Fault Diagnosis Method for Multi-Component Mechanical Systems Based on Graph Theory Decoupling and Probabilistic Fusion

Abstract

This invention relates to a fault diagnosis method for multi-component mechanical systems based on graph theory decoupling and probabilistic fusion, which can improve the efficiency and accuracy of equipment fault diagnosis. The method is characterized by obtaining operating parameters of the multi-component mechanical system through sensors; dividing the system into multiple observable subsystems based on the observability and output reachability of the operating parameters; establishing a state-space model of the multi-component mechanical system based on each subsystem; using the sensor-measured data as input, processing it through unscented Kalman filtering to obtain the output residual of the state-space model; calculating the conditional probability from the output residual based on Bayesian principles; simultaneously classifying the measured data using a support vector machine to obtain the posterior probability; fusing the conditional probability and posterior probability using a Bayesian linear mixture method to obtain a new probability; using the fused probability as the analysis standard; and combining it with a threshold to output the state assessment result of the multi-component mechanical system.

Description

Technical fields:

[0001] This invention relates to the field of complex equipment fault diagnosis technology, specifically a fault diagnosis method for multi-component mechanical systems based on graph theory decoupling and probabilistic fusion that can significantly improve the efficiency and accuracy of equipment fault diagnosis. Background technology:

[0002] Complex equipment is often formed by the coupling of multiple components or functional units. During operation, there are many sources of failure, and the failure of a part will affect the overall operation of the equipment. At the same time, the component failures of such complex equipment are often not obvious in the early stages and are not easy to detect and isolate, which poses a hidden danger to the normal operation of the equipment.

[0003] Taking marine propulsion systems as an example, the numerous components and high degree of coupling between them make it difficult to perform status monitoring, fault detection, and isolation during operation, thus affecting the safety of ship navigation. To address this issue, sensors are installed to determine directly observable parameters, and the operating status of the propulsion system is monitored based on these parameters. This requires determining the overall state-space model parameters based on the operating characteristics of the propulsion system. However, the overall state-space model for marine propulsion systems has excessively high dimensionality, resulting in a large computational burden. Summary of the Invention:

[0004] This invention addresses the shortcomings and deficiencies of existing technologies by proposing a fault diagnosis method for multi-component mechanical systems based on graph theory decoupling and probabilistic fusion, which can significantly improve the efficiency and accuracy of equipment fault diagnosis.

[0005] This invention achieves its purpose through the following measures:

[0006] A fault diagnosis method for multi-component mechanical systems based on graph theory decoupling and probabilistic fusion is characterized by: obtaining operating parameters of the multi-component mechanical system through sensors; dividing the system into multiple observable subsystems based on the observability and output reachability of the operating parameters; establishing a state-space model of the multi-component mechanical system based on each subsystem; using the sensor-measured data as input, processing it through unscented Kalman filtering to obtain the output residual of the state-space model; calculating the conditional probability from the output residual based on Bayesian principles; simultaneously classifying the measured data using a support vector machine to obtain the posterior probability; fusing the conditional probability and the posterior probability using a Bayesian linear mixture method to obtain a new probability; using the fused probability as the analysis standard; and combining it with a threshold to output the state assessment result of the multi-component mechanical system.

[0007] The state-space model of the multi-component mechanical system described in this invention is achieved through the following:

[0008] For any multi-component mechanical system, at time k, the minimum number of parameters x are used. k If x can comprehensively and accurately describe the dynamic characteristics of the system, then k This is called the state variable of the system, and its relationship with the state variable at the previous moment is as follows:

[0009] x k =f(x) k-1 ,u k-1 )+w k (3)

[0010] In the formula, f is the system state transition equation; u is the control variable, i.e., the set of variables affecting the system state; w is the system noise, including errors in the system state transition equation, modeling errors, etc.; k-1 represents the time t = k-1; x k-1 u k-1 These are the state and control variables at time k-1.

[0011] For the system's output variable y, let it be the set of observable variables of the system, and let its relationship with the state variables at time k be:

[0012] y k =g(x k ,u k )+v k (4)

[0013] In the formula, g is the measurement conversion equation; v k To measure noise, such as sensor noise error; u k Let be the control variable. Then, combining equations (3) and (4) gives the state model of the system.

