CN108363876B - Test optimization selection method considering key faults - Google Patents

Test optimization selection method considering key faults Download PDF

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CN108363876B
CN108363876B CN201810152724.6A CN201810152724A CN108363876B CN 108363876 B CN108363876 B CN 108363876B CN 201810152724 A CN201810152724 A CN 201810152724A CN 108363876 B CN108363876 B CN 108363876B
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马羚
叶文
吕晓峰
王凤琴
刘瑜
汪兴海
吕鑫燚
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Abstract

The invention discloses a test optimization selection method considering key faults, which comprises the following steps: obtaining a fault-test correlation matrix, establishing an optimization model, solving the optimization model and the like. The method analyzes the importance of the key fault from the perspective of system safety, then establishes a test optimization selection model considering the key fault by taking the minimum test cost as an optimization target and taking the fault detection rate, the isolation rate, the key fault detection rate and the isolation rate as constraints based on a correlation matrix, and finally solves the problem by adopting a binary particle swarm algorithm based on centroid improvement and inertia weight adaptive adjustment. The invention can effectively eliminate the serious threat to equipment safety caused by the missing detection of key faults.

Description

Test optimization selection method considering key faults
Technical Field
The invention belongs to the technical field of testing and fault diagnosis, and relates to a test optimization selection method considering key faults.
Background
With the continuous improvement of the complexity of electronic equipment, the problems of poor testability, high test cost, high test diagnosis difficulty and the like are gradually exposed in use. An important task of test diagnosis is test optimization selection, that is, a group of test sets meeting the requirement of testability parameter indexes are selected from a set formed by all possible tests of the system, and the test cost is minimum. The test optimization selection problem belongs to a typical set coverage and combination optimization problem, and the solving difficulty is high. The common greedy algorithm, the and-or graph search algorithm, the AO method and the like have the problems of high computational complexity, local convergence, combined explosion and the like, and are difficult to adapt to a complex system.
In recent years, with the rise of intelligent optimization algorithms, researchers at home and abroad have started to pay attention to the application research of the intelligent optimization algorithms in test optimization selection, such as methods based on genetic algorithms, methods based on particle swarm optimization, and methods based on quantum evolution algorithms. The methods all use the minimum test cost as an optimization target, use the fault detection rate and the fault isolation rate as constraint conditions to establish a mathematical model, and then obtain a test optimization selection result through optimization of an intelligent optimization algorithm, so that the method is widely applied. Although the optimal solution searched by the algorithm can minimize the test cost and meet the requirement of testability indexes, the abandonment of some tests possibly causes part of small-probability critical faults which cannot be detected and isolated, and further causes serious burden on the safe operation and subsequent maintenance of the system. In view of the above, it is necessary to develop a test optimization selection problem for critical faults to reduce the life cycle cost of the system.
Disclosure of Invention
In view of the above, the present invention provides a directional method for effectively detecting and isolating critical faults. Firstly, analyzing the importance of a key fault from the perspective of system safety; and then based on the correlation matrix, establishing a test optimization selection model considering key fault detection rate and isolation rate indexes by taking the minimum test cost as an optimization target and taking the fault detection rate and the fault isolation rate as constraints, and solving by adopting a binary particle swarm algorithm based on centroid improvement and inertial weight and based on population diversity adaptive adjustment to realize the test optimization selection of the system.
The technical solution of the method of the invention is now described as follows:
the invention relates to a test optimization selection method considering key faults, which is characterized by comprising the following steps: the method comprises the following steps:
step 1: through a correlation modeling method, namely, through methods such as fault tree analysis, simulation analysis and the like, correlation relations among system faults, key faults and tests are analyzed, a fault-test correlation matrix can be obtained, and therefore the next test optimization selection work can be carried out. If F is ═ F1,f2,…,fmIs the failure set of the system, FkeyFor the set of all critical faults in the system, T ═ T1,t2,…,tnIs a set of optional tests, λ ═ λ1,λ2,…,λm]For the prior probability vector of each failure mode, C ═ C1,c2,…,cn]The cost vectors for each test. The fault-test correlation matrix is shown below:
Figure BDA0001580295330000011
where the rows of the matrix represent failure modes and the columns represent test sets. Matrix element ftijIndicates a fault fiAnd test tjCorrelation of ft ij1 denotes fault fiCan be tested tjDetected, ft ij0 denotes fault fiCan not be tested tjAnd (4) detecting.
