Vibration monitoring sensor measuring point optimization layout method

Abstract

The invention discloses a vibration monitoring sensor measuring point optimization layout method, which comprises the following steps of: firstly, extracting fault characteristics of a diesel engine in different states, constructing a percentage difference matrix, and providing a data basis for subsequent optimization; secondly, based on the percentage difference matrix and a sensor fault threshold, establishing a fault distinguishing matrix for judging distinguishability between different states; then, designing a multi-objective optimization function, and balancing the fault distinguishing capability of a sensor arrangement scheme and the number of sensors; further, a multi-objective optimization algorithm is utilized to optimize the sensor arrangement scheme, and an optimal sensor arrangement scheme is searched; thirdly, continuously iteratively screening each generation of non-dominated solution by using an optimization algorithm, combining the non-dominated solutions into a non-dominated solution set, and updating and outputting the non-dominated solution set based on a Pareto algorithm; and finally, screening a sensor arrangement scheme meeting the requirements of high index fault coverage rate, few sensors and high distinguishing capability as an optimal sensor arrangement scheme.

Description

Technical Field

[0001] This invention relates to the field of sensor layout optimization, specifically to a method for optimizing the layout of sensor measuring points for vibration monitoring of mechanical equipment based on the degree of fault difference and multi-objective optimization. Background Technology

[0002] As a core power unit in the industrial sector, the operational stability of diesel engines in key industries such as shipbuilding and power generation directly determines the continuity and economy of production. With the upgrading of industrial technology, diesel engines are developing towards higher parameters, and failure modes are becoming increasingly complex, placing stringent requirements on the real-time performance and accuracy of health monitoring. As the data entry point for the monitoring system, the arrangement of sensors directly affects the effectiveness of fault diagnosis. Excessive arrangement can lead to structural redundancy and information interference, while insufficient arrangement can fail to capture key features, especially when sensors fail, resulting in monitoring blind spots.

[0003] In existing research, patent CN 117350056 A provides a method for optimizing the arrangement of diesel engine monitoring sensors based on the Pareto particle swarm optimization algorithm. This method selects a sensor arrangement scheme with the fewest sensors that can still distinguish all faults even after any sensor fails, ensuring that the diesel engine's fault differentiation capability is not affected by sensor failure. It effectively reduces the number of sensors and provides multiple alternative arrangement schemes. Patent CN112052952A combines conditional entropy, attribute importance, and the number of sensors to design a fitness function. By using the number of sensors and information as conflict objectives, it uses a genetic algorithm to search for the optimal sensor arrangement scheme with the fewest sensors and the largest amount of information. However, neither of these methods considers the situation where the fault differentiation capability of the sensor scheme can be maintained after multiple sensor failures. This invention addresses this by proposing redundant constraints, ensuring that the optimization algorithm pre-places multiple sensors in the same or multiple locations of the equipment, thus preventing the sensor scheme from losing its fault differentiation capability after sensor failure. Summary of the Invention:

[0004] The technical solution adopted by this invention to solve the above problems is: a method for optimizing the layout of measuring points of vibration monitoring sensors for mechanical equipment based on fault difference degree and multi-objective optimization, characterized by including the following steps:

[0005] Step 1: Extract fault characteristics of diesel engines under different conditions and construct a percentage difference matrix to provide a data foundation for subsequent optimization.

[0006] Step 1.1, Obtain initial data: Define the diesel engine state set K = {k1, k2, ..., k m}, where k1 represents the normal state, k2 to k mLet m represent the total number of states, and let m represent the fault state. We obtain diesel engine operating data from n vibration monitoring sensors for each state in the diesel engine state set K, resulting in the initial matrix G = G_0. i,j :

[0007]

[0008] Where i represents the diesel engine status, 1≤i≤m, and j represents the sensor number, 1≤j≤n;

[0009] Step 1.2, based on the initial matrix G = G i,j Obtain the percentage difference matrix B = {b1, b2, ..., b} h ,...b m For each state k h ,in accordance with

[0010]

