CN108345730B - Dam safety multi-source fusion diagnosis method - Google Patents
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Abstract
The invention discloses a dam safety multi-source fusion diagnosis method, which comprises the following steps: (1) acquiring a basic probability distribution function of the multi-point effect quantity by means of a mathematical statistics method, a reliability theory and an expert scoring method; (2) computing an assigning weight matrix [ evi ] among the basic probability distribution function strips; (3) calculating a focus weighted matrix [ foc ] among the basic probability distribution functions; (4) constructing a comprehensive evidence weighting matrix [ cor ]; (5) carrying out weighted average on the basic probability distribution functions of all evidences by using a comprehensive evidence weighting matrix [ cor ]; (6) and (3) performing n-1 times of fusion on the weighted and averaged basic probability distribution function by using a D-S evidence fusion theory, and further realizing comprehensive diagnosis and analysis of the safety condition of the dam. According to the invention, by analyzing monitoring data of each measuring point of dam deformation, seepage and other effect quantities and performing fusion analysis on multi-source effect quantity monitoring data, the deformation safety of the dam, seepage and other effect quantities at each point is obtained, and the method has extremely good practical application and popularization values.
Description
Technical Field
The invention relates to a dam safety multi-source fusion diagnosis method, and belongs to the field of dam monitoring.
Background
Reservoir dam engineering mostly exists in a complex working environment, is acted by upstream huge water pressure, temperature change, even earthquake and the like during service, and simultaneously has the problems of aging, pathological changes, even deformation abnormality, seepage abnormality and the like of the dam engineering in different degrees due to the performance degradation of dam building materials, unreasonable human factors existing in the design, construction and operation management processes and the like. If defects and hidden dangers of the dam cannot be found in time, the safety condition of the dam can be deteriorated, and catastrophic accidents such as dam break can be caused in serious cases.
In order to organically unify monitoring data of each effect quantity in time and space, make up for the defects of incompleteness of single effect quantity in information description, inaccuracy and uncertainty of local information and the like, and obtain the diagnosis capability of the dam safety condition superior to the single effect quantity, the invention provides a dam safety condition analysis and evaluation method based on multi-source effect quantity monitoring data fusion. Common data fusion methods are: weighted average method, Bayes method, Kalman filtering, fuzzy mathematic method, neural network method, D-S evidence reasoning method, etc., and Table 1 lists the characteristics of the commonly used data fusion method.
TABLE 1 basic characteristics of the conventional data fusion method
As can be seen from the above table, the classical Dempster-Shafer (D-S) evidence reasoning theory can be used for fusion analysis of multi-source effect monitoring data and further reasoning dam service behavior because the uncertainty of multi-source information can be better grasped and processed under the condition of no prior probability. However, under the condition of high evidence conflict, important problems that the fusion rule fails or focal elements are fused and exploded so as to obtain reasoning results of inverse intuition and paradoxical theory and the like exist, and the classical D-S evidence theory needs to be improved during application.
Based on the background, according to the calculated deformation, seepage and stress safety degrees of all points, mutual influences among the effect quantities of dam deformation, seepage, stress and the like are fully considered, and from the view point of multi-source data fusion, a dam safety degree multi-source fusion diagnosis technology is invented, a calculation model of the whole safety degree of the dam is established, and key index identification influencing the safety condition of the dam is realized.
Disclosure of Invention
The purpose of the invention is as follows: in order to overcome the defects in the prior art, the invention provides a dam safety degree multi-source fusion diagnosis method, which analyzes the monitoring data of each measuring point of the dam deformation, seepage and other effect quantities and performs fusion analysis on the multi-source effect quantity monitoring data to obtain the deformation, seepage and other time-varying safety of the dam at each point, effectively improves the capability of effectively identifying the dam safety, and has excellent practical application and popularization values.
