CN110568069B

CN110568069B - Beam bridge damage identification method based on average value of acceleration ratio and GPSA (general purpose analysis System) algorithm

Info

Publication number: CN110568069B
Application number: CN201910859338.5A
Authority: CN
Inventors: 阳洋; 成泉; 沈小俊
Original assignee: Chongqing University
Current assignee: Chongqing University
Priority date: 2019-09-11
Filing date: 2019-09-11
Publication date: 2021-09-14
Anticipated expiration: 2039-09-11
Also published as: CN110568069A

Abstract

The invention belongs to the technical field of bridge damage identification, and particularly relates to a beam bridge damage identification method based on an average value of acceleration ratio and a GPSA algorithm, which comprises the following steps: the method comprises the following steps of adopting two detection vehicles with fixed intervals and known parameters to stop at different positions on a bridge floor, then collecting response signals of sensors mounted on the vehicles, finally calculating the acceleration response signals of nodes on the bridge floor in a reverse mode through a theoretical formula, using the average value of the ratio of the acceleration responses of the nodes of the adjacent bridge floor as a target vector, and using the bending rigidity coefficient of each beam unit as an optimization variable in a simply supported beam optimization model, namely the bending rigidity of the beam unit calculated by finite elements in the model is as follows: and finally, taking a two-norm of the relative error between the target vector and the model vector as a target function value of the GPSA optimization, namely identifying the damage position and the damage degree.

Description

Beam bridge damage identification method based on average value of acceleration ratio and GPSA (general purpose analysis System) algorithm

Technical Field

The invention belongs to the technical field of bridge damage identification, and particularly relates to a beam bridge damage identification method based on an average value of acceleration ratio and a GPSA algorithm.

Background

The bridge structure is inevitably damaged due to long-term traffic and natural disasters. Bridge modal parameters such as frequency, mode and damping of the bridge are important information in structural diagnosis. Through the change of the modal parameters, the damage condition of the bridge can be identified. The traditional method is to directly analyze signals acquired by sensors arranged on a bridge, but the traditional monitoring problems of optimal arrangement of the sensors, difficulty in processing mass data and the like exist. Poplar and the like internationally propose indirect measurement technology for the first time, namely, a test vehicle is used for running on a bridge, and the frequency of the bridge is identified based on sensor signals collected on the test vehicle. Then, many scholars at home and abroad carry out a series of researches on the basis, and Keenahan and Obbrien preliminarily identify the damping ratio change of the bridge theoretically by analyzing the acceleration difference frequency spectrum of two axes. Oshima et al extracts bridge modes through a multi-vehicle composition test system, and then uses average MAC indexes to identify damage. Obbrien et al separately extracts bridge modes by using an improved short-time Fourier transform method for an axle coupling model, and extracts bridge frequencies by combining Empirical Mode Decomposition (EMD) to perform damage identification research without road surface roughness. Keenahan and Obbrien propose an optimization method capable of replacing a standard signal processing technology through simulation, and the optimization method is used for overcoming the nonlinear relation between a mobile vehicle acquisition signal and an axle coupling system. Li and Au propose a method to identify the damage condition of the bridge from the response of the moving vehicle based on genetic algorithms. Hester and Gonzalez show that the range of the filtered bridge acceleration response is expanded with the damage degree even under the action of high-speed load by using a three-dimensional axle coupling model. OBrien and Keenahan use test vehicles equipped with Traffic Speed Deflectors (TSD) in the process of identifying damage to bridges, by means of which the deck roughness of the bridge can be measured. Yin presents a semi-analytic solution for a moving vehicle at an initial speed and constant acceleration and deceleration through a simply supported bridge. He and the like perform wavelet transformation processing on bridge dynamic response under the moving load and perform numerical simulation research on single damage. Zhu et al summarized the inverse problem of axle coupling response identifying moving vehicle loads and bridge structural parameters, indicating that the current numerical simulation is still immature, that many factors need to be considered from practical application, and that there is a lack of experimental verification. Kong is based on an axle coupling system, a transfer rate relation is established by using a frequency response function between a bridge and a test vehicle dynamic response, and a transfer rate damage index (TDI) is established to identify the damage of the bridge. Yebin and poplar perpetual bin, etc. invert the sensor signal collected from the test car in motion to the response of the contact point between the test car in motion and the bridge deck, and higher-order bridge frequency is extracted.

Most of the above damage identification methods are limited to primarily judging whether the structure is damaged, and the judgment of the damaged position and the damaged degree is still insufficient.

