CN107844850B - Two-type prediction set safety evaluation method based on data possibility-reliability distribution - Google Patents

Two-type prediction set safety evaluation method based on data possibility-reliability distribution Download PDF

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CN107844850B
CN107844850B CN201710752507.6A CN201710752507A CN107844850B CN 107844850 B CN107844850 B CN 107844850B CN 201710752507 A CN201710752507 A CN 201710752507A CN 107844850 B CN107844850 B CN 107844850B
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王肖霞
杨风暴
朱博秀
张飞飞
姜星
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North University of China
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Abstract

The invention belongs to the field of evaluation of actual projects such as large buildings, public facilities, precision equipment and the like, and particularly relates to a two-type prediction set safety evaluation method based on data possibility-reliability distribution. The method firstly defines a two-type prediction set and related concepts thereof on the basis of probability distribution and reliability distribution, and provides a similarity measurement method between the two-type prediction sets; then, determining a heterogeneous data security level scale according to the evaluation requirement, establishing joint distribution, and respectively fusing heterogeneous data to be evaluated in two-type distribution by using a weighted fusion method; and finally, calculating the similarity measure between the fusion distribution and the safety level scale thereof, determining the position of the centroid in the projection plane of the joint scale, and judging the safety level. Experimental results show that when the method is used for judging the safety level of the tailing dam, the granularity of an evaluation result can be effectively reduced, the problem of erroneous judgment is reduced, and convenience is brought to accurate judgment of the safety level of the dam body.

Description

Two-type prediction set safety evaluation method based on data possibility-reliability distribution
Technical Field
The invention belongs to the field of evaluation of actual projects such as large buildings, public facilities, precision equipment and the like, and particularly relates to a two-type prediction set safety evaluation method based on data possibility-reliability distribution.
Background
The expert prediction data and the sensor monitoring data reflect the operation conditions of actual projects (such as large buildings, public facilities, precise equipment and the like) from different sides, and the effective evaluation of the future safety level of the expert prediction data and the sensor monitoring data is an important guarantee for avoiding the occurrence of serious catastrophic accidents. Most of the existing evaluation methods are based on various uncertainties (such as randomness, fuzziness, possibility and the like) of data, and the safety level is judged by using probability theory, fuzzy set theory, possibility theory and the like, so that the existing evaluation methods have strong pertinence and wide application value in a specific uncertainty environment. The main purpose of the safety assessment is not only to determine the study object in time after the accident or failure occurs, but also to predict the future development trend of the study object when the tiny abnormal symptom occurs. In addition, a large amount of experimental data cannot be obtained when researching evaluation objects which cannot be subjected to destructive tests, such as tailing dams, side slopes, space equipment and the like. That is, how to predict the working state or ability of a research object at a certain time or in a certain period of time in the future by using small sample data is a problem to be solved urgently in some specific projects at present. Only if the problem is solved, people can prevent the further development and deterioration of the situation by taking measures at proper time, thereby effectively preventing or avoiding the occurrence of accidents. The probability distribution is a quantitative description method of the occurrence difficulty of the "event" given by zadeh in the probability space, emphasizes the embodiment of the occurrence difficulty of the element under the occurrence condition of the "event", is the possible occurrence degree of the element when the "event" does not occur, and has the advantages of less required sample information, less calculation amount and the like. Thus, likelihood distributions are more suitable for metric and post fusion and decision processing of uncertainty data in the evaluation than probability distributions, fuzzy distributions, and the like.
The credibility of the data is another important factor which influences the actual engineering evaluation result besides the uncertainty, and reflects the difference of the capability of the data source (such as expert experience, comprehension force, sensor performance, operation condition and the like), and if the difference is ignored, the misjudgment of safety level is caused. Therefore, how to reflect the credibility and uncertainty of the data in the judgment of the safety level in the actual engineering is an important way for ensuring the comprehensive and efficient evaluation result.
Disclosure of Invention
The idea that the two-type fuzzy set respectively represents the element fuzziness and the primary membership function fuzziness in the fuzzy set by using the primary membership function and the secondary membership function provides reference for describing the credibility and uncertainty of the data in the text. Therefore, the method is provided for converting the first type distribution into the second type distribution capable of reflecting the data reliability, and describing the credibility and the uncertainty of the data by using a reliability distribution function and a probability distribution function respectively so as to improve the universality of the evaluation method and solve the misjudgment of the security level.
The invention provides a two-type prediction set security evaluation method based on data possibility-reliability distribution, which utilizes a similar matrix and a centroid matrix among two-type prediction sets to research the relationship between evaluation data and a security level scale in heterogeneous data joint evaluation and determines the evaluation result of a security level according to the position of a centroid point in a projection plane.
