CN113705721B - Joint probability density function difference diagnosis method for beam bridge support group void diseases - Google Patents
Joint probability density function difference diagnosis method for beam bridge support group void diseases Download PDFInfo
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Abstract
The invention discloses a joint probability density function difference diagnosis method for bridge support group void diseases, which comprises the steps of constructing a bridge support group wireless monitoring network by adopting a wireless inclinometer, acquiring corner displacement monitoring data of support measuring points, dividing the bridge support group supports into a plurality of cluster groups according to symmetry relations, calculating void diagnosis factors by using joint probability density function differences between supports in the same cluster group in a reference state and a to-be-diagnosed state, calculating void diagnosis factor thresholds by using joint probability density function differences between supports in the same cluster group in the reference state, judging whether the bridge support group has void diseases by combining the plane positions of the support measuring points of the bridge support group, and determining the support positions of the void diseases. The invention is suitable for solving the problem of monitoring and diagnosing the void diseases of the beam bridge support groups in actual operation.
Description
Technical Field
The invention belongs to the field of health monitoring of beam bridge structure support void diseases in actual operation, and relates to a joint probability density function difference diagnosis method of beam bridge support group void diseases.
Background
The bridge support is an important structural device for transmitting load between the upper structure and the lower structure of the bridge, coordinating deformation and ensuring the safety of the bridge body. The support void is the most serious support disease, and the influence on the stress of the bridge structure is extremely large, so that the safety, the integrity and the applicability of the bridge structure in the operation period are seriously hindered, and the effective technical means are urgently needed to monitor and accurately diagnose the void disease of the bridge support. At present, most of bridge support disease detection works are regular inspection of the bridge support, and the detection method comprises manual observation, image snapshot, image feature recognition based on deep learning and the like, but the essence of the detection method is that the appearance of the support is directly observed, the detection method is influenced by the position of the support and the environment, and the accuracy of an observation result is difficult to guarantee. In addition, there is a method for detecting the bearing diseases based on the dynamic response of the bridge structure, but the acquisition of dynamic response data has extremely high requirements on equipment, and is limited by the restrictions of high cost, large power consumption, complicated installation, difficult wiring and the like of the detection equipment. In the disease monitoring of bridge supports, research work has focused on two aspects: the method comprises the steps of installing various sensors inside a bridge support to directly monitor parameters such as pressure and the like, and arranging displacement sensors outside the bridge support to directly monitor parameters such as displacement and the like. The structure of the support is damaged, the function of the support is limited, and the sensor under the action of high stress has low survival rate and short service life, so that the research result is only remained in a laboratory stage; the latter is the monitoring method that actual engineering used more, adopts displacement sensor such as stay cord displacement meter, amesdial to monitor the displacement of some supports that are in the beam-ends often, and more is considering the longitudinal deformation of the roof beam body under the temperature effect, and the diagnosis to support void disease helps little. Meanwhile, it is noted that all supports (support groups) in the bridge jointly form boundary conditions of the bridge structure, and the occurrence of void diseases of a single support directly changes the boundary conditions of the whole structure, however, the existing bridge support detection and monitoring methods are all used for analyzing and evaluating the states of the single support, and cannot consider the influence of the void diseases of the support on the whole bridge structure. Therefore, the support void is taken as a disease type which seriously affects the safety of the bridge structure, and the problem of diagnosis of the support void is not solved by the existing technical means. In recent years, with the rise of wireless sensing technology, the bridge support void disease monitoring has new technical means, the characteristics of low power consumption, ad hoc network and wireless transmission of a wireless sensor network can be utilized to carry out long-term online multipoint monitoring on the bridge support group, and the diagnosis problem of the bridge support group void disease is solved through monitoring data analysis.
Disclosure of Invention
The invention provides a joint probability density function difference diagnosis method for beam bridge support group void diseases, which aims to solve the problems of lack of a beam bridge support group void disease monitoring method and low accuracy of diagnosis results in actual operation.