Step 2: establishment of optimization model
Step 2.1: and establishing an optimization target, namely testing cost. Assume that the selected test set is TSThen the test cost is:
Figure BDA0001580295330000021
step 2.2: and establishing optimized constraint conditions, namely fault detection rate, fault isolation rate, key fault detection rate and key fault isolation rate. The method comprises the following specific steps:
step 2.2.1: and calculating the fault detection rate. Fault fiTested set TSThe detection conditions are as follows: fault fiThe corresponding row vector is not a zero vector, i.e.
Figure BDA0001580295330000022
Wherein N isSSet T for testSThe number of tests contained in (1). Set test set TSThe set of detectable faults is FDNamely:
Figure BDA0001580295330000023
thus, the failure detection rate can be calculated by:
Figure BDA0001580295330000024
step 2.2.2: and calculating the fault isolation rate. If fault fiAnd fault fjThe corresponding row vectors are respectively FisAnd FjsThen fail fiAnd fault fjCan be tested set TSThe condition of isolation is that a fault fiAnd fjAll can be TSDetect, and vector FisAnd FjsIs not identical, i.e.
Figure BDA0001580295330000025
In the formula (I), the compound is shown in the specification,
Figure BDA0001580295330000026
and the XOR operation of the vectors is represented, when the operation result is 0, the corresponding elements of the two vectors are the same, otherwise, the operation result is 1. Set test set TSSet of isolatable faults is FINamely:
Figure BDA0001580295330000027
thus, the fault isolation rate can be calculated by:
Figure BDA0001580295330000028
step 2.2.3: and calculating the detection rate of the key faults. The critical failure detection rate is defined as: the ratio of the sum of prior probabilities of correctly detected critical faults to the sum of prior probabilities of all critical faults is determined in a defined manner over a defined time. Let the set of all critical fault components in the system be FkeyTest set TSThe set of key faults that can be detected is FDkeyNamely:
Figure BDA0001580295330000029
thus, the critical failure detection rate can be calculated by:
Figure BDA0001580295330000031
step 2.2.4: and calculating the isolation rate of the critical fault. The critical fault isolation rate is defined as: the ratio of the number of critical faults correctly isolated to the number of single replaceable units to the number of critical faults detected at the same time is determined in a defined manner over a defined period of time. Let FIkeyIs TSThe set of all critical faults that can be isolated then has:
Figure BDA0001580295330000032
thus, the critical fault isolation rate can be calculated by:
Figure BDA0001580295330000033
step 2.3: and establishing a test optimization selection mathematical model considering the key faults. The objective of test optimization selection considering the key faults is to select the optimal complete test for the system, namely, the selected test set meets the indexes of fault detection rate and fault isolation rate, the effective detection and isolation of the key faults are realized, and meanwhile, the test cost of the test set is minimum. Therefore, by combining the formulas (1) to (5), the test optimization selects the mathematical model as:
Figure BDA0001580295330000034
in the formula (I), the compound is shown in the specification,
Figure BDA0001580295330000035
the fault detection rate, the fault isolation rate, the key fault detection rate and the key fault isolation rate required by the system are respectively.
And step 3: solution of optimization model
The traditional method has good performance for solving the test optimization selection problem with a certain set scale, but as the set scale is increased, accurate results are difficult to obtain quickly. The problem is a combined optimization problem, and the solving difficulty is multiplied along with the increase of the system scale. Based on the method, an improved binary particle swarm algorithm is adopted for solving.
