Multi-objective optimization synergistic orthotropic steel bridge deck slab damage acoustic emission localization method

Abstract

The invention discloses a multi-objective optimization synergistic orthotropic steel bridge deck slab damage acoustic emission positioning method. Comprising the steps that 1, acoustic emission signals of the orthotropic steel bridge deck in the working state are collected through acoustic emission sensors on the four vertexes of a rectangular area to be detected; 2, deducing a shortest path formula for transmitting the acoustic emission signals from potential damage sources at different positions to the acoustic emission sensor; 3, the arrival time of a first arrival mode of the acoustic emission signals is extracted according to the Akaike information criterion, a frequency dispersion curve of the acoustic emission signals is obtained, the characteristic frequencies and wave velocities of the first arrival mode and the A0 mode are determined respectively, and the arrival time of the A0 mode of the acoustic emission signals is determined; 4, establishing a multi-objective optimization model for orthotropic steel bridge deck damage positioning according to the determined multi-mode arrival time and wave velocity parameters; and 5, solving the multi-objective optimization model through a hierarchical sequence method by taking the first layer of the multi-objective optimization model as an important objective function, and evaluating the position of the damage. According to the invention, the damage position can be accurately identified.

Description

Technical Field

[0001] The invention belongs to the field of civil engineering structure health monitoring and damage identification, and in particular relates to a multi-objective optimization and efficiency-enhanced orthogonal anisotropic steel bridge deck damage acoustic emission positioning method. Background Art

[0002] Orthotropic steel bridge decks are complex thin-walled spatial structures welded from decks, longitudinal U-ribs and transverse diaphragms. This structure has the advantages of light weight, high load-bearing capacity and convenient construction, and is the preferred bridge deck structure for medium and long span bridges. However, due to heavy vehicle loads, long-term environmental impacts, structural characteristics and manufacturing processes, fatigue cracks in orthotropic steel bridge decks are prominent, resulting in significant reductions in structural performance and driving comfort. Therefore, whether fatigue cracks in orthotropic steel bridge decks can be accurately located is crucial to the operation and maintenance of bridges throughout their life cycle. Summary of the invention

[0003] The purpose of the present invention is to provide a multi-objective optimization and efficiency-enhanced acoustic emission positioning method for orthotropic steel bridge deck damage, which overcomes the difficulty of multiple solutions in traditional acoustic emission positioning methods, can achieve more accurate damage positioning, and provide a scientific basis for the timely maintenance and repair of orthotropic steel bridge decks.

[0004] In order to solve the above technical problems, the specific technical solutions of the present invention are as follows:

[0005] A multi-objective optimization and efficiency-enhanced orthotropic steel bridge deck damage acoustic emission positioning method comprises the following steps:

[0006] Step S1, collecting acoustic emission signals of the orthotropic steel bridge deck in a working state through acoustic emission sensors at four vertices of the rectangular area to be measured;

[0007] Step S2, according to the complex spatial thin-wall geometric structure of the orthotropic steel bridge deck, deriving the shortest path formula for the acoustic emission signal propagating from the potential damage sources at different positions to the acoustic emission sensor;

[0008] Step S3, using the Akaike information criterion to extract the arrival time of the first arrival mode of the acoustic emission signal, obtaining the dispersion curve of the acoustic emission signal through the lamb wave dispersion theory, determining the characteristic frequency and wave velocity of the first arrival mode and the A0 mode respectively, and determining the arrival time of the A0 mode of the acoustic emission signal by wavelet transform;

[0009] Step S4, establishing a multi-objective optimization model for orthotropic steel bridge deck damage location using the shortest path derived in step S2 and the multi-mode arrival time and wave velocity parameters determined in step S3;

[0010] S5. Taking the first layer of the multi-objective optimization model as the important objective function, the multi-objective optimization model is solved by the hierarchical sequence method to evaluate the location of the acoustic emission source, that is, the location of the damage.

[0011] Further, in step S2, the acoustic emission signal transmits energy in the plate structure in the most effective path, that is, the shortest path, which is called the geodesic distance; the orthotropic steel bridge deck is a thin-walled space structure composed of a panel and a U-rib welded together, the longitudinal direction of the orthotropic steel bridge deck is along the extension direction of the U-rib, and the transverse direction is along the cross-sectional direction of the U-rib opening, and has multiple acoustic emission signal propagation paths; the acoustic emission signal propagates through the panel and the U-rib; the geodesic distance is related to the path of the initial arrival component of the acoustic emission signal, and theoretically the geodesic distance is the path of the initial arrival component of the acoustic emission signal; the orthotropic steel bridge deck is l long and w wide, the U-rib opening width is w1, the bottom width is u1, the depth is h, the U-rib cross-section length is u, and there are two dividing lines on the U-rib defined by the following formula:

[0012]

[0013] Among them, w2 is the distance from the weld on the panel to the acoustic emission sensor in the transverse direction, u2 is the distance from the dividing line on the U rib to the bottom of the U rib in the transverse direction, and u3 is the distance from the dividing line on the U rib to the weld in the transverse direction. Based on the two dividing lines and the weld, the steel bridge deck is divided into four areas. The U rib is unfolded into a plane to obtain two sub-domains D1 and D2 of the optimized search of the orthogonal anisotropic steel bridge deck. The sub-domain D1 corresponds to the panel, and the sub-domain D2 corresponds to the U rib. The coordinate system is established with the center of the panel as the coordinate origin. The expressions of the two sub-domains are as follows:

[0014]

[0015] The coordinate system of the subdomain D1 is represented by x f and f , the coordinate system of the subdomain D2 is represented by x u and u .