The invention aims at realizing the following technical scheme:
a joint probability density function difference diagnosis method for beam bridge support group void diseases comprises the following steps:
step one: installing wireless inclinometers at all supports of a beam bridge, constructing a beam bridge support group wireless sensor monitoring network, acquiring corner displacement monitoring data of the support measuring points X, Y in two directions, and carrying out clustering division on the supports in the support group and dividing the supports into a plurality of clustering groups by utilizing the symmetry relation of the support positions in the beam bridge support group;
step two: selecting proper time nodes for each support measuring point in the same cluster group to divide monitoring data into reference state monitoring data and to-be-diagnosed state monitoring data, and calculating a linear normalized joint probability density matrix under the reference state and the to-be-diagnosed state of each support measuring point;
step three: calculating a joint probability density function difference matrix between every two support measuring points of the same cluster group in the reference state by using a method of reserving a cross validation for the linear normalized joint probability density matrix in the reference state of each support measuring point in the same cluster group in the second step, removing diagonal elements, taking the mean value of each row of the matrix, and multiplying a guarantee coefficient to be used as a void diagnosis factor threshold value of the corresponding support measuring point in the cluster group;
step four: calculating joint probability density function difference matrixes between every two support measuring points of the same cluster group in a reference state and a to-be-diagnosed state by using a method of reserving a cross validation for linear normalization joint probability density matrixes under the to-be-diagnosed state of each support measuring point in the same cluster group in the second step, removing diagonal elements, and taking the average value of each row of the matrixes as a void diagnosis factor of the corresponding support measuring point in the cluster group; comparing the void diagnosis factor of the support measuring point with the void diagnosis factor threshold of the corresponding support measuring point in the third step, and when the void diagnosis factor is smaller than or equal to the void diagnosis factor threshold, the support is not affected by the void disease; when the void diagnostic factor is greater than the void diagnostic factor threshold, the support is affected by the void disease;
step five: and repeating the second step to the fourth step until the void diagnosis factors of all the support measuring points in all the clustering groups are subjected to abnormal judgment, and judging the locations of the void supports by combining the plane arrangement of the support measuring points of the beam bridge support group.
Compared with the prior art, the invention has the following advantages:
the joint probability density function difference diagnosis method for the bridge support group void diseases is characterized in that a wireless monitoring network of the bridge support group is built by adopting a wireless inclinometer with high cost performance by means of a wireless sensing technology, and the corner displacement monitoring data of each support measuring point are obtained. Meanwhile, the method divides the beam bridge support group supports into a plurality of cluster groups according to the symmetry relation, calculates the void diagnosis factors by utilizing the joint probability density function difference between every two supports in the same cluster group under the reference state and the to-be-diagnosed state, calculates the void diagnosis factor threshold value by utilizing the joint probability density function difference between every two supports in the same cluster group under the reference state, judges whether the beam bridge support group has void diseases by comparing the void diagnosis factors of all supports with the corresponding void diagnosis factor threshold value and combining the plane positions of the support measurement points of the beam bridge support group supports, and determines the support positions of the void diseases. The monitoring method provided by the invention can be directly applied to the bridge support group support void disease monitoring, and the provided diagnosis method can realize the diagnosis of the bridge support group support void disease and the determination of the void support position, and is suitable for solving the problems of the bridge support group void disease monitoring and diagnosis in actual operation.
Drawings
Fig. 1 is a schematic diagram of a four-span continuous beam bridge structure.
Fig. 2 is a schematic diagram of a beam bridge support group void disease monitoring system.
Fig. 3 is a schematic diagram of a cluster division result of beam bridge supports.
Fig. 4 is a plan view of a void support in the simulation of a void disease of a beam bridge support group.
Fig. 5 is a graph of a digitally simulated monitored data time course (for example, a # 1 pedestal).
Fig. 6 is a schematic diagram of the monitoring data and the status division of the monitoring data of the angular displacement of the support measuring point.
FIG. 7 is a graph of joint probability density functions for two supports of the same cluster set in a reference state.
FIG. 8 is a graph of joint probability density functions for two supports of the same cluster set under a condition to be diagnosed.
FIG. 9 is a graph of diagnostic factors and thresholds for the run-out of each pedestal in the same cluster set in a reference state.
Fig. 10 is a graph of diagnostic results of the void diagnostic factors of the supports in the same cluster group under the condition to be diagnosed.
FIG. 11 is a schematic diagram of the calculation of a joint probability density function difference matrix.
Fig. 12 is a schematic plan view of a diagnosis result of the void diseases of the beam bridge bearing groups.