The technical scheme is as follows: in order to solve the technical problem, the dam safety multi-source fusion diagnosis method comprises the following steps:
(1) acquiring a basic probability distribution function of the multi-point effect quantity by means of a mathematical statistics method, a reliability theory and an expert scoring method;
(2) calculation of an assignment matrix [ evi ] between bars of the basic probability distribution function: judging the independence of focal elements among the basic probability distribution functions, correcting the basic probability distribution functions by means of a correction matrix [ d ], obtaining a compatibility coefficient matrix [ r ] among the basic probability distribution function strips by utilizing a Cauchy-Schwarz inequality, and obtaining an evidence weighting matrix [ evi ] among the basic probability distribution function strips by the matrix [ r ];
(3) focus element weighting matrix [ foc ] between basic probability distribution functions]The calculation of (2): judging the independence of focal elements among the basic probability distribution functions, and utilizing a correction formula to aim at each focal element PkConstructing a focal element compatibility matrix
By focal element compatibility matrix
Obtaining focus evidence weighting matrix [ foc ] between basic probability distribution functions]；
(4) Constructing a comprehensive evidence weighting matrix [ cor ];
(5) carrying out weighted average on the basic probability distribution functions of all evidences by using a comprehensive evidence weighting matrix [ cor ];
(6) and (3) performing n-1 times of fusion on the weighted and averaged basic probability distribution function by using a D-S evidence fusion theory, and further realizing comprehensive diagnosis and analysis of the safety condition of the dam.
Preferably, the optimized wavelet basis function is used for extracting the trend component of the effect quantity of a certain point of the dam, a sudden change analysis model of the safety condition of the dam is built according to the trend component, the judgment of whether the deformation, seepage or stress condition of the point changes at a certain moment is realized, and the safety degree of the point of the dam at any moment is determined by the following formula.
Preferably according to
Calculating the obtained dam time-varying safety degree R (R) (t), wherein i is the serial number of a dam effect measuring point, and i is 1,2, … and n; ri(t) safety of the ith effect quantity at time t, NΔ＞0(t) and NΔ＜0(t) represents the number of mutations (Δ > 0) and no mutation (Δ < 0) occurring up to time t, respectively, and is combined with a normalized normal distribution β ═ Φ-1And (R), wherein phi (·) is a standard normal distribution function, beta is a reliability coefficient, three warning lines for the difference judgment of the dam safety degree are drawn by referring to relevant specifications, and the safety degree of a single point is calculated to construct the warning lines.
Preferably, the three warning lines are 0.844, 0.954 and 0.997, the safety degree is less than 0.844, the dam is abnormal, the safety degree is between 0.844 and 0.954, the dam is abnormal, the safety degree is between 0.954 and 0.997, the dam is basically normal, the safety degree is more than 0.997, and the dam is normal.
Preferably, in step (4), [ cor ] ═ α [ evi ] + (1- α) [ foc ], where: alpha is more than or equal to 0 and less than or equal to 1.
In the present invention, step (1): and acquiring a basic probability distribution function of the multi-point effect quantity by means of a mathematical statistics method, a reliability theory, expert scoring and other methods. The basic probability distribution function is composed of point safety degree, and the specific method is as follows:
the method comprises the steps of extracting a trend component of an effect quantity of a certain point of the dam by using a preferred wavelet basis function, establishing a sudden change analysis model of the safety condition of the dam according to the trend component, judging whether the deformation, seepage or stress condition of the point changes at a certain moment, and determining the safety degree of the dam at any moment by using the following formula.
In the formula: i is the serial number of the dam effect measuring point, i is equal to1,2,…,n；Ri(t) represents the safety of the ith effect quantity at the time t; n is a radical ofΔ＞0(t) and NΔ＜0(t) represents the number of mutations (Δ > 0) and (Δ < 0) which did not occur by the time t, respectively.
