0018]

[0019] in, and They are Moment and The error in the estimation of the fault-free state at time t; for Fault-free residual at time t;

[0020] The residual system equation of the system with fault is:

[0021]

[0022] in, and They are Moment and The fault state estimation error at time t; for The faulty residual at time.

[0023] Furthermore, in step S102, the method for calculating the residual feasible set is:

[0024] The residual feasible set is represented by a centrosymmetric polyhedron, and the centrosymmetric polyhedron of the system fault-free residual system is:

[0025]

[0026] in, represents the Minkowski sum, represents a linear mapping, For trouble-free system Moment residual centrosymmetric polytope, For trouble-free system The center vector of the moment residual centrosymmetric polytope, For trouble-free system Generator matrix of the moment residual centrosymmetric polytope; For trouble-free system The centrosymmetric polytope of the state estimation error at the moment, For trouble-free system The center vector of the central symmetric polyhedron of the state estimation error at the moment, For trouble-free system The generator matrix of the central symmetric polyhedron of the state estimation error at the moment, For trouble-free system The centrosymmetric polytope of the state estimation error at the moment, for Centrosymmetric polytope that measures noise at every moment;

[0027] The central symmetric polytope of the faulty residual system is:

[0028]

[0029] in, For faulty systems The centrosymmetric polytope of the moment residual, For faulty systems The center vector of the moment residual centrosymmetric polytope, For faulty systems Generator matrix of the moment residual centrosymmetric polytope; For faulty systems The centrosymmetric polytope of the state estimation error at the moment, For faulty systems The center vector of the central symmetric polyhedron of the state estimation error at the moment, For faulty systems The generator matrix of the central symmetric polyhedron of the state estimation error at the moment, For faulty systems The centrosymmetric polytope of the state estimation error at the moment, For faulty systems Centrosymmetric polytopes of moment faults.

[0030] Furthermore, in step S103, the method for calculating the minimum detectable fault index is: by calculating the fault state Centrosymmetric polytopes of time residuals and fault-free states When the intersection of the centrosymmetric polytopes of the moment residuals is an empty set, The fault with the minimum value is recorded as the minimum detectable fault:

[0031]

[0032]

[0033] in, is the minimum value operator, Matrix is ​​the given weight matrix;

[0034] Convert the above formula into a mixed integer quadratic programming problem and solve it:

[0035]

[0036]

[0037]

[0038] in, 、 、 To solve the Lagrange multiplier, for No. elements, for No. elements, is the transpose, 、 is the binary variable to be determined, 、 are the vector and scalar to be determined, and for The number of rows and columns, 、 Known to be The lower and upper bounds of 、 They are The center and generator matrix of the new polyhedron generated by applying the transformation theorem of the empty polyhedron intersection condition at all times; , , is the weight matrix, For trouble-free system The generator matrix of the moment residual centrosymmetric polytope, For faulty systems The generator matrix of the moment residual centrosymmetric polytope, is the weight matrix;

[0039] Calculate the minimum detectable fault index of the fault detection system .

[0040] A second aspect of the present invention provides an evaluation device, which includes a data acquisition module, a system model parameter identification module, a minimum detectable fault index calculation module, a communication decoding module, and a host computer storage and analysis module;

[0041] The data acquisition module is used to collect measurement information output by the sensor of the system to be detected;

[0042] The system model parameter identification module is connected to the data acquisition module and is used to identify the system model parameters in real time through the output information measured by the system sensors, and to modify the nominal system parameter matrix using particle swarm parameter identification and least squares parameter identification methods;

[0043] The minimum detectable fault index calculation module is connected to the system model parameter identification module, and after obtaining the parameters of the system model, calculates the minimum detectable fault index at each moment according to the performance evaluation method described in the first aspect of the present invention;

[0044] The communication decoding module is connected to the minimum detectable fault index calculation module, performs communication decoding on the minimum detectable fault index and sends the data to the host computer storage and analysis module;

[0045] The host computer storage and analysis module stores the measurement information output by the sensor, the identified model parameters and the minimum detectable fault index, and analyzes the stored results.

[0046] A third aspect of the present invention provides an application of a performance evaluation method for a member fault detection method to a rotary steerable drilling tool, comprising the following steps:

[0047] S201. Establishing a system model of the rotary steerable drilling tool based on its physical and electrical characteristics, and identifying model parameters of the rotary steerable drilling tool; combining the system state observer equation to obtain residual system equations for the system in a fault-free state and a faulty state;

[0048] S202, using a centrosymmetric polyhedron to characterize the measurement noise range of the rotary steerable drilling tool, and obtaining a residual centrosymmetric polyhedron of the rotary steerable drilling tool system based on the computational properties of the centrosymmetric polyhedron;

[0049] S203. Taking minimization of the weighted bi-norm of the vector composed of the current fault and its variation as the optimization objective, maximize the distance between the residual centrosymmetric polytopes in the faulty and non-faulty states of the rotary steerable drilling tool at the current moment, and obtain the minimum detectable current fault index of the rotary steerable drilling tool system; the minimum detectable current fault index is the fault amplitude at which the residual feasible sets of the faulty and non-faulty states of the system to be detected are just separated at the sampling moment.

