Bridge damage identification method based on statistical noise reduction

Abstract

The invention discloses a bridge damage identification method based on statistical noise reduction. The method comprises the following steps: step 1, obtaining bridge dynamic response data; 2, preprocessing the dynamic response data by means of a statistical algorithm, removing common factor components containing noise in the dynamic response data, and obtaining special factors; 3, performing secondary processing on the dynamic response data before and after damage to obtain a special factor matrix, and sequentially calculating a covariance index and an acceleration energy index; 4, performing data fusion on the covariance index and the acceleration energy index to obtain a damage identification index, and identifying a bridge damage position according to the damage identification index; the method has the advantages of high robustness, high recognition precision and difficulty in damage misjudgment.

Description

Technical Field

[0001] The invention belongs to the technical field of bridge detection and bridge health monitoring, and specifically relates to a bridge damage identification method based on statistical noise reduction. Background Art

[0002] Bridges play a very important role in people's livelihood and economy, especially when the bridge is in operation. In recent years, large-scale bridge engineering technology has been developing rapidly, but bridge safety accidents have also occurred frequently during operation. In order to effectively protect the safety of people's lives and property, bridge health monitoring has become a research hotspot in civil engineering. [1-3] , due to the long service life of bridges, the environmental conditions of bridges are also different, and the loads acting on bridges are highly random, so the potential risk of damage is relatively high. Since bridge damage often develops from local damage, and it is difficult to find internal damage through appearance inspection, if the damaged position is not found in time for repair and reinforcement, it will affect the bearing capacity and durability of the bridge. If the damage is allowed to accumulate over time, it is easy to cause serious bridge safety accidents, bringing immeasurable economic damage and social impact. Therefore, the research on damage identification of bridges during their service period is of great practical significance.

[0003] At present, the damage identification method based on vibration testing [4-8] It has been widely used in bridge damage identification. [9] The identification formulas of stiffness damage index and mass damage index were derived, and the frequency was used to identify the damage of the structure.

[10] A new method is proposed to use the flexibility matrix before and after structural damage, and to perform two differences on the columns and rows of the flexibility matrix difference to obtain the flexibility difference curvature matrix, and use the diagonal elements as a new method to detect structural damage indicators. And damage identification is completed through this indicator.

[0004] The problem with the existing technology is that during the actual operation of the bridge, the response of the structure will inevitably be affected by external interference factors such as noise and temperature. The influence of temperature can be weakened by screening data from the same period and time, while noise has a large randomness, and the noise in different time periods is different, which affects the accuracy of damage identification; at the same time, since the early damage of the bridge is relatively small, it is difficult to identify with the existing technology. At the same time, since the early damage of the bridge is relatively small, a single damage indicator [11，12] It may not be able to fully reflect local damage information, which may easily lead to misjudgment of the damage.

[0005] References

[0006] [1] Pan Yongjie, Cai Degou, Feng Zhongwei, et al. Analysis and thinking on the current status of technical standards for bridge structure health monitoring[J]. Railway Construction, 2022, 62(10): 8-16.

[0007] [2] Wang Lingbo, Wang Qiuling, Zhu Zhao, et al. Research status and prospects of bridge health monitoring technology[J]. China Journal of Highway and Transport, 2021, 34(12): 25-45. DOI: 10.19721 / j.cnki.1001-7372.2021.12.003.

[0008] [3] Guo Jian, Gu Zhengwei, Sun Bingnan, et al. Bridge health monitoring method based on wavelet analysis [J]. Engineering Mechanics, 2006(12):129-135.

[0009] [4] Yang Yang, Xu Wenming, Tan Xiaokun, Tang Yan, Liu Liyuan. Research on damage identification of statistical moment curvature beam bridge based on vehicle-bridge coupled vibration [J / OL]. China Journal of Highway and Transport: 1-16 [2023-05-05]

[0010] [5] Tian Yongding, Zhang Jian. Research progress on rapid testing and flexibility identification of bridges based on mobile impact vibration[J]. China Civil Engineering Journal, 2022, 55(10): 46-61. DOI: 10.15951 / j.tmgcxb.21080835.

[0011] [6] Shu Xiaoyu, Li Xuefeng, Wang Chengyu. Research on multi-damage identification of uniform cross-section continuous beam bridge based on vehicle-bridge coupled vibration[J]. Journal of Hefei University of Technology (Natural Science Edition), 2023, 46(01): 81-87+103.