Calculating the time-varying safety degree R (R) (t) of the dam according to the formula (1) and combining the standard normal distribution beta (phi)-1(R) (wherein phi (-) is a standard normal distribution function, beta is a reliability coefficient), and three warning lines for the judgment of the difference of the dam safety degree are drawn by referring to the relevant specifications:
the idea of drawing up the warning line in the formula (2) is as follows: the third warning line is the probability that the system corresponding to the area of the horizontal axis of the standard normal distribution density function in the range of [ -3,3] is in a safe state; the second warning line is the probability that the system corresponding to the area of the horizontal axis of the standard normal distribution density function in the range of [ -2,2] is in a safe state; the first guard line is also the most strict guard line, and is obtained when the reliability coefficient β takes 1 from R ═ Φ (β). The three warning lines divide the safety condition of the dam into four areas, namely normal, basically normal, abnormal and abnormal, as shown in figure 2.
Step (2): calculation of an assignment matrix [ evi ] between bars of the basic probability distribution function: judging the independence of focal elements among the basic probability distribution functions; correcting the basic probability distribution function by means of the correction matrix [ d ], and obtaining a compatibility coefficient matrix [ r ] among the basic probability distribution function strips by utilizing a Cauchy-Schwarz inequality; obtaining an evidence weighting matrix [ evi ] among the basic probability distribution function strips from the matrix [ r ];
the nature of the conflict between the two evidences is that there is a difference in the degree of support for the same focal element. If the supporting degrees of the same focal element are similar, the compatibility is good, otherwise, the compatibility is poor. The compatibility between any two basic probability assignment function bars is measured by a compatibility coefficient r.
Cauchy-Schwarz inequality: assuming that second moments of random variables X and Y are present:
|E(XY)|2≤E(X2)E(Y2) (3)
sufficient requirements for the establishment of the equal sign are that P { Y ═ tX } ═ 1, and t ═ const. E (X)2＝D(X)+(E(X))2D (X) represents the variance of X, and E (X) represents the mean of X.
With the idea of the Cauchy-Schwarz inequality, in the recognition framework Θ, the basic probability distribution functions of two evidences are: m is1And m2Requirement m in combination with the basic probability distribution functioniCriterion of > 0, assuming m1And m2Coefficient of inter-compatibility r (m)1,m2) Comprises the following steps:
in the recognition framework Θ, m1And m2Coefficient of inter-compatibility r (m)1,m2) The following conditions are satisfied:
1)0≤r(m1,m2)≤1；
2)r(m1,m2)＝r(m2,m1)；
3)
4)
wherein A isi、BjAre respectively m1And m2The focal length of (1);
5) coefficient of compatibility r (m)1,m2) The measurement result of (2) should meet the intuitive requirement.
Requirements 1) to 3) can be demonstrated by the Cauchy-Schwarz inequality in combination with the basic probability distribution function basic requirements.
Requires 4) proof of sufficiency. When r (m)1,m2) When 0, then (E (m)1m2))2Is 0, then m1m2When m is {0}, m is known1And m2Does not have a common focal element AiAnd which satisfies: m is more than 01(Ai),m2(Ai) Is less than 1, so (U.A)i)∩(∪Bj) Phi holds. Conversely, the necessity may also be justified.
Requirement 5) verification by example 1.
Example 1: in the recognition frame Θ, Θ ═ a, B, C, three pieces of evidence are constructed as follows:
calculated using equation (4): r (m)1,m2)＝0.965，r(m1,m3) 0.105, which satisfies the intuitive requirement, so condition 5) is also proved.
In the recognition framework Θ, the evidence strip m is aimed ati(i 1.. n), and m is calculated from formula (4)iAnd mjInter-compatibility coefficient, a compatibility coefficient matrix [ r ] can be obtained]：
The compatibility coefficient between the basic probability distribution function strips in the formula (4) is only suitable for the single focal element in the calculation example 1, and the focal element subsets are corrected to fulfill the condition that the focal element subsets between any two basic probability distribution functions are not independent from each other so as to achieve the purpose of expansion. Example 2 is listed to illustrate the problem.
Example 2: in the recognition framework Θ, Θ ═ a, B, C, D, E, F, three basic probability distribution functions are constructed as follows:
from visual analysis, evidence m1And m2Has a basic probability distribution function compatibility stronger than that of the evidence m1And m3Is compatible, but is calculated using equation (4): r (m)1,m2) 0.942 but r (m)1,m3) When 1, it is clear that the fusion result is rather intuitive and paradoxical.