[0050] Furthermore, the system model of the rotary steerable drilling tool is:

[0051]

[0052]

[0053] in, for The system state vector at the moment, that is, the motor Shaft current , permanent magnet synchronous motor speed , stabilize the platform speed and tool face angle , for The system state vector at time t, 、 、 、 and They are At time instants, the system input vector, unknown input vector, system output vector, measurement noise vector, and sensor fault vector, is the singular matrix of the known singular system, 、 and are the known system matrix, input matrix and output matrix respectively, For the system The parameter uncertainty matrix of the matrix, is the unknown input distribution matrix, is the noise distribution matrix, is the fault distribution matrix;

[0054] The observer used is of the form:

[0055]

[0056] in, 、 is the observer parameter matrix; the observer parameter matrix satisfies ; is the 4-dimensional identity matrix; for The system output vector at the moment; is the observer parameter matrix;

[0057] Time state estimation error , residual , noise variation , fault variation , 、 They are The moment-to-moment noise vector, sensor fault vector, and the residual system of the rotary steerable drilling tool with and without faults are as follows:

[0058]

[0059]

[0060] in, for The error in the estimation of the fault-free state at time t; and They are Moment and The fault state estimation error at time t; for The faulty residual at time.

[0061] Furthermore, the error-free central symmetric polytope , residual centrosymmetric polytope , the central symmetric polytope of the faulty system state estimation error , residual centrosymmetric polytope The iteration is expressed as:

[0062]

[0063]

[0064] in, is the parameter model uncertainty matrix The parameter matrix obtained by taking the maximum value is and Respectively Moment and The error in the estimation of the state of the fault-free system at any moment, For trouble-free system The center vector of the central symmetric polyhedron of the state estimation error at the moment, For trouble-free system +1 moment state estimation error centrosymmetric polytope generating matrix, For trouble-free system The center vector of the central symmetric polyhedron of the state estimation error at the moment, For trouble-free system The generator matrix of the central symmetric polyhedron of the state estimation error at the moment, and Respectively Moment and There is always an error in the estimation of the fault system state, For faulty systems The center vector of the central symmetric polyhedron of the state estimation error at the moment, For faulty systems The generator matrix of the central symmetric polyhedron of the state estimation error at the moment, For faulty systems The center vector of the central symmetric polyhedron of the state estimation error at the moment, For faulty systems The generator matrix of the central symmetric polyhedron of the state estimation error at the moment, for The system state vector at time t, for The centrosymmetric polytope of the system state vector at time t, for Generator matrix of the centrosymmetric polytope of the system state vector at time instant; for The noise variation at each moment, for The central symmetric polyhedron of the momentary noise variation, for Generator matrix of the centrosymmetric polyhedron of momentary noise variation; for The noise vector at time instant, for The centrosymmetric polytope of the noise vector at time instant, for Generator matrix of the centrosymmetric polytope of the moment noise vector; for The change of fault at each moment, for The centrosymmetric polyhedron of the moment fault variation, for The center vector of the centrosymmetric polyhedron of the moment fault variation; for The moment fault vector, for Centrosymmetric polytopes of moment faults, for The center vector of the centrosymmetric polytope of the moment fault vector; and Respectively The residuals of the fault-free system and the faulty system at time instants, For trouble-free system The center vector of the moment residual centrosymmetric polytope, For trouble-free system The generating matrix of the residual centrosymmetric polytope at time +1, For faulty systems The center vector of the moment residual centrosymmetric polytope, For faulty systems Generator matrix of the residual centrosymmetric polytope at time +1.

[0065] Furthermore, the calculation method of the centrosymmetric polyhedron of the error and residual of the state estimation of the fault-free system is:

[0066]

[0067] The calculation method of the centrosymmetric polyhedron of the faulty system state estimation error and residual is:

[0068]

[0069] in, , , 、 They are 、 is the matrix after dimensionality reduction, and the dimensionality reduction process is as follows:

[0070] against dimensional centrosymmetric polytope and integers , and satisfies , is the center vector of the centrosymmetric polyhedron, is the Minkowski sum operation, Generate a matrix for a centrosymmetric polyhedron, for the number of rows, For the general The matrix obtained by arranging the column vectors of in descending order of Euclidean norm is: for dimensional hypercube, then the matrix after dimensionality reduction is , and there are Established, among which for dimensional hypercube, Depend on Before column vectors, for Remove part, satisfy: , is a matrix No. Rank Column element.

[0071] Furthermore, the minimum detectable current fault index is calculated as follows:

[0072]

[0073] The above formula is transformed into a mixed integer quadratic programming problem. The problem is solved by writing a solver in MATLAB software using the YALMIP toolkit and using the CPLEX commercial solver:

[0074]

[0075] in, 、 、 To solve the Lagrange multiplier, for No. elements, for No. elements, is the transpose, 、 is the binary variable to be determined, 、 are the vector and scalar to be determined, and for The number of rows and columns, 、 Known to be The lower and upper bounds of , .