Step 3.1: improved binary particle swarm algorithm based on centroid
For the updating of the particle speed, two abstract particles, namely an individual optimal mass center and a population mass center, are introduced into a particle speed updating formula so as to improve the information interaction among the particles and effectively improve the optimizing speed and quality; the position updating mode of the particles is the same as that of the basic binary particle swarm algorithm. The specific formula is as follows:
Figure BDA0001580295330000041
in the formula (I), the compound is shown in the specification,
Figure BDA0001580295330000042
is the mass center of the population,
Figure BDA0001580295330000043
an optimal centroid for the individual; m is the population scale; omega is the inertial weight;
Figure BDA0001580295330000044
and
Figure BDA0001580295330000045
the d-dimension components of the position and the speed of the particle i in the t +1 th iteration respectively;
Figure BDA0001580295330000046
and
Figure BDA0001580295330000047
respectively finding an individual extreme value and a global extreme value from the d-dimension component of the particle i to the t-dimension iteration; c. C1、c2、c3In order to accelerate the factor(s) of the vehicle,
Figure BDA0001580295330000048
Figure BDA0001580295330000049
and
Figure BDA00015802953300000410
is a positive real number randomly generated between intervals (0, 1).
Step 3.2: fitness calculation
The particle swarm algorithm evaluates the quality of particles through fitness, and the convergence speed and precision of the algorithm are directly influenced by the quality of the calculation method. The specific steps for calculating the particle fitness by considering the key fault indexes are as follows:
step 3.2.1: assuming that the population evolves to the kth generation, the current population is
Figure BDA00015802953300000411
The ith particle in the population
Figure BDA00015802953300000412
The selected test set is TiAnd T isiThe set of detected faults is FiCalculating the test set T from equation (2)iFault detection rate of (a)FD(Ti). If it is
Figure BDA00015802953300000413
It jumps to step 3.2.5; otherwise, skipping to the step 3.2.2;
step 3.2.2: from TiGet unselected test sets
Figure BDA00015802953300000414
According to FiDeriving a set of undetected faults
Figure BDA00015802953300000415
Step 3.2.3: to the test set
Figure BDA00015802953300000416
Each test t inkCalculating the cost-to-efficiency ratio:
Figure BDA00015802953300000417
wherein, F (t)k) To test tkSet of detectable faults, p (f)i) As a set of faults
Figure BDA00015802953300000418
Can be tested for tkDetected fault fiA priori probability of ckTo test tkThe cost of the test. Selecting the test with the highest cost-to-efficiency ratio to join the test set TiAnd adding the detected faults into a fault set Fi；
Step 3.2.4: computing test set TiIf the fault detection rate is
Figure BDA0001580295330000051
Jump to step 3.2.5, otherwise update
Figure BDA0001580295330000052
And
Figure BDA0001580295330000053
skipping to step 3.2.2;
step 3.2.5: let TiThe set of detected critical faults is FikeyCalculating the test set T from equation (4)iCritical failure detection rate of
Figure BDA00015802953300000515
If it is
Figure BDA00015802953300000516
Go to step 3.2.9, otherwise go to step 3.2.6;
step 3.2.6: from TiGet unselected test sets
Figure BDA0001580295330000054
According to FikeyDeriving a set of undetected critical faults
Figure BDA0001580295330000055
Step 3.2.7: to the test set
Figure BDA0001580295330000056
Each test t inkCalculating the cost-to-efficiency ratio:
Figure BDA0001580295330000057
wherein, Fkey(tk) To test tkSet of detectable critical faults, p (f)i) Is a set of critical faults
Figure BDA0001580295330000058
Can be tested for tkDetected critical fault fiA priori probability of ckTo test tkThe cost of the test. Selecting the test with the highest cost-to-efficiency ratio to join the test set TiAnd adding the detected faults into a key fault set Fikey；
Step 3.2.8: computing test set TiCritical failure detection rate of
Figure BDA0001580295330000059
If it is
Figure BDA00015802953300000510
Jump to step 3.2.9, otherwise update
Figure BDA00015802953300000511
And
Figure BDA00015802953300000512
skipping to step 3.2.6;
step 3.2.9: calculating test set T according toiThe fitness value of (a):
Figure BDA00015802953300000513
step 3.3: inertial weight adaptive adjustment
The inertia weight reflects the influence of the speed of the previous generation particles on the speed of the current generation particles, and the value of the inertia weight directly influences the local search capability and the global search capability of the particles. The state of the particles is judged according to the population diversity, so that the inertia weight is dynamically changed, and the algorithm has good searching capability. The quantification of the population diversity is to judge the beginning of the state of the particles, and the population diversity is measured by adopting the average point distance from an individual to a centroid, and the calculation formula is as follows:
Figure BDA00015802953300000514
where k is the number of iterations, M is the population size, D is the particle dimension, pjAnd L is half of the maximum diagonal distance of the search space, which is the centroid of the population.