[0014] The unscented Kalman filtering process described in this invention selects multiple sigma points based on the current operating point, calculates the mean and covariance of this set of points through unscented transformation, and performs filtering calculations accordingly. Specifically, it includes the following steps:

[0015] Step 1-1: Initialize the mean weights and error covariance weights of the state variables:

[0016]

[0017]

[0018] In the formula ω m ω c ω represents the weights of the mean of the state variables and the weights of the covariance of the errors of the state variables; c,0 ω represents the weight of the error covariance of the state variable at t=0. c,kλ represents the weight of the error covariance of the state variable at time t = k. 2 (n dim +κ)-n dim , represents the distance between the sigma point and the mean; α is the distribution range of the sigma point near the mean, and according to the literature, α = 0.001; β is the prior knowledge of the mean distribution, and according to the literature, β = 2; κ is similar to α, and is a second-order scaling parameter, and according to the literature, κ = 0; n dim It is the dimension of the sampled data;

[0019] Step 1-2: Calculate the sigma point and make predictions:

[0020]

[0021]

[0022] In the formula P xx Let be the state variable and its error covariance corresponding to the (i+1)th sigma point; u is the state variable corresponding to the first sigma point at t = k-1; k-1 This is the control variable when t = k-1; Let be the state variable corresponding to the first sigma point at t = k-1; Let $\ma$ be the error covariance of the state variable corresponding to the first sigma point at $t = k-1$. Let be the state variable at time t = k; The state transition equation at time t = k; The output variable at time t = k; Here is the measurement transformation equation at time t = k. μ is the mean of the state variables; These are the state variables and output variables predicted by the sigma points;

[0023] Steps 1-3: Calculate the state variables and error covariance:

[0024]

[0025]

[0026] In the formula Let k be the state variables and their error covariance calculated by the unscented transformation at time k. Let ω be the covariance of the systematic error at time k; m,i The weights are the mean values ​​of the state variables corresponding to the (i+1)th sigma point at time t = k. Let be the state variable corresponding to the (i+1)th sigma point at t = k; The error covariance of the state variable is calculated at t=k; Let be the state variable corresponding to the (i+1)th sigma point at t = k;

[0027] Steps 1-4: Calculate the output variables and error covariance:

[0028]

[0029]

[0030] In the formula The output variable and its error covariance are calculated by the unscented transformation at time k; It is the covariance of the measurement error at time k; ω is the output variable calculated at t = k. mi The weights are the mean values ​​of the state variables corresponding to the (i+1)th sigma point at time t = k. Let ω be the output variable corresponding to the (i+1)th sigma point at time t=k; ci The weights of the covariance of the state variable corresponding to the (i+1)th sigma point at t=k; Let be the state variable corresponding to the (i+1)th sigma point at t = k; The output variable error covariance is calculated at t=k;

[0031] Steps 1-5: Calculate Kalman gain and residuals:

[0032]

[0033]

[0034]

[0035] In the formula P xy It is the error covariance between the state variable and the output variable; K is the Kalman gain, e is the residual; P xy,k Let K be the error covariance between the state variables and the output variables at time t = k; k The Kalman gain at time t = k; e is the inverse matrix of the output variable error covariance calculated at t=k; k The residual at time t=k

[0036] Steps 1-6: Update state variables and error covariance:

[0037]

[0038]

[0039] In the formula, x, Pxx These are the updated state variables and their error covariance, respectively.

[0040] The method for obtaining the conditional probabilities of multiple models in this invention specifically includes the following steps:

[0041] Step 2-1: Assume that in a multi-component mechanical system at time k, there exists n mode One possible running state H i (i = 1, 2, ... n) mode If the state at time k is only related to the previous time k-1, then based on the data measured at time k and before, the system is currently in operation H. j The conditional probability of a state is represented by a first-order Markov chain as follows:

[0042] p j,k =p(H j |J k (18)

[0043] In the formula p j,k It is in state H at time k. j The probability of;

[0044] H j It is the j-th running state, where 1≤j≤n mode ;

[0045] J k It is the historical data set at time k, i.e., J k =(y0,y1,y2,...y k ), where y is the measurement data;

[0046] Step 2-2: Based on the filtering residuals and covariance of each model, the conditional probability density of each state is expressed as:

[0047]

[0048] In the formula f p (y k |H i J k ) is the state H corresponding to time k. i The conditional probability density;

[0049] e i,k ,P zz,i,k These are the residuals and covariance generated by UKF filtering at time k;

[0050] Step 2-3: Combining equations (18) and (19), update the conditional probability of each state at time k according to Bayes' theorem as follows:

[0051]

[0052] In the formula The corresponding state H obtained from the multi-model calculation at time k. i The conditional probability;

[0053] n mode It represents the number of possible states.