Disclosure of Invention

Aiming at the defects in the prior art, the invention provides the beam bridge damage identification method based on the average value of the acceleration ratio and the GPSA algorithm, which can judge whether the structure is damaged or not, and can judge the damage position and the damage degree.

In order to solve the technical problems, the invention adopts the following technical scheme:

the method for identifying the damage of the beam bridge based on the average value of the acceleration ratio and the GPSA algorithm comprises the following steps of:

the first step is as follows: two detection vehicles with fixed spacing and known parameters are adopted to stop at different positions on the bridge floor, then response signals of sensors mounted on the vehicles, namely acceleration signals, are collected, and the acceleration response signals at nodes on the bridge floor are calculated reversely;

the second step is that: filtering the signals obtained in the first step in a first-order bridge frequency to obtain response signals only containing the first-order frequency of the bridge, then making a ratio of every two signals, performing deletion selection processing according to a set deletion threshold comparison value to obtain a stable ratio sequence of acceleration responses of two points on the bridge floor, and finally taking the average value of each sequence as a target vector;

the third step: in the simply supported beam optimization model, the bending stiffness coefficient of each beam unit is used as an optimization variable, namely the bending stiffness of the beam unit calculated by finite elements in the model is as follows: the rigidity coefficient EI can also obtain an optimized model vector which takes the bending rigidity coefficient as a variable and is formed by the average value of the acceleration response ratios of the adjacent nodes of the bridge deck;

the fourth step: and identifying the damage position and the damage degree by adopting a two-norm of the relative error between the target vector and the model vector as an objective function value of the GPSA optimization.

Drawings

FIG. 1 is a schematic diagram of an embodiment of a beam bridge damage identification method based on an average value of acceleration ratio values and a GPSA algorithm;

FIG. 2 is a numerical model diagram of an embodiment of a beam bridge damage identification method based on an average value of acceleration ratio values and a GPSA algorithm of the present invention;

FIG. 3 is a theoretical first-order bridge acceleration signal diagram in an embodiment of the method for identifying damage to a beam bridge based on an average value of acceleration ratios and a GPSA algorithm of the present invention;

FIG. 4 is a graph of acceleration signals after band-pass filtering in an embodiment of a beam bridge damage identification method based on an average value of acceleration ratio values and a GPSA algorithm of the present invention;

FIG. 5 is an acceleration comparison graph in an embodiment of the method for identifying damage to a beam bridge based on an average value of acceleration ratios and a GPSA algorithm according to the present invention;

FIG. 6 is a graph comparing acceleration on a bridge deck in an embodiment of a beam bridge damage identification method based on an average value of acceleration ratios and a GPSA algorithm according to the present invention;

FIG. 7 is a distribution diagram of ratio values over time after the acceleration responses of No. 2 and No. 3 nodes on a bridge surface are calculated back by a working condition 1 in the embodiment of the beam bridge damage identification method based on the average value of the acceleration ratio values and the GPSA algorithm and first-order bridge frequency responses are filtered;

FIG. 8 is a distribution diagram of ratio values over time after the acceleration responses of nodes No. 3 and No. 4 on a bridge surface are calculated back by a working condition 1 in the embodiment of the beam bridge damage identification method based on the average value of the acceleration ratio values and the GPSA algorithm and first-order bridge frequency responses are filtered;

FIG. 9 is a ratio sequence distribution diagram obtained after the working condition 1 filters FIG. 7 in the embodiment of the beam bridge damage identification method based on the average value of the acceleration ratio and the GPSA algorithm of the present invention;

FIG. 10 is a ratio sequence distribution diagram obtained after the working condition 1 filters FIG. 8 in the embodiment of the method for identifying damage to a beam bridge based on an average value of acceleration ratios and a GPSA algorithm;

FIG. 11 is a graph of a stiffness optimization recognition result of a working condition 1 in an embodiment of a beam bridge damage recognition method based on an average value of acceleration ratio values and a GPSA algorithm;

FIG. 12 is a graph of a stiffness optimization recognition result of a working condition 2 in an embodiment of a beam bridge damage recognition method based on an average value of acceleration ratios and a GPSA algorithm;

FIG. 13 is a graph of a stiffness optimization recognition result of working condition 3 in an embodiment of a beam bridge damage recognition method based on an average value of acceleration ratios and a GPSA algorithm of the present invention;

FIG. 14 is a graph of a stiffness optimization recognition result of a working condition 4 in an embodiment of a beam bridge damage recognition method based on an average value of acceleration ratio values and a GPSA algorithm;

FIG. 15 is a graph of a stiffness optimization recognition result of a working condition 5 in an embodiment of a beam bridge damage recognition method based on an average value of acceleration ratios and a GPSA algorithm.