The threshold value of the population diversity is:
Figure BDA0001580295330000061
in the formula, MaxIter and CurIter are the maximum iteration times and the current iteration times of the algorithm, and a and b are adjustment parameters and take values of (0, 1).
The inertial weight adaptive adjustment strategy based on the population diversity is as follows:
Figure BDA0001580295330000062
in the formula (f)gFitness value, f, for a globally optimal particleavgIs the average fitness value, omega, of all the particles at presentmaxAnd ωminThe maximum and minimum values of ω, respectively. Omega2The inertial weight is dynamically changed for the adjustable portion.
Step 3.4: the specific steps of carrying out test optimization selection by using a binary particle swarm algorithm with improved centroid are as follows:
step 3.4.1: obtaining a system fault-test correlation matrix FT using a correlation modelm×nInitializing algorithm parameters including population size Popsize and learning factor c1、c2、c3Inertia weight ωmax、ωminConstants α, β, γ and λ, maximum number of iterations Nmax；
Step 3.4.2: setting a population iteration counter i to be 0, calculating the fitness value of each individual in the population X (i) according to the step 3.2, comparing and updating the extreme values of the individuals in the population
Figure BDA0001580295330000063
And global extremum
Figure BDA0001580295330000064
Step 3.4.3: adjusting the inertial weight by adopting a self-adaptive strategy according to the step 3.3, calculating the population centroid and the individual optimal centroid, and updating the population speed and position according to the formula (7); obtaining a next generation population X (i +1), and updating a counter i ═ i + 1;
step 3.4.4: if the number of iterations i > NmaxIf yes, the algorithm is ended, and the step 3.4.5 is skipped; otherwise go to step 3.4.2;
step 3.4.5: output of
Figure BDA0001580295330000065
As a result of test optimization selection.
An optimal complete test set considering the key faults can be obtained through the process, and therefore test optimization selection considering the key faults is completed.
Compared with the prior art, the invention has the advantages that: aiming at the problem that the key fault is easy to be missed in the traditional test optimization selection method because the key fault is a small-probability fault, from the viewpoint of contradiction between balance test cost and system safety, the key fault detection rate and key fault isolation rate indexes are added into a test optimization selection model, and a binary particle swarm algorithm based on centroid improvement and inertia weight self-adaptive adjustment is adopted for solving. The method can effectively eliminate the serious threat to equipment safety caused by the missing detection of the key faults on the premise of ensuring the optimization target of 'lowest test cost'.
Drawings
FIG. 1 is a flow chart of the method of the present invention
FIG. 2 is a graph of the method history fitness change
Detailed Description
The method according to the invention will now be described in more detail with reference to the accompanying drawings and examples:
examples
Taking a superheterodyne receiver system as an example, the fault-test correlation matrix is shown in Table 1, t1～t36For 36 tests, f1～f22Representing 22 faults respectively.
TABLE 1 Fault-test correlation matrix for superheterodyne systems
Figure BDA0001580295330000071
Table 2 shows the prior probability of each fault and three key faults of the system, assuming that the test cost of each candidate test is 1.