[0054] The acquisition of the SVM posterior probability in this invention specifically includes the following steps:

[0055] Step 3-1: Find a hyperplane within the ensemble space formed by multiple sets of data.

[0056]

[0057] In the formula, h, —Hyperplane function and sample function;

[0058] w — weight vector;

[0059] a——Sample data;

[0060] τ—threshold;

[0061] Make it satisfy the optimal problem:

[0062]

[0063]

[0064] In the formula, C is the penalty function;

[0065] ξ—slack variable;

[0066] b — The category corresponding to the sample.

[0067] Step 3-2: Using the Lagrange dual function, the optimization problem (23) is rewritten as:

[0068]

[0069]

[0070] In the formula, α is the Lagrange coefficient;

[0071] κ — Gaussian kernel function;

[0072] Let α * For the solution of equation (24), the solution for the threshold τ and the weight vector w is expressed as:

[0073]

[0074]

[0075] Substituting equation (25) into equation (23), we obtain the classification discriminant function of the vector machine as follows:

[0076]

[0077] Step 3-3: The posterior probability of the SVM classifying the current state is expressed as:

[0078]

[0079] In the formula —At time k, the SVM classifies the input into state H. i The posterior probability;

[0080] x, y — the input and output of SVM;

[0081] A, B – Coefficients obtained by fitting the SVM training data.

[0082] The method described in this invention for fusing conditional probability and posterior probability using Bayesian linear mixture to obtain a new probability is as follows: Referring to the Bayesian linear mixture method, the fused probability is expressed as:

[0083] In the formula —SVM-MM pair of state H at time k i Calculate the conditional probability.

[0084] α p —The weights of the probabilities calculated from the multi-model calculation.

[0085] The present invention uses the fused probability as the analysis standard and combines it with a threshold to output the state evaluation result of a multi-component mechanical system. Specifically, it fuses the conditional probability of MM and the posterior probability of SVM to form a new conditional probability. Considering the speed requirements of fault diagnosis, a minimum value (0.001) is set for each probability to ensure timely response. Then, the current state is evaluated based on a pre-set threshold.

[0086] j k =arg|p i,k >p thtreshold |i=1,2...n mode | (29)

[0087] In the formula p threshold The probability threshold is set to 0.95. If the value exceeds this threshold, the corresponding state is considered to exist; if the value is below this threshold, the corresponding state is considered to not exist.

[0088] Compared with existing technologies, this invention fully considers the strong coupling characteristics of multi-component mechanical systems. It decouples such mechanical systems by combining observables with graph theory, thereby reducing the computational load of the decoupled subsystems. At the same time, considering the difficulty in early fault diagnosis, it uses the posterior probability of support vector machines and the conditional probability of multiple models to improve the speed of fault detection and isolation of traditional multi-model methods. Attached image description:

[0089] Appendix Figure 1 This is a directed graph of the overall machine parameters in Embodiment 1 of the present invention.

[0090] Appendix Figure 2 This is a directed graph of the intercooler parameters in Embodiment 1 of the present invention.

[0091] Appendix Figure 3 This is a schematic diagram of the improved multi-model fault diagnosis process in Embodiment 1 of the present invention.

[0092] Appendix Figure 4 This is a schematic diagram of the diagnostic results of the intercooler fault in Embodiment 1 of the present invention, wherein... Figure 4 (a) indicates fault S1. Figure 4 (b) indicates fault S2. Detailed implementation method:

[0093] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0094] Example 1:

[0095] This example uses a multi-component marine propulsion system to propose a fault diagnosis method for multi-component marine propulsion systems based on graph theory decoupling and probabilistic fusion.

[0096] First, construct the directed graph of the entire marine propulsion system:

[0097] Based on the sensor location map, the thermodynamic parameters that can be directly measured in marine power plants are listed in Table 1.

[0098] Table 1 Measurement parameters of marine power plants

[0099]

[0100] Considering the operating characteristics of marine propulsion systems, the state variables, output variables, and control variables in the overall state-space model can be expressed as follows:

[0101]

[0102] By treating each variable in the state model as an object and representing it through vertices, and using the thermodynamic relationships between the variables as the lines connecting the vertices, the marine propulsion system can be represented as a directed graph. Elliptical icons correspond to observable variables, while rectangular icons correspond to intermediate variables that cannot be directly measured. For example... Figure 1 As shown.