[0076] The present invention calculates the minimum detectable fault index of different set membership fault detection methods. The smaller the minimum detectable fault index, the smaller the fault that can be detected by the fault detection method, and the better the performance of the set membership fault detection method. The minimum detectable fault index is related to the design parameters of the observer and the design of the control system. Therefore, by calculating the minimum detectable fault index, it can not only be used to guide the design optimization of the observer, but also be applied to the design of the control system and the correction of the system model parameters, making the control system operation more stable. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] Figure 1 This is a flow chart of an embodiment of the present invention;

[0078] Figure 2 This is a module connection diagram of another embodiment of the present invention;

[0079] Figure 3 This is a flow chart of another embodiment of the present invention;

[0080] Figure 4 This is a flow chart of another embodiment of the present invention;

[0081] Figure 5 For the ( )to ( ) starts calculating the minimum detectable current fault amplitude curve;

[0082] Figure 6 For the ( )to ( ) starts to calculate the minimum detectable current fault amplitude change curve.

[0083] Figure 7 This is the residual result diagram obtained after adding the calculated minimum detectable fault.

[0084] Figure 8 This is the fault alarm result. DETAILED DESCRIPTION

[0085] Model-based fault diagnosis techniques can be divided into probabilistic methods based on statistical properties and deterministic methods based on set membership theory. Deterministic methods can characterize system uncertainty using set-membership geometries such as centrosymmetric polytopes. Then, based on set membership operations combined with set-membership geometry logic, model analysis can be used to obtain theoretical bounds for system state estimation errors and residuals, thereby enabling fault detection. Because the noise characteristics of actual uncertainty are often difficult to accurately determine, while the approximate range of noise can be readily determined, the main purpose of this invention is to design quantitative evaluation metrics for the performance of fault detection methods using set membership methods.

[0086] The present invention provides a method and device for designing a minimum detectable fault index of a set membership fault detection method and its application in a rotary steerable drilling tool, which can dynamically and automatically calculate the minimum detectable fault index of a rotary steerable drilling tool under a set membership fault detection method. The minimum detectable fault index at each moment can be used to evaluate the performance of the set membership fault detection method. This can be further combined with the observer design process to guide the design of the observer, improve the performance of the set membership fault detection method, and thus enhance the reliability of the rotary steerable drilling tool, improve drilling efficiency, and reduce oil and gas production costs.

[0087] Compared with research on fault detection performance evaluation indicators within the framework of statistical theory, relatively few results have been reported within the framework of set membership theory. Existing minimum detectable fault analysis methods based on invariant sets can only obtain the steady-state value of the minimum detectable fault at the final steady state, and are unable to solve the minimum detectable fault for each dynamic process. In some cases, some systems require a long time to reach steady state, or even alarm during the dynamic process but not during the steady state. Therefore, existing methods are highly conservative when analyzing the sensor diagnosability of rotary steerable drilling tools, or even fail to analyze them. Furthermore, the diverse and complex forms of strong interference during drilling further complicate fault diagnosability analysis. Therefore, it is necessary to design minimum detectable fault indicators for the system's dynamic process under strong interference.

[0088] An embodiment of the first aspect of the present invention provides a performance evaluation method for a set membership fault detection method, wherein the performance of the fault detection method is evaluated based on the minimum detectable fault index of the fault detection method, wherein the minimum detectable fault index is the distance between the fault residual set membership and the fault-free residual feasible set of the system to be detected, and the system to be detected is the system to be fault detected.

[0089] like Figure 1 As shown, the performance evaluation method includes:

[0090] S101. For the system to be detected, combining the used observer equation, obtain the residual system equations of the system in the fault-free state and the faulty state;

[0091] The system to be detected can be a linear system or a nonlinear system. It only needs to design a suitable observer or processing method to make the residual system of the system to be detected a linear discrete time-invariant system. The following description assumes that the system to be detected is a linear discrete time-invariant system containing a fault.

[0092] In this embodiment, the linear discrete time-invariant system containing a fault is:

[0093]

[0094] in, 、 、 、 、 They are System state vector, system input vector, system output vector, measurement noise vector, sensor fault vector, is the system matrix, is the input matrix, is the output matrix, is the noise distribution matrix; is the fault distribution matrix.

[0095] The observer equation is:

[0096]

[0097] in, 、 They are The observed values ​​of the system state and output vector at time t, for The system state vector at time t, is the observer parameter matrix, The design of affects the observer's estimate of the system state.

[0098] The state estimation error is:

[0099] The residual is:

[0100] The fault-free residual system equation is:

[0101]

[0102] in, , They are interference and noise when the system is fault-free, for The number of rows in the column vector, for The number of rows in the column vector. , , , is the parameter matrix of the residual system when there is no fault, for The number of rows in the column vector, for The number of rows in the column vector; where and Respectively represent Order and dimensional Euclidean space.

[0103] Substitute the parameters of the linear discrete time-invariant system equation containing the fault and the observer equation parameters into, , , , , interference when the system has no faults is the system noise , then the system no-fault residual system equation is:

[0104]

[0105] in and They are Moment and The error in the estimation of the fault-free state at time t; for The residual in the fault-free state at time t;

[0106] The fault residual equation of the system is:

[0107]

[0108] in, , They are interference and noise when the system fails. , , , , , is the parameter matrix when the residual system has faults, for The number of rows in the column vector.

