Marine diesel engine sensor configuration strategy optimization method and system based on improved NSGA-II algorithm

Abstract

The invention belongs to the technical field of diesel engine intelligent monitoring, and discloses a marine diesel engine sensor configuration strategy optimization method and system based on an improved NSGA-II algorithm, and the method comprises the steps: firstly, determining diesel engine alternative sensors and a to-be-detected fault mode, and constructing a to-be-optimized sensor configuration strategy set; and then inputting a to-be-optimized sensor configuration strategy set into the improved NSGA-II algorithm, then calculating a fitness function of each sensor configuration strategy in the to-be-optimized sensor configuration strategy set, and finding an optimal sensor configuration strategy after optimization iteration. According to the method, the monitoring effect of different sensor combinations on the running state of the diesel engine can be fully explored, and the optimal diesel engine sensor configuration strategy capable of accurately recognizing each to-be-detected fault mode through the minimum number of sensors is found.

Description

Technical Field

[0001] The present invention relates to the technical field of diesel engine intelligent monitoring, and in particular to a method and system for optimizing ship diesel engine sensor configuration strategy based on an improved NSGA-II algorithm. Background Art

[0002] Marine diesel engines occupy a primary position in ship main engines due to their excellent power performance and extremely high combustion efficiency. In order to ensure the safe and reliable operation of marine diesel engines, sensors are needed to accurately and reliably monitor their operating status and perform fault diagnosis in a timely manner. However, there are many types of operating status parameters that can be monitored by diesel engines, including temperature signals, pressure signals, vibration signals, acoustic emission signals, etc. However, considering the sensor procurement cost and the difficulty of maintenance and replacement, it is unrealistic to use all parameters for status monitoring. Therefore, it is necessary to carry out research on sensor optimization configuration strategies to achieve accurate and reliable monitoring of marine diesel engine operating data under the condition of a limited number of sensors, distinguish all fault modes to be detected, and reduce the difficulty of sensor installation, maintenance and replacement. This is of great significance to ensure the safe and reliable operation of marine diesel engines.

[0003] After searching the literature on the prior art, it was found that the public document "Research on Leakage Risk Warning Method Based on Rule Reasoning and Moving Slope Coding" (China University of Petroleum (East China), 2022) proposed a method for optimizing leakage risk monitoring parameters based on sensitivity analysis. The public document describes itself as: "The Pearson correlation coefficient method and multivariate regression analysis method are used to analyze the correlation and sensitivity of the comprehensive logging parameters to the leakage volume when overflow and well leakage risks occur, and the parameters with high sensitivity are selected according to the sensitivity coefficients of each parameter for overflow and well leakage risk monitoring." There are 15 parameters for monitoring leakage risks. Based on the method proposed in this document, the parameters for monitoring leakage risks can be reduced to 3. However, its shortcoming is that this document only optimizes monitoring parameters based on correlation coefficient ranking and sensitivity coefficient ranking, and fails to fully explore the monitoring effects of different monitoring parameter combinations on overflow risks and well leakage risks. The public document "Research on Simulation Analysis and Diagnosis Methods of Typical Faults of Marine Diesel Engines" (Jiangsu University of Science and Technology, 2022) proposes a diesel engine monitoring parameter simplification method based on rough sets and genetic algorithms. The document describes itself as: "Based on the rough set attribute simplification theory, the fitness function of the genetic algorithm is constructed with the goal of minimizing the number of elements in the monitoring parameter subset and maintaining the same ability to distinguish the monitoring parameter subset. First, the fault sample data is discretized by the K-means algorithm, and then the attributes of the full set of monitoring parameters are simplified to calculate the optimal monitoring parameter subset for fault diagnosis. As a result, 14 monitoring parameters can be reduced to 7 items." The shortcoming is that when constructing the fitness function of the genetic algorithm, the document directly sets the fitness function as the sum of the quantity index of the monitoring parameter subset and the fault discrimination index, and does not assign weights to the two indicators. When the order of magnitude of the two indicator values ​​differ too much, it is very easy to cause the search results to converge to the optimal only on one optimization indicator, but not on other optimization indicators. That is, the optimal monitoring parameter subset obtained is actually a local optimal solution. Summary of the invention

[0004] In order to solve the above technical problems, the present invention provides a method and system for optimizing the sensor configuration strategy of a ship diesel engine based on an improved NSGA-II algorithm, which can deeply explore the solution space, fully explore the monitoring effect of different sensor combinations on the operating status of the diesel engine, avoid the risk of falling into local optimality, and thus find the optimal diesel engine monitoring sensor configuration strategy, thereby achieving the goal of accurately isolating each fault mode to be detected through fewer sensors.

[0005] The present invention provides a method for optimizing the configuration strategy of a ship diesel engine sensor based on an improved NSGA-II algorithm, the method comprising:

[0006] Step 1: Determine the diesel engine candidate sensor set and the set of fault modes to be detected, and construct the sensor configuration strategy set to be optimized;

[0007] Step 2: Take the sensor configuration strategy set to be optimized as the input of the improved NSGA-II algorithm, and calculate the number of monitoring sensors and the fault isolation rate of the fault mode to be detected for each sensor configuration strategy in the sensor configuration strategy set to be optimized;

[0008] Step 3: Calculate the fitness function y1 of the improved NSGA-II algorithm according to the number of monitoring sensors, and calculate the fitness function y2 of the improved NSGA-II algorithm according to the fault isolation rate. Use the fitness functions y1 and y2 to evaluate the pros and cons of each sensor configuration strategy, guide the optimization iteration direction of the improved NSGA-II algorithm, and then obtain the optimal sensor configuration strategy.

[0009] Preferably, in step 1,

[0010] The diesel engine candidate sensor set is: S = {s1, s2, ..., s n}, where s j are sensors at different monitoring locations, j = 1, 2, ..., n;

[0011] The set of failure modes to be detected is F = {f1, f2, ..., f m}, where f i are the fault modes of the diesel engine to be tested, i=1,2,…,m;

[0012] Randomly select different numbers of sensors from the candidate sensor set S to form a sensor configuration strategy x q , then the sensor configuration strategy set to be optimized is: S w ={x1,x2,…,x p}, where q = 1, 2, ..., p, i.e. the sensor configuration strategy set S to be optimized w Contains p sensor configuration strategies.