Detailed Description

In order that those skilled in the art can better understand the present invention, the following technical solutions are further described with reference to the accompanying drawings and examples.

1. Method flow

Two detection vehicles with fixed spacing and known parameters are adopted, as shown in figure 1, the detection vehicles stop at different positions on the bridge floor, then response signals (acceleration signals) of sensors mounted on the detection vehicles are collected, and finally the acceleration response signals at the nodes on the bridge floor are calculated reversely through a theoretical formula. And taking the average value of the ratio of the acceleration responses of the nodes of the adjacent bridge surfaces as a target vector. And in the simply supported beam optimization model, the bending stiffness coefficient of each beam unit is taken as an optimization variable, namely the bending stiffness of the beam unit calculated by finite elements in the model is as follows: and finally, taking a two-norm of the relative error between the target vector and the model vector as an objective function value of the GPSA optimization.

2. Description of the principles of the GPSA optimization algorithm

The generalized pattern search algorithm (gps a) principle is illustrated with an example:

calculating minf (x)₁，x₂)＝x₁(x₁-x₂-7)+3x₂(x₂-1)

a) Assume an initial vector of

The initial mesh size is 1, the mesh reduction factor is 0.5, the mesh enlargement factor is 2, and the number of basic pattern vectors is 2N, i.e., 2 × 2 — 4, each of which is

b) Find f (x)₀) 0 and the pattern vectors needed for the first iteration are respectively

To find

c) Will be provided with

Are respectively connected with f (x)₀) By comparison, it is found that

Set the initial vector of the second step iteration to x₁Simultaneously order

Because the first iteration finds the ratio f (x)₀) The point of 0 is small, and this case is considered as a successful iteration, where the mode vector should be the grid size of the previous step multiplied by the grid magnification factor 2, multiplied by the base mode vector, and added with x₁Namely:

calculate and compare f (x) separately₁) And

if the vector smaller than the function value of the previous iteration cannot be found in the function values of all the mode vectors, the iteration is regarded as failed, and the basic mode vector is multiplied by a grid reduction factor of 0.5, then multiplied by the grid size of the previous iteration and added with the initial vector of the previous iteration to obtain a new mode vector.

d) Repeating the steps a) to c) until the size of the iteration grid is smaller than a set threshold value, such as 1e-7, at which time the iteration is terminated, and regarding the point which is minimum in the function value in the final mode vector as a minimum value point, and ending the search.

Numerical simulation

1. Numerical simulation model

The numerical model is shown in fig. 2, the bridge is a simple beam, which is divided into 10 units, which are respectively represented by circled numbers (r) and (r) … … (r), and meanwhile, the total number of 11 nodes is represented by

numbers

1 and 2 … … 11, the bending stiffness of each unit is represented by EI, the span of the bridge is 30m, and the distance between two detected vehicles is 3 m. Under the condition of not interrupting traffic, the

vehicles

1 and 2 are stopped at the No. 2 and No. 3 node positions respectively at the beginning to acquire signals for a period of time, and the signals are regarded as a group of signals. And then the

vehicles

1 and 2 move to the

node positions

3 and 4 respectively to collect signals for a period of time, and the process is repeated until the

vehicles

1 and 2 respectively reach the

node positions

9 and 10. The total number of 8 groups of acceleration signals is 8, the 8 groups of signals are filtered in the same frequency band (such as a first-order bridge frequency) to obtain response signals only containing the first-order frequency of the bridge, the 8 groups of signals are subjected to ratio pairwise, deletion processing is carried out according to a set deletion threshold value comparison value to obtain 8 stable ratio sequences of acceleration responses of two points on the bridge floor, and finally the average value of each sequence is taken as a target vector.

Explanation of acceleration sequence deletion principle: it can be theoretically demonstrated that the ratio of acceleration responses of certain orders at two points on the bridge surface does not change along with time, and is a fixed value, but certain signal leakage conditions exist after the acceleration responses on the bridge surface are filtered, as shown in fig. 3, 4 and 5. This leakage can cause instability in the acceleration signal ratio as shown in fig. 6.