[0011] Calculate the percentage difference between other states and this state to obtain the percentage difference matrix b. h Represented as:

[0012]

[0013] Among them, G h,j This represents the monitoring data of sensor j under state h, b h Let a represent the percentage difference matrix between each state in the h-th state and the current state, where h ranges from 1 to m; i,j This represents the percentage difference between the monitoring data of the j-th sensor in state i and state h, where 1 ≤ i ≤ m, 1 ≤ j ≤ n, and a i,j =0 indicates that under the j-th sensor, the percentage difference between the i-th state and the h-th state is 0; the h-th row represents the percentage difference between each sensor under the h-th state and the h-th state, all of which are 0;

[0014] Step 2: Based on the percentage difference matrix and sensor fault threshold, establish a fault differentiation matrix to determine the distinguishability between different states.

[0015] Step 2.1, Adaptively update sensor thresholds based on collected fault case data: Define each sensor threshold Thd = {th1, th2, ..., th...} n}, the fault threshold th corresponding to the j-th sensor j ;

[0016] Step 2.2: Compare the percentage difference in each column of the percentage difference matrix with the corresponding fault threshold, i.e., the percentage difference in column j is compared with the threshold value in column th. j Compare, if ai,j >th j This indicates that the states differ significantly, let d p,l Setting d to 1 allows for differentiation; conversely, setting d to 0 indicates that the states are relatively close. p,l Taking 0 makes it difficult to distinguish.

[0017] Step 2.3, using the fault differentiation threshold Thd and the percentage difference matrix b h The fault differentiation matrix D = {d1, d2, ..., d} is constructed. m}, D h =(d i,j ) m×n Represented as:

[0018] th1 th2…th n

[0019]

[0020] Fault Differentiation Matrix D under state h h Represented as:

[0021]

[0022] Where d i,j This represents the fault differentiation value of sensor j between state i and state h, where i ranges from 1 to m; j ranges from 1 to n; d i,j The value range of d is 0 and 1. i,j A value of 0 indicates that sensor j has a small difference between state i and state h. If the sum of all values ​​in a row is 0, then state i and state h form an equivalence cluster. h Since the percentage difference in row h is all 0, it is obviously all below the threshold. Therefore, it belongs to the same equivalence cluster as itself. Conversely, if the sum of an entire row is not 0, it is classified according to the redundancy quantification constraint in step 2.4.

[0023] Step 2.4, define redundancy quantification constraints:

[0024] Calculate the row sum of the p-th row in the matrix for each pair of states (p, h):

[0025]

[0026] Where row_sum is the total number of sensors that can distinguish the state pair, 1≤p≤m;

[0027] Redundancy is defined as:

[0028] ry = row_sum - y

[0029] Where y is the preset minimum number of distinguishing sensors, y≥1.

[0030] To address the degree of difference between different fault pairs in diesel engines, a minimum redundancy requirement is set through a redundancy constraint matrix: for example, fault pairs with minor differences require ry≥1, i.e., row_sum≥2 and row_sum-y≥1; for fault pairs with significant differences, ry≥0 can be set, i.e., row_sum≥1 and row_sum-y≥0, to ensure that the sensor can still maintain its distinguishing ability when it fails.

[0031] The redundancy constraint matrix is ​​defined as follows:

[0032]

[0033] A redundancy is set between each pair of faults. Before modification, the default redundancy is 0, i.e., row_sum = y = 1. Therefore, according to the conclusion in step 2.3: if the redundancy between state i and state h is not 0, calculate the row sum of the i-th row:

[0034]

[0035] Step 2.5, Calculation of individual sensor discrimination capability:

[0036] The percentage differences exceeding a threshold in the same column of each percentage difference matrix are summed to represent the discrimination capability of a single sensor, expressed as:

[0037]

[0038] Where A s,j This represents the discrimination capability of the j-th sensor in sensor scheme s, where the value of j ranges from 1 to n;

[0039] Step 3: Design a multi-objective optimization function to balance the fault differentiation capability and the number of sensors in the sensor layout scheme.