[0013] Preferably, in step 2,

[0014] The number of monitoring sensors for each sensor configuration strategy in the sensor configuration strategy set to be optimized is calculated as follows:

[0015]

[0016] Among them, |x q |Configure policy for sensor x q The number of sensors in the candidate sensor set S, |S| is the number of sensors in the candidate sensor set S, |S| = n;

[0017] Statistical failure mode set F = {f1,f2,...,f m Each failure mode f iThe number of fault modes to be detected that are correctly isolated Combined failure mode f i The number of failure mode samples to be tested Calculate the fault isolation rate FIR:

[0018]

[0019] Preferably, in step 3,

[0020] The calculation formulas of fitness functions y1 and y2 include:

[0021]

[0022] The fitness functions y1 and y2 are used to evaluate the pros and cons of each sensor configuration strategy, guide the optimization iteration direction of the improved NSGA-II algorithm, and then obtain the optimal sensor configuration strategy including:

[0023] Step 3.1: Configure the sensor to be optimized with the strategy set S w is the initial population;

[0024] Step 3.2: Calculate the fitness functions y1 and y2 of each sensor configuration strategy in the population;

[0025] Step 3.3: stratify the population according to the fast non-dominated sorting algorithm;

[0026] Step 3.4: Calculate the crowding degree of each sensor configuration strategy in the population;

[0027] Step 3.5: Select the parent sensor configuration strategy suitable for reproduction according to the tournament selection algorithm;

[0028] Step 3.6: Search for the next-generation sensor configuration strategy based on the position and velocity update mechanism of the BPSO algorithm;

[0029] Step 3.7: Merge the parent population and the child population;

[0030] Step 3.8: Retain the elite sensor configuration strategy from the merged population as the new population according to the elite strategy;

[0031] Step 3.9: Repeat steps 3.2 to 3.8 until the maximum number of iterations Iter is reached, and use the elite sensor configuration strategy as the sensor optimization configuration strategy set;

[0032] The sensor optimization configuration strategy set is: S best ={x1,x2,...,x l}, that is, the sensor optimization configuration strategy set S bestContains l optimized sensor configuration strategies, each sensor configuration strategy contains different sensors, and the optimized sensor configuration strategy is in the form of:

[0033]

[0034] Among them, i=1,2,…,n.

[0035] The present invention also provides a ship diesel engine sensor configuration strategy optimization system based on an improved NSGA-II algorithm, the system is used to implement any one of the methods described, the system comprises: a construction module, a calculation module and an iteration module;

[0036] The construction module is used to determine the diesel engine candidate sensor set and the to-be-detected fault mode set, and to construct the sensor configuration strategy set to be optimized;

[0037] The calculation module is used to calculate the number of monitoring sensors and the fault isolation rate of the fault mode to be detected for each sensor configuration strategy in the sensor configuration strategy set to be optimized, using the sensor configuration strategy set to be optimized as the input of the improved NSGA-II algorithm;

[0038] The iteration module is used to calculate the fitness function y1 of the improved NSGA-II algorithm according to the number of monitoring sensors, and calculate the fitness function y2 of the improved NSGA-II algorithm according to the fault isolation rate. The fitness functions y1 and y2 are used to evaluate the pros and cons of each sensor configuration strategy, guide the optimization iteration direction of the improved NSGA-II algorithm, and then obtain the optimal sensor configuration strategy.

[0039] Preferably, in the building block,

[0040] The diesel engine candidate sensor set is: S = {s1, s2, ..., s n}, where s j are sensors at different monitoring locations, j = 1, 2, ..., n;

[0041] The set of failure modes to be detected is F = {f1,f2,...,f m}, where f i are the fault modes of the diesel engine to be tested, i=1,2,...,m;

[0042] Randomly select different numbers of sensors from the candidate sensor set S to form a sensor configuration strategy x q , then the sensor configuration strategy set to be optimized is: S w ={x1,x2,...,x p}, where q = 1, 2, ..., p, i.e. the sensor configuration strategy set S to be optimized wContains p sensor configuration strategies.

[0043] Preferably, in the calculation module,

[0044] The number of monitoring sensors for each sensor configuration strategy in the sensor configuration strategy set to be optimized is calculated as follows:

[0045]

[0046] Among them, |x q |Configure policy for sensor x q The number of sensors in the candidate sensor set S, |S| is the number of sensors in the candidate sensor set S, |S| = n;

[0047] Statistical failure mode set F = {f1,f2,...,f m Each failure mode f i The number of fault modes to be detected that are correctly isolated Combined failure mode f i The number of failure mode samples to be tested Calculate the fault isolation rate FIR:

[0048]

[0049] Preferably, in the iteration module,

[0050] The calculation formulas of fitness functions y1 and y2 include:

[0051]

[0052] The fitness functions y1 and y2 are used to evaluate the pros and cons of each sensor configuration strategy, guide the optimization iteration direction of the improved NSGA-II algorithm, and then the optimal sensor configuration strategy is obtained, including: initialization unit, fitness function calculation unit, stratification unit, crowding calculation unit, selection unit, update unit, merging unit, retention unit, iteration unit,

[0053] The initialization unit is used to configure the sensor configuration strategy set S to be optimized. w is the initial population;

[0054] The fitness function calculation unit is used to calculate the fitness functions y1 and y2 of each sensor configuration strategy in the population;

[0055] The stratification unit is used to stratify the population according to a fast non-dominated sorting algorithm;

[0056] The congestion calculation unit is used to calculate the congestion of each sensor configuration strategy in the population;

[0057] The selection unit is used to select a parent sensor configuration strategy suitable for reproduction according to a tournament selection algorithm;

[0058] The updating unit is used to search for the sub-generation sensor configuration strategy according to the position and speed update mechanism of the BPSO algorithm;

[0059] The merging unit is used to merge the parent population with the offspring population;

[0060] The retaining unit is used to retain the elite sensor configuration strategy from the merged population as a new population according to the elite strategy;

[0061] The iteration unit is used to repeat the fitness function calculation unit to the retention unit until the maximum number of iterations Iter is reached, and the elite sensor configuration strategy is used as the sensor optimization configuration strategy set;

[0062] The sensor optimization configuration strategy set is: S best ={x1,x2,…,x l}, that is, the sensor optimization configuration strategy set S best Contains l optimized sensor configuration strategies, each sensor configuration strategy contains different sensors, and the optimized sensor configuration strategy is in the form of:

[0063]

[0064] Among them, i=1,2,…,n.