[0012] [7] Li Huimin, Dong Meimei, Xiong Xiong, Xiong Deng. A review of research on structural damage identification based on vibration[J]. Building Structures, 2021, 51(04): 45-50+38. DOI: 10.19701 / j.jzjg.2021.04.007.

[0013] [8]Luo J,Huang M,Xiang C,et al.A Novel Method for DamageIdentification Based on Tuning-Free Strategy and Simple PopulationMetropolis-Hastings Algorithm[J].Internati onal Journal of StructuralStability and Dynamics,2023,23(04).DOI:10.1142 / S0219455423500438.

[0014] [9] Wang Zhisong, Guo Huiyong, Li Zhengliang. Research on different structural damage identification methods based on frequency response[J]. Engineering Mechanics, 2008(06):6-13.

[0015]

[10] Li Yongmei, Zhou Xiyuan, Gao Xiangyu. Structural damage identification method based on flexibility difference curvature matrix[J]. Engineering Mechanics, 2009, 26(02): 188-195+202.

[0016]

[11] Wei Jun, Du Yongxiao, Wu Zhiqiang, Huang Dunwen, Liu Kang. Damage identification of beam structures based on modal strain energy and Bayesian theory[J]. Journal of Railway Science and Engineering, 2019, 16(08): 2052-2061. DOI: 10.19713 / j.cnki.43-1423 / u.2019.08.023.

[0017]

[12] Zeng Bin, Zhou Zhen, Zhang Qingfang, Xu Qing. Multi-position damage identification and noise resistance analysis of truss string based on data fusion[J]. Journal of Building Structures, 2020, 41(S1): 36-43. DOI: 10.14006 / j.jzjgxb.2020.S1.005. Summary of the invention

[0018] The purpose of the present invention is to provide a bridge damage identification method based on statistical noise reduction to address the problems existing in the prior art. The method can separate the measurement noise from the dynamic response of the bridge, and then construct a basic damage index based on the dynamic response. By fusion of data and integration of multiple damage indicators, the reliability and efficiency of the damage identification method can be improved to avoid misjudgment of damage. The scheme has the advantages of high robustness, high recognition accuracy and low risk of misjudgment of damage.

[0019] To achieve the above object, the technical solution adopted by the present invention is: a bridge damage identification method based on statistical noise reduction, comprising the following steps:

[0020] Step 1: Obtain bridge dynamic response data;

[0021] Step 2: Preprocess the dynamic response data based on statistical algorithms to remove common factor components containing noise in the dynamic response data and obtain special factors;

[0022] Step 3: Perform secondary processing on the dynamic response data before and after the injury to obtain the special factor matrix, and calculate the covariance index and acceleration energy index in turn;

[0023] Step 4: The covariance index and the acceleration energy index are fused to obtain the damage identification index, and the damage location of the bridge is identified according to the damage identification index.

[0024] In the above scheme, step 1 is to collect dynamic response data of each position of the bridge under load by setting vibration sensors on the bridge. Step 2 is to find common factors by calculating the response matrix to reduce the influence of noise on the dynamic response data of the bridge. Step 3 is to calculate the covariance index and acceleration energy index as the basic indicators for damage identification by secondary processing of the dynamic response data before and after damage. Step 4 is to construct a damage identification index by combining the covariance index and acceleration energy index through data fusion to identify the damage position of the bridge.

[0025] Furthermore, step 2 includes first performing coordinate rotation on the factor matrix of the dynamic response data to obtain the factor loading matrix, then calculating the factor score coefficient matrix and each factor, and then calculating the special factor.

[0026] By rotating the factor axis, that is, rotating the coordinates, the loads of the original variables on the principal components are redistributed, so that the loads of the original variables on the common factors are polarized, so that the principal components can be explained by the original variables with large loads. This process can also observe the degree to which the hidden factors extract the original feature information, thereby achieving the effect of eliminating noise.

[0027] Furthermore, before performing step 2, the correlation of the dynamic response data is judged, and when the correlation of the dynamic response data meets the requirements, secondary processing is performed.

[0028] Furthermore, the covariance index includes covariance difference curvature, and the covariance difference curvature calculation formula is as follows:

[0029]

[0030] Where: CCR i is the covariance difference curvature of the measuring point i, crc i is the covariance of measuring point i, and h is the distance between two adjacent measuring points.

[0031] Covariance is a statistic used in statistics to measure the overall error between two variables. By introducing it into bridge damage identification, the change trend between the columns of the acceleration response matrix before and after damage can be measured and evaluated, thereby identifying damage to the bridge.