FIG. 13 is a flow chart of a joint probability density function difference diagnostic method for beam bridge abutment group void disease.
Detailed Description
The following description of the present invention is provided with reference to the accompanying drawings, but is not limited to the following description, and any modifications or equivalent substitutions of the present invention should be included in the scope of the present invention without departing from the spirit and scope of the present invention.
The invention provides a joint probability density function difference diagnosis method for beam bridge support group void diseases, which is shown in fig. 13 and comprises the following steps:
step one: and installing wireless inclinometers with high cost performance at all the supports of the bridge, constructing a bridge support group wireless sensor monitoring network, acquiring corner displacement monitoring data of the support measuring points X, Y in two directions, and carrying out clustering division on the supports in the support group and dividing the supports into a plurality of clustering groups by utilizing the symmetry relation of the support positions in the bridge support group.
In the step, the clustering and dividing method of the support group comprises the following steps:
the method comprises the following steps: let the bridge support crowd set as Z, divide into N cluster group with the support in the bridge support crowd according to symmetry relation, it is defined as:
wherein Z is k K is more than or equal to 1 and less than or equal to N, and is the set of the kth support clustering group in the beam bridge support group;
step two: set Z of kth support clustering group in bridge support group k It is defined as:
wherein Z is i For the ith support in the kth support cluster group, i is more than or equal to 1 and less than or equal to n k ，n k The number of the supports in the kth support clustering group.
Step two: and selecting proper time nodes for each support measuring point in the same cluster group, dividing the monitoring data into reference state monitoring data and to-be-diagnosed state monitoring data, and calculating a linear normalized joint probability density matrix under the reference state and the to-be-diagnosed state of each support measuring point.
In the step, the method for calculating the joint probability density matrix after the state division and the linear normalization of the corner displacement monitoring data comprises the following steps:
step two,: setting X-direction corner displacement monitoring data set of support measuring points in kth support clustering group as matrix
The Y-direction corner displacement monitoring data set of the support measuring points in the kth support clustering group is a matrix +.>
X-direction angular displacement monitoring data set X of ith support measuring point i And Y-direction angular displacement monitoring data set Y i The definitions are respectively as follows:
in the method, in the process of the invention,
for the j-th sampling result of the X-direction angular displacement of the i-th support measuring point,/th sampling result is given>
For the j-th sampling result of the Y-direction angular displacement of the i-th support measuring point, i is more than or equal to 1 and less than or equal to n k ，1≤j≤m，n k The number of the supports in the kth support clustering group is the number of corner displacement sampling times;
step two: taking a suitable intermediate time point m in the monitoring time period 0 (1≤m 0 M) dividing the angular displacement monitoring data into a reference state and a state to be diagnosed, and collecting the X-direction angular displacement monitoring data under the reference state
Y-direction corner displacement monitoring data set>
And X-direction angular displacement monitoring data set in the state to be diagnosed +.>
Y-direction corner displacement monitoring data set>
The definitions are respectively as follows:
in the method, in the process of the invention,
the c-th sampling result of the X-direction angular displacement of the i-th support measuring point is also the c-th sampling result of the X-direction angular displacement of the i-th support measuring point in a reference state; />
Mth of the X-direction angular displacement of the ith support measuring point 0 The +d-1 sampling result is also the d sampling result of the X-direction angular displacement of the i-th support measuring point under the state to be diagnosed; />
The c-th sampling result of the Y-direction angular displacement of the i-th support measuring point is also the c-th sampling result of the Y-direction angular displacement of the i-th support measuring point in the reference state; />
Mth for the Y-direction angular displacement of the ith support measuring point 0 The +d-1 sampling result is also the d sampling result of the Y-direction angular displacement of the i-th support measuring point under the state to be diagnosed; c is more than or equal to 1 and less than or equal to m 0 ，1≤d≤m-m 0 ；
Step two, three: x, Y angular displacement monitoring data set for ith support in reference state