The invention is realized by adopting the following technical scheme: the two-type prediction set safety assessment method based on data probability-confidence distribution comprises the following steps:
step 1: determining safety level scales of two types of data monitored by an expert system and a sensor according to system safety regulations, establishing joint distribution and determining projection surface areas of each safety level because the scales are used as level judgment bases and the credibility given to a credibility distribution function of the safety level scales is 1;
step 2: determining evaluation data { I ] in the expert system according to the contents of each evaluation item of the security level i1,2, … n and a weight { w |E1,wE2,…,wEnReference data { M } in sensor monitoring j1,2, …, m and weight { w |S1,wS2,…,wSmAnd using two type prediction sets based on data probability-confidence distribution
Figure BDA0001391448750000031
Is shown as respectively
Figure BDA0001391448750000032
And
Figure BDA0001391448750000033
and step 3: respectively synthesizing the probability distribution function and the reliability distribution function of the reference data in each type of data by using a weighted fusion method to obtain the fusion distribution of the two types of data
Figure BDA0001391448750000034
And 4, step 4: calculating the similarity and the mass center between the fusion distribution obtained in the step 3 and the safety level scale, and establishing a corresponding matrix;
and 5: determining specific position points of the centroids of the two types of parameter data in the projection plane of the safety level scale according to the similarity measure matrix and the centroid matrix in the step 4, and if the specific position points of the two types of parameter data are in the same projection plane of the safety level scale, judging that the system is in the safety level; if the rule is not satisfied, go to step 6;
step 6: and determining the gravity center position of the projection surface of each safety level scale, calculating the distance between the gravity center position and the specific position point of the mass center of the reference data, and judging the safety level of the system by using a shortest distance method.
Compared with the existing evaluation method, the method has the following advantages:
(1) the two-type prediction set description method capable of reflecting the data reliability is provided, and a processor provides support for accurate measurement of data and reduction of the separation degree of a post-processing result by using a three-dimensional function;
(2) the method utilizes the similarity measure and the mass center between the two types of prediction sets to respectively determine the relation between the test data and the safety level scale, and further provides an evaluation result through the position of the evaluation result in the projection of the joint scale, thereby solving the problems of large granularity and misjudgment of the evaluation result caused by the existing evaluation method;
(3) experimental results show that the method is suitable for safety assessment of the tailing dam, and people can obtain the optimal solution of a reliability distribution function by researching comparison and analysis of assessment results under different reliability distributions.
Drawings
FIG. 1 is a diagram of probability traces (FOPs) and related quantities.
FIG. 2 is a schematic illustration of a confidence distribution.
FIG. 3 is a diagram of a two-type predictor set graph.
FIG. 4 is a schematic diagram of the evaluation method.
FIG. 5 is a diagram illustrating a security level scale of a sensor and an expert system class when a Gaussian distribution is taken as an example.
Fig. 6 shows the joint distribution of the two types of security level scales in fig. 5 and a projection thereof.
Fig. 7 shows the joint distribution of the two types of safety level scales and the projection thereof in the embodiment.
FIG. 8 is a schematic diagram illustrating determination of a position point in a projection plane in an embodiment.
Fig. 9 is a schematic diagram illustrating a relationship between the determination result position point a and the uncertainty area B in consideration of the reliability in the embodiment.