TABLE 2 System Fault Prior probability and Critical Fault
Fault of Failure rate Critical fault Fault of Failure rate Critical fault
f1 0.00185 f12 0.00185
f2 0.00923 f13 0.00923
f3 0.18500 f14 0.18500
f4 0.00185 f15 0.00923
f5 0.00185 f16 0.00185 Is that
f6 0.00923 f17 0.00923
f7 0.00185 f18 0.00185
f8 0.00923 f19 0.00185 Is that
f9 0.18500 f20 0.00185 Is that
f10 0.18500 f21 0.00185
f11 0.18500 f22 0.00185
The fault detection rate and the fault isolation rate of the system are not lower than 95%, and the key fault detection rate and the key fault isolation rate are not lower than 98%. The other parameters are: m60, ωmax＝1.2，ωmin＝0.4，Nmax＝200，α＝β＝γ＝0.5，c1＝c2＝c31.4962. After 30 independent operations, the number of iterations in each operation process is 200, and the finally obtained change curve of the fitness of the particles in the past generation is shown in fig. 2. As can be seen in the figure, the globally optimal solution converges on iteration to around the 50 th generation. The optimal solution is [0,0,0,0,0,0,0,1,0,0,0,1,0,0,0, 0,0,0,0,1,0,1,0, 0,0,0,0,0,0,0,0]I.e. the selected test set is t8,t12,t16,t26,t28,t30,t31,t34}。

Claims (2)

1. A test optimization selection method considering critical faults is characterized by comprising the following steps:
step 1: the correlation relationship between system fault and test is analyzed by a correlation modeling method, namely a fault tree analysis method and a fault mode influence and hazard analysis method to obtain a fault-test correlation matrix FTm×nTherefore, the next testing optimization selection work is carried out;
matrix FTm×nThe method specifically comprises the following steps:
Figure FDA0003180524220000011
wherein, the rows of the matrix represent failure modes, and the columns represent test sets; matrix element ftijIndicates a fault fiAnd test tjIs in the correlation relationship of i ∈ [1, m ∈ ]],j∈[1,n]；ftij1 denotes fault fiCan be tested tjDetected, ftij0 denotes fault fiCan not be tested tjDetecting;
step 2: establishing a test optimization selection mathematical model considering the key faults;
the mathematical model is specifically as follows:
Figure FDA0003180524220000012
in the formula (I), the compound is shown in the specification,
Figure FDA0003180524220000013
selecting a test cost of a test set for the system; lambda [ alpha ]FD、λFI、
Figure FDA0003180524220000014
Respectively obtaining the fault detection rate, the fault isolation rate, the key fault detection rate and the key fault isolation rate of the selected test set;
Figure FDA0003180524220000015
Figure FDA0003180524220000016
respectively the fault detection rate, the fault isolation rate, the key fault detection rate and the key fault isolation rate required by the system;
key fault detection rate of system in step 2
Figure FDA0003180524220000017
And critical fault isolation rate
Figure FDA0003180524220000018
The method specifically comprises the following steps:
1) the key fault detection rate of the system is as follows: the ratio of the sum of the prior probabilities of the correctly detected key faults to the sum of the prior probabilities of all key faults is determined by a determined method within a determined time;
let the set of all critical fault components in the system be FkeyTest set TSThe set of key faults that can be detected is FDkeyNamely:
Figure FDA0003180524220000019
the critical fault detection rate is calculated from:
Figure FDA0003180524220000021
2) the key fault isolation rate of the system is as follows: correctly isolating the ratio of the number of critical faults to the number of single replaceable units to the number of critical faults detected at the same time in a prescribed way within a prescribed time;
let FIkeyIs TSThe set of all critical faults that can be isolated then has:
Figure FDA0003180524220000022
the critical fault isolation rate is calculated from:
Figure FDA0003180524220000023
and step 3: the method adopts a centroid improved binary particle swarm algorithm to solve an optimization model, and specifically comprises the following steps:
step 3.1: improved binary particle swarm algorithm based on centroid
Step 3.2: fitness calculation
The specific steps for calculating the particle fitness by considering the key fault indexes are as follows:
step 3.2.1: assuming that the population evolves to the kth generation, the current population is
Figure FDA0003180524220000024
The ith particle in the population
Figure FDA0003180524220000025
The selected test set is TiAnd T isiThe set of detected faults is FiCalculating a test set TiFault detection rate of (a)FD(Ti) (ii) a If it is
Figure FDA0003180524220000026
Go to step 3.2.5; otherwise, skipping to the step 3.2.2;
step 3.2.2: from TiTo obtainUnselected test sets