[0065] Compared with the prior art, the present invention has the following beneficial effects:

[0066] The present invention provides a method and system for optimizing the sensor configuration strategy of a marine diesel engine based on an improved NSGA-II algorithm. First, the candidate sensors and the failure modes to be detected of the diesel engine are determined, and a set of sensor configuration strategies to be optimized is constructed; then the set of sensor configuration strategies to be optimized is input into the improved NSGA-II algorithm, and then the fitness function of each sensor configuration strategy in the set of sensor configuration strategies to be optimized is calculated, and after optimization iterations, the optimal sensor configuration strategy is found. The present invention can fully explore the monitoring effect of different sensor combinations on the operating status of the diesel engine, and find the optimal diesel engine sensor configuration strategy that can accurately identify each failure mode to be detected with the least number of sensors. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] In order to more clearly illustrate the technical solution of the present invention, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0068] Figure 1 A flow chart of a method for optimizing configuration of ship diesel engine sensors based on an improved NSGA-II algorithm according to an embodiment of the present invention;

[0069] Figure 2 Schematic diagram of chromosome encoding method according to an embodiment of the present invention. DETAILED DESCRIPTION

[0070] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0071] It should be noted that, unless otherwise defined, the technical terms or scientific terms used in the embodiments of the present disclosure should be understood by people with ordinary skills in the field to which the present disclosure belongs. The "first", "second" and similar words used in the embodiments of the present disclosure do not indicate any order, quantity or importance, but are only used to distinguish different components. "Including" or "comprising" and similar words mean that the elements or objects appearing before the word cover the elements or objects listed after the word and their equivalents, without excluding other elements or objects. "Connect" or "connected" and similar words are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0072] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0073] Embodiment 1

[0074] like Figure 1 As shown, the embodiment of the present invention provides a method for optimizing the configuration of ship diesel engine sensors based on the improved NSGA-II algorithm. First, the candidate sensors and the fault modes to be detected of the diesel engine are determined, and a set of sensor configuration strategies to be optimized is constructed; then the set of sensor configuration strategies to be optimized is input into the improved NSGA-II algorithm, and then the fitness function of each sensor configuration strategy in the set of sensor configuration strategies to be optimized is calculated. After optimization iterations, the optimal sensor configuration strategy is found. Finally, the present invention verifies the effectiveness of the above method through examples, and the present invention is specifically implemented through the following technical solutions:

[0075] Step 1: Determine the diesel engine candidate sensor set S and the failure mode set F to be detected, and construct the sensor configuration strategy set S to be optimized w , obtain the operation monitoring data of the diesel engine under each fault mode to be detected, and normalize the monitoring data;

[0076] Step 2: Configure the strategy set S based on the sensor configuration to be optimized in step 1 w As the input of the improved NSGA-II algorithm, calculate S w The number of monitoring sensors qt of each sensor configuration strategy and the fault isolation rate FIR of the fault mode to be detected;

[0077] Step 3: Take the quantity index qt of the sensor configuration strategy in step 2 as the fitness function y1 of the improved NSGA-II algorithm, calculate the fitness function y2 of the improved NSGA-II algorithm according to the fault isolation rate FIR, and use the fitness functions y1 and y2 to evaluate the pros and cons of each sensor configuration strategy, guide the optimization iteration direction of the improved NSGA-II algorithm, and then obtain the optimal sensor configuration strategy.

[0078] Furthermore, the diesel engine candidate sensor set in step 1 is S = {s1, s2, ..., s n}, where s j are sensors at different monitoring locations, j = 1, 2, ..., n; the set of failure modes to be detected is F = {f1, f2, ..., f m}, where f i are the fault modes to be detected of the diesel engine, i = 1, 2, ..., m, in particular, f1 is the normal operation mode of the diesel engine; different numbers of sensors are randomly selected from the candidate sensor set S to form the sensor configuration strategy x q , then the sensor configuration strategy set to be optimized is S w ={x1,x2,...,x p}, where q = 1, 2, ..., p, i.e. the sensor configuration strategy set S to be optimized w Contains p sensor configuration strategies.

[0079] The preprocessing method of diesel engine operation monitoring data is as follows: t rows of monitoring data samples are collected in each fault mode to be detected, and the initial value of the monitoring data in the normal operation mode f1 of the diesel engine is used as the basis to normalize the monitoring data in each fault mode of the diesel engine. The formula is:

[0080]

[0081] Where i = 1, 2, ..., m, j = 1, 2, ..., n; x i,j (k) represents when the diesel engine is in fault mode f iWhen the monitoring sensor s j The kth diesel engine operation monitoring data sample collected, k = 1, 2, ..., t; x 1,j (1) is the monitoring sensor s in the normal operation mode f1 of the diesel engine j The first data sample collected, i.e. the initial value; x′ i,j (k) is the normalized data. i Taking as an example, the data form after monitoring data preprocessing is shown in Table 1.

[0082] Table 1 Diesel engine operation monitoring data after pretreatment

[0083]

[0084] Furthermore, the sensor configuration strategy x is calculated in step 2 q The steps of the sensor quantity index qt and the fault isolation rate FIR of the fault mode to be detected are:

[0085] (1) Calculate the sensor configuration strategy x q The quantitative index qt is calculated as follows:

[0086]

[0087] Among them, |x q |Configure policy for sensor x q is the number of sensors in the candidate sensor set S, |S| is the number of sensors in the candidate sensor set S, |S|=n.

[0088] (2) Based on the failure mode f i As an example, the diesel engine fault mode reference vector v is calculated based on the first c rows of data samples in Table 1. i , the calculation formula is:

[0089]

[0090] Where, c = t / 10, v i (j) indicates failure mode f i Next, the reference vector v i The value at the jth position.

[0091] The remaining tc rows of data samples in Table 1 are taken as the fault mode samples to be detected, and their true labels are the fault mode f i Similarly, we obtain the samples of the failure modes to be detected under other failure modes. Each row of the failure mode samples to be detected is a failure mode vector v to be detected. p , as shown in Table 2.