Therefore, the comparison signal needs to be processed, a deletion threshold is set by referring to the theoretical ratio of the lossless bridge model, a deletion range can be obtained by adding or subtracting the threshold to the reference value, the ratio is reserved in the range, and the deletion is carried out when the ratio exceeds the range. For example, if the reference value of the acceleration ratio of the

nodes

2 and 3 on the bridge is 0.7 and the threshold value is set to ± 0.01, the ratio is retained between (0.69 and 0.71), deletion beyond this range is performed, and finally, the data after deletion is averaged to obtain a target value.

2. Numerical simulation results

Setting a damage working condition 1: three cells set to 10% and the censoring threshold set to 0.01

1) The distribution of the ratio over time after the acceleration responses of the nodes No. 2 and No. 3 on the bridge surface are back calculated and the first-order bridge frequency response is filtered is shown in FIG. 7, and it can be known from FIG. 7 that the ratio swings around the theoretical value of 0.53, but because certain spectrum leakage exists in the band-pass filtering, a part of the ratio is distorted, and the ratio deviates far from the theoretical value of 0.53, so that the ratio needs to be further screened. Similarly, the acceleration response ratio of other nodes on the bridge surface has certain distortion conditions, such as the ratio of No. 3 node to No. 4 node (principle of the invention)Theoretical value 0.73) over time as shown in fig. 8. In addition, the theoretical ratio of the first-order bridge acceleration response among all the nodes can be determined according to the theoretical mode of the simply supported bridge

Obtained as shown in Table a

TABLE a

Node making ratio	2 to 3	3 to 4	4 to 5	5 to 6	6 to 7	7 to 8	8 to 9	9 to 10
									Theoretical size	0.53	0.73	0.85	0.95	1.05	1.18	1.38	1.9

2) Setting a threshold value of 0.01, and screening the ratio sequence in the step 1) by combining the theoretical value of the ratio of the two nodes, wherein the screening conditions are as follows: ratios within the range of 0.01 of the theoretical value remain, and deletions outside the range. The resulting ratio sequences after screening of FIGS. 7 and 8 are shown in FIGS. 9 and 10, respectively.

3) Averaging each ratio signal after screening, namely dividing the sum of the ratios after screening by the number of the ratios to obtain a target vector V for optimization_Target(total of 8 averages).

4) The model vector V can be obtained in the same way_{Model (model)}Finally, a two-norm relative error between the model vector and the target vector is obtained, and the stiffness coefficient which enables the two-norm to be minimum is optimized by using a GPSA algorithm

The damage position and the damage degree of the bridge can be identified.

The stiffness coefficient optimization identification result of the working condition 1 is shown in fig. 11, the abscissa in fig. 11 represents the unit number, the ordinate represents the stiffness coefficient of the optimization identification, the lossless value is 1, and less than 1 represents that the unit is damaged.

Setting a damage working condition 2: three units set 20% damage, threshold: 0.01

The stiffness optimization recognition results are shown in fig. 12.

Setting a damage working condition 3: three and eight units are respectively provided with 20 percent of damage, and the threshold value is 0.01

The stiffness optimization results are shown in fig. 13.

Setting a damage working condition 4: three and eight units are respectively provided with 20 percent and 30 percent of damage, and the threshold value is 0.025

The recognition optimization results are shown in fig. 14.

Setting a damage working condition 5: three and four units are respectively provided with 20 percent and 30 percent of damage, and the threshold value is 0.025

The recognition optimization results are shown in fig. 15.

Finally, the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting, although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions may be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all of them should be covered in the claims of the present invention.

Claims

1. The method for identifying the damage of the beam bridge based on the average value of the acceleration ratio and the GPSA algorithm is characterized by comprising the following steps of:

the second step is that: filtering the signals obtained in the first-order bridge frequency to obtain response signals only containing the first-order frequency of the bridge, then making a ratio of every two signals, and performing deletion processing according to a set deletion threshold comparison value, wherein the deletion threshold is set to be 0.01, so that a stable ratio sequence of acceleration responses of two points on the bridge surface is obtained, and finally, taking the average value of each sequence as a target vector;

the third step: in the simply supported beam optimization model, the bending stiffness coefficient of each beam unit is used as an optimization variable, namely the bending stiffness of the beam unit calculated by finite elements in the model is as follows: obtaining an optimized model vector which is formed by the average value of acceleration response ratios of adjacent nodes of the bridge floor by taking the bending stiffness coefficient as a variable;

the fourth step: taking a two-norm of the relative error between the target vector and the model vector as an objective function value of the GPSA optimization, wherein the minimum value of the two-norm is

When optimizing recognitionIf the rigidity coefficient is equal to 1, judging that the bridge is not damaged; if the stiffness coefficient identified by optimization is less than 1, damage to the unit is represented.