[0109] Substitute the parameters of the linear discrete time-invariant system equation containing the fault and the observer equation parameters into, , , , , , , interference when the system has no faults is the system noise , then the residual system equation of the system with fault is:

[0110]

[0111] in, and They are Moment and The fault state estimation error at time t; for The residual error under fault condition at time t.

[0112] The initial estimation error vector and noise vector of the system are unknown but bounded, expressed as , , , , , .in Indicates a A collection of dimensions.

[0113] According to the operation rules and theorems of the corresponding geometric bodies, we can get The feasible set representation of the residual vector of the residual system with and without faults at each moment: , .

[0114] S102, using a geometric representation of the measurement noise range and combining it with a set membership operation to obtain a residual feasible set representation of a linear discrete time-invariant system containing a fault in a fault-free state and a fault-containing state;

[0115] The member aggregate can be a centrosymmetric polyhedron, an ellipsoid, a parallelepiped or other geometric solids. Different geometric solids have different computational properties. For example, the properties of a centrosymmetric polyhedron are as follows:

[0116] The centrosymmetric polytope is defined as:

[0117]

[0118] in, is the center vector of the centrosymmetric polyhedron, is the Minkowski sum operation, Generate a matrix for a centrosymmetric polyhedron, for the number of rows, is the unit hypercube, is the dimension of the polyhedron.

[0119] The operation rules for centrosymmetric polytopes are:

[0120]

[0121]

[0122] Among them, the matrix , represents the Minkowski sum, two sets and The Minkowski sum of is defined as , Represents a linear map, a centrosymmetric polyhedron With a matrix The linear mapping of can be obtained by the standard matrix product operation: .

[0123] The method for calculating the residual feasible set in this embodiment is:

[0124] The residual feasible set is represented by a centrosymmetric polyhedron, and the centrosymmetric polyhedron of the system fault-free residual system is:

[0125]

[0126] in, For trouble-free system Moment residual centrosymmetric polytope, For trouble-free system The center vector of the moment residual centrosymmetric polytope, For trouble-free system Generator matrix of the moment residual centrosymmetric polytope; For trouble-free system The centrosymmetric polytope of the state estimation error at the moment, For trouble-free system The center vector of the central symmetric polyhedron of the state estimation error at the moment, For trouble-free system The generator matrix of the central symmetric polyhedron of the state estimation error at the moment, For trouble-free system The centrosymmetric polytope of the state estimation error at the moment, For trouble-free system Centrosymmetric polytope that measures noise at every moment;

[0127] The central symmetric polytope of the faulty residual system is:

[0128]

[0129] in, For faulty systems The centrosymmetric polytope of the moment residual, For faulty systems The center vector of the moment residual centrosymmetric polytope, For faulty systems Generator matrix of the moment residual centrosymmetric polytope; For faulty systems The centrosymmetric polytope of the state estimation error at the moment, For faulty systems The center vector of the central symmetric polyhedron of the state estimation error at the moment, For faulty systems The generator matrix of the central symmetric polyhedron of the state estimation error at the moment, For faulty systems The centrosymmetric polytope of the state estimation error at the moment, For faulty systems Centrosymmetric polytopes of moment faults.

[0130] S103 , determining a minimum detectable fault index of a linear discrete time invariant system, wherein the minimum detectable fault index is the distance between the residual feasible sets of a faulty state and a non-faulty state of the linear discrete time invariant system containing a fault at a maximum sampling time.

[0131] The method for calculating the minimum detectable fault index in step S103 is: by calculating the fault state Centrosymmetric polytopes of time residuals and fault-free states When the intersection of the centrosymmetric polytopes of the moment residuals is an empty set, The fault with the minimum value is recorded as the minimum detectable fault:

[0132]

[0133] in, is the minimum value operator, The matrix is ​​the given weight matrix.

[0134] The optimization problem means that the minimum fault value is defined as the minimum fault value that makes the feasible set of residual vectors with and without faults have no intersection under the corresponding set membership fault detection method. .in The matrix is ​​a weighted matrix, which is used to adjust the solution weight relationship between different faults.

[0135] The intersection of the feasible sets of residual vectors with and without faults is empty, which means that the actual system residual is located in the membership set of the residual vector set with faults. Or the set of fault-free residual vectors It is used to determine whether a fault occurs, thereby achieving the purpose of fault detection.

[0136] The intersection of centrosymmetric polytopes is empty transformation theorem: given a centrosymmetric polytope and ,but The necessary and sufficient conditions are:

[0137] Applying the above theorem, let , , we can get

[0138] Convert the above formula into a mixed integer quadratic programming problem and solve it:

[0139]

[0140]

[0141]

[0142] in, 、 、 To solve the Lagrange multiplier, for No. elements, for No. elements, is the transpose, 、 is the binary variable to be determined, 、 are the vector and scalar to be determined, and for The number of rows and columns, 、 Known to be The lower and upper bounds of 、 They are The center and generator matrix of the new polyhedron generated by applying the transformation theorem of the empty polyhedron intersection condition at all times;

[0143] , ;

[0144] Calculate the minimum detectable fault index of the fault detection system .