[0016] Furthermore, in step S2, the formula for the shortest path from the damage source to the four acoustic emission sensors is derived as follows:

[0017]

[0018]

[0019] Among them, d1, d2, d3, and d4 are the geodesic paths of the potential damage sources at different locations to reach the four acoustic emission sensors. The shortest path from the source to the sensor calculated by formulas (3)-(6) is considered to be the actual propagation distance of the acoustic emission signal.

[0020] Furthermore, in step S4, the proposed multi-objective optimization model expression is:

[0021]

[0022] Among them, E(x f ,y f ,x u ,y u ) and E'(x f ,y f ,x u ,y u ) are the first-level objective function and the second-level objective function of the multi-objective optimization model respectively; Δt ij is the arrival time of the first arrival mode of the acoustic emission signal collected by the i-th sensor and the j-th sensor; d i and d j are the geodesic distances from the damage source to the i-th sensor and the j-th sensor respectively; v s is the wave velocity of the first arrival mode of the acoustic emission signal; in the second level objective function of the multi-objective optimization model, d i,M is the propagation distance of the acoustic emission signal calculated using formula (8):

[0023] d i,M =(t i,A -t i,S )×v S ×v A / (v S -v A ) (8)

[0024] In formula (9), t i,S and t i,A are the arrival times of the acoustic emission signal in the first arrival mode and A0 mode, respectively, and v A is the wave velocity of the A0 mode of the acoustic emission signal.

[0025] Furthermore, in step S5, the steps of solving the multi-objective optimization model using the hierarchical sequence method are as follows:

[0026] Step S5.1, set E(x f ,y f ,x u ,y u ) is an important objective function of the multi-objective optimization model, E'(x f ,y f ,x u ,y u )

[0027] It is the second most important objective function;

[0028] Step S5.2: Genetic algorithm is used to calculate the function E(x f ,y f ,x u ,y u )

[0029] Optimize and find the optimal solution set Ω;

[0030] Step S5.3: If Ω is unique, then output the damage location. If Ω is not unique, then search for the next most important objective function E'(x f ,y f ,x u ,y u ) obtains the coordinates of the minimum value and outputs the location of the acoustic emission source, that is, the location of the damage.

[0031] The multi-objective optimization and efficiency-enhanced orthotropic steel bridge deck damage acoustic emission positioning method of the present invention has the following advantages:

[0032] (1) The present invention is a multi-objective optimization and efficiency-enhanced acoustic emission positioning method for orthotropic steel bridge deck damage. The formula for calculating the shortest distance between the damage source and the sensor is derived based on the complex spatial thin-walled geometric structure of the orthotropic steel bridge deck.

[0033] (2) The present invention is a multi-objective optimization and synergistic method for locating damage of orthotropic steel bridge decks using acoustic emission. The multi-objective optimization model used for locating damage of orthotropic steel bridge decks overcomes the difficulty that traditional optimization-based positioning methods cannot be applied to acoustic emission positioning of spatial thin-walled structures.

[0034] (3) The present invention is a method for locating damaged acoustic emission of orthotropic steel bridge decks with multi-objective optimization and synergy. According to the accuracy differences of multiple modes of arrival time of acoustic emission signals in the multi-objective model, the first layer of the multi-objective optimization model is used as the important objective function. The multi-objective optimization model is solved by the hierarchical sequence method to obtain more accurate damage source location. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 A flow chart of a multi-objective optimization and efficiency-enhanced orthotropic steel bridge deck damage acoustic emission positioning method of the present invention;

[0036] Figure 2 This is a schematic diagram of the geometric structure of the ribbed surface of a typical orthotropic steel bridge deck;

[0037] Figure 3 Schematic diagram of an artificial lead breaking test specimen of a steel bridge deck specimen according to an embodiment of the present invention;

[0038] Figure 4 A schematic diagram of test point distribution according to an embodiment of the present invention;

[0039] Figure 5 It is a schematic diagram of the artificial lead breaking experiment setting of the steel bridge deck specimen of the present invention;

[0040] Figure 6 Schematic diagram of arrival time extraction for typical acoustic emission signals and Akaike Information Criterion;

[0041] Figure 7 This is a schematic diagram of the theoretical dispersion curve of Lamb waves of a 20 mm thick Q345 steel plate according to an embodiment of the present invention;

[0042] Figure 8 It is a typical acoustic emission signal spectrum diagram;

[0043] Fig. 9 It is a spectrum diagram of the first arrival mode of an embodiment of the present invention;

[0044] Fig.10 This is a schematic diagram of A0 mode arrival time determination according to an embodiment of the present invention;

[0045] Fig.11 The verification result of a multi-objective optimization and efficiency-enhanced orthotropic steel bridge deck damage acoustic emission localization method of the present invention;

[0046] Fig.12 This is the verification result of the traditional optimization-based positioning method. DETAILED DESCRIPTION

[0047] In order to better understand the purpose, structure and function of the present invention, a multi-objective optimization and efficiency-enhanced orthotropic steel bridge deck damage acoustic emission positioning method of the present invention is further described in detail below in conjunction with the accompanying drawings.

[0048] Embodiment 1:

[0049] The main content of this embodiment is the artificial lead breaking experiment of steel bridge deck specimens, which is used to verify the effectiveness and practicality of the multi-objective optimization and efficiency-enhanced orthogonal anisotropic steel bridge deck damage acoustic emission positioning method proposed in this patent. Figure 1 shown.

[0