[0032] Furthermore, the acceleration energy index includes acceleration energy curvature, and the acceleration energy curvature is calculated by the central difference method. k The acceleration energy characteristic function AE is calculated and obtained. k The calculation formula is as follows:

[0033]

[0034] Where: is the acceleration of node k at time t.

[0035] The acceleration energy curvature is introduced to measure and evaluate the change trend of the acceleration energy before and after damage, and then the damage of the bridge is identified.

[0036] Furthermore, in step 4, a data fusion formula is used to fuse the covariance index and the acceleration energy index. The data fusion formula is as follows:

[0037]

[0038] Where: m 1i is the basic probability distribution function of the covariance of the i-element beam, m 2i is the basic probability distribution function of the acceleration energy of the i-element beam, AECR k is the acceleration energy curvature of the measuring point k.

[0039] Furthermore, in step 4, a damage warning line is set to determine whether damage occurs. The calculation formula of the damage warning line is as follows:

[0040]

[0041] Where: DI i is the damage index of the dynamic response structure of the i-element beam; DI max is the maximum value of the structural damage index of each unit beam segment; S is the safety factor. When , it is determined that damage has occurred in the kth unit.

[0042] Furthermore, step 2 includes building a special factor model:

[0043] ε=Af-X

[0044] Where X is the data matrix, A is the factor loading matrix, f is the common factor of the data matrix X, and ε is the special factor.

[0045] Furthermore, in step 1, when the moving load passes through the bridge, the dynamic response data of several vibration sensors preset on the bridge at each moment of duration n are recorded as follows:

[0046]

[0047] Where: m is the measuring point number; X mn is the dynamic response of the bridge at the nth moment collected at the mth measuring point of the structure.

[0048] Furthermore, the vibration sensors are arranged at equal distances along the length direction of the bridge.

[0049] Vibration sensors are set equidistantly to facilitate damage identification and calculation.

[0050] Compared with the prior art, the present invention has the following beneficial effects:

[0051] (1) The damage identification index obtained by data fusion can effectively improve the effect of damage identification, avoid misjudgment and omission of damage when using a single damage index, and improve the accuracy of damage identification;

[0052] (2) This method processes the dynamic response data and removes the common factor components to reduce the interference of noise on damage identification and improve the damage identification effect;

[0053] (3) The method proposed in this paper can better identify the damage location when dealing with a single minor damage accompanied by a large noise level and when dealing with multiple minor damages accompanied by a noise level below 20%, and has good applicability. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 is a fusion flow chart of an embodiment of the present invention;

[0055] Figure 2 A schematic diagram of a bridge model in an embodiment of the present invention;

[0056] Figure 3 It is a bridge damage index 1 identification diagram of working condition 1 in an embodiment of the present invention;

[0057] Figure 4 It is a damage indicator 2 identification diagram of working condition 1 in an embodiment of the present invention;

[0058] Figure 5 This is a damage index fusion identification diagram for working condition 1 in an embodiment of the present invention;

[0059] Figure 6 This is a damage index fusion identification diagram for working condition 3 in an embodiment of the present invention;

[0060] Figure 7 This is a fusion diagram of damage index data for working condition 2 in an embodiment of the present invention;

[0061] Figure 8 This is a damage index data fusion diagram for working condition 4 in an embodiment of the present invention;

[0062] Fig. 9 Comparison chart before and after adding noise to the acceleration signal;

[0063] Fig.10 This is the data fusion index diagram for condition 1 under 10% noise;

[0064] Fig.11 This is the data fusion index diagram for condition 1 under 30% noise;

[0065] Fig.12 It is the covariance damage index diagram of working condition 1 under different noises;

[0066] Fig.13 This is the data fusion index diagram for working condition 2 under 10% noise; DETAILED DESCRIPTION

[0067] The technical solution of the present invention will be clearly and completely described below in conjunction with the drawings in the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention. In the description of the present invention, it should be noted that the terms front, back, left, right, etc. indicate directions or positional relationships based on the directions or positional relationships shown in the drawings, or the directions or positional relationships in which the product is usually placed when in use. They are only for the convenience of describing the present invention or simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed or operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention.

[0068] The KMO (Kaiser-Meyer-Olkin) test statistic is an indicator used to compare the simple correlation coefficient and partial correlation coefficient between variables. It is mainly used in factor analysis of multivariate statistics. The KMO statistic takes values ​​between 0 and 1.