Detailed Description
The two-type prediction set safety assessment method based on data possibility-reliability distribution comprises the following steps:
step 1: determining safety level scales of two types of data monitored by an expert system and a sensor according to system safety regulations, wherein the sensor monitoring data are A, B, C, D four safety level scales; the expert system data are four safety level scales I, II, III and IV, the scales are used as the level judgment basis, the credibility given to the credibility distribution function of the safety level scales is 1, the safety level scale joint distribution is established, and the projection surface area of each safety level is determined;
step 2: determining evaluation data { I ] in the expert system according to the contents of each evaluation item of the security level i1,2, … n and a weight { w |E1,wE2,…,wEnReference data { M } in sensor monitoring j1,2, …, m and weight { w |S1,wS2,…,wSmAnd using two type prediction sets based on data probability-confidence distribution
Figure BDA0001391448750000051
Is shown as respectively
Figure BDA0001391448750000052
And
Figure BDA0001391448750000053
and step 3: respectively synthesizing the probability distribution function and the reliability distribution function of the reference data in each type of data by using a weighted fusion method to obtain the fusion distribution of the two types of data
Figure BDA0001391448750000054
And 4, step 4: calculating the similarity measure S between the fusion distribution obtained in the step 3 and the safety level scale by using a calculation formulaJAnd its center of mass
Figure BDA0001391448750000056
Establishing corresponding matrix
Figure BDA0001391448750000055
Figure BDA0001391448750000065
Wherein the content of the first and second substances,
Figure BDA0001391448750000066
four safety grade scales for expert system class data represented by the two-type prediction set;
Figure BDA0001391448750000068
and
Figure BDA0001391448750000067
for the similarity measure and the mass center between the data fusion distribution of the parameters and the corresponding safety level scale,
Figure BDA0001391448750000061
four safety scales for sensor monitoring class data expressed by the two-type prediction set;
Figure BDA0001391448750000062
and
Figure BDA0001391448750000063
fusing the similarity measure and the mass center between the distribution and the corresponding safety level scale for the class of parameter data;
and 5: determining specific position points of the centroids of the two types of parameter data in the projection plane of the safety level scale according to the similarity measure matrix and the centroid matrix in the step 4, and if the specific position points of the two types of parameter data are in the same projection plane of the safety level scale, judging that the system is in the safety level; if the rule is not satisfied, go to step 6;
step 6: and determining the gravity center position of the projection surface of each safety level scale, calculating the distance between the gravity center position and the specific position point of the mass center of the reference data, and judging the safety level of the system by using a shortest distance method.
In specific implementation, the definition process of the two-type prediction set and the similarity measurement method is as follows:
two type prediction set
To elicit the definition of the two-type prediction set, the concepts of probability distribution and confidence distribution are given below:
probability distribution definition: suppose (U, F (U), (U) and II) are probability spaces, X is a value variable on a finite universe of discourse U, and
Figure BDA0001391448750000069
if it is
Figure BDA0001391448750000064
The fuzzy constraint associated with X is R (X), then the probability distribution II associated with the variable XXIs composed of
∏X＝R(X) (1)
Let piXIs a nXThe probability distribution function of (1), the probability of the variable X taking the value of X is
πX(x)＝Poss(X＝x) (2)
Which describes the size of the x value possibilities.
Possibility trace definition: suppose that
Figure BDA0001391448750000071
For any one of the two-type prediction sets on the finite discourse field X, then
Figure BDA0001391448750000072
The union of the Cartesian product of any point X on X and the point probability distribution will constitute a planar region referred to as
Figure BDA0001391448750000073
Can be expressed as
Figure BDA0001391448750000074
When in use
Figure BDA00013914487500000715
When the upper value is a continuous domain, then
Figure BDA0001391448750000075
Belief distribution definition: assuming (U, F (U) and n) as a probability space, X is a value variable on a finite universe of discourse U, piX(x) As a function of the probability distribution of the variable X, let f: X πX(x)→[0,1]For a collection-valued mapping, then
Figure BDA0001391448750000076
To say, call
Con(FOP)＝f(x×πX(x)) (5)
Is piX(x) The confidence distribution of (2) is shown in fig. 2, which describes the confidence level of the probability corresponding to the variable of the X value.
From the likelihood distribution definition and the confidence distribution definition, the FOP in the two-type prediction set represents the confidence distribution function
Figure BDA0001391448750000077
In that
Figure BDA00013914487500000716
The two-dimensional value space above.
Definition of the two-type prediction set: it is assumed that U is a finite domain of discourse,
Figure BDA0001391448750000078
if any prediction set on the variable X is taken as the value of the prediction set, then
Figure BDA0001391448750000079
Satisfy the requirement of
Figure BDA00013914487500000710
At first, call
Figure BDA00013914487500000711
Is a two-type prediction set over a finite universe of discourse U. Wherein the content of the first and second substances,
Figure BDA00013914487500000712
in order to be a function of the probability distribution,
Figure BDA00013914487500000713
is a reliability distribution function. When in use
Figure BDA00013914487500000714
In time, the two-type prediction set is called the interval two-type prediction set.
When there are finite discourse domains X and JxWhen the distribution is continuous or discrete, the two-type prediction set
Figure BDA00013914487500000717
Can be expressed as
Figure BDA0001391448750000081
Based on the definition of the type two prediction set and the definition of the reliability distribution, a graph of the type two prediction set corresponding to FIG. 2 can be drawn, as shown in FIG. 3. As can be seen from fig. 3, for
Figure BDA0001391448750000089
FOP is a set of belief distribution function support sets.
Similarity measurement method
Definition of the-alpha plane of the type II prediction set: if it is
Figure BDA00013914487500000810
Is a prediction set of two types, alpha ∈ [0,1 ]]Is a constant, then
Figure BDA0001391448750000082
At first, call
Figure BDA0001391448750000083
Is the-alpha surface of the two-type prediction set.