Performing linear normalization transformation, and recording the transformed set as +.>
X, Y angular displacement monitoring data set of ith support under to-be-diagnosed state +.>
Performing linear normalization transformation, and recording the transformed set as +.>
It is defined as:
in the method, in the process of the invention,
the maximum value of the displacement of the ith support measuring point X, Y to the rotation angle under the reference state and the state to be diagnosed is +.>
Similarly, let go of>
The minimum value of X, Y displacement of the ith support measuring point to the corner under the reference state and the state to be diagnosed is +.>
Respectively forming a set by the minimum value of the angular displacement of the X, Y of the ith support measuring point in the reference state and the state to be diagnosed;
the conversion coefficient of X, Y of the ith support measuring point to the corner displacement under the reference state and the diagnosis state is determined by the plane position symmetrical relation of the two support measuring points to be calculated, and the value is 1 or-1; />
Step two, four: x, Y angular displacement monitoring data set of ith support measuring point after linear normalization under reference state and to-be-diagnosed state
Setting X, Y two-dimensional random variable of angular displacement of the ith support measuring point in a reference state as +.>
X, Y two-dimensional random variable of angular displacement under to-be-diagnosed state is +.>
The definition domain is { (x, y) |x E [0,1 ]],y∈[0,1]If each domain interval is equally divided into s subintervals of length Δ=1/s, the domain is equally divided into s×s subintervals, i.e.:
0＝x 0 ＜x 1 ＜x 2 ＜…＜x s-1 ＜x s ＝1；
0＝y 0 ＜y 1 ＜y 2 ＜…＜y s-1 ＜y s ＝1；
step two, five: setting square subinterval { (x, y) |x E (x) falling in definition field (e line, f column) under ith support measuring point reference state and to-be-diagnosed state e-1 ,x e ],y∈(x f-1 ,x f ]Respectively have } therein
And->
The probability of an event can be estimated from the frequency of the event, as known from Bernoulli's law of large numbers, then the two-dimensional random variables in the reference state and the state to be diagnosed are +.>
And->
Probability of falling within the square subinterval +.>
And->
The method comprises the following steps of:
in particular, when e=1 or f=1, the left boundary of the definition field is preferable, and so on;
the joint probability density matrix of the ith support in the reference and to-be-diagnosed states, respectively
And->
It is defined as:
step three: and (3) calculating a joint probability density function difference matrix between every two support measuring points of the clustering group in the reference state by using a method of reserving a cross validation for the linear normalized joint probability density matrix in the reference state of each support measuring point in the same clustering group in the step (II), removing diagonal elements, taking the mean value of each row of the matrix, and multiplying a guarantee coefficient to be used as a void diagnosis factor threshold value of the corresponding support measuring point in the clustering group.
In the step, the method for determining the threshold value of the void diagnostic factor of each support measuring point comprises the following steps:
step three: setting joint probability density matrixes of a support and a support measuring point in a k support clustering group in a reference state
And->
In order to center the shape of the joint probability density matrix of two support measuring points during calculation, the joint probability density matrix of the b support measuring point can be selected>
Appropriate expansion is carried out to obtain->
The expansion method comprises the following steps:
wherein, l is a positive integer, which can be properly valued, and is generally a positive integer of which l is about s/8;
step three, two: matrix expanded in step three
Sub-of window size sxs is fetchedMatrix->
The definition is as follows:
wherein g and h are positive integers, g is not less than 1 and h is not more than 2l;
sub-matrix of the order
And matrix->
Difference is made to obtain a difference matrix->
And summing the absolute values of its elements as a joint probability density matrix difference +.>
The definition is as follows:
when g, h traverses 1 to 2l, joint probability density matrix differences
A difference matrix of size 2l×2l can be constructed>
The definition is as follows:
taking a difference matrix
The smallest element of (2) as the joint probability density matrix difference at this time +.>
The definition is as follows:
and step three: when a, b in the third step are respectively taken through n in the kth support clustering group k When the support measuring points are arranged, the joint probability density matrix difference
Can be formed into a size of n k ×n k Difference matrix->
The definition is as follows:
wherein, the main diagonal element is 0;
from a matrix of differences
A void diagnostic factor threshold eta for the a-th support can be determined a It is defined as follows:
where λ is a guaranteed coefficient, and generally 2 is taken.