[0145] The quantitative evaluation problem of fault detection performance can be transformed into an optimization problem for solution.

[0146]

[0147] This embodiment calculates the minimum detectable fault index for different set membership fault detection methods. A smaller minimum detectable fault index indicates a smaller fault that can be detected by the fault detection method, and the set membership fault detection method has better performance. The minimum detectable fault index is related to the design parameters of the observer and the design of the control system. Therefore, calculating the minimum detectable fault index can not only guide observer design optimization, but also be applied to control system design and correction of system model parameters, making the control system more stable.

[0148] This embodiment realizes the separation of real-time residual sets and solves the minimum detectable fault index; and compares and evaluates the performance of fault diagnosis methods under the set membership framework based on the minimum detectable fault index.

[0149] Compared with the traditional method of using transfer function to perform set membership method to design quantitative indicators for fault diagnosis performance evaluation, the advantages of this method include:

[0150] 1. The fault diagnosis performance quantitative evaluation design method of the present invention can realize the fault diagnosis performance evaluation under the set membership method;

[0151] 2. The fault diagnosis performance quantitative evaluation design method of the present invention can overcome the disadvantages of the invariant set method that loses process information and can only obtain the final minimum detectable fault in the steady state, and can evaluate each fault in the dynamic process of the system. Analyze and solve the minimum detectable fault at the moment;

[0152] 3. Through the design method for quantitative evaluation of fault diagnosis performance of the present invention, the performance of the fault diagnosis method based on the set membership method proposed for rotary steerable drilling tools can be quantitatively evaluated by applying the idea of ​​this method;

[0153] 4. The evaluation index obtained by the present invention has better applicability for systems that need a long time to reach a steady state and only alarm during a dynamic process in certain situations.

[0154] like Figure 2 As shown, the second embodiment of the present invention provides a performance evaluation device 40 for a collective fault detection method, including a data acquisition module 401, a system model parameter identification module 402, a minimum detectable fault index calculation module 403, a communication decoding module 404, and a host computer storage and analysis module 405.

[0155] The data acquisition module 401 is used to collect measurement information output by the sensors of the system under test 50 and transmit this information to the system model parameter identification module 402 via the CAN bus. The sensors are sensors used to measure various parameters in the system under test 50. The vectors measured by these sensors constitute the state vectors of the system state equation, i.e., the system output vectors. The system model parameter identification module 402 is connected to the data acquisition module 401 and is used to identify the system model parameters in real time based on the output information measured by the system sensors. Methods such as particle swarm parameter identification and least squares parameter identification can be used to modify the nominal system parameter matrix to meet the model parameter accuracy requirements of the minimum detectable fault index design method. The minimum detectable fault index calculation module 403 is connected to the system model parameter identification module. After obtaining the system model parameters, it calculates the minimum detectable fault index at each moment according to the performance evaluation method of the set membership fault detection method and transmits it to the communication decoding module 404 via the CAN bus. The communication decoding module 404 is connected to the minimum detectable fault index calculation module 403, performs communication decoding through the communication decoding module 403, and outputs the index calculation results to the host computer storage and analysis module 405. The communication decoding module 404 can be a CAN analyzer, a CAN-to-USB module, etc. The host computer storage and analysis module 405 stores the sensor measurement information, the identified model parameters, and the minimum detectable fault index, and analyzes the stored results. The sensor measurement information is used to determine whether the system has a fault, the type of fault, and the fault size. The identified model parameters are used to determine whether the observer design can be improved. The minimum detectable fault index is used to analyze the quality of different observer design methods and can be used as one of the optimization design indicators to guide observer design. The performance evaluation method of the set membership fault detection method is the same as that of the previous embodiment and will not be repeated here.

[0156] In practical applications, the disturbance situation during drilling is complex. There are periodic disturbances caused by the axial, circumferential, and torsional vibrations of the drill tool, as well as trend disturbances that increase with drilling depth and pressure. The probabilistic characteristics of uncertainties such as noise are often difficult to obtain accurately, and it is more reasonable to model them as bounded signals.

[0157] In this embodiment, the system to be tested 50 may be a rotary steerable drilling tool. The data acquisition module 401 is used to collect measurement information output by the rotary steerable drilling tool sensor and transmit the information to the system model parameter identification module 402 via the CAN bus to identify the mathematical model of the rotary steerable drilling tool.

[0158] In this paper, model uncertainty is characterized using centrosymmetric polytopes. Numerous fault detection methods have been proposed under bounded uncertainty. Selecting the optimal fault detection method and guiding its design and optimization requires establishing appropriate quantitative metrics for evaluating fault detection performance. Due to the presence of noise, minor faults can be easily submerged in the noise signal, making them difficult to detect. The minimum detectable fault (MDF) characterizes the minimum detectable fault size within a specific system and method, thus serving as a direct indicator for evaluating the performance of fault detection methods.

[0159] This embodiment collects sensor data of the system to be tested, identifies system model parameters, and dynamically and automatically calculates the minimum detectable fault of the rotary steerable drilling system fault detection method and outputs the result to the host computer storage and analysis module 405.