[0103] Next, we decouple and construct a subsystem model: taking the intercooler as an example, its main parameters include the outlet gas temperature T. sac and intercooler efficiency η sac To establish a state-space model of the intercooler, it must be made observable, that is, T must be... sac η sac Output is achievable, such as Figure 2 As shown.

[0104] in accordance with Figure 2 To fully reflect the operating characteristics of the system, the model of the intercooler subsystem needs to include at least five parameters: the gas mass flow rate and temperature at the compressor outlet, the gas temperature at the intercooler outlet, the intercooler efficiency, and the intercooler cooling water temperature. Therefore, the state model of the intercooler can be represented as follows:

[0105] y sac =f sac (x sac )+u sac (ΔT cool ,Δη sac (2)

[0106] In the formula y sac —Output of the intercooler state model

[0107] x sac —Input to the intercooler state model

[0108] f sac —Based on the intercooler's operating mechanism and structure, T sac =T comp -(η sac +Δη sac )[T comp -(T cool +ΔT cool )];

[0109] Regarding the intercooler's operating condition, potential faults such as clogged air filters or poor main cooling water circulation may exist, thus affecting its efficiency η. sac Drop or cooling water temperature T cool Changes in parameters such as elevation are addressed in the state model by adjusting the control variable u. sacThe numerical values ​​are modified to obtain the corresponding fault representation model, which is then merged with the normal state model to form a filter bank for the intercooler. Subsequently, the measured data is used as input to the filter bank and filtered using the unscented Kalman filter. The conditional probability is calculated using Bayesian principles based on the residuals generated by each state model; this probability reflects the likelihood of the assumed state occurring. Additionally, the residuals of the normal state model are used as input to a pre-trained support vector machine, enabling it to classify the current state and calculate the corresponding posterior probability. The posterior probability is then fused with the conditional probabilities of the multiple models using a Bayesian linear fusion method to form a new conditional probability, thereby improving the speed of fault detection and isolation by the multiple models. Finally, the current operating state of the marine propulsion system is evaluated based on the fused conditional probability and a threshold, achieving fault diagnosis and isolation, as shown in the figure.

[0110] Next, we establish the system state model: For a mechanical system, at time k, we use the parameter set x with the minimum number of parameters. k This allows for a comprehensive and accurate description of the system's dynamic characteristics, then x k This is called the state variable of the system, and its relationship with the state variable at the previous moment is as follows:

[0111] x k =f(x) k-1 ,u k-1 )+w k (3)

[0112] In the formula, f is the system state transition equation;

[0113] u — control variables, the set of variables that affect the state of the system;

[0114] w—System noise, including errors in the system state transition equations, modeling errors, etc.;

[0115] k-1 — indicates the time t = k-1

[0116] For the output variable y of the system, it is generally chosen to be the set of observable variables of the system. Let its relationship with the state variables at time k be:

[0117] y k =g(x k ,u k )+v k (4)

[0118] In the formula, g represents the measurement conversion equation;

[0119] v k —Measurement noise, such as sensor noise error, etc.

[0120] Then, by combining equations (3) and (4), we can express the state model of the system.

[0121] UKF selects multiple sigma points based on the current operating point, calculates the mean and covariance of this set of points through unscented transformation, and uses this to perform filtering calculations. Because UKF retains all the information of the nonlinear function, it only needs to iterate and calculate each sigma point in each step, which has higher accuracy and speed than EKF.

[0122] (2) Calculate the sigma point and make predictions:

[0123]

[0124]

[0125] In the formula P xx —The state variables and their error covariance corresponding to the i-th sigma point;

[0126] μ—the mean of the state variables;

[0127] —State and output variables predicted by sigma points;

[0128] (3) Calculate the state variables and error covariance:

[0129]

[0130]

[0131] In the formula These are the state variables and their error covariance calculated from the unscented transformation at time k; It is the covariance of the systematic error at time k.

[0132] (4) Calculate the output variables and error covariance:

[0133]

[0134]

[0135] In the formula —The output variable and its error covariance calculated by the unscented transformation at time k;

[0136] — Covariance of measurement error at time k.

[0137] (5) Calculate the Kalman gain and residual:

[0138]

[0139]

[0140]

[0141] In the formula P xy —The error covariance between state variables and output variables;

[0142] K—Kalman gain;

[0143] e – residual.