Figure FDA0003180524220000027
According to FiDeriving a set of undetected faults
Figure FDA0003180524220000028
Step 3.2.3: to the test set
Figure FDA0003180524220000029
Each test t inkCalculating the cost-to-efficiency ratio:
Figure FDA00031805242200000210
wherein, F (t)k) To test tkSet of detectable faults, p (f)i) As a set of faults
Figure FDA00031805242200000211
Can be tested for tkDetected fault fiA priori probability of ckTo test tkThe test cost of (2); test set T is added to the test with the highest cost-to-efficiency ratioiAnd adding the detected faults into a fault set Fi；
Step 3.2.4: computing test set TiIf the fault detection rate is
Figure FDA00031805242200000212
Jump to step 3.2.5, otherwise update
Figure FDA00031805242200000213
And
Figure FDA00031805242200000214
skipping to step 3.2.2;
step 3.2.5: let TiThe set of detected critical faults is FikeyCalculating the test set T from equation (1)iCritical failure detection rate of
Figure FDA00031805242200000215
If it is
Figure FDA00031805242200000216
Go to step 3.2.9, otherwise go to step 3.2.6;
step 3.2.6: from TiGet unselected test sets
Figure FDA0003180524220000031
According to FikeyDeriving a set of undetected critical faults
Figure FDA0003180524220000032
Step 3.2.7: to the test set
Figure FDA0003180524220000033
Each test t inkCalculating the cost-to-efficiency ratio:
Figure FDA0003180524220000034
wherein, Fkey(tk) To test tkSet of detectable critical faults, p (f)i) Is a set of critical faults
Figure FDA0003180524220000035
Can be tested for tkDetected critical fault fiA priori probability of ckTo test tkThe test cost of (2); test set T is added to the test with the highest cost-to-efficiency ratioiAnd adding the detected faults into a key fault set Fikey；
Step 3.2.8: computing test set TiCritical failure detection rate of
Figure FDA0003180524220000036
If it is
Figure FDA0003180524220000037
Jump to step 3.2.9, otherwise update
Figure FDA0003180524220000038
And
Figure FDA0003180524220000039
skipping to step 3.2.6;
step 3.2.9: calculating test set T according toiThe fitness value of (a):
Figure FDA00031805242200000310
step 3.3: inertial weight adaptive adjustment based on population diversity
Step 3.4: carrying out test optimization selection by using a binary particle swarm algorithm with improved mass center;
an optimal complete test set considering the key faults is obtained through the steps, and therefore test optimization selection considering the key faults is completed.
2. The method of claim 1, wherein the test optimization selection method considering critical faults is characterized in that: step 3.4 specifically comprises the following substeps:
step 3.4.1: obtaining a matrix FT by correlation modelingm×nInitializing algorithm parameters including population size Popsize and learning factor c1、c2、c3Inertia weight ωmax、ωminConstants α, β, γ and λ, maximum number of iterations Nmax；
Step 3.4.2: setting a population iteration counter i to be 0, calculating the fitness value of each individual in the population X (i) according to the step 3.2, comparing and updating the extreme values of the individuals in the population
Figure FDA00031805242200000311
And global extremum
Figure FDA00031805242200000312
Step 3.4.3: adjusting the inertial weight by adopting a self-adaptive strategy according to the step 3.3, calculating the population centroid and the individual optimal centroid, and updating the population speed and position according to the following formula:
Figure FDA0003180524220000041
in the formula (I), the compound is shown in the specification,
Figure FDA0003180524220000042
is the mass center of the population,
Figure FDA0003180524220000043
an optimal centroid for the individual; m is the population scale; omega is the inertial weight;
Figure FDA0003180524220000044
and
Figure FDA0003180524220000045
the d-dimension components of the position and the speed of the particle i in the t +1 th iteration respectively;
Figure FDA0003180524220000046
and
Figure FDA0003180524220000047
respectively finding an individual extreme value and a global extreme value from the d-dimension component of the particle i to the t-dimension iteration; c. C1、c2、c3As an acceleration factor, r1 t、
Figure FDA0003180524220000048
Figure FDA0003180524220000049
And
Figure FDA00031805242200000410
positive real numbers randomly generated between intervals (0, 1); then obtaining a next generation population X (i +1), and updating a counter i to i + 1;
step 3.4.4: if the number of iterations i>NmaxIf yes, the algorithm is ended, and the step 3.4.5 is skipped; otherwise go to step 3.4.2;
step 3.4.5: output of
Figure FDA00031805242200000411
As a result of test optimization selection.
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