[0069] When the sum of squares of simple correlation coefficients among all variables is much larger than the sum of squares of partial correlation coefficients, the closer the KMO value is to 1, the stronger the correlation among variables is, and the more suitable the original variables are for factor analysis; when the sum of squares of simple correlation coefficients among all variables is close to 0, the closer the KMO value is to 0, the weaker the correlation among variables is, and the less suitable the original variables are for factor analysis.

[0070] The Bartlett test is a test for the correlation between variables in factor analysis. When the correlation is strong, the KMO value is close to 1. Generally, KMO>0.9 is very suitable for factor analysis.

[0071] Statistical algorithms usually refer to algorithms that use statistical principles to process data. They are used for data collection, analysis, and interpretation, including principal component analysis and covariance algorithms.

[0072] Principal Component Analysis (PCA) is a principal component analysis technique that uses the idea of ​​dimensionality reduction to mainly study how to explain the correlation between multiple variables through a few principal components. Each principal component is a linear combination of the original variables, so that they retain as much information of the original variables as possible, and the principal components are independent of each other. There are two purposes of principal component analysis: one is to compress the data, and the other is to explain the data. This method can reduce complex factors to several principal components, eliminate redundant information, simplify complex problems, and obtain more scientific and accurate information, so that the model can better reflect the real situation. In order to avoid information loss when compressing data, PCA is improved.

[0073] In view of the explanatory defects of the actual meaning of PCA, in order to make the common factors better explained, the loads of the original variables on the principal components are redistributed by rotating the factor axis, that is, rotating the coordinates, so that the loads of the original variables on the common factors are polarized, so that the principal components can be explained by the original variables with large loads. This process can also observe the degree of extraction of the original feature information by the hidden factors, so as to achieve the effect of eliminating noise.

[0074] The Varimax criterion is a factor rotation method that aims to simplify factor interpretation by maximizing the variance of the factor loading matrix. The Varimax method adjusts the factor loading matrix through an iterative process so that the absolute value of each factor loading is as large or small as possible, making the factor interpretation clearer and more intuitive.

[0075] Covariance, also known as covariance, is used to describe the degree of linear correlation between two random variables.

[0076] DS evidence theory is a method for dealing with uncertainty information fusion. Its applications include machine fault detection in Matlab. Information fusion methods include comprehensive averaging method, Bayesian estimation method, DS method, etc.

[0077] The core principle of DS evidence theory is to deal with the synthesis of multi-source uncertain information through concepts such as basic probability assignment function BPA, trust function and likelihood function. BPA is a function defined on all subsets of the recognition framework, which represents the degree of trust in each proposition. The trust function represents the overall degree of trust in a proposition, while the likelihood function represents the degree of non-negation of the proposition. When there are multiple independent sources of evidence, the basic probability assignments of these sources can be combined using the Dempster combination rule to obtain a comprehensive trust assignment.

[0078] like Figure 1-13 As shown, a bridge damage identification method based on statistical noise reduction includes the following steps:

[0079] Step 1: Obtain bridge dynamic response data;

[0080] Step 2: Preprocess the dynamic response data based on statistical algorithms to remove common factor components containing noise in the dynamic response data and obtain special factors;

[0081] Step 3: Perform secondary processing on the dynamic response data before and after the injury to obtain the special factor matrix, and calculate the covariance index and acceleration energy index in turn;

[0082] Step 4: The covariance index and the acceleration energy index are fused to obtain the damage identification index, and the damage location of the bridge is identified according to the damage identification index.

[0083] In the above scheme, step 1 is to collect the dynamic response data of each position of the bridge under the action of load by setting a number of vibration sensors on the bridge. Step 2 is to find the common factors and the common factors and special factors by calculating the response matrix, and remove the common factors to reduce the influence of noise on the dynamic response data of the bridge. Step 3 is to calculate the covariance index and the acceleration energy index as the basic indicators for damage identification by secondary processing of the dynamic response data before and after damage. Step 4 is to construct the damage identification index by data fusion and comprehensive covariance index and acceleration energy index to identify the damage position of the bridge.

[0084] For a B-dimensional data X, assuming it has l common factors, through statistical analysis and calculation, X can be expressed as:

[0085]

[0086] Where f1, f2, ..., f n is the n common factors of data X; A pj is the pth common factor f p The jth component x in X j The load on j For x j special factor.