[0160] like Figure 3 As shown, the third embodiment of the present invention provides an application of the performance evaluation method of the integrated fault detection system to a rotary steerable drilling tool, comprising the following steps:

[0161] S201: Establish a system model of the rotary steerable drilling tool based on its physical and electrical characteristics, and identify model parameters of the rotary steerable drilling tool. Combined with the system state observer equation, residual system equations for both a fault-free state and a faulty state are obtained. The model parameters of the rotary steerable drilling tool can be obtained by a model parameter identification module using output information measured by system sensors, or by mathematical modeling.

[0162] Specifically, the system model of the rotary steerable drilling tool stabilization platform is:

[0163]

[0164]

[0165] in, for The state vector of the system at the moment, that is, the motor Shaft current , permanent magnet synchronous motor speed , stabilize the platform speed and tool face angle , for The state vector of the system at time t, 、 、 、 and They are System input vector, unknown input vector, output vector, noise vector and fault vector at each moment, is the singular matrix of the known singular system, 、 and are the known system matrix, input matrix and output matrix respectively, For the system The parameter uncertainty matrix of the matrix, is the unknown input distribution matrix, is the noise distribution matrix, is the fault distribution matrix. System model parameters can be obtained through system parameter identification or mathematical modeling. In this embodiment, the data model of the rotary steerable drilling tool stabilization platform is obtained through mathematical modeling and the model is initialized. The system parameters are specifically:

[0166] , , , , , , , , ,

[0167] in 、 and For The motor load torque, drill collar speed and Shaft current fault value, is the sampling time interval of the system, 、 、 、 、 、 and They are the system stator winding resistance, stator winding inductance, constant, torque constant, friction factor, total inertia and pole pair number, is the 4-dimensional identity matrix. and They are The perturbation value of stator winding resistance and torque constant parameters at time , for time Model uncertainty of shaft current, For the Current fault amplitude at the sampling point.

[0168] The observer used is of the form:

[0169]

[0170] Among them, the observer parameter matrix 、 and Design parameters for the observer, and the observer parameters satisfy .

[0171] Time state estimation error , residual , noise variation , fault variation , the residual system of the rotary steerable drilling tool with and without faults is as follows, and the set membership is initialized:

[0172]

[0173] .

[0174] S202. Use a centrosymmetric polyhedron to characterize the measurement noise range of the rotary steerable drilling tool, and obtain a centrosymmetric polyhedron of the residual system of the rotary steerable drilling tool system based on the computational properties of the centrosymmetric polyhedron.

[0175] A centrosymmetric polyhedron is defined as:

[0176]

[0177] in, is the center vector of the centrosymmetric polyhedron, is the Minkowski sum operation, Generate a matrix for a centrosymmetric polyhedron, is the unit hypercube, is the dimension of the polyhedron.

[0178] Fault-free state estimation error centrosymmetric polytope , residual centrosymmetric polytope The iteration formula is as follows:

[0179] Centrally Symmetric Polytope of State Estimation Error of Faulty System , residual centrosymmetric polytope The iteration is expressed as:

[0180]

[0181] in, is the parameter matrix obtained by taking the maximum value of the matrix parameter model uncertainty, and Respectively Moment and The error in the estimation of the state of the fault-free system at any moment, and Respectively Moment and There is always an error in the estimation of the fault system state, for The system state vector at time t, for The centrosymmetric polytope of the system state vector at time t, for Generator matrix of the centrosymmetric polytope of the system state vector at time instant; for The noise variation at each moment, for The central symmetric polyhedron of the momentary noise variation, for Generator matrix of the centrosymmetric polyhedron of momentary noise variation; for The noise vector at time instant, for The centrosymmetric polytope of the noise vector at time instant, for Generator matrix of the centrosymmetric polytope of the moment noise vector; for The change of fault at each moment, for The centrosymmetric polyhedron of the moment fault variation, for The center vector of the centrosymmetric polyhedron of the moment fault variation; for The moment fault vector, for Centrosymmetric polytopes of moment faults, for The center vector of the centrosymmetric polytope of the moment fault vector; , Respectively The residuals of the fault-free system and the faulty system at time instants.

[0182]

[0183]

[0184] In this embodiment, 、 、 is a constant that does not change with time, then , , .

[0185] Then the above formula is:

[0186]

[0187]

[0188] in, The system is in a fault-free state The central vector of the centrosymmetric polyhedron of the moment error, The system is in a fault-free state The central vector of the moment error centrosymmetric polyhedron, The system is in a fault-free state The centrosymmetric polytope generator matrix of the moment error; The system is in a fault-free state The center vector of the centrosymmetric polytope of the moment residual, The system is in a fault-free state The center vector of the moment residual centrosymmetric polytope, The system is in a fault-free state Centrosymmetric polytope generator matrix for the moment residuals.

[0189] The system is in a fault state The central vector of the centrosymmetric polyhedron of the moment error, The system is in a fault state The central vector of the moment error centrosymmetric polyhedron, The system is in a fault state The centrosymmetric polytope generator matrix of the moment error; The system is in a fault state The center vector of the centrosymmetric polytope of the moment residual, The system is in a fault state The center vector of the moment residual centrosymmetric polytope, The system is in a fault-free state Centrosymmetric polytope generator matrix for the moment residuals.