[0092] Table 2 Samples of diesel engine failure modes to be tested

[0093]

[0094] (3) Combined with the fault mode reference vector v i and the failure mode vector v p , calculate the sensor configuration strategy x q The fault isolation rate FIR is calculated as follows:

[0095] Calculate the fault mode vector v to be detected by grey correlation analysis p With each failure mode reference vector v i The grey relational degree between them is obtained, and the grey relational degree sequence r=[r1,r2,...,r m ], sort the grey correlation degree sequence from large to small, and classify the fault mode to be detected as the fault mode reference vector corresponding to the maximum grey correlation degree value, that is, the maximum grey correlation degree value in the grey correlation degree sequence r is r i , then the fault mode vector v p The predicted label is f i .

[0096] Take the fault mode vector v of the diesel engine to be detected p is the reference sequence, each fault mode reference vector v i is the comparison sequence, then the grey correlation coefficient ζ between the reference sequence and the corresponding dimension j in the comparison sequence i (j) The calculation formula is as follows:

[0097]

[0098] Among them, Δ min =min i min j |v i (j)-v p (j)| is the minimum difference between the two levels, Δ max =max i max j |v i (j)-v p (j) are the maximum difference between the two levels, Δ=|v i (j)-v p (j)|, ρ is the resolution coefficient.

[0099] Then the fault mode vector v p and the failure mode reference vector v i The grey relational degree r i The calculation formula is as follows:

[0100]

[0101] Get the fault mode vector v to be detected p With each failure mode reference vector v i After the grey relational degree sequence r is obtained, the grey relational degree sequence r can be sorted to complete the fault mode vector v to be inspected. p Fault isolation.

[0102] Statistical failure mode set F = {f1,f2,…,f m Each failure mode f i The number of fault modes to be detected that are correctly isolated Combined failure mode f i The number of failure mode samples to be tested Calculate the fault isolation rate FIR:

[0103]

[0104] Furthermore, the calculation formulas of the fitness functions y1 and y2 in step 3 are:

[0105]

[0106] The improved method of the NSGA-II algorithm in step 3 is:

[0107] (1) Chromosome encoding method, such as Figure 2 Shown

[0108] Configure policy with sensor x q To improve the chromosome of NSGA-II algorithm, the chromosome encoding is as follows Figure 2 As shown, each sensor configuration strategy x q are represented by a binary vector. When the sensor configuration strategy x q When the jth sensor is included, the corresponding value is 1, otherwise the corresponding value is 0.

[0109] (2) Improvement of NSGA-II algorithm

[0110] In order to fully explore the monitoring effect of different sensor combinations on the operating status of diesel engines and find the optimal diesel engine sensor configuration strategy that can accurately identify each fault mode to be detected with the least number of sensors, the NSGA-II algorithm is improved based on the position and speed update mechanism of the BPSO algorithm. Specifically, the crossover and mutation operations of the traditional NSGA-II algorithm are replaced by the position and speed update mechanism of the BPSO algorithm, but the BPSO algorithm's dependence on the optimal position of the group is abandoned, and only the individual optimal position of each particle is retained and updated, aiming to use the excellent dynamic search characteristics of the BPSO algorithm to conduct a deep search in the neighborhood of the parent population, thereby significantly improving the algorithm's search ability for the optimal sensor configuration strategy.

[0111] The particle velocity update formula is as follows, which is determined by the particle velocity, the distance between the particle's current position and the individual's optimal position:

[0112] v qj (t+1)=w(t)·v qj (t)+c·r1·(p qj -x qj (t)), (8)

[0113] Where q = 1, 2, ..., p, p is the population size, that is, the sensor configuration strategy set S to be optimized w The number of sensor configuration strategies in ; j = 1, 2, ..., n, n is the particle dimension, n = |S|; c is the individual learning factor, p qj is the optimal position of the individual, x qj The current position of the particle, r1∈(0,1) is a random factor; is the dynamic inertia weight, t I is the number of particle swarm iterations, and w0 is the initial weight.

[0114] According to the probability mapping algorithm, the particle position is updated with the Sigmoid function sig(v qj )=(1+exp(-v qj )) -1 Mapping the velocity to [0,1] as the particle flip probability, the particle position update formula is:

[0115]

[0116] Where r2∈[0,1] is a random number.

[0117] In step 3, the steps of searching for the optimal sensor configuration strategy based on the improved NSGA-II algorithm are:

[0118]

[0119]

[0120] Among them, the fast non-dominated sorting algorithm:

[0121] Calculate the objective functions y1 and y2 of all diesel engine sensor configuration strategies in each iteration, and statistically dominate the sensor configuration strategy x q The number of strategies n q , and the configured policy x q The set of strategies S that dominates q , and then execute the following fast non-dominated sort algorithm pseudo code:

[0122]

[0123] Among them, the congestion calculation method is:

[0124] The crowdedness q of the sensor configuration strategy distance The calculation method is:

[0125]

[0126] Where e=1,…,k, e is the number of evaluation indicators, is the evaluation index y k The maximum value of y k (q+1) and y k (q-1) is based on y k After sorting the population, the sensor configuration strategy x q Evaluation index value of adjacent sensor configuration strategy.

[0127] Among them, the tournament selection strategy:

[0128] From the population with non-dominated sorting and crowding calculation, two sensor configuration strategies are randomly selected with replacement as two contestants. The ranking levels of the two contestants are compared, and the contestant with the smaller ranking is selected as the parent sensor configuration strategy. If the ranking levels of the two contestants are the same, the contestant with the larger crowding degree is selected as the parent sensor configuration strategy. Until the parent sensor configuration strategy set S f The size is 0.75p.

[0129] Among them, the position and speed update mechanism of the BPSO algorithm is used to search for the next-generation sensor configuration strategy:

[0130] Receive the parent sensor configuration policy set S f , calculate the parent sensor configuration strategy set S f The fitness F of each sensor configuration strategy xq in q (x)=λ1y1(x)+λ2y2(x), where λ1=λ2=0.5;

[0131] 1) If the fitness of the particle's current position is less than the fitness of the individual optimal position, the individual optimal position is updated and the current position is taken as the individual optimal position p qj ;

[0132] 2) Determine whether the number of particle swarm iterations reaches iter=5;

[0133] 3) If iter=5 is not reached, the position vector and velocity vector of each particle are updated according to formula (8) and formula (9), and steps 2) to 4) are repeated; if the number of particle swarm iterations iter=5, the output individual optimal position is the offspring sensor configuration strategy set S c.