[0040] Step 3.1, determine the fault equivalence cluster: based on the fault differentiation matrix D = {d1, d2, ..., d...} m The state set K is divided into several fault equivalence clusters v. x ={K1,K2,…,K t}, where t≤m represents the number of equivalent clusters.

[0041] Step 3.2, define the optimization sub-function:

[0042] (1) Fault coverage sub-function f1: measures the number of fault equivalence clusters. The fewer the number of equivalence clusters, the higher the fault coverage.

[0043]

[0044] The effective calculation of the fault coverage sub-function must satisfy the redundancy constraint pre-verification: if the redundancy of any pair of faults in the fault differentiation matrix corresponding to the sensor layout scheme is lower than the minimum requirement in the redundancy constraint matrix, then f1 is directly forced to be 0, and the scheme is marked as an invalid solution; only when the redundancy of all fault pairs satisfies the constraint that ry> the preset value, and the number of equivalent clusters t conforms to the logic, will f1 be taken according to the original formula.

[0045] (2) Sensor Quantity Subfunction f2: Measures the number of sensors in the sensor layout scheme. The fewer the number of sensors, the lower the cost.

[0046]

[0047] (3) Fault discrimination capability sub-function f3: measures the sum of the discrimination capabilities of each sensor for each fault state. The more sensors there are, the stronger the discrimination capability.

[0048]

[0049] Where t represents the number of fault clusters, m represents the number of states in the state set, m-1 represents the number of fault states, N represents the number of sensors in the diesel engine condition monitoring sensor set L, |s| represents the number of sensors in sensor layout scheme s, and A s This represents the sum of the capabilities of all sensors in sensor arrangement scheme s to distinguish each normal or faulty state from other states.

[0050] Step 3.3, based on the fault differentiation matrix D under sensor layout scheme s. d ={D1, D2, ..., D m} and equivalent cluster v x Given the number of sensors and the sensor fault discrimination capability under sensor layout scheme s, the multi-objective optimization function F for designing the sensor layout scheme is expressed as:

[0051] F = [f1, f2, f3]

[0052] Step 3.4: In the multi-objective optimization problem, since there is a conflict between the fault discrimination capability sub-function f3 and the sensor quantity sub-function f2, there is no unique optimal solution. Therefore, the Pareto non-dominated algorithm is used to select a set of approximate Pareto optimal solutions.

[0053] Step 3.5 is implemented through the following steps: Compare the objective function values ​​[f1, f2, f3] of all sensor placement schemes pairwise and record the non-dominated solutions; retain the non-dominated solutions to form a temporary solution set NDset, and set the crowding degree of the solutions with the largest and smallest objective values ​​in the temporary solution set to infinity to ensure they are not deleted; in maintaining the solution set, prioritize retaining solutions with high crowding degree and delete redundant solutions to ensure that the non-dominated solutions are evenly distributed in the objective space, avoiding the algorithm from converging to a local optimum; iteratively update the solution set, and the final Pareto front output is the set of optimal sensor placement schemes.

[0054] Step 4: Optimize the sensor layout scheme using a multi-objective optimization algorithm to find the optimal sensor layout scheme.

[0055] Step 4.1, randomly generate an initial population P = (s1, s2, ..., s z Let z be the number of individuals in the population, and each individual in the population represents a sensor placement scheme. The sensor placement scheme is represented by a binary vector Vn = (l1, l2, ..., ln). n ) indicates that l i ∈{0,1}, i=1,2,…,n, where l i =0 indicates that the i-th sensor in the state monitoring sensor set L is not included in the sensor layout scheme, and vice versa; n represents the total number of sensors.

[0056] Step 4.2 Before evaluating each sensor deployment scheme in the population, the row sum and redundancy of all fault pairs must be calculated using the fault differentiation matrix in Step 2 to perform redundancy constraint verification: If the redundancy of any pair of faults is lower than the constraint value in the redundancy constraint matrix, the scheme is directly marked as an invalid solution and will not participate in the Pareto non-dominated solution screening.