To solve the above existing problems, a medium matrix [ d ] is introduced]A concept. Assuming that N pairwise mutually exclusive focal elements are included in a complete recognition framework Θ, P is a subspace formed by all subsets in Θ, and P ═ P1…Pi…Pn},n＝2NObviously, the matrix [ d ]]Is an n × n matrix, and the elements in the matrix are as follows:
in the formula: the symbol | | · | | represents the number of elements therein. It can be seen that when the focal element subsets are independent of each other between any two basic probability distribution functions, the matrix [ d ] degenerates to a unit matrix.
Before calculating the compatibility coefficient between the basic probability distribution function strips, a matrix d is used]Correcting the basic probability distribution function mi'＝mi[d]And then fusing the basic probability distribution functions. Similarly, taking example 2 as an example, the modified compatibility coefficient is r (m)1,m2)＝0.962，r(m1,m3) The modified result is ideal and better reflects the compatibility between the pieces of basic probability assignment function, 0.429.
After correcting the basic probability distribution function strips by the matrix [ d ], calculating a compatibility coefficient by using a formula (4) to obtain a compatibility coefficient matrix [ r ], and weighting the basic probability distribution function by the matrix [ r ] to obtain a basic probability distribution function weighting matrix [ evi ].
In the recognition framework Θ, it is assumed that there are n basic probability distribution functions, i.e. n pieces of evidence: m isi(i 1.. n), then the compatibility matrix [ r ]]Is an n × n matrix. Evidence miIs assumed to be evii：
In the formula: sum [ r ] represents the sum of all elements of the matrix [ r ].
Then the weighting matrix of the basic probability distribution function obtained by the compatibility coefficients among the basic probability distribution function strips is:
[evi]＝[evi1 evi2 … evin]T (10)
as shown in formula (9), sum [ evi ] is 1.
And (3): focus element weighting matrix [ foc ] between basic probability distribution functions]And (4) calculating. Judging the independence of focal elements among the basic probability distribution functions; using a correction formula (11), for each focal element PkConstructing a focal element compatibility matrix
By focal element compatibility matrix
Obtaining focus evidence weighting matrix [ foc ] between basic probability distribution functions]。
The generation of the inter-evidence conflict not only comprises the inter-item conflict of the basic probability distribution function, but also comprises the inter-focal element conflict of the basic probability distribution function. Assume that m exists in two basic probability distribution functionsi(Pk) And mj(Ph) (i ≠ j), which would be due to PkAnd PhThe differences present create collisions, referred to as focal element collisions between the underlying probability distribution functions.
The focal element compatibility coefficient between the basic probability distribution functions needs to be capable of measuring the compatibility between focal elements, and the following requirements are met: if the supporting degrees of the same focal element are similar, the compatibility is good, otherwise, the compatibility is poor. And (4) leading out definition of focal element compatibility coefficients among basic probability distribution functions. In the recognition frame Θ, Θ ═ θ1,θ2,…,θnP is a subspace of Θ, for
BPAF for both lines of evidence is mi(Pk) And mj(Pk) (i ≠ j), assume that two pieces of evidence pertain to focal element PkOf (2) a compatibility coefficient Ri,j(Pk) Comprises the following steps:
when there are n pieces of basic probability distribution functions, i.e., n pieces of evidence, in the recognition frame Θ, the focal element P is referred tokCan constitute a reference to the focal element PkOf a compatibility matrix
Namely, it is
Equation (11) applies to the case where the evidence focal element subsets in equation 1 are independent of each other, i.e., Pi∩Pj|i≠jPhi, for evidence of a focal element in analogous example 2, Pi∩Pj|i≠jAnd if the mutual independence is not achieved, evidence fusion cannot be carried out.