[0134] Among them, elite retention strategy:

[0135] Parent sensor configuration policy set S f Configure the policy set S with the child sensor c The sizes are all 0.75p, and they are merged into a configuration strategy set of size 1.5p. After fast non-dominated sorting, the configuration strategies with lower non-dominated ranks (such as rank1 and rank2) are used as new parents. If their size does not reach p, the configuration strategies with high congestion in the next configuration strategy layer with higher non-dominated ranks (such as rank3) are added to the new parents until the size of the configuration strategy set is p. This configuration strategy set is the elite configuration strategy set.

[0136] The sensor optimization configuration strategy set is S best ={x1,x2,…,x l}, that is, the sensor optimization configuration strategy set S best Contains l optimized sensor configuration strategies, each sensor configuration strategy contains different sensors, and the optimized sensor configuration strategy is as follows:

[0137]

[0138] Where i=1,2,…,n.

[0139] Embodiment 2

[0140] The embodiment of the present invention provides a method for optimizing the configuration of ship diesel engine sensors based on an improved NSGA-II algorithm, which is specifically implemented by the following technical solutions:

[0141] Step 1: Determine the diesel engine candidate sensor set S and the failure mode set F to be detected, and construct the sensor configuration strategy set S to be optimized w , obtain the operation monitoring data of the diesel engine under each fault mode to be detected, and normalize the monitoring data;

[0142] Step 2: Configure the strategy set S based on the sensor configuration to be optimized in step 1 w As the input of the improved NSGA-II algorithm, calculate S w The number of monitoring sensors qt of each sensor configuration strategy and the fault isolation rate FIR of the fault mode to be detected;

[0143] Step 3: Take the quantity index qt of the sensor configuration strategy in step 2 as the fitness function y1 of the improved NSGA-II algorithm, calculate the fitness function y2 of the improved NSGA-II algorithm according to the fault isolation rate FIR, and use the fitness functions y1 and y2 to evaluate the pros and cons of each sensor configuration strategy, guide the optimization iteration direction of the improved NSGA-II algorithm, and then obtain the optimal sensor configuration strategy.

[0144] Furthermore, in step 1, the diesel engine alternative sensor set S includes 9 sensor positions, that is, n=9, S={s1,s2,…,s9}, where s1 is the lubricating oil temperature after the lubricating oil pump, s2 is the lubricating oil temperature before the filter, s3 is the lubricating oil temperature after the filter, s4 is the cooling water outlet temperature of the cooler, s5 is the lubricating oil pressure after the lubricating oil pump, s6 is the lubricating oil pressure before the filter, s7 is the lubricating oil pressure after the filter, s8 is the lubricating oil inlet pressure, and s9 is the cooling water outlet pressure of the cooler.

[0145] The failure mode set to be detected is F, which includes 5 failure modes, that is, m=5, F={f1, f2, ..., f5}, where f1 is the normal operation mode, f2 is the filter blockage failure, f3 is the bypass valve leakage failure, f4 is the cooler fouling failure, and f5 is the filter leakage failure.

[0146] Randomly select different numbers of sensors from the candidate sensor set S to form a sensor configuration strategy x q , then the sensor configuration strategy set to be optimized is S w ={x1,x2,...,x p}, where p = 50, that is, S w Contains 50 sensor configuration strategies.

[0147] The temperature (℃) and pressure (bar) data of each measuring point in the normal operation mode f1 and other fault modes of the diesel engine at 1800rpm and 250kW are collected. The preprocessing method of the diesel engine operation monitoring data is: based on the initial value of the monitoring data in the normal operation mode f1 of the diesel engine, the monitoring data of each operating state of the diesel engine is normalized, and the formula is:

[0148]

[0149] where i∈[1,5], j=[1,9]; x i,j (k) represents when the diesel engine is in fault mode f i When the sensor s j The kth data collected, k = 1, 2, ..., t, that is, t rows of data samples are collected in each fault mode, t = 1000; x 1,j (1) is the first row of data samples under the normal operation mode f1 of the diesel engine, xi ' ,j (k) is the preprocessed data, and the preprocessed data format is shown in Table 3.

[0150] Table 3 Diesel engine monitoring data after preprocessing

[0151]

[0152]

[0153] Furthermore, the sensor configuration strategy x is calculated in step 2 q The steps of the sensor quantity index qt and the fault isolation rate FIR of the fault mode to be detected are:

[0154] (1) Calculate the sensor configuration strategy x q The quantitative index qt is calculated as follows:

[0155]

[0156] Among them, |x q |Configure policy for sensor x q |S|=n=9 is the number of sensors in the candidate sensor set S.

[0157] (2) Calculate the diesel engine fault mode reference vector v based on the first c rows of data samples in Table 2 i , the calculation formula is:

[0158]

[0159] Where, c = t / 10 = 100, v i (j) indicates failure mode f i Next, the reference vector v i The value at the jth position.

[0160] Thus, the normal operating mode reference vector v1, the filter blockage fault mode reference vector v2, the bypass valve leakage fault mode reference vector v3, the cooler fouling fault mode reference vector v4, and the filter leakage fault mode reference vector v5 are obtained, as shown in Table 4.

[0161] Table 4 Reference vectors of various fault modes

[0162]

[0163] The remaining 900 rows of data samples in Table 2 are taken as the fault mode samples to be detected, and their true labels are fault mode f i Similarly, we obtain the samples of the failure modes to be detected under other failure modes. Each row of the failure mode samples to be detected is a failure mode vector v to be detected.p , some of the fault mode vectors to be detected are shown in Table 5.

[0164] Table 5 Some of the failure mode vectors to be detected

[0165]

[0166] (3) Combined with the fault mode reference vector v i and the failure mode vector v p , calculate the sensor configuration strategy x q The fault isolation rate FIR is calculated as follows:

[0167] Calculate the fault mode vector v to be detected by grey correlation analysis p With each failure mode reference vector v i The gray correlation degree between them is obtained, and the gray correlation degree sequence r = [r1, r2, ..., r5] is obtained. The gray correlation degree sequence is sorted from large to small, and the fault mode to be detected is classified as the fault mode reference vector corresponding to the maximum gray correlation value, that is, the maximum gray correlation value in the gray correlation degree sequence r is r i , then the fault mode vector v p The predicted label is f i .