[0144] (6) Update the state variables and error covariance:

[0145]

[0146]

[0147] In the formula, x, P xx —The updated state variables and their error covariance.

[0148] Calculate the conditional probabilities of multiple models:

[0149] For multiple possible operating states, corresponding models are established and filtered separately. The model with the smallest filtered residual corresponds to the state closest to the current operating state. Based on this principle, it is assumed that the marine propulsion system has n states at time k. mode One possible running state H i (i = 1, 2, ... n) mode If the state at time k is only related to the previous time k-1, then based on the data measured at time k and before, the system is currently in operation H. j The conditional probability of a state is represented by a first-order Markov chain as follows:

[0150] p j,k =p(H j |J k (18)

[0151] In the formula p j,k —At time k, the state is H j The probability of;

[0152] H j —The j-th running state, where 1≤j≤n mode ;

[0153] J k —The historical data set at time k, i.e., J k =(y0,y1,y2,...y k ), where y is the measurement data.

[0154] Furthermore, based on the filtering residuals and covariance of each model, the conditional probability density of each state can be expressed as:

[0155]

[0156] In the formula f p (y k |H i J k — The state H corresponding to time k i The conditional probability density;

[0157] e i,k ,P zz,i,k —The residuals and covariance generated by UKF filtering at time k.

[0158] Combining equations (18) and (19), the conditional probability of each state at time k is updated according to Bayes' theorem as follows:

[0159]

[0160] In the formula —The corresponding state H obtained from multi-model calculation at time k i The conditional probability;

[0161] n mode — The number of possible states.

[0162] Calculate the posterior probability of the SVM:

[0163] The principle of SVM is to find a hyperplane within the ensemble space formed by multiple sets of data:

[0164]

[0165] In the formula, h, —Hyperplane function and sample function;

[0166] w — weight vector;

[0167] a——Sample data;

[0168] τ—threshold.

[0169] Make it satisfy the optimal problem:

[0170]

[0171]

[0172] In the formula, C is the penalty function;

[0173] ξ—slack variable;

[0174] b — The category corresponding to the sample.

[0175] Using the Lagrange dual function, the optimization problem (23) can be rewritten as:

[0176]

[0177]

[0178] In the formula, α is the Lagrange coefficient;

[0179] κ — Gaussian kernel function.

[0180] Let α * For the solution of equation (24), the solution for the threshold τ and the weight vector w can be expressed as:

[0181]

[0182]

[0183] Substituting equation (25) into equation (23), we obtain the classification discriminant function of the vector machine as follows:

[0184]

[0185] During fault diagnosis, the actual measured data contains noise and outliers, requiring denoising and normalization before it can be used for SVM training or prediction. UKF denoises the current data while preserving higher-order terms; simultaneously, the differences between various faults and normal states are reflected in the residuals after filtering by the normal model. Therefore, the residuals generated by the normal model filtering various states can be considered as data samples after denoising and feature extraction, used for SVM training or prediction. Thus, by training the SVM using the residuals from various operating states, its function of classifying operating conditions is achieved. Correspondingly, the posterior probability of the SVM classifying the current state can be expressed as:

[0186]

[0187] In the formula —At time k, the SVM classifies the input into state H. i The posterior probability;

[0188] x, y — the input and output of SVM;

[0189] A, B – Coefficients obtained by fitting the SVM training data.

[0190] Perform probability fusion:

[0191] Probabilistic fusion combines information from two different sources, while ensuring the mathematical completeness and consistency of the fused probabilities. Since the inputs to both multi-model and SVM originate from the same state, and p... MM and p SVM Since the probability distributions are the same, the Bayesian mixture method can be used for fusion. Common Bayesian mixture methods include linear and logarithmic forms. This invention refers to the Bayesian linear mixture method, and the fused probability can be expressed as:

[0192]

[0193] In the formula —SVM-MM pair of state H at time k i Calculated conditional probability

[0194] α p —The weights of the probabilities calculated from the multi-model calculation.

[0195] The conditional probabilities of MM and the posterior probabilities of SVM are fused to form new conditional probabilities. Considering the speed requirements of fault diagnosis, a minimum value (0.001) is set for each probability to ensure timely response. Then, based on a pre-set threshold, the current state can be evaluated.