Step four: calculating joint probability density function difference matrixes between every two support measuring points of the same cluster group in a reference state and a to-be-diagnosed state by using a method of reserving a cross validation for linear normalization joint probability density matrixes under the to-be-diagnosed state of each support measuring point in the same cluster group in the second step, removing diagonal elements, and taking the average value of each row of the matrixes as a void diagnosis factor of the corresponding support measuring point in the cluster group; comparing the void diagnosis factor of the support measuring point with the void diagnosis factor threshold of the corresponding support measuring point in the third step, and when the void diagnosis factor is smaller than or equal to the void diagnosis factor threshold, the support is not affected by the void disease; when the void diagnostic factor is greater than the void diagnostic factor threshold, the mount is affected by the void disease.
In the step, the method for determining the void diagnosis factor of the support measuring point comprises the following steps:
step four, first: taking n in k-th support clustering group under reference state and to-be-diagnosed state k The normalized joint probability density matrix of the support measuring points can be regarded as different support measuring points in the reference state and the to-be-diagnosed state, namely 2n in the kth support clustering group k Measuring points of the support, 2n k The joint probability density matrixes of the a-th support and the b-th support are taken to be respectively measured
And->
Wherein a is more than or equal to 1 and b is more than or equal to 2n k ；
Step four, two: the calculation of the void diagnosis factors of the support is the same as the joint probability density matrix expansion method when the threshold value of the void diagnosis factors is calculated, namely: joint probability density matrix for the b-th support measurement point according to the method of the third step
Appropriate expansion is carried out to obtain->
And step four, three: the calculation method of the void diagnosis factor of the support is the same as the calculation method of the joint probability density matrix difference when the threshold value of the void diagnosis factor is calculated, namely: calculating the joint probability density matrix difference delta between the a-th support measuring point and the b-th support measuring point according to the method of the third step and the second step a,b ；
And step four: by using the joint probability density matrix difference delta obtained in the fourth step and the third step a,b The size of the constitution is 2n k ×2n k Is defined as follows:
wherein, the main diagonal element is 0;
from the difference matrix delta, the diagnostic factor delta for the run-out of the a-th support can be determined a It is defined as follows:
the calculated void diagnostic factors comprise the void diagnostic factors of the support measuring points in the reference state and the to-be-diagnosed state, the void diagnostic factors of the support measuring points in the to-be-diagnosed state are taken to be compared with the void diagnostic factor threshold value of the corresponding support measuring point calculated in the third step, and if the void diagnostic factors are smaller than or equal to the void diagnostic factor threshold value, the support measuring point is not affected by the void diseases; if the void diagnostic factor is greater than the void diagnostic factor threshold, the support measurement point is affected by the void disease.
Step five: and repeating the second step to the fourth step until the void diagnosis factors of all the support measuring points in all the clustering groups are subjected to abnormal judgment, and judging the locations of the void supports by combining the plane arrangement of the support measuring points of the beam bridge support group.
The beam bridge support group void disease monitoring method provided by the invention utilizes a wireless sensing technology, utilizes a high-cost performance wireless inclinometer to construct a beam bridge support group wireless monitoring network, acquires the corner displacement monitoring data of each support measuring point, is different from the traditional wired single-point monitoring method of the support, and realizes the distributed multipoint monitoring of the support group while avoiding complex wiring. The bridge support group void disease diagnosis method provided by the invention utilizes the high similarity of the rotation angle displacement monitoring data of the support measuring points under the same or similar environmental load and traffic load action of the supports in the same cluster group with symmetry relation, and diagnoses the bridge support group void disease by taking the joint probability density function difference between the supports in the same cluster group in a reference state and a to-be-diagnosed state as a void diagnosis factor, thereby breaking through the traditional limitation of diagnosing a single support, considering the influence of support void on other supports and the whole bridge structure from the perspective of the support group, realizing the diagnosis of the bridge support group void disease and the determination of the void support position, and having important significance for accurately diagnosing the bridge support void disease.
The following tests were used to verify the effect of the invention:
this test takes the four-span continuous beam bridge structure shown in fig. 1 as an example. In order to simulate the support void diseases, the effective bearing area of the support is reduced.
The test is specifically as follows:
and installing a high-cost performance wireless inclinometer at each support position of the four-span continuous beam bridge, constructing a beam bridge support group wireless sensor monitoring network, and acquiring corner displacement monitoring data of the support measuring points X, Y in two directions, wherein the monitoring network is shown in figure 2.
And carrying out clustering group division on the beam bridge support groups according to the symmetry relation of the support positions, wherein the division result is shown in figure 3.