[0168] Take the diesel engine failure mode vector v p is the reference sequence, each fault mode reference vector v i is the comparison sequence, then the grey correlation coefficient ζ between the reference sequence and the corresponding dimension j in the comparison sequence i (j) The calculation formula is as follows:

[0169]

[0170] Among them, Δ min =min i min j |v i (j)-v p (j)| is the minimum difference between the two levels, Δ max =max i max j |v i (j)-v p (j)| are the maximum differences between the two levels, Δ=|v i (j)-v p (j)|, ρ=0.5 is the resolution coefficient.

[0171] Then the fault mode reference vector v i and the failure mode vector v p The grey relational degree r iThe calculation formula is as follows:

[0172]

[0173] Calculate the fault mode vector v to be detected p With each failure mode reference vector v i After the grey relational degree sequence r=[r1,r2,...,r5] is obtained, the grey relational degree sequence r can be sorted from large to small to complete the fault mode vector v to be inspected. p Fault isolation.

[0174] Statistical failure mode set F = {f1,f2,...,f5} each failure mode f i The number of fault modes to be detected that are correctly isolated Combined failure mode f i The number of failure mode samples to be tested Calculate the fault isolation rate FIR:

[0175]

[0176] Furthermore, the calculation formulas of the fitness functions y1 and y2 in step 3 are:

[0177]

[0178] The improved method of the NSGA-II algorithm in step 3 is:

[0179] (1) Chromosome encoding method

[0180] Configure policy with sensor x q To improve the chromosome of NSGA-II algorithm, the chromosome encoding is as follows Figure 2 As shown, each sensor configuration strategy x q are represented by a binary vector. When the sensor configuration strategy x q When the jth sensor is included, the corresponding value is 1, otherwise the corresponding value is 0.

[0181] (2) Improvement of NSGA-II algorithm

[0182] In order to fully explore the monitoring effect of different sensor combinations on the operating status of diesel engines and find the optimal diesel engine sensor configuration strategy that can accurately identify each fault mode to be detected with the least number of sensors, the NSGA-II algorithm is improved based on the position and speed update mechanism of the BPSO algorithm. Specifically, the crossover and mutation operations of the traditional NSGA-II algorithm are replaced by the position and speed update mechanism of the BPSO algorithm, but the BPSO algorithm's dependence on the optimal position of the group is abandoned, and only the individual optimal position of each particle is retained and updated, aiming to use the excellent dynamic search characteristics of the BPSO algorithm to conduct a deep search in the neighborhood of the parent population, thereby significantly improving the algorithm's search ability for the optimal sensor configuration strategy.

[0183] The particle velocity update formula is as follows, which is determined by the particle velocity, the distance between the particle's current position and the individual's optimal position:

[0184] v qj (t+1)=w(t)·v qj (t)+c·r1·(p qj -x qj (t)),

[0185] Where q = 1, 2, ..., p, p = 50 is the population size, that is, the sensor configuration strategy set S to be optimized w The number of sensor configuration strategies in; j = 1, 2, ..., n, n = |S| = 9; c = 2 is the individual learning factor, p qj is the optimal position of an individual, x qj The current position of the particle, r1∈(0,1) is a random factor; is the dynamic inertia weight, t I =10 is the number of particle swarm iterations, and w0=1.2 is the initial weight.

[0186] According to the probability mapping algorithm, the particle position is updated with the Sigmoid function sig(v qj )=(1+exp(-v qj )) -1 Mapping the velocity to [0,1] as the particle flip probability, the particle position update formula is:

[0187]

[0188] Where r2∈[0,1] is a random number.

[0189] In step 3, the steps of searching for sensor optimization configuration strategy based on the improved NSGA-II algorithm are as follows:

[0190]

[0191]

[0192] According to the above steps, the optimal configuration strategy set of diesel engine lubrication system sensors is searched, and the obtained sensor configuration solution set is shown in Table 6.

[0193] Table 6 Diesel engine lubrication system sensor configuration set

[0194]

[0195] The searched diesel engine lubrication system sensor optimization configuration strategy set can achieve a 100% fault isolation rate in the feature vector set of the state to be tested, and the number of sensors can be reduced to 4. A total of 6 optimal sensor configuration strategies are searched, which can provide more flexible and diverse alternative strategies for practical engineering applications.

[0196] The technical solution of the present invention,

[0197] The present invention can fully explore the monitoring effects of different sensor combinations on the operating status of a diesel engine, and find the optimal diesel engine sensor configuration strategy that can accurately identify each fault mode to be detected with the least number of sensors.

[0198] It should be noted that the method of the embodiment of the present disclosure can be performed by a single device, such as a computer or a server. The method of the present embodiment can also be applied in a distributed scenario and completed by multiple devices cooperating with each other. In the case of such a distributed scenario, one of the multiple devices can only perform one or more steps in the method of the embodiment of the present disclosure, and the multiple devices will interact with each other to complete the described method.

[0199] It should be noted that some embodiments of the present disclosure are described above. Other embodiments are within the scope of the attached claims. In some cases, it should be understood that the size of the serial number of each step in the above embodiment does not mean the order of execution, and the execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiment of the present invention. The actions or steps recorded in the claims can be performed in an order different from that in the above embodiment and still achieve the desired results. In addition, the process depicted in the accompanying drawings does not necessarily require the specific order or continuous order shown to achieve the desired results. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0200] Embodiment 3

[0201] Based on the same inventive concept, corresponding to any of the above-mentioned embodiments and methods, the present invention also provides a ship diesel engine sensor configuration strategy optimization system based on an improved NSGA-II algorithm, the system is used to implement any of the methods described, the system includes: a construction module, a calculation module and an iteration module;

[0202] The construction module is used to determine the diesel engine candidate sensor set and the failure mode set to be detected, and to construct the sensor configuration strategy set to be optimized;

[0203] The calculation module is used to use the sensor configuration strategy set to be optimized as the input of the improved NSGA-II algorithm, and calculate the number of monitoring sensors and the fault isolation rate of the fault mode to be detected for each sensor configuration strategy in the sensor configuration strategy set to be optimized;

[0204] The iteration module is used to calculate the fitness function y1 of the improved NSGA-II algorithm according to the number of monitoring sensors, and to calculate the fitness function y2 of the improved NSGA-II algorithm according to the fault isolation rate. The fitness functions y1 and y2 are used to evaluate the pros and cons of each sensor configuration strategy, guide the optimization iteration direction of the improved NSGA-II algorithm, and then obtain the optimal sensor configuration strategy.