[0196] j k =arg|p i,k >p thtreshold |i=1,2...n mode | (29)

[0197] In the formula p threshold —The probability threshold is set to 0.95. If the value exceeds this threshold, the corresponding state is considered to exist.

[0198] If the value is below this threshold, the corresponding state is considered not to exist.

[0199] Taking a filter clogging issue in an intercooler as an example, the clogging doesn't happen instantly. Instead, it gradually evolves from a clean and unobstructed state to becoming clogged with contaminants over time, leading to a decrease in intercooler efficiency. Therefore, the fault involves an evolutionary process. However, traditional multi-model diagnostic methods require waiting for the fault to evolve to a certain stage before it can be detected and isolated. In this invention, probability fusion can improve the diagnostic speed. During the fault evolution process, measured data... As input, the probability of occurrence of three intercooler states (normal S0, filter blockage S1, and poor main cooling water circulation S2) at different times is calculated using an improved multi-model approach.

[0200] Table 2 Performance Indicators for Intercooler Fault Diagnosis

[0201]

[0202] Table 2 shows the weight coefficients α of three methods (MM, SVM-MM1, and SVM-MM2). p =0.98, α of SVM-MM2 p The performance index (α = 0.95) shows that after incorporating the posterior probability of SVM, the detection and isolation speed of SVM-MM are improved, and the speed increases with the weighting coefficient α. p The decrease leads to a greater increase. For example, Figure 4 As shown in (a), during the diagnosis of fault S1, before step 171, the conditional probability calculated by MM for state S0 is... All values ​​were greater than 0.95, and after step 171, they decreased to less than 0.95, indicating that MM considered the intercooler to be in normal condition before step 171, but detected an abnormality in the intercooler in step 171; at the same time, MM checked the intercooler in step 176. If the calculated value exceeds 0.95, the intercooler is considered to be operating in state S1, meaning the filter blockage fault has been correctly isolated. For SVM-MM, when α... p When it equals 0.98, it is in step 168. The calculated value was below 0.95, indicating an anomaly was detected; and the result calculated in step 175... Exceeding the threshold, the intercooler is considered to be in state S1, representing a 4.23% improvement in detection speed and a 1.32% improvement in isolation speed compared to MM. When the weighting coefficient is further reduced, at α... p At a value of 0.95, the diagnostic speed of SVM-MM is further improved, by 32.39% and 1.32% respectively compared to MM. For the diagnosis of fault S2, from... Figure 4 Analysis in (b) shows that SVM-MM also has a faster diagnostic speed, improving by 5.00% and 4.35%, and 35.00% and 6.09%, respectively. However, both MM and SVM-MM experienced false alarms for a period of time, with the calculated probability of fault S1 exceeding 0.95. This is because in the early stages of the evolution of fault S2, parameter fluctuations are not significant or exhibit characteristics of S1, thus increasing the probability of p1. In the posterior probability calculations of SVM from steps 141 to 174, the probability of S1 is generally higher than 0.9, further verifying this reason. However, SVM has higher sensitivity than MM. Therefore, after probability fusion, SVM-MM reduced the alarm duration by 8.47% (SVM-MM1) and 40.68% (SVM-MM2) compared to MM, indicating that SVM-MM has better robustness. The weighting coefficient α pThe value of not only affects the speed of fault detection and isolation in MM, but also determines the degree of influence of SVM on the uncertainty of classification results. The smaller the weight coefficient, the higher the probability of fusion calculated by SVM as p. SVM The greater the weight of the variable, the faster the detection and isolation speed will be. However, the impact of SVM uncertainty will also increase. Therefore, when applying SVM-MM for fault diagnosis, the selection should be based on the SVM's prediction accuracy on the training data and the degree to which the model reflects the actual fault.

[0203] Compared with existing technologies, this invention fully considers the strong coupling characteristics of multi-component mechanical systems. It decouples such mechanical systems by combining observables with graph theory, thereby reducing the computational load of the decoupled subsystems. At the same time, considering the difficulty in early fault diagnosis, it uses the posterior probability of support vector machines and the conditional probability of multiple models to improve the speed of fault detection and isolation of traditional multi-model methods.