[0190] , , 、 They are 、 To solve the problem of excessive dimensionality caused by the Minkowski sum operation, the matrix is ​​reduced in dimension. The dimensionality reduction process is as follows:

[0191] consider dimensional centrosymmetric polytope and integers , for -dimensional hypercube, and satisfies ,definition For the general The matrix obtained by arranging the column vectors of the matrix in descending order of the Euclidean norm is , and there are Established.

[0192] in, for dimensional hypercube, Depend on Before column vectors, defined for Remove part, and satisfy: Finally, the residual error of the system with or without fault is calculated. , the centrosymmetric polyhedron in the fault-free state , a centrosymmetric polyhedron with a faulty state .

[0193] S203. Taking minimization of the weighted bi-norm of the vector composed of the current fault and its variation as the optimization objective, maximize the distance between the residual centrosymmetric polytopes in the faulty and non-faulty states of the rotary steerable drilling tool at the current moment, and obtain the minimum detectable current fault index of the rotary steerable drilling tool system.

[0194] The calculation method of the minimum detectable current fault index is as follows:

[0195]

[0196] The above formula is transformed into a mixed integer quadratic programming problem. The problem is solved by writing a solver in MATLAB software using the YALMIP toolkit and using the CPLEX commercial solver:

[0197]

[0198] in, 、 、 To solve the Lagrange multiplier, for No. elements, for No. elements, 、 is the binary vector to be found, 、 are the vector and scalar to be determined, and for The number of rows and columns, 、 Known to be The lower and upper bounds of , .

[0199] Solve the given mixed integer quadratic programming problem scalar 、 , the solution is the fault vector Amplitude, recalculate the central symmetric polyhedron in the fault-free state , Centrally symmetric polytope with fault state .

[0200] like Figure 4 As shown in the figure, the residual calculation method and fault alarm logic under the centrosymmetric polyhedral method are as follows:

[0201] S301, model initialization, given the observer parameters designed according to a certain method, set initialization;

[0202] S302: Calculate residual error in the system with faults , centrally symmetric polyhedron in the fault-free state , Centrally symmetric polyhedron in faulty state ;

[0203] S303, the central symmetric polyhedron in the fault-free state , Centrally symmetric polyhedron in faulty state Use the interval envelope to calculate the center of the residuals with and without faults 、 ;

[0204] S304. Calculate the boundary of the fault-free residual polyhedron , the boundary of the faulty residual polytope ,in, Expressed as The first row of the array Column elements, is the upper bound of the fault-free residual polyhedron, is the lower bound of the fault-free residual polyhedron, is the upper bound of the faulty residual polytope, is the lower bound of the faulty residual polytope, Generate a matrix for a centrosymmetric polytope with no fault residuals and the matrix generated by the centrosymmetric polytope with fault residuals The number of columns;

[0205] S305, calculation fault alarm signal .

[0206] Figure 6 For the ( )to ( ) and calculate the minimum detectable current fault result.

[0207] Figure 7 The residual result diagram is obtained after adding the calculated minimum detectable current fault.

[0208] Figure 8 This is the fault alarm result.

[0209] It can be seen from the test results that the minimum detectable fault designed by the proposed method can achieve the perfect separation of the faulty centrosymmetric polyhedron and the fault-free centrosymmetric polyhedron. The centrosymmetric polyhedron can well contain the actual residual signal. The correct fault alarm can be achieved through the inclusion relationship between the actual residual signal and the centrosymmetric polyhedron interval, thus completing the design of the minimum detectable fault under the set membership framework.

[0210] It should be noted that the matrix dimensions mentioned in this patent have appropriate dimensions by default. The above content is a detailed description made in combination with a specific rotary steerable drilling tool stable platform model, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions.