[0205] In this embodiment, in the construction module,

[0206] The diesel engine candidate sensor set is: S = {s1, s2, ..., s n}, where s j are sensors at different monitoring locations, j = 1, 2, ..., n;

[0207] The set of failure modes to be detected is F = {f1,f2,...,f m}, where f i are the fault modes of the diesel engine to be tested, i=1,2,...,m;

[0208] Randomly select different numbers of sensors from the candidate sensor set S to form a sensor configuration strategy x q , then the sensor configuration strategy set to be optimized is: S w ={x1,x2,...,x p}, where q = 1, 2, ..., p, i.e. the sensor configuration strategy set S to be optimized w Contains p sensor configuration strategies.

[0209] In this embodiment, in the calculation module,

[0210] The number of monitoring sensors for each sensor configuration strategy in the sensor configuration strategy set to be optimized is calculated as follows:

[0211]

[0212] Among them, |x q |Configure policy for sensor x q The number of sensors in the candidate sensor set S, |S| is the number of sensors in the candidate sensor set S, |S| = n;

[0213] Statistical failure mode set F = {f1,f2,...,f m Each failure mode f i The number of fault modes to be detected that are correctly isolated Combined failure mode f i The number of failure mode samples to be tested Calculate the fault isolation rate FIR:

[0214]

[0215] In this embodiment, in the iteration module,

[0216] The calculation formulas of fitness functions y1 and y2 include:

[0217]

[0218] The fitness functions y1 and y2 are used to evaluate the pros and cons of each sensor configuration strategy, guide the optimization iteration direction of the improved NSGA-II algorithm, and then the optimal sensor configuration strategy is obtained, including: initialization unit, fitness function calculation unit, stratification unit, crowding calculation unit, selection unit, update unit, merging unit, retention unit, iteration unit,

[0219] The initialization unit is used to configure the sensor strategy set S to be optimized. w is the initial population;

[0220] The fitness function calculation unit is used to calculate the fitness functions y1 and y2 of each sensor configuration strategy in the population;

[0221] The stratification unit is used to stratify the population according to the fast non-dominated sorting algorithm;

[0222] The crowding degree calculation unit is used to calculate the crowding degree of each sensor configuration strategy in the population;

[0223] The selection unit is used to select a parent sensor configuration strategy suitable for reproduction according to a tournament selection algorithm;

[0224] The updating unit is used to search for the configuration strategy of the child sensor according to the position and speed updating mechanism of the BPSO algorithm;

[0225] The merging unit is used to merge the parent population with the child population;

[0226] The retaining unit is used to retain the elite sensor configuration strategy from the merged population as a new population according to the elite strategy;

[0227] The iteration unit is used to,repeat the fitness function calculation unit to the retention unit until the maximum,iteration number Iter is reached, and the elite sensor configuration strategy is used as the sensor,optimization configuration strategy set;

[0228] The sensor optimization configuration strategy set is: S best ={x1,x2,...,x l}, that is, the sensor optimization configuration strategy set S best Contains l optimized sensor configuration strategies, each sensor configuration strategy contains different sensors, and the optimized sensor configuration strategy is in the form of:

[0229]

[0230] Among them, i=1,2,…,n.

[0231] The system of the above embodiment is used to implement a corresponding ship diesel engine sensor configuration strategy optimization method based on the improved NSGA-II algorithm in any of the above embodiments, and has the beneficial effects of the corresponding method embodiments, which will not be repeated here.

[0232] It should be noted that the above-mentioned ship diesel engine sensor configuration strategy optimization system based on the improved NSGA-II algorithm is embodied in the form of a functional unit. The term "module" here can be implemented in the form of software and / or hardware, and is not specifically limited to this.

[0233] For example, a "module" may be a software program, a hardware circuit, or a combination of the two that implements the above functions. The hardware circuit may include an application specific integrated circuit (ASIC), an electronic circuit, a processor (such as a shared processor, a dedicated processor, or a group processor, etc.) and a memory for executing one or more software or firmware programs, a combined logic circuit, and / or other suitable components that support the described functions.

[0234] The embodiments of the present disclosure are intended to cover all such substitutions, modifications and variations that fall within the broad scope of the appended claims. Therefore, any omissions, modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the embodiments of the present disclosure should be included in the scope of protection of the present disclosure.

Claims

1. A method for optimizing the configuration strategy of ship diesel engine sensors based on an improved NSGA-II algorithm, characterized in that: The method comprises: Step 1: Determine the diesel engine candidate sensor set and the set of fault modes to be detected, and construct the sensor configuration strategy set to be optimized; Step 2: Take the sensor configuration strategy set to be optimized as the input of the improved NSGA-II algorithm, and calculate the number of monitoring sensors and the fault isolation rate of the fault mode to be detected for each sensor configuration strategy in the sensor configuration strategy set to be optimized; Step 3: Calculate the fitness function y1 of the improved NSGA-II algorithm according to the number of monitoring sensors, and calculate the fitness function y2 of the improved NSGA-II algorithm according to the fault isolation rate. Use the fitness functions y1 and y2 to evaluate the pros and cons of each sensor configuration strategy, guide the optimization iteration direction of the improved NSGA-II algorithm, and then obtain the optimal sensor configuration strategy.

2. The method according to claim 1, characterized in that In the step 1, The diesel engine candidate sensor set is: S = {s1, s2, ..., s n }, where s j are sensors at different monitoring locations, j = 1, 2, ..., n; The set of failure modes to be detected is F = {f1, f2, ..., f m }, where f i are the fault modes of the diesel engine to be tested, i=1,2,…,m; Randomly select different numbers of sensors from the candidate sensor set S to form a sensor configuration strategy x q , then the sensor configuration strategy set to be optimized is: S w ={x1,x2,...,x p }, where q = 1, 2, ..., p, i.e. the sensor configuration strategy set S to be optimized w Contains p sensor configuration strategies.