In the recognition frame Θ, Θ ═ θ1,θ2,…,θnP is a subspace of theta, and two evidence basic probability distribution functions are respectively set as mi:…,mi(Pk) … and mj:…,mj(Ph) …, assume mjMiddle mj(Ph) (h ═ 1.., n.) for mi(Pk) Of (2) a compatibility coefficient Ri,j(Pk) Comprises the following steps:
in the formula: the symbol | | · | | represents the number of elements therein. When P is presentk∩PhWhen Φ, equation (13) is reduced to equation (11). When there are n pieces of basic probability distribution functions, i.e., n pieces of evidence, in the recognition frame Θ, the focal element P is referred tokThe compatibility coefficients of (A) can also form a compatibility matrix
The complete identification frame theta comprises N pairwise mutually exclusive focal elements, P is a subspace formed by all subsets in theta, and P is { P ═ P1…Pm…PM}，M＝2NAssume that there are n basic probability distribution functions: m isiN, an inter-focal-element compatibility matrix can be completed according to formula (13)
Of course, it is clear that
Is an n × n matrix, k is 1,2, …, M. Order:
the evidence weighting matrix obtained by the compatibility coefficient between the focal elements is:
[foc]＝[foc1 foc2 …focn]T (16)
as shown in formula (15), sum [ foc ] is 1.
And (4): a composite evidence weighting matrix [ cor ] is constructed according to equation (17).
The focal element compatibility matrix [ r ] between the bars of the basic probability distribution function and the basic probability distribution function]And
the obtained weighting matrix [ evi ]]And [ foc]Satisfies the following conditions: if the support degrees of the focusing elements are similar, the compatibility is strong and the weight is great; otherwise, the compatibility is poor and the weight is small. Using a composite evidence weighting matrix cor]Implement the Pair matrix [ evi]And [ foc]Unification of (1):
[cor]＝α[evi]+(1-α)[foc] (17)
in the formula: alpha is more than or equal to 0 and less than or equal to 1.
And (5): and carrying out weighted average on the basic probability distribution functions of all evidences by using the comprehensive evidence weighting matrix [ cor ].
And (6): and (3) performing n-1 times of fusion on the weighted and averaged basic probability distribution function by using a D-S evidence fusion theory, and further realizing comprehensive diagnosis and analysis of the safety condition of the dam.
Has the advantages that: the dam safety multi-source fusion diagnosis method of the invention analyzes the monitoring data of each measuring point of the effective quantity such as dam deformation, seepage and the like, the fusion analysis is carried out on the multi-source effect quantity monitoring data to shield the larger uncertainty and even high conflict of the single-point analysis method, the uncertainty of multi-source information can be better grasped and processed under the condition of no prior probability based on the D-S evidence theory, the time-varying safety degree such as dam deformation, seepage and the like at each point is obtained, on the basis, a D-S evidence theory is introduced, the integral time-varying safety degree of the dam is obtained by reasoning through the fusion analysis of the calculated value of the time-varying point safety degree, and further, comprehensive diagnosis and evaluation of the dam safety condition are realized according to the criterion, the capability of effectively identifying the dam safety is effectively improved, and the method has extremely good practical application and popularization values.
Drawings
FIG. 1 is a flow chart of a dam safety multi-source fusion diagnosis method of the invention;
FIG. 2 is a diagram of the determination criteria of the safety condition of the dam in step (1) of the present invention;
FIG. 3 is a diagram illustrating the process of the 22# dam segment deformation and the safety degree evolution of seepage points in the present invention;
FIG. 4 is a diagram illustrating the overall safety evolution process of a typical dam segment according to the present invention.
Detailed Description
The present invention will be further described with reference to the accompanying drawings.