The void diseases of the support are simulated by reducing the effective bearing area of the support, and the plane position of the void support is shown in figure 4.
Collecting monitoring data of the first 6 months under a reference state of a four-span continuous beam bridge structure, and monitoring data of the last 9 months under a to-be-diagnosed state, wherein the bearing void disease occurs in 12 months, a time course curve of the monitoring data of the rotation angle displacement of a 1# bearing measuring point is shown in fig. 5, and a monitoring data dividing method is shown in fig. 6;
and calculating a normalized joint probability density function of each support measuring point in the same cluster group under a reference state, wherein a joint probability density function diagram of the 1# support and the 5# support is shown in fig. 7. And calculating a normalized joint probability density function of two support measuring points in the same cluster group under the to-be-diagnosed state, wherein a joint probability density function diagram of the 1# support and the 5# support is shown in fig. 8.
And calculating a joint probability density function difference matrix between every two support measuring points of the cluster group in a reference state by using a cross verification method, removing diagonal elements, taking the average value of each row of the matrix, and multiplying the average value by a guarantee coefficient to serve as a void diagnosis factor threshold value of each support measuring point of the cluster group, as shown in fig. 9. And calculating joint probability density function difference matrixes between every two support measuring points of the clustering group in a reference state and a to-be-diagnosed state, taking the average value of each row of the matrix as a void diagnosis factor of each support measuring point of the clustering group after diagonal elements are removed, and comparing the void diagnosis factor with a diagnosis factor threshold of the corresponding support measuring point, wherein the diagnosis result is shown in figure 10. Wherein the joint probability density function difference matrix calculation is shown in fig. 11.
The position of the void support can be judged according to the diagnosis result of each support measuring point by combining the plane position of the beam bridge support group, and the judgment result is shown in fig. 12.
In summary, the monitoring method provided by the invention can realize long-term monitoring of the angular displacement of each support measuring point X, Y of the beam bridge support group in two directions, and the diagnosis method for the void diseases can realize accurate diagnosis of the void diseases of the beam bridge support group and determination of the locations of the void supports.
Claims (4)
1. A joint probability density function difference diagnosis method for beam bridge support group void diseases is characterized by comprising the following steps:
step one: installing wireless inclinometers at all supports of a beam bridge, constructing a beam bridge support group wireless sensor monitoring network, acquiring corner displacement monitoring data of the support measuring points X, Y in two directions, and carrying out clustering division on the supports in the support group and dividing the supports into a plurality of clustering groups by utilizing the symmetry relation of the support positions in the beam bridge support group;
step two: for each support measuring point in the same cluster group, selecting a proper time node to divide monitoring data into reference state monitoring data and state monitoring data to be diagnosed, calculating a linear normalized joint probability density matrix under the reference state and the state to be diagnosed of each support measuring point, and calculating a joint probability density matrix after the state division and the linear normalization of the corner displacement monitoring data comprises the following steps:
step two,: setting X-direction corner displacement monitoring data set of support measuring points in kth support clustering group as matrix
The Y-direction corner displacement monitoring data set of the support measuring points in the kth support clustering group is a matrix +.>
X-direction angular displacement monitoring data set X of ith support measuring point i And Y-direction angular displacement monitoring data set Y i The definitions are respectively as follows:
in the method, in the process of the invention,
for the j-th sampling result of the X-direction angular displacement of the i-th support measuring point,/th sampling result is given>
For the ith support measuring pointThe j-th sampling result of the Y-direction angular displacement is that i is more than or equal to 1 and n is more than or equal to n k ，1≤j≤m，n k The number of the supports in the kth support clustering group is the number of corner displacement sampling times;
step two: taking a suitable intermediate time point m in the monitoring time period 0 ，1≤m 0 M is less than or equal to, the angular displacement monitoring data are divided into a reference state and a state to be diagnosed, and then X-direction angular displacement monitoring data set is carried out under the reference state
Y-direction corner displacement monitoring data set>
And X-direction angular displacement monitoring data set in the state to be diagnosed +.>
Y-direction corner displacement monitoring data set>
The definitions are respectively as follows:
in the method, in the process of the invention,