[0057] Step 4.3: Initialize a non-dominated solution set ND before optimization. Using the multi-objective optimization function F = [f1, f2, f3] for sensor placement schemes, evaluate each individual in the population that passes redundancy check based on the Pareto algorithm: Calculate the three sub-functions f1, f2, f3 for each individual. Iterate through all individuals in the population, comparing the objective function values ​​pairwise between different individuals. If individual a's f1, f2, f3 are all no worse than individual b's, and at least one objective is strictly better than b's, then a dominates b, b is excluded from ND, a is marked as a non-dominated solution, and all non-dominated solutions are entered into the initial non-dominated solution set ND.

[0058] Step 4.4: Select and record the initial global optimal individual position s from ND. g,d and the individual's historical best position s i,dThe solution with f1=1 and the highest crowding is selected first as the initial optimal position of the optimization algorithm;

[0059] Step 5: Iteratively filter the non-dominated solutions of each generation using optimization algorithms, merge them into the non-dominated solution set, and update the non-dominated solution set NDset based on the Pareto algorithm.

[0060] Step 5.1: Receive the solution set ND as the population to be optimized, initialize the non-dominated solution set NDset, set the stopping iteration condition to stop the iteration when no new non-dominated solution appears for 10 consecutive iterations or when the maximum number of iterations Imax is reached, and set the auxiliary parameters of the initial population: the initial velocity of the particle swarm is a random number between [0,1], and the crossover mutation probability of the genetic algorithm.

[0061] Step 5.2: Update the velocity vector and position vector of each individual or the gene values ​​and arrangement order in the individual chromosomes based on the initial optimal position obtained in Step 4.

[0062] Step 5.3: Verify redundancy constraints. If the redundancy of any pair of faults is lower than the constraint value in the redundancy constraint matrix, the solution is directly marked as an invalid solution and will not participate in the Pareto non-dominated solution screening.

[0063] Step 5.4: Use the multi-objective optimization function F = [f1, f2, f3] of the sensor deployment scheme to evaluate the three objective function values ​​of each individual in the population;

[0064] Step 5.5: Select and record the position s of the current global best individual in the population. g,d and the individual's historical best position s i,d The solution with f1=1 and the highest crowding is selected as the direction of optimization. At the same time, the current population is merged with the non-dominated solution set NDset, and non-dominated solutions are selected based on the Pareto algorithm to update the non-dominated solution set NDset.

[0065] Step 5.6: Determine if no new non-dominated solution appears for 10 consecutive iterations. If so, stop the iteration and output the non-dominated solution set NDset. Otherwise, repeat steps 2 to 5 until no new non-dominated solution appears for 10 consecutive iterations or the maximum number of iterations is reached. Then stop the iteration and output the non-dominated solution set NDset.

[0066] Step Six: Filter the non-dominated solution set according to the required conditions:

[0067] Step 6.1: To achieve full fault coverage, it is necessary to filter and retain solutions where the fault coverage sub-function f1 = 1.

[0068] Step 6.2: In order to ensure that the selected sensor solutions have a greater ability to distinguish faults, the ability to distinguish faults is classified as follows: Under the condition of satisfying full fault coverage, sensor solutions with excellent distinguishing ability are given priority.

[0069]

[0070] Step 6.3: Under the constraints of satisfying full fault coverage and excellent discrimination capability, select the scheme with the fewest number of sensors as the optimal sensor layout scheme. Attached image description:

[0071] (1) Appendix Figure 1 Overall flowchart of the sensor measurement point layout optimization method

[0072] (2) Appendix Figure 2 Flowchart for step four

[0073] (3) Appendix Figure 3 Flowchart for step five

[0074] (4) Appendix Figure 4 Line chart comparing specific implementation results Detailed implementation method:

[0075] Based on diesel engine failure examples, and in accordance with the appendix Figure 1 The overall process of optimizing the sensor measurement point layout and verifying the optimal layout scheme set is as follows:

[0076] The first step is to obtain diesel engine data and construct a percentage difference matrix:

[0077] k1 indicates a wear failure in the large end bearing, k2 indicates a wear failure in the small end bearing, k3 indicates a wear failure in the main bearing, and k4 indicates a knocking failure. 1-20 The vibration acceleration measurements are taken at 20 measuring points on the diesel engine, in mm / s². 2 .