For each α ∈ [0,1 ]]In the case of a composite material, for example,
Figure BDA0001391448750000084
convertible into a special set of two-type predictions, i.e.
Figure BDA0001391448750000085
That is to say that the position of the first electrode,
Figure BDA0001391448750000086
the values of the reliability distribution functions are all alpha. Now two type prediction set
Figure BDA00013914487500000811
Can be expressed as
Figure BDA0001391448750000087
Expanding the similarity measure among the ordinary fuzzy sets, and when alpha belongs to [0,1 ]]When the values are different, a series of similarity measures among different sets can be obtained
Figure BDA0001391448750000088
Giving a similarity measure of two prediction sets of
Figure BDA0001391448750000091
Wherein alpha isjJ (j) is 1,2, …, M) and represents ajEach value must contain 1.
Combinations (10) and (11) can be given
Figure BDA0001391448750000092
Measure of inter-similarity of
Figure BDA0001391448750000093
Since the union operator U represents a supremum or maximum value, so
Figure BDA0001391448750000094
Fail to reflect each αjThe magnitude of the similarity measure in the case of value. The following can reflect all
Figure BDA0001391448750000095
And alphajOf information
Figure BDA0001391448750000096
Center of mass of
Figure BDA0001391448750000097
When in use
Figure BDA0001391448750000098
As a monotonic function of alpha
Figure BDA0001391448750000099
Otherwise
Figure BDA00013914487500000910
Wherein S is alphajA subset of the remaining part after the supremum is removed.
When a certain system security level is determined, two types of results, namely SL ═ f (SL)monitor,SLstate). Wherein SL is the final judgment result of the system; SL (Long-side)monitorA judgment result of a sensor monitoring class; SL (Long-side)stateA judgment result of the expert system class; f (-) is a decision function, which is determined from Table 1. When the similarity measure centroid satisfies the rule 1, the system state is at the security level; when rule 2 is satisfied, the system state is a blue early warning level; when the rule 3 is met, the system state is at a yellow early warning level, and the operating conditions of the dam body and related facilities need to be monitored and controlled; when rule 4 is satisfied, the system state is a red warning level.
TABLE 1 basis for system security level determination
Figure BDA0001391448750000101
If the similarity measurement centroid does not meet the table 1, it is indicated that the two types of determination results have conflict, and the centroid CG (CG ═ CG) of the projection surface of the security level joint scale is calculated at this time1A,CG11A,CG111A,CG1VAAnd determining the distance between the position of the centroid and the gravity center of each safety grade scale, and judging the safety grade of the system according to the shortest distance method.
Taking an upstream tailing dam under the flag of a certain enterprise in Shanxi province as an example to evaluate the safety level of the dam body, the tailing dam is in the middle of the design life. On the basis of the safety level evaluation items, the expert group respectively determines four levels of safety level scales (shown in table 2) of the sensor class and the expert system class, and the joint distribution and projection surfaces of the four levels are respectively shown in fig. 7. For convenience of representation, the data form in table 2 and the following tables is represented by the following rules: the data of the type II predictor set of the Gaussian type are expressed by expectation and variance; the two-type predictor set data of the triangle type is expressed in the form of a probability distribution.
TABLE 2 safety class reference Scale
Figure BDA0001391448750000102
Figure BDA0001391448750000111
The main parameters of the sensor monitoring net are determined to be the reservoir water level, the infiltration line, the dry beach length and the dam body displacement according to the tailing dam parameter selection rule, and the main parameters of the expert system are a tailing dam leakage control system, a flood discharge system, a drainage well system and the dam body appearance (such as cracks and depressions on the dam surface). On the basis of preprocessing and analyzing the main parameter data, the representation form and the weight of the two-type prediction set are determined, and are respectively shown in tables 3 and 4.