the c-th sampling result of the X-direction angular displacement of the i-th support measuring point is also the c-th sampling result of the X-direction angular displacement of the i-th support measuring point in a reference state; />
Mth of the X-direction angular displacement of the ith support measuring point 0 The +d-1 sampling result is also the d sampling result of the X-direction angular displacement of the i-th support measuring point under the state to be diagnosed; />
The c-th sampling result of the Y-direction angular displacement of the i-th support measuring point is also the c-th sampling result of the Y-direction angular displacement of the i-th support measuring point in the reference state; />
Mth for the Y-direction angular displacement of the ith support measuring point 0 The +d-1 sampling result is also the d sampling result of the Y-direction angular displacement of the i-th support measuring point under the state to be diagnosed; c is more than or equal to 1 and less than or equal to m 0 ，1≤d≤m-m 0 ；/>
Step two, three: x, Y angular displacement monitoring data set for ith support in reference state
Performing linear normalization transformation, and recording the transformed set as +.>
X, Y angular displacement monitoring data set of ith support under to-be-diagnosed state +.>
Performing linear normalization transformation, and recording the transformed set as +.>
It is defined as:
in the method, in the process of the invention,
the maximum value of the displacement of the ith support measuring point X, Y to the rotation angle under the reference state and the state to be diagnosed is +.>
In the same way, the processing method comprises the steps of,
the minimum value of X, Y displacement of the ith support measuring point to the corner under the reference state and the state to be diagnosed is +.>
X, Y the i-th support measuring point is oriented to the corner position under the reference state and the state to be diagnosed respectivelyA set of shifted minima;
the conversion coefficients of X, Y of the ith support measuring point to the angular displacement under the reference state and the diagnosis state are respectively;
step two, four: x, Y angular displacement monitoring data set of ith support measuring point after linear normalization under reference state and to-be-diagnosed state
Setting X, Y two-dimensional random variable of angular displacement of the ith support measuring point in a reference state as +.>
X, Y two-dimensional random variable of angular displacement under to-be-diagnosed state is +.>
The definition domain is { (x, y) x E [0,1 ]],y∈[0,1]If each domain interval is equally divided into s subintervals of length Δ=1/s, the domain is equally divided into s×s subintervals, i.e.:
0＝x 0 ＜x 1 ＜x 2 ＜…＜x s-1 ＜x s ＝1；
0＝y 0 ＜y 1 ＜y 2 ＜…＜y s-1 ＜y s ＝1；
step two, five: setting square subinterval { (x, y) x E (x) falling in definition field (e, f, column) under ith support measuring point reference state and to-be-diagnosed state e-1 ,x e ],y∈(x f-1 ,x f ]Respectively have } therein
And->
The observed values are known from Bernoulli's law of large numbersThe probability of a piece can be estimated from the frequency of events, then the two-dimensional random variables in the reference state and the state to be diagnosed
And->
Probability of falling within the square subinterval +.>
And->
The method comprises the following steps of:
the joint probability density matrix of the ith support in the reference and to-be-diagnosed states, respectively
And->
It is defined as: />
Step three: calculating a joint probability density function difference matrix between every two support measuring points of the same cluster group in the reference state by using a method of reserving a cross validation for the linear normalized joint probability density matrix in the reference state of each support measuring point in the same cluster group in the second step, removing diagonal elements, taking the mean value of each row of the matrix, and multiplying a guarantee coefficient to be used as a void diagnosis factor threshold value of the corresponding support measuring point in the cluster group;
step four: calculating joint probability density function difference matrixes between every two support measuring points of the same cluster group in a reference state and a to-be-diagnosed state by using a method of reserving a cross validation for linear normalization joint probability density matrixes under the to-be-diagnosed state of each support measuring point in the same cluster group in the second step, removing diagonal elements, and taking the average value of each row of the matrixes as a void diagnosis factor of the corresponding support measuring point in the cluster group; comparing the void diagnosis factor of the support measuring point with the void diagnosis factor threshold of the corresponding support measuring point in the third step, and when the void diagnosis factor is smaller than or equal to the void diagnosis factor threshold, the support is not affected by the void disease; when the void diagnostic factor is greater than the void diagnostic factor threshold, the support is affected by the void disease;
step five: and repeating the second step to the fourth step until the void diagnosis factors of all the support measuring points in all the clustering groups are subjected to abnormal judgment, and judging the locations of the void supports by combining the plane arrangement of the support measuring points of the beam bridge support group.