[0087] Simplifying the above formula into a mathematical model, it can be written as:

[0088] X=Af+ε (2)

[0089] The special factor model can be obtained. As long as the common factors of each component in the original data are calculated, the components of the common factors in the original data can be eliminated. This will reduce the impact of environmental factors such as noise and temperature on the structural dynamic response data during the damage detection process. Noise exists in all dynamic response data and belongs to the common factor part, so the purpose of extracting special factors is to reduce the impact of noise factors.

[0090] Furthermore, step 2 includes building a special factor model:

[0091] ε=Af-X (3)

[0092] Where X is the data matrix, A is the factor loading matrix, f is the common factor of the data matrix X, and ε is the special factor.

[0093] Furthermore, in step 4, a data fusion formula is used to fuse the covariance index and the acceleration energy index. The data fusion formula is as follows:

[0094]

[0095] Where: m 1i is the basic probability distribution function of the covariance of the i-element beam, m 2i is the basic probability distribution function of the acceleration energy of the i-element beam, AECR k is the acceleration energy curvature of the measuring point k.

[0096] Through data fusion, comprehensive covariance and acceleration energy indicators are used to identify damage and improve identification accuracy and efficiency.

[0097] The theory of evidence was first proposed by Dempster and then continuously improved by Shafter. This theory can determine the basic probability assignment of uncertain events and integrate them through its specific rules to solve uncertainty problems.

[0098] By applying this theory to damage identification of civil engineering structures, the damage identification results of multiple independent sensors can be assigned probabilities and the data of multiple sensors can be fused through its operation rules.

[0099] Assume that θ is the damage identification framework or hypothesis space of the continuous beam structure:

[0100] θ={θ1,θ2,…,θ n} (4)

[0101] Where: θ i (i=1,2,…,n) is the damage of the i-th unit of the continuous beam. Its power set 2 θA function for the basic probability distribution in the recognition framework is called the mass function, 0≤mass≤1, satisfying mass(φ)=0 and

[0102] When there are n sensors, there are n mass functions and their synthesis rules are as follows:

[0103]

[0104] in,

[0105]

[0106] In this scheme, combined with the synthesis rules of evidence theory, multi-sensor data fusion is extended to multi-damage indicator data fusion to improve the bridge damage identification effect.

[0107] Furthermore, in step 1, when the moving load passes through the bridge, the dynamic response data of several vibration sensors preset on the bridge at each moment of duration n are recorded as follows:

[0108]

[0109] Where: m is the measuring point number; X mn is the dynamic response of the bridge at the nth moment collected at the mth measuring point of the structure.

[0110] In order to obtain effective special factors, the special factors can only be better explained when the dynamic response data matrix samples are sufficient and the dynamic response data of each measuring point have a certain correlation. Therefore, before calculation, the Kaiser-Meyer-Olkin (KMO) test and Bartlett test are required to determine whether the response matrix can effectively find common factors.

[0111]

[0112] The element r in the i-th row and j-th column of the matrix C ij is the Pearson correlation coefficient of variables Di and Dj (i=1,2,...,m,j=1,2,...,n).

[0113] Based on the PCA algorithm, the coordinate axes are rotated to keep the load size of the same type of features on each factor consistent, thereby improving the practical significance of the factors. The Varimax criterion is a common method of coordinate rotation, which maximizes the load variance of all factors to make the differences between factors more prominent.

[0114] Furthermore, step 2 includes first performing coordinate rotation on the factor matrix of the dynamic response data to obtain the factor loading matrix, then calculating the factor score coefficient matrix and each factor, and then calculating the special factor.

[0115] By rotating the factor axis, that is, rotating the coordinates, the loads of the original variables on the principal components are redistributed, so that the loads of the original variables on the common factors are polarized, so that the principal components can be explained by the original variables with large loads. This process can also observe the degree to which the hidden factors extract the original feature information, thereby achieving the effect of eliminating noise.

[0116] Based on the PCA algorithm, the coordinate axes are rotated to keep the load size of the same type of features on each factor consistent, thereby improving the practical significance of the factors. The Varimax criterion is a common method of coordinate rotation, which maximizes the load variance of all factors to make the differences between factors more prominent.

[0117] First, principal component analysis is performed to find the principal components D1…D N , and then based on the principal component, rotate the coordinate axis to obtain the factor loading matrix A as shown in formula (8):

[0118]

[0119] Using the Anderson-Rubin regression estimation method, we can calculate the factor score coefficient matrix G and the various factors as shown in equations (9) and (10):

[0120] G=C -1 A (9)

[0121]

[0122] From equations (9) and (10), we can get:

[0123]

[0124] From formula (11), we can obtain ε=[ε1,ε2,…,ε n ].