[0078]

[0079] 1. Table 1 shows the diesel engine fault data:

[0080]

[0081]

[0082] The initial matrix G = G is formed from the data in the table above. 4×20 ;

[0083] 2. Establish the percentage difference matrix for each state, as shown below:

[0084] From the initial matrix G = G 4×20 Calculate the percentage difference 'a' between each pair of sensor states. i，j Obtain the percentage difference matrix b h .

[0085]

[0086] The specific calculations are as follows:

[0087] k1's characteristic fault matrix b1

[0088]

[0089] k2's characteristic fault matrix b2

[0090]

[0091] k3's characteristic fault matrix b3

[0092]

[0093] k4's characteristic fault matrix b4

[0094]

[0095] Step 2: Construct the fault differentiation matrix:

[0096] Using percentage difference matrix b h The fault discrimination matrix D is obtained by comparing each column of data with the corresponding threshold of the sensor. h ;

[0097] th1 th2…th 20

[0098]

[0099] The specific calculations are as follows:

[0100] 1. Based on the collected fault case data, the sensor threshold is adaptively updated. In this example, the sensor sequence threshold Thd is set to [0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05];

[0101] 2. Each column of the above matrix is ​​compared with the threshold to obtain the fault differentiation matrix D = {D1, D2, D3, D4}; the matrix is ​​shown below:

[0102] Fault differentiation matrix D1 of k1

[0103]

[0104] Calculate the sum of each row. The first row has a sum of 0, the second row has a sum of 7, the third row has a sum of 20, and the fourth row has a sum of 20. Thus, the four states can be distinguished.

[0105] Fault differentiation matrix D2 of k2

[0106]

[0107] Calculate the sum of each row. The first row has a sum of 7, the second row has a sum of 0, the third row has a sum of 20, and the fourth row has a sum of 20. Thus, the four states can be distinguished.

[0108] Fault Differentiation Matrix D3 of k3

[0109]

[0110] Calculate the sum of each row to get the first row sum to be 20, the second row sum to be 20, the third row sum to be 0, and the fourth row sum to be 20. Then the four states can be distinguished.

[0111] Fault Differentiation Matrix D4 of k4

[0112]

[0113] Calculate the sum of each row. The first row sums to 20, the second row sums to 20, the third row sums to 20, and the fourth row sums to 0. Thus, the four states can be distinguished.

[0114] 3. Define the redundancy constraint matrix:

[0115]

[0116] The third step is to optimize the sensor placement scheme using a multi-objective optimization algorithm:

[0117] This example uses the multi-objective particle swarm optimization algorithm, based on the attached... Figure 2 With appendix Figure 3 Optimize the middle steps:

[0118] A random particle swarm P with 50 particles is generated. The maximum number of iterations for particle swarm optimization is set to 100, and the initial inertia weight w is set to 1.2. Each particle is evaluated based on calculated f1, f2, and f3 using a multi-objective optimization function. The optimal arrangement schemes are shown in the table below.

[0119]

[0120]

[0121] While ensuring fault coverage, the optimal solution reduces the number of sensors from 20 to 4-6. Taking the sensor layout scheme in the table above as an example, the line graph comparing the objective function values ​​of the schemes is attached. Figure 4 As shown; from the appendix Figure 4 It can be seen that: Schemes 3 and 4 have a fault coverage sub-function value of 1, which guarantees full fault coverage, while the other schemes cannot achieve full fault differentiation coverage; the fault differentiation capabilities of Schemes 3 and 4 are both greater than 8.4, which is in the excellent range; comparing the number of sensors in the two schemes, Scheme 3 has fewer sensors and lower sensor cost than Scheme 4, therefore Scheme 3 is selected as the optimal sensor layout scheme, that is, the optimal sensor layout scheme is {l2, l4, l8, l... 17 , l 20 The results show that measuring points should be arranged at the cylinder head, housing, shock absorber, and flywheel to ensure that the sensor arrangement meets the requirements of high coverage, small number of sensors, and strong discrimination capability.