Claims

1. A performance evaluation method for a set fault detection method is applied to a rotary steerable drilling tool, characterized in that: The following steps are involved: S201. Establish a system model of the rotary steerable drilling tool based on its physical and electrical characteristics, and identify model parameters of the rotary steerable drilling tool. Combined with the system state observer equation, obtain residual system equations for the system in a fault-free state and a faulty state. The system model of the rotary steerable drilling tool is: in, for The system state vector at the moment, that is, the motor Shaft current , permanent magnet synchronous motor speed , stabilize the platform speed and tool face angle , for The system state vector at time t, 、 、 、 and They are At time instants, the system input vector, unknown input vector, system output vector, measurement noise vector, and sensor fault vector, is the singular matrix of the known singular system, 、 and are the known system matrix, input matrix and output matrix respectively, For the system The parameter uncertainty matrix of the matrix, is the unknown input distribution matrix, is the noise distribution matrix, is the fault distribution matrix; S202, using a centrosymmetric polyhedron to characterize the measurement noise range of the rotary steerable drilling tool, and obtaining a residual centrosymmetric polyhedron of the rotary steerable drilling tool system based on the computational properties of the centrosymmetric polyhedron; S203, minimizing the weighted bi-norm of the current fault and its variation vector as the optimization objective, maximizing the distance between the residual centrosymmetric polytopes in the faulty and non-faulty states of the rotary steerable drilling tool at the current moment, and obtaining a minimum detectable current fault index of the rotary steerable drilling tool system; the minimum detectable current fault index is the fault amplitude at which the residual feasible sets of the faulty and non-faulty states of the system to be detected are just separated at the sampling moment; The calculation method of the minimum detectable current fault index is as follows: in, is the minimum value operator, , for The sensor fault vector at time instant, is the fault variation, For a given weight matrix, is a residual centrosymmetric polyhedron, is a residual centrosymmetric polyhedron; The above formula is transformed into a mixed integer quadratic programming problem. The problem is solved by writing a solver in MATLAB software using the YALMIP toolkit and using the CPLEX commercial solver: in, 、 、 To solve the Lagrange multiplier, for No. elements, for No. elements, is the transpose, 、 is the binary variable to be determined, , are the vector and scalar to be determined, and for The number of rows and columns, 、 Known to be The lower and upper bounds of , is the identity matrix, is the observer parameter matrix, is the observer parameter matrix, 、 They are The center and generator matrix of the new polyhedron generated by applying the transformation theorem of the empty polyhedron intersection condition at all times; , , For trouble-free system The center vector of the central symmetric polyhedron of the state estimation error at the moment, For faulty systems The center vector of the central symmetric polyhedron of the state estimation error at the moment, For trouble-free system The generator matrix of the moment residual centrosymmetric polytope, For faulty systems Generator matrix of the moment residual centrosymmetric polytope; The minimum detectable current fault indicator is obtained by calculation.

2. The use according to claim 1, characterized in that The observer used is of the form: in, is the observer parameter matrix; the observer parameter matrix satisfies ; is the 4-dimensional identity matrix; for The system output vector at the moment; Time state estimation error , residual , noise variation , fault variation , 、 They are The moment-to-moment noise vector, sensor fault vector, and the residual system of the rotary steerable drilling tool with and without faults are as follows: in, for The error in the estimation of the fault-free state at time t; and They are Moment and The fault state estimation error at time t; for The faulty residual at time.

3. The use according to claim 2, characterized in that Fault-free state estimation error centrosymmetric polytope , residual centrosymmetric polytope , the central symmetric polytope of the faulty system state estimation error , residual centrosymmetric polytope The iteration is expressed as: in, is the parameter model uncertainty matrix The parameter matrix obtained by taking the maximum value is and Respectively Moment and The error in the estimation of the state of the fault-free system at any moment, For trouble-free system The center vector of the central symmetric polyhedron of the state estimation error at the moment, For trouble-free system +1 moment state estimation error centrosymmetric polytope generating matrix, For trouble-free system The generator matrix of the central symmetric polyhedron of the state estimation error at the moment, and Respectively Moment and There is always an error in the estimation of the fault system state, For faulty systems The center vector of the central symmetric polyhedron of the state estimation error at the moment, For faulty systems The generator matrix of the central symmetric polyhedron of the state estimation error at the moment, For faulty systems The generator matrix of the central symmetric polyhedron of the state estimation error at the moment, for The system state vector at time t, for The centrosymmetric polytope of the system state vector at time t, for Generator matrix of the centrosymmetric polytope of the system state vector at time instant; for The noise variation at each moment, for The centrosymmetric polyhedron of the momentary noise variation, for Generator matrix of the centrosymmetric polyhedron of momentary noise variation; for The noise vector at time instant, for The centrosymmetric polytope of the noise vector at time instant, for Generator matrix of the centrosymmetric polytope of the moment noise vector; for The change of fault at each moment, for The centrosymmetric polyhedron of the moment fault variation, for The center vector of the centrosymmetric polyhedron of the moment fault variation; for The moment fault vector, for The centrosymmetric polytope of the fault vector at time instant, for The center vector of the centrosymmetric polytope of the moment fault vector; and Respectively The residuals of the fault-free system and the faulty system at time instants, For trouble-free system The center vector of the moment residual centrosymmetric polytope, For trouble-free system The generator matrix of the residual centrosymmetric polytope at time +1, For faulty systems The center vector of the moment residual centrosymmetric polytope, For faulty systems Generator matrix of the residual centrosymmetric polytope at time +1.

4. The use according to claim 3, characterized in that The calculation method of the centrosymmetric polyhedron of the state estimation error and residual of the fault-free system is: The calculation method of the centrosymmetric polyhedron of the faulty system state estimation error and residual is: in, 、 They are 、 is the matrix after dimensionality reduction, and the dimensionality reduction process is as follows: against dimensional centrosymmetric polytope and integers , and satisfies , is the center vector of the centrosymmetric polyhedron, is the Minkowski sum operation, Generate a matrix for a centrosymmetric polyhedron, for the number of rows, For the general The matrix obtained by arranging the column vectors of the matrix in descending order of the Euclidean norm is , and there are Established, among which for dimensional hypercube, Depend on Before column vectors, for Remove Part of the matrix satisfy: , is a matrix No. Rank Column element.

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