[0125] Furthermore, before performing step 2, the correlation of the dynamic response data is judged, and when the correlation of the dynamic response data meets the requirements, secondary processing is performed.

[0126] In order to obtain effective special factors, the special factors can be better explained only when the dynamic response data matrix samples are sufficient and the dynamic response data of each measuring point have a certain correlation.

[0127] Before calculation, Kaiser-Meyer-Olkin (KMO) test and Bartlett test are needed to determine whether the response matrix can effectively find common factors. If the dynamic response data are completely correlated, some data need to be deleted.

[0128] The expected values ​​are E[X] and E[Y] respectively. The covariance crc(X,Y) between two real random variables X and Y is defined as shown in formula (12):

[0129] crc(X,Y)=E[(XE[X])(YE[Y])]

[0130] =E[XY]-2E[Y]E[X]+E[X]E[Y]

[0131] =E[XY]-E[X]E[Y] (12)

[0132] Where: E[X] is the matrix composed of the acceleration response of the bridge before damage, and E[Y] is the matrix composed of the acceleration response of the bridge after damage.

[0133] After finding the covariance between the columns of the acceleration response matrix, the difference curvature of the covariance between two adjacent points is solved to highlight the damage.

[0134] Furthermore, the covariance index includes covariance difference curvature, and the covariance difference curvature calculation formula is as follows:

[0135]

[0136] Where: CCR i is the covariance difference curvature of the measuring point i, crc i is the covariance of measuring point i, and h is the distance between two adjacent measuring points.

[0137] Covariance is a statistic used in statistics to measure the overall error between two variables. By introducing it into bridge damage identification, the change trend between the columns of the acceleration response matrix before and after damage can be measured and evaluated, thereby identifying damage to the bridge.

[0138] Furthermore, the acceleration energy index includes acceleration energy curvature, and the acceleration energy curvature is calculated by the central difference method. k Calculate and obtain.

[0139] Where: is the acceleration of node k at time t.

[0140] The acceleration energy curvature is introduced to measure and evaluate the change trend of the acceleration energy before and after damage, and then the damage of the bridge is identified.

[0141] Acceleration energy is expressed as shown in (14):

[0142]

[0143] Where: m k is the mass at the k node, is the acceleration of node k at time t.

[0144] The damage characteristic function AE based on the concept of acceleration energy is k It can be expressed as shown in formula (15):

[0145]

[0146] After obtaining the acceleration energy difference before and after the injury, the AE k Calculate the acceleration energy curvature AECR k .

[0147] CCR is obtained by calculation i and AECR k After that, it is fused according to the DS evidence theory operation rules, and then the basic probability distribution function (BPA) is calculated. The final fusion result is the damage index (DI) of this paper.

[0148] Furthermore, in step 4, a damage warning line is set to determine whether damage occurs. The calculation formula of the damage warning line is as follows:

[0149]

[0150] Where: DI i is the damage index of the dynamic response structure of the i-element beam; DI max is the maximum value of the structural damage index of each unit beam segment; S is the safety factor. When , it is determined that damage has occurred in the kth unit.

[0151] Since the smaller the S value, the more conservative the judgment condition, in this embodiment, the S value is the average of the two.

[0152] Furthermore, the vibration sensors are arranged at equal distances along the length direction of the bridge.

[0153] Vibration sensors are set equidistantly to facilitate damage identification and calculation.

[0154] The fusion steps are as follows:

[0155] ① Obtain the dynamic response of the bridge before and after damage;

[0156] ② Perform KMO correlation test and Bartlett test on the dynamic response data of the bridge before and after damage;

[0157] ③Use statistical algorithms to process the bridge dynamic response data containing measurement noise, find common factors and special factors, and eliminate the influence of noise;

[0158] ④ Perform secondary calculation on the dynamic response data before and after the damage to obtain the special factor matrix to calculate the covariance and acceleration energy;

[0159] ⑥ Use DS evidence theory to fuse the above damage indicators;

[0160] ⑦ Identify the damage location of the bridge based on the structural damage identification indicators.