2. The method for diagnosing joint probability density function difference of void diseases of beam bridge support groups according to claim 1, wherein in the first step, the method for clustering and dividing the support groups is as follows:
the method comprises the following steps: let the bridge support crowd set as Z, divide into N cluster group with the support in the bridge support crowd according to symmetry relation, it is defined as:
wherein Z is k K is more than or equal to 1 and less than or equal to N, and is the set of the kth support clustering group in the beam bridge support group;
step two: set Z of kth support clustering group in bridge support group k It is defined as:
wherein Z is i For the ith support in the kth support cluster group, i is more than or equal to 1 and less than or equal to n k ，n k The number of the supports in the kth support clustering group.
3. The method for diagnosing joint probability density function difference of girder bridge abutment group void diseases according to claim 1, wherein in the third step, the method for determining the void diagnosis factor threshold value of each abutment measuring point is as follows:
step three: setting joint probability density matrixes of a support and a support measuring point in a k support clustering group in a reference state
And->
In order to center the shape of the joint probability density matrix of two support measuring points during calculation, the joint probability density matrix of the b support measuring point is selected>
Appropriate expansion is carried out to obtain->
The expansion method comprises the following steps:
wherein l is a positive integer;
step three, two: matrix expanded in step three
The submatrix with window size s x s is fetched>
The definition is as follows:
wherein g and h are positive integers, g is not less than 1 and h is not more than 2l;
sub-matrix of the order
And matrix->
Difference is made to obtain a difference matrix->
And summing the absolute values of its elements as a joint probability density matrix difference +.>
The definition is as follows:
when g, h traverses 1 to 2l, joint probability density matrix differences
A difference matrix of size 2l×2l is formed>
The definition is as follows:
taking a difference matrix
The smallest element of (2) as the joint probability density matrix difference at this time +.>
The definition is as follows:
and step three: when a, b in the third step are respectively taken through n in the kth support clustering group k When the support measuring points are arranged, the joint probability density matrix difference
The composition size is n k ×n k Difference matrix->
The definition is as follows:
wherein, the main diagonal element is 0;
from the differenceValue matrix
A void diagnostic factor threshold eta for the a-th support can be determined a It is defined as follows:
where λ is a guaranteed coefficient.
4. The method for diagnosing joint probability density function difference of girder bridge abutment group void diseases according to claim 1, wherein in the fourth step, the method for determining the void diagnostic factor of the abutment measuring point is as follows:
step four, first: taking n in k-th support clustering group under reference state and to-be-diagnosed state k The normalized joint probability density matrix of the support measuring points can be regarded as different support measuring points in the reference state and the to-be-diagnosed state, namely 2n in the kth support clustering group k Measuring points of the support, 2n k The joint probability density matrixes of the a-th support and the b-th support are taken to be respectively measured
And->
Wherein a is more than or equal to 1 and b is more than or equal to 2n k ；
Step four, two: the calculation of the void diagnosis factors of the support is the same as the joint probability density matrix expansion method when the void diagnosis factors are calculated at threshold values, and the joint probability density matrix of the b support measuring point is obtained according to the method of the third step
Appropriate expansion is carried out to obtain->
And step four, three: the calculation of the void diagnosis factor of the support is the same as the calculation method of the joint probability density matrix difference when the threshold value of the void diagnosis factor is calculated, and the joint probability density matrix difference delta of the a-th support measuring point and the b-th support measuring point is calculated according to the method of the third step a,b ；
And step four: by using the joint probability density matrix difference delta obtained in the fourth step and the third step a,b The size of the constitution is 2n k ×2n k Is defined as follows:
wherein, the main diagonal element is 0;
from the difference matrix delta, the diagnostic factor delta for the run-out of the a-th support can be determined a It is defined as follows:
the calculated void diagnostic factors comprise the void diagnostic factors of the support measuring points in the reference state and the to-be-diagnosed state, the void diagnostic factors of the support measuring points in the to-be-diagnosed state are taken to be compared with the void diagnostic factor threshold value of the corresponding support measuring point calculated in the third step, and if the void diagnostic factors are smaller than or equal to the void diagnostic factor threshold value, the support measuring point is not affected by the void diseases; if the void diagnostic factor is greater than the void diagnostic factor threshold, the support measurement point is affected by the void disease.
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