Claims

1. A method for optimizing layout of vibration monitoring sensor measurement points, characterized by: Comprising the following steps: Step one: extract the fault characteristics of diesel engine under different states, build the percentage difference matrix, provide data basis for subsequent optimization; Step two: based on the percentage difference matrix and sensor fault threshold, establish the fault discrimination matrix, which is used to judge the distinguishability between different states; Step three: design a multi-objective optimization function to balance the fault discrimination ability of sensor arrangement scheme and the number of sensors; Step four: use multi-objective optimization algorithm to optimize the sensor arrangement scheme and find the optimal sensor arrangement scheme; Step five: use optimization algorithm to continuously iterate and screen each generation of non-dominated solution, merge in non-dominated solution set and update non-dominated solution set NDset based on Pareto algorithm; Step six: screen the non-dominated solution set.

2. The method of claim 1, wherein, Step one is specifically: Step 1.1, Obtain initial data: Define the diesel engine state set K = {k1, k2, ..., k m }, where k1 represents the normal state, k2 to k m Let m represent the total number of states, and let m represent the fault state. We obtain diesel engine operating data from n vibration monitoring sensors for each state in the diesel engine state set K, resulting in the initial matrix G = G_0. i,j : Where i represents the diesel engine status, 1≤i≤m, and j represents the sensor number, 1≤j≤n; Step 1.2, based on the initial matrix G = G i,j , obtain the percentage difference matrix B = {b1, b2,..., b h ,...b m}; for each state k h , according to calculate the percentage difference degree of other states with this state, get the percentage difference matrix b h expressed as: Where G h,j represents the monitoring data of the jth sensor in the hth state, b h represents the percentage difference matrix of each state with the hth state in the hth state, h ranges from 1 to m; a i,j represents the percentage difference of the ith state and the jth sensor monitoring data in the hth state, 1≤i≤m, 1≤j≤n, a i,j = 0 indicates that the percentage difference of the ith state and the hth state is 0 under the jth sensor; the hth row indicates the percentage difference of each sensor in the hth state and the hth state, all of which are 0.

3. The method of claim 2, wherein, Step two is specifically: Step 2.1, update the fault decision threshold adaptively according to the collected fault case data: define each sensor threshold Thd = {th1, th2, …, thn}, the jth sensor corresponds to the fault threshold thj n . j ; Step 2.2, compare each column percentage difference value in the percentage difference matrix with the corresponding fault threshold value, i.e. the percentage difference value of the jthcolumn with the th j a i,j >th j , it means that the states are quite different, let d i,j = 1, which can be distinguished, otherwise it means that the states are quite similar, let d i,j = 0, which is difficult to distinguish; Step 2.3, use of fault differentiation threshold Thd and percentage difference matrix b h The fault differentiation matrix D = {dl, d2,..., dn} is established m}, D h = (d i,j ) m×n is expressed as: fault discrimination matrix D in state h h is expressed as: wherein d i,j represents the fault discrimination value of sensor j between state i and state h, i ranges from 1 to m; j ranges from 1 to n; d i,j ranges from 0, 1, d i,j value of 0 indicates that sensor j has a small difference between state i and state h, if the value of the sum of the whole row is 0, then state i and state h are an equivalent cluster, D h the hth row in D is obviously below the threshold value because the percentage difference is all 0, so itself and itself are the same equivalent cluster, on the contrary, if the value of the sum of the whole row is not 0, then classification is performed according to the redundancy quantization constraint in step 2.4; Step 2.4, define redundancy quantification constraint: calculate the row sum of each pair of states (p, h) in the p-th row of the matrix: where row_sum is the total number of sensors that can distinguish the pair of states, 1≤p≤m; define redundancy as ry=row_sum-y, where y is a preset minimum number of distinguishing sensors, y≥1; For the difference degree of different fault pairs of diesel engine, the minimum redundancy requirement is set through the redundancy constraint matrix: for the fault pairs with slight difference, ry≥1, i.e. row_sum≥2, row_sum-y≥1; for the fault pairs with significant difference, ry≥0, i.e. row_sum≥1, row_sum-y≥0, so as to ensure the distinguishing ability when the sensor fails; the redundancy constraint matrix is defined as follows: A redundancy is set between each pair of faults, and the default redundancy before modification is 0, i.e. row_sum=y=1; then according to the conclusion of step 2.3, if the redundancy of state i and state h is not 0, the row sum of the i-th row is calculated If the following condition is met Step 2.5, single sensor distinguishability calculation: The sum of all the percentage difference values over the threshold in the same column in each percentage difference matrix is defined as the discrimination ability of the individual sensor, denoted as: where A s,j denotes the discrimination ability of the jth sensor in the sensor scheme s, with j ranging from 1 to n.