[0161] use Figure 2 The finite element simply supported beam bridge model shown in the figure is used as an example for dynamic response analysis. The bridge is made of concrete, with a total length of 24m. The unit is divided into 0.8m units, totaling 30 units. The cross-section is a rectangular cross-section. The material parameter settings are: elastic modulus E = 3.45 × 10 4 MPa, density ρ=2.549kg / m 3 , Poisson's ratio μ = 0.2, section inertia moment I = 2.8m 4 . The vehicle is simplified as a moving concentrated load, with a vehicle weight of 200kN and a vehicle speed of 10m / s. This paper uses Midas software to build a model, and applies the full transient method to calculate the dynamic response of a simply supported beam bridge under a uniform moving load. The finite element model is the basic model in the analysis of self-vibration characteristics. The Newmark time integration method is used to load the finite element model in load steps. In each load step, the load is added to the node of the main beam unit, and all load steps are solved at one time. Finally, the dynamic response of each measuring point in the time history is obtained as the original data. Sensors are evenly arranged under the bridge, with one sensor arranged under each node, and the sensors are numbered in unit order. The simply supported beam is 24m long. If a vehicle passes over the bridge deck at a speed of 10m / s, it takes 2.4 seconds. Considering that too long a collection time will result in too much data, the simulation data collection ends at 3 seconds, and the collection step is 0.01s.

[0162] When a structure is damaged, it is related to the change of structural stiffness. Therefore, the damage of a simply supported beam is simulated by stiffness reduction in this paper. Considering that there are many influencing factors in the dynamic response in engineering practice, and the allowable error of measurement in engineering is 5%, this paper assumes that 5% damage is defined as minor damage. The damage condition is set as single damage and two damages. The specific conditions are shown in Table 1:

[0163] Table 1: Damage conditions

[0164]

[0165] According to the above method, each working condition is calculated respectively, and the basic damage index 1 is defined as the absolute value of the acceleration energy difference curvature, and the basic damage index 2 is defined as the absolute value of the covariance curvature. The calculation results are as follows:

[0166] ① Single damage condition

[0167] In order to better reflect the damage identification process, taking working condition 1 as an example, the damage index 1, damage index 2 and the fused damage index identification are plotted as shown in the figure. Figure 3-Figure 5 shown.

[0168] pass Figure 5 It can be judged that damage has occurred between nodes 12 and 13, that is, unit 12, and the peaks of other locations are all below the damage warning line, which can well identify the damage location. Figure 3 , Figure 4 When a single damage indicator is used for identification, the waveform of the location where no damage occurs also has obvious fluctuations, which can easily lead to misjudgment of the damage result. After data fusion, the waveform is clearer than that of a single damage indicator, and the noise effect is significantly reduced, which can well identify the damage.

[0169] The damage identification diagram formed after data fusion calculation of the dynamic response data of working condition 3 is as follows: Figure 6 As shown in the figure, it can be determined that damage has occurred at unit 12, and the peaks at other locations are all below the damage warning line, and the damage identification effect is good. Figure 5 , Figure 6 It can be seen that with the increase of the degree of damage, the peak extreme point of the final identification result of working condition 3 is slightly smaller than that of working condition 1, and the waveform coordinate points of the other undamaged positions are all improved, but the fluctuation is not large and relatively gentle, which will not cause misjudgment.

[0170] Judging from the recognition results, this method has good recognition effect in the single damage recognition process and is feasible.

[0171] ② Two injuries

[0172] The multiple damage conditions are condition 2 and condition 4. The identification results are as follows: Figure 7 , Figure 8 As shown in the figure, when two minor damages occur, this method can accurately identify the locations of the two minor damages, and the waveforms of the other undamaged parts do not fluctuate greatly, and the peak extreme points are all below the damage warning line. As the degree of damage increases to 10%, the waveform trend is generally consistent with that when minor damage occurs, but the extreme points are significantly increased. Comprehensive analysis shows that this method is feasible and effective for multiple damage identification and has good results.

[0173] In order to verify the denoising effect of this method, Gaussian white noise is added to the structure. Gaussian white noise can simulate real-world noise, such as wind and waves, to simulate actual noise.

[0174] The signal with noise can be expressed by equation (18):

[0175] y d,noise =y d +E p N noise σ(y d ) (18)

[0176] Where: y d,noise is the dynamic response with noise, y d is the dynamic response in the noise-free state, E p is the noise level, N noise is a random number sequence with a mean of 0 and a standard deviation of 1, σ(y d ) is the standard deviation of the dynamic response in the noise-free state.

[0177] When the bridge is damaged in the early stage, the damage is minor. Fig. 9 This is the comparison of acceleration response before and after adding 30% noise at the mid-span of working condition 2. It can be seen that the acceleration response after adding noise can no longer be directly used to construct damage indicators. Therefore, it is necessary to perform noise reduction before performing a series of fusion calculations.