Claims

1. A fault diagnosis method for multi-component marine propulsion systems based on graph theory decoupling and probabilistic fusion, characterized in that, First, the directed graph of the marine propulsion system is constructed: Based on the sensor point map, the state variables, output variables, and control variables in the overall state-space model are represented by combining the directly measured thermodynamic parameters of the marine propulsion system with the operating characteristics of the system: （1）， In the state model, each variable is treated as an object and represented by a vertex. The thermodynamic relationship between each variable is used as the connection between vertices to represent the marine power plant as a whole as a directed graph. Next, the subsystem model is decoupled and constructed. The parameters of the intercooler include the outlet gas temperature. and intercooler efficiency To establish a state-space model of the intercooler, it must be made observable, that is, to make... , To fully reflect the operating characteristics of the system, the model of the intercooler subsystem needs to include five parameters: the gas mass flow rate and temperature at the compressor outlet, the gas temperature at the intercooler outlet, the intercooler efficiency, and the intercooler cooling water temperature. Therefore, the state model of the intercooler is represented as follows: (2), In the formula This is the output of the intercooler state model. ; It is the input of the intercooler state model. ; It is constructed based on the operating mechanism of the intercooler. ; The intercooler's operating condition is affected by issues such as a clogged air filter or poor main cooling water circulation, which can lead to reduced efficiency. Decrease or cooling water temperature The increase is achieved by adjusting the control variables in the state model. The numerical values ​​are modified to obtain the corresponding fault representation model, which is then merged with the normal state model to form a filter bank for the intercooler. Subsequently, the measured data is used as input to the filter bank and filtered using the unscented Kalman method. The conditional probability is calculated based on the residuals generated by each state model using the Bayesian principle, which reflects the likelihood of the assumed state occurring. The residuals of the normal state model are used as input to a pre-trained support vector machine to classify the current state and calculate the corresponding posterior probability. The posterior probability and the conditional probability of the multiple models are fused using the Bayesian linear fusion method to form a new conditional probability, thereby improving the speed of fault detection and isolation by the multiple models. Finally, the current operating state of the marine power unit is evaluated based on the fused conditional probability and threshold, realizing fault diagnosis and isolation. The state-space model is achieved through the following: For any multi-component mechanical system, in Use the set of parameters with the smallest number at all times. If it can comprehensively and accurately describe the dynamic characteristics of the system, then This is called the state variable of the system, and its relationship with the state variable at the previous moment is as follows: （3）， In the formula The system state transition equations; Control variables are the set of variables that affect the state of the system. This refers to system noise, including errors in the system state transition equations and modeling errors. Indicates being in The moment; , for State variables and control variables at any given time; For the system's output variables Let be the set of variables that the system can observe, and let them be in The relationship between time and state variables is as follows: （4）， In the formula For measurement transformation equations; For measuring noise; To control variables, Then, by combining equations (3) and (4), we can express the state model of the system.

2. The fault diagnosis method for multi-component marine propulsion systems based on graph theory decoupling and probabilistic fusion according to claim 1, characterized in that, The unscented Kalman filtering process selects multiple sigma points based on the current operating point, calculates the mean and covariance of this set of points through unscented transformation, and performs filtering calculations accordingly. Specifically, it includes the following steps: Step 1-1: Initialize the mean weights and error covariance weights of the state variables: （5）， （6）， In the formula , These are the weights of the mean of the state variables and the weights of the covariance of the errors of the state variables; for The weights of the error covariance of the state variables at that time; for The weights of the error covariance of the state variables at time. , representing the distance between the sigma point and the mean; It is the distribution range of the sigma points around the mean, taking... ; It is prior knowledge of the mean distribution, taking ; and This is a secondary scaling parameter; take the value. It is the dimension of the sampled data; Step 1-2: Calculate the sigma point and make predictions: （7）， （8）， In the formula For the first The state variables corresponding to each sigma point; for The state variable corresponding to the first sigma point; for Time control variables; for The state variable corresponding to the first sigma point; for The error covariance of the state variable corresponding to the first sigma point; for The state variable at any given time; for The state transition equation at time t; for Output variables at any given time; for The conversion equation for measuring time. The mean of the state variables; , These are the state variables and output variables predicted by the sigma points; Steps 1-3: Calculate the state variables and error covariance: （9）， （10）， In the formula , for The state variables and their error covariance calculated from the unscented transformation at time 1; for Covariance of the time-series systematic error; for The weight of the mean of the state variable corresponding to the (i+1)th sigma point; for The state variable corresponding to the (i+1)th sigma point; for The state variable error covariance is calculated at that time. for The state variable corresponding to the (i+1)th sigma point; Steps 1-4: Calculate the output variables and error covariance: （11）， （12） ， In the formula , yes The output variables and their error covariance calculated by the unscented transformation at each time step; yes Covariance of time measurement error; for The output variable is calculated at that time; for The weight of the mean of the state variable corresponding to the (i+1)th sigma point; for The output variable corresponding to the (i+1)th sigma point at time i; for The weights of the covariance of the state variable corresponding to the (i+1)th sigma point; for The state variable corresponding to the (i+1)th sigma point; for The output variable error covariance is calculated at the time. Steps 1-5: Calculate the Kalman gain and residuals: （13）， （14）， （15）， In the formula It is the error covariance between the state variables and the output variables; It is Kalman gain. It is a residual; for The error covariance between the state variables and the output variables at any given time; for Kalman gain at time step; for The inverse matrix of the error covariance of the output variable is calculated at the same time; for The residuals at time step, steps 1-6: update the state variables and error covariance: （16）， （17）， In the formula , These are the updated state variables and their error covariance, respectively.