4. The method of claim 3, wherein, Step three is specifically: Step 3.1, determining fault equivalence clusters: according to the fault distinguish matrix D = {d1, d2, …, d m} divide the state set K into several fault equivalence clusters v x = {K1, K2, …, K t}, where t ≤ m, represents the number of equivalence clusters; Step 3.2, define the optimization sub-function: (1) Fault coverage sub-function f1: measures the number of fault equivalence clusters, the fewer the number of equivalence clusters, the greater the fault coverage: The effective calculation of the fault coverage sub-function needs to satisfy the redundancy constraint precondition check: if there is any pair of faults in the fault differentiation matrix corresponding to the sensor layout scheme whose redundancy is lower than the minimum requirement in the redundancy constraint matrix, then f1 is directly forced to be 0, marking the scheme as an invalid solution; only when the redundancy of all fault pairs meets the constraint, i.e. ry> preset value, and the number of equivalence clusters t meets the logic, f1 is valued according to the original formula; (2) Sensor quantity sub-function f2: measures the number of sensors in the sensor arrangement, the fewer the sensors, the lower the cost: (3) Fault discrimination capability sub-function f3: measures the sum of the discrimination capability of each sensor for each fault state, the more the number of sensors, the stronger the discrimination capability: where t represents the number of fault clusters, m represents the number of states in the state set, m-1 represents the number of fault states, N represents the number of sensors in the diesel engine state monitoring sensor set L, |s| represents the number of sensors in the sensor arrangement scheme s, A s represents the sum of the ability of all sensors in the sensor arrangement scheme s to distinguish from other states based on each normal or fault state; Step 3.

3. Obtain the fault distinguish matrix D under the sensor arrangement scheme s d = {D1, D2,..., D m} and the equivalent cluster v x Obtain the number of sensors under the sensor arrangement scheme s and the sensor fault distinguish ability Design the sensor arrangement scheme multi-objective optimization function F, represented as: F = [f1, f2, f3] Step 3.4, in the multi-objective optimization problem, since there is a conflict between the fault discrimination ability sub-function f3 and the number of sensors sub-function f2, there is no unique optimal solution, which needs to be screened by Pareto non-dominated algorithm to find the approximate Pareto optimal solution set; Step 3.5, specifically by the following steps: compare the target function values [f1, f2, f3] of all sensor arrangement schemes two by two, record the non-dominated solution; keep the non-dominated solution to form a temporary solution set NDset, set the crowding degree of the solution with the maximum and minimum target value of the temporary solution set to infinity to ensure that it is not deleted; in solution set maintenance, preferentially keep the solution with high crowding degree, delete redundant solution, ensure that the non-dominated solution is evenly distributed in the target space, and avoid the algorithm converging to the local optimal area; update the solution set iteratively, and the final output of the Pareto front is the optimal solution set of sensor arrangement.