Example (b): the invention relates to a dam safety degree multi-source fusion diagnosis technology, which takes dam engineering of a certain reservoir as an example, takes the safety degree of each measuring point of a typical dam section as an effect quantity characteristic characterization parameter, namely an evidence source, shown in figures 3 to 4, the deformation and seepage actual measurement values of the dam section are shown in tables 2(a) and 2(b), and the data in tables 2(a) and 2(b) are utilized to carry out the data according to the data
The dam time-varying safety degree R ═ R (t) is obtained through calculation, wherein i is a dam effect measuring point number, and i ═ 1,2, …, n; ri(t) represents the safety degree of the ith effect quantity at the time t, the specific calculation results are shown in (a) and (b) in fig. 4, and in the identification frame theta, theta is equal to { theta ═ in1,θ2,θ3Construct five BPAFs, as in Table 3, for 22#In the engineering example, the attribute of the intra-evidence source focal elements is single and no intermixing is shown as a formula (7), so that alpha in the formula (17) is taken as 1, and a comprehensive evidence weighting matrix [ cor ] is set]＝[evi]And (4) referring to a table 4, listing a comprehensive weighting matrix of the typical dam section, reasoning the overall safety degree of the typical dam section by using the improved D-S evidence, referring to an attached figure 4, and carrying out safety condition evaluation by means of the transfer criterion of the step (6).
TABLE 2(a) seepage measured value of 22# dam segment
TABLE 2(b) measured values of 22# dam segment deformation
TABLE 3 initial evidence BPAF value Table
Table 422#Comprehensive weighting matrix for each measuring point of dam section
From FIG. 4It can be seen that: 22#The whole dam section is located between the second warning line and the first warning line, the safety condition of the dam is diagnosed to be a serious abnormal state, and the safety degree of the dam is in a slow rising trend after reinforcement and reinforcement.
Claims (3)
1. A dam safety multi-source fusion diagnosis method is characterized by comprising the following steps:
(1) acquiring a basic probability distribution function of the multi-measuring-point effect quantity of the safety degree of the dam by means of a mathematical statistics method, a reliability theory and an expert scoring method;
(2) calculation of an assignment matrix [ evi ] between bars of the basic probability distribution function: judging the independence of focal elements among the basic probability distribution functions, correcting the basic probability distribution functions by means of a correction matrix [ d ], obtaining a compatibility coefficient matrix [ r ] among the basic probability distribution function strips by utilizing a Cauchy-Schwarz inequality, and obtaining an evidence weighting matrix [ evi ] among the basic probability distribution function strips by the matrix [ r ];
(3) focus element weighting matrix [ foc ] between basic probability distribution functions]The calculation of (2): judging the independence of focal elements among the basic probability distribution functions, and utilizing a correction formula to aim at each focal element PkConstructing a focal element compatibility matrix
By focal element compatibility matrix
Obtaining focus evidence weighting matrix [ foc ] between basic probability distribution functions]；
(4) Constructing a composite evidence weighting matrix [ cor ] ═ α [ evi ] + (1- α) [ foc ], wherein: alpha is more than or equal to 0 and less than or equal to 1;
(5) carrying out weighted average on the basic probability distribution functions of all evidences by using a comprehensive evidence weighting matrix [ cor ];
(6) and (5) performing n-1 times of fusion on the weighted average basic probability distribution function by using a D-S evidence fusion theory.
2. According to claimThe dam safety multi-source fusion diagnosis method in claim 1 is characterized in that: extracting the trend component of the effect quantity of a certain point of the dam by using a wavelet basis function, establishing a safety condition mutation analysis model of the dam, judging whether the deformation, seepage or stress condition of the point is different at a certain moment, and further using a formula
Determining the point safety degree R (R) (t) of the dam at any moment, wherein i is the serial number of a dam effect measuring point, and i is 1,2, …, n; ri(t) safety of the ith effect quantity at time t, NΔ＞0(t) and NΔ＜0(t) represents the number of mutations (Δ > 0) and no mutation (Δ < 0) occurring up to time t, respectively, and is combined with a normalized normal distribution β ═ Φ-1And (R), wherein phi (·) is a standard normal distribution function, beta is a reliability coefficient, and three warning lines for judging the difference of the dam safety degree are drawn by taking the reference of the dam safety monitoring standard.
3. The dam safety multi-source fusion diagnosis method according to claim 2, characterized in that: the three warning lines are 0.844, 0.954 and 0.997, the safety degree is less than 0.844, the dam is abnormal, the safety degree is between 0.844 and 0.954, the dam is abnormal, the safety degree is between 0.954 and 0.997, the dam is basically normal, the safety degree is greater than 0.997, and the dam is normal.
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