TABLE 3 actual sensor Module parameters information and weight coefficients
Figure BDA0001391448750000112
TABLE 4 evaluation information and weight coefficient of expert system module
Figure BDA0001391448750000113
And (3) synthesizing the probability distribution function and the reliability distribution function of the two types of parameter information by using an equation (15) to obtain the comprehensive distribution of the two types of information. Calculating similarity measure between various comprehensive distributions and the safety level scale in the table 2 by using the formulas (10) to (12), and establishing corresponding matrix
Figure BDA0001391448750000114
Figure BDA0001391448750000115
Determining a centroid matrix
Figure BDA0001391448750000121
Figure BDA0001391448750000122
Determining the coordinate x of the mass center in each module according to the matrixcentroid＝0.500， ycentroid0.575. By using (x)centroid,ycentroid) And (0.500,0.575) determining a specific position point A (shown in FIG. 8) of the test data in the projection surface of the safety level scale, which indicates that the dam body state is safe and at a blue early warning level. If the support set reliability is not considered, the reliability of the reliability distribution function is all 1, the position of the evaluation data in the projection plane of the safety level scale is an uncertainty area B (as shown in fig. 8), the dam body state cannot be directly judged, and the judgment can be carried out only by adopting the distance between the evaluation data and the cluster center point of each level. The distances of the central location point of uncertainty region B from the central location points of the four classes of safety classes when calculated separately for the supremum and infimum of the probability trace are shown in table 5.
TABLE 5 distance between the center point of area B and the center point of each safety class
Figure BDA0001391448750000123
As can be seen from table 5, when the distances between the supremum and infimum centers of the FOP and the centers of the safety classes are calculated by using the shortest distance method, the safety classes determined are all yellow warning classes, which indicates that the dam body, the seepage drainage facility, and the like need to take measures such as reinforcement and maintenance. The method is completely contradictory to the judged safety level when the reliability distribution is considered, and the evaluation result obtained by utilizing the binary prediction set is consistent with the actual situation after the dam body design combination expert group affirmation.
To further illustrate the advantages of the method herein, FIG. 9 shows the relationship of the decision location point A to the uncertainty region B when confidence is considered. The position difference of the point A in the area B reflects the distribution trend of the support concentration reliability corresponding to the test data, namely, the point A is used as the center and gradually decreases towards the periphery. When the point A is superposed with the outer curve of the area B, the maximum reliability of the certainty boundary on the probability trace is explained; when the point A is superposed with the inner measuring curve of the area B, the maximum reliability of the certainty boundary under the possibility trace is shown. That is, the size of the A-point location is determined by the belief distribution function. Thus, the methods herein can also be used to compare and analyze results as one studies different confidence distributions.

Claims (1)

1. The two-type prediction set safety assessment method based on data possibility-reliability distribution is characterized by comprising the following steps of:
step 1: determining safety level scales of two types of data monitored by an expert system and a sensor according to system safety regulations, wherein the sensor monitoring data are A, B, C, D four safety level scales; the expert system data are four safety level scales I, II, III and IV, because the scales are used as the level judgment basis, the credibility given to the credibility distribution function of the safety level scales is 1, the safety level scale joint distribution is established, and the projection surface area of each safety level is determined;
step 2: determining evaluation data { I ] in the expert system according to the contents of each evaluation item of the security leveli1,2, … n and a weight { w |E1,wE2,…,wEnReference data { M } in sensor monitoringj1,2, …, m and weight { w |S1,wS2,…,wSmAnd using two type prediction sets based on data probability-reliability distribution
Figure FDA0001391448740000011
Is shown as respectively
Figure FDA0001391448740000012
And
Figure FDA0001391448740000013
and step 3: respectively synthesizing the probability distribution function and the reliability distribution function of the reference data in each type of data by using a weighted fusion method to obtain the fusion distribution of the two types of data
Figure FDA0001391448740000014
And 4, step 4: calculating the similarity measure S between the fusion distribution obtained in the step 3 and the safety level scale by using a calculation formulaJAnd its center of mass
Figure FDA0001391448740000015
Establishing corresponding matrix
Figure FDA0001391448740000016
Figure FDA0001391448740000021
Wherein the content of the first and second substances,
Figure FDA0001391448740000022
Figure FDA0001391448740000023
four safety level scales for expert system class data represented by the two-type prediction set;
Figure FDA0001391448740000024
and
Figure FDA0001391448740000025
for the similarity measure and the mass center between the data fusion distribution of the parameters and the corresponding safety level scale,
Figure FDA0001391448740000026
four safety scales for sensor monitoring class data expressed by the two-type prediction set;
Figure FDA0001391448740000027
and
Figure FDA0001391448740000028
performing similarity measurement and mass center between the data fusion distribution of the parameters and the corresponding safety level scale;
and 5: determining specific position points of the centroids of the two types of parameter data in the projection plane of the safety level scale according to the similarity measure matrix and the centroid matrix in the step 4, and if the specific position points of the two types of parameter data are in the same projection plane of the safety level scale, judging that the system is in the safety level; if the rule is not satisfied, go to step 6;
step 6: and determining the gravity center position of the projection surface of each safety level scale, calculating the distance between the gravity center position and the mass center position of the parameter data, and judging the safety level of the system by using a shortest distance method.
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