5. The method of claim 4, wherein, Step four is specifically: Step 4.1, randomly generate an initial population P = (s1, s2, …, s z ), z is the number of individuals in the population, each individual in the population is a sensor arrangement, and the sensor arrangement is represented by a binary vector Vn= (l1, l2, …, ln), where l n j ∈{0,1}, j = 1, 2, …, n, where l j = 0 indicates that the jth sensor in the set of state monitoring sensors L is not included in the sensor arrangement, and vice versa; n represents the total number of sensors;​ Step 4.2, before evaluating each sensor arrangement scheme in the population, the redundancy constraint verification needs to be performed by calculating the row sum and redundancy of all fault pairs through the fault discrimination matrix in step two: if the redundancy of any pair of faults is lower than the constraint value in the redundancy constraint matrix, the scheme is directly marked as invalid solution and does not participate in the Pareto non-dominated solution screening; Step 4.3, initialize a non-dominated solution set ND before optimization, use the multi-objective optimization function F=[f1, f2, f3] of sensor arrangement scheme to evaluate each individual of the scheme that passes the redundancy check in the population based on Pareto algorithm: calculate the three sub-functions f1, f2, f3 of each individual, traverse all individuals in the population, compare the target function values of different individuals two by two, if the f1, f2, f3 of individual a are not inferior to individual b, and at least one target is strictly superior to b, then a dominates b, b is excluded from ND, a is marked as non-dominated solution, and all non-dominated solutions are recorded into the initial non-dominated solution set ND; Step 4.4, Select and record the initial global optimum individual position s from the ND population g,d and the individual historical optimum position s i,d The solution with f1=1 and the largest crowding distance is selected as the initial optimum position of the optimization algorithm.

6. The method of claim 5, wherein, Step five is specifically: Step 5.1, receiving the solution set ND as the population to be optimized, initializing the non-dominated solution set NDset, setting the stop iteration condition as stopping iteration when new non-dominated solutions do not appear for 10 times continuously or the maximum iteration number is reached, setting the initial population auxiliary parameters: the initial speed of the particle swarm is a random number between [0, 1], the crossover mutation probability of the genetic algorithm; Step 5.2, updating the speed vector and position vector of each individual or the gene value and arrangement order in the individual chromosome according to the initial optimal position obtained in step four; Step 5.3, checking the redundancy constraint, if the redundancy of any pair of faults is lower than the constraint value in the redundancy constraint matrix, the scheme is directly marked as invalid solution and does not participate in the Pareto non-dominated solution screening; Step 5.4, evaluating the three objective function values of each individual in the population by using the sensor arrangement scheme multi-objective optimization function F = [f1, f2, f3]; Step 5.5, screen and record the global optimal individual position s of the current generation from the population g,d and the individual historical optimal position s i,d Preferentially select the solution with f1=1 and the largest crowding distance as the optimization direction; meanwhile, combine the current population and the non-dominated solution set NDset, screen the non-dominated solution based on the Pareto algorithm, and update the non-dominated solution set NDset; Step 5.6, judging whether new non-dominated solutions do not appear for 10 times continuously, if yes, stopping iteration and outputting the non-dominated solution set NDset; otherwise, repeating steps 5.2 to 5.5 until new non-dominated solutions do not appear for 10 times continuously or the maximum iteration number is reached, then stopping iteration and outputting the non-dominated solution set NDset.

7. The method of claim 6, wherein, Step six is specifically: Step 6.1, in order to meet the fault full coverage index, solutions with fault coverage sub-function f1 = 1 need to be screened and retained; Step 6.2, in order to make the screened sensor scheme have greater ability to distinguish faults, the ability to distinguish faults is classified as follows: under the condition of meeting the fault full coverage, the sensor scheme with excellent ability to distinguish faults is preferentially selected; Pass Good Excellent 8.0≤f3≤8.2 8.2<f3≤8.4 f3>8.4 Step 6.3, under the constraint condition of meeting the fault full coverage and the ability to distinguish faults in the excellent interval, the scheme with the least number of sensors is selected as the optimal sensor arrangement scheme.

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