3. The method according to claim 2, characterized in that In the step 2, The number of monitoring sensors for each sensor configuration strategy in the sensor configuration strategy set to be optimized is calculated as follows: Among them, |x q |Configure policy for sensor x q The number of sensors in the candidate sensor set S, |S| is the number of sensors in the candidate sensor set S, |S| = n; Statistical failure mode set F = {f1,f2,…,f m Each failure mode f i The number of fault modes to be detected that are correctly isolated Combined failure mode f i The number of failure mode samples to be tested Calculate the fault isolation rate FIR:

4. The method according to claim 3, characterized in that In step 3, The calculation formulas of fitness functions y1 and y2 include: The fitness functions y1 and y2 are used to evaluate the pros and cons of each sensor configuration strategy, guide the optimization iteration direction of the improved NSGA-II algorithm, and then obtain the optimal sensor configuration strategy including: Step 3.1: Configure the sensor to be optimized with the strategy set S w is the initial population; Step 3.2: Calculate the fitness functions y1 and y2 of each sensor configuration strategy in the population; Step 3.3: stratify the population according to the fast non-dominated sorting algorithm; Step 3.4: Calculate the crowding degree of each sensor configuration strategy in the population; Step 3.5: Select the parent sensor configuration strategy suitable for reproduction according to the tournament selection algorithm; Step 3.6: Search for the next-generation sensor configuration strategy based on the position and velocity update mechanism of the BPSO algorithm; Step 3.7: Merge the parent population and the child population; Step 3.8: Retain the elite sensor configuration strategy from the merged population as the new population according to the elite strategy; Step 3.9: Repeat steps 3.2 to 3.8 until the maximum number of iterations Iter is reached, and use the elite sensor configuration strategy as the sensor optimization configuration strategy set; The sensor optimization configuration strategy set is: S best ={x1,x2,…,x l }, that is, the sensor optimization configuration strategy set S best Contains l optimized sensor configuration strategies, each sensor configuration strategy contains different sensors, and the optimized sensor configuration strategy is in the form of: Among them, i=1,2,…,n.

5. A ship diesel engine sensor configuration strategy optimization system based on an improved NSGA-II algorithm, the system is used to implement the method described in any one of claims 1 to 4, characterized in that: The system comprises: a construction module, a calculation module and an iteration module; The construction module is used to determine the diesel engine candidate sensor set and the to-be-detected fault mode set, and to construct the sensor configuration strategy set to be optimized; The calculation module is used to calculate the number of monitoring sensors and the fault isolation rate of the fault mode to be detected for each sensor configuration strategy in the sensor configuration strategy set to be optimized, using the sensor configuration strategy set to be optimized as the input of the improved NSGA-II algorithm; The iteration module is used to calculate the fitness function y1 of the improved NSGA-II algorithm according to the number of monitoring sensors, and calculate the fitness function y2 of the improved NSGA-II algorithm according to the fault isolation rate. The fitness functions y1 and y2 are used to evaluate the pros and cons of each sensor configuration strategy, guide the optimization iteration direction of the improved NSGA-II algorithm, and then obtain the optimal sensor configuration strategy.

6. The system according to claim 5, characterized in that In the building blocks, The diesel engine candidate sensor set is: S = {s1, s2, ..., s n }, where s j are sensors at different monitoring locations, j = 1, 2, ..., n; The set of failure modes to be detected is F = {f1,f2,...,f m }, where f i are the fault modes of the diesel engine to be tested, i=1,2,...,m; Randomly select different numbers of sensors from the candidate sensor set S to form a sensor configuration strategy x q , then the sensor configuration strategy set to be optimized is: S w ={x1,x2,...,x p }, where q = 1, 2, ..., p, i.e. the sensor configuration strategy set S to be optimized w Contains p sensor configuration strategies.

7. The system according to claim 6, characterized in that In the calculation module, The number of monitoring sensors for each sensor configuration strategy in the sensor configuration strategy set to be optimized is calculated as follows: Among them, |x q |Configure policy for sensor x q The number of sensors in the candidate sensor set S, |S| is the number of sensors in the candidate sensor set S, |S| = n; Statistical failure mode set F = {f1,f2,…,f m Each failure mode f i The number of fault modes to be detected that are correctly isolated Combined failure mode f i The number of failure mode samples to be tested Calculate the fault isolation rate FIR:

8. The system according to claim 7, characterized in that In the iteration module, The calculation formulas of fitness functions y1 and y2 include: The fitness functions y1 and y2 are used to evaluate the pros and cons of each sensor configuration strategy, guide the optimization iteration direction of the improved NSGA-II algorithm, and then the optimal sensor configuration strategy is obtained, including: initialization unit, fitness function calculation unit, stratification unit, crowding calculation unit, selection unit, update unit, merging unit, retention unit, iteration unit, The initialization unit is used to configure the sensor configuration strategy set S to be optimized. w is the initial population; The fitness function calculation unit is used to calculate the fitness functions y1 and y2 of each sensor configuration strategy in the population; The stratification unit is used to stratify the population according to a fast non-dominated sorting algorithm; The congestion calculation unit is used to calculate the congestion of each sensor configuration strategy in the population; The selection unit is used to select a parent sensor configuration strategy suitable for reproduction according to a tournament selection algorithm; The updating unit is used to search for the sub-generation sensor configuration strategy according to the position and speed update mechanism of the BPSO algorithm; The merging unit is used to merge the parent population with the offspring population; The retaining unit is used to retain the elite sensor configuration strategy from the merged population as a new population according to the elite strategy; The iteration unit is used to repeat the fitness function calculation unit to the retention unit until the maximum number of iterations Iter is reached, and the elite sensor configuration strategy is used as the sensor optimization configuration strategy set; The sensor optimization configuration strategy set is: S best ={x1,x2,...,x l }, that is, the sensor optimization configuration strategy set S best Contains l optimized sensor configuration strategies, each sensor configuration strategy contains different sensors, and the optimized sensor configuration strategy is in the form of: Among them, i=1,2,…,n.

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