[0178] In this robustness analysis, the fusion results of working condition 1 under 10% and 30% noise conditions are given. The damage identification results are shown in Figure 10-11 As shown in the figure, it can be seen that when the bridge has minor damage and the damage is single, even if the noise level reaches 30%, this method can still identify the damage location well, and all waveforms in the undamaged area are below the warning line. As the noise increases, the waveforms in the undamaged area fluctuate slightly.

[0179] Depend on Fig.12 It can be clearly seen that as the noise increases, the waveform of the undamaged part changes in a certain trend. Generally speaking, as the noise increases, the waveform of the undamaged part gradually increases. This shows that the noise reduction effect of this noise reduction method is negatively correlated with the noise level.

[0180] In order to better verify the robustness of this method, the working condition 2 is used to verify the recognition effect when two minor damages occur. The fusion results of working condition 2 under 10% noise are given. The damage recognition results are shown in Fig.13 .

[0181] By analyzing the situation when multiple minor damages occur and the noise level is 10%, this method can still identify the damage location well. The waveform of the undamaged part is relatively flat and does not exceed the warning line. In this paper, the value of S is relatively conservative when setting the warning line. If the safety factor S is reasonably increased, it can be adapted to identify the damage location when the noise level is high.

[0182] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A bridge damage identification method based on statistical noise reduction, characterized in that: The steps include: Step 1: Obtain bridge dynamic response data; Step 2: Preprocess the dynamic response data based on statistical algorithms to remove common factor components containing noise in the dynamic response data and obtain special factors; Step 3: Perform secondary processing on the dynamic response data before and after the damage, obtain the special factor matrix, and calculate the covariance index and acceleration energy index in turn; Step 4: The covariance index and the acceleration energy index are fused to obtain the damage identification index, and the damage location of the bridge is identified according to the damage identification index.

2. The bridge damage identification method based on statistical noise reduction according to claim 1 is characterized in that: Step 2 includes first performing coordinate rotation on the factor matrix of the dynamic response data to obtain the factor loading matrix, then calculating the factor score coefficient matrix and each factor, and then calculating the special factors.

3. The bridge damage identification method based on statistical noise reduction according to claim 1 is characterized in that: Before performing step 2, the correlation of the dynamic response data is judged. When the correlation of the dynamic response data meets the requirements, secondary processing is performed.

4. The bridge damage identification method based on statistical noise reduction according to claim 1 is characterized in that: The covariance index includes the covariance difference curvature, and the covariance difference curvature calculation formula is as follows: Where: is the covariance difference curvature of the measuring point i, is the covariance of measuring point i, and h is the distance between two adjacent measuring points.

5. The bridge damage identification method based on statistical noise reduction according to claim 4 is characterized in that: The acceleration energy index includes the acceleration energy curvature, which is calculated by the central difference method. The acceleration energy characteristic function is calculated and obtained. The calculation formula is as follows: Where: is the acceleration of node k at time t.

6. The bridge damage identification method based on statistical noise reduction according to claim 5 is characterized in that: In step 4, the data fusion formula is used to fuse the covariance index and the acceleration energy index. The data fusion formula is as follows: Where: is the basic probability distribution function of the covariance of the i-element beam, is the basic probability distribution function of the acceleration energy of the i-element beam, is the acceleration energy curvature of the measuring point k.

7. The bridge damage identification method based on statistical noise reduction according to claim 1 is characterized in that: In step 4, a damage warning line is set to determine whether damage occurs. The calculation formula of the damage warning line is as follows: Where: is the damage index of the dynamic response structure of the i-element beam; is the maximum value of the structural damage index of each unit beam segment; S is the safety factor. When , it is determined that damage has occurred in the kth unit.

8. The bridge damage identification method based on statistical noise reduction according to claim 1 is characterized in that: Step 2 involves building a special factor model: Where X is the data matrix, A is the factor loading matrix, and f is the common factor of the data matrix X. is a special factor.

9. The bridge damage identification method based on statistical noise reduction according to claim 8 is characterized in that: In step 1, when the moving load passes through the bridge, the dynamic response data of several vibration sensors preset on the bridge at each moment of duration n are recorded as follows: Where: m is the measuring point number; X mn is the dynamic response of the bridge at the nth moment collected at the mth measuring point of the structure.

10. The bridge damage identification method based on statistical noise reduction according to claim 9 is characterized in that: The vibration sensors are arranged at equal distances along the length direction of the bridge.

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