3. The fault diagnosis method for multi-component marine propulsion systems based on graph theory decoupling and probabilistic fusion according to claim 2, characterized in that, Obtaining the conditional probabilities of multiple models specifically includes the following steps: Step 2-1: Assume a multi-component mechanical system in Always exist One possible running state , ,and The state at any given moment is only related to the state at the previous moment. If relevant, then through Data measured at or before this time, currently in operation. The conditional probability of a state is represented by a first-order Markov chain as follows: （18） In the formula Is Always in a state of readiness The probability of; It is the first There are several operating states, among which ; yes The historical data set at any given moment, i.e. , For measurement data; Step 2-2: Based on the filtering residuals and covariance of each model, the conditional probability density of each state is expressed as: （19） In the formula yes Time corresponding to state The conditional probability density; , yes The residuals and covariance generated by UKF filtering at each time step; Step 2-3: Combining equations (18) and (19), according to Bayes' theorem... The conditional probability of each state at time step 1 is updated as follows: （20） In the formula yes The corresponding state calculated by the multi-model at each time step The conditional probability; It represents the number of possible states.

4. The fault diagnosis method for multi-component marine propulsion systems based on graph theory decoupling and probabilistic fusion according to claim 3, characterized in that, Obtaining the posterior probability of SVM specifically includes the following steps: Step 3-1: Find a hyperplane within the ensemble space formed by multiple sets of data: （22）， In the formula , These are hyperplane functions and sample functions; It is a weight vector; It is sample data; It is a threshold; to make it satisfy the optimal problem: （23）， In the formula It is a penalty function. It is a slack variable. It is the category corresponding to the sample. Step 3-2: Using the Lagrange dual function, the optimization problem (23) is rewritten as: (24), where It is the Lagrange multiplier; It is a Gaussian kernel function; set up If the solution to equation (24) is the threshold, then and weight vector The solution is expressed as: （25） ， Substituting equation (25) into equation (23), we obtain the classification discriminant function of the vector machine as follows: （26） ， Step 3-3: The posterior probability of the SVM classifying the current state is expressed as: （27） ， In the formula yes At time 1, the SVM classifies the input into states. The posterior probability; , These are the inputs and outputs of the SVM; , These are coefficients obtained by fitting the SVM training data.

5. The fault diagnosis method for multi-component marine propulsion systems based on graph theory decoupling and probabilistic fusion according to claim 4, characterized in that, The method of fusing conditional probability and posterior probability using Bayesian linear mixture to obtain a new probability is as follows: Referring to the Bayesian linear mixture method, the fused probability is expressed as: （28）， In the formula for Time SVM-MM pair of states Calculate the conditional probability. The weights are the probabilities calculated for the corresponding multi-model calculations.

6. The fault diagnosis method for multi-component marine propulsion systems based on graph theory decoupling and probabilistic fusion according to claim 5, characterized in that, The method of using the fused probability as the analysis standard and combining it with a threshold to output the state evaluation result of the multi-component mechanical system is as follows: the conditional probability of MM and the posterior probability of SVM are fused to form a new conditional probability. Considering the speed requirements of fault diagnosis, a minimum value (0.001) is set for each probability to ensure timely response. Then, the current state is evaluated based on the pre-set threshold. （29）， In the formula The probability threshold is set to 0.

95. If the value exceeds this threshold, the corresponding state is considered to exist; if the value is below this threshold, the corresponding state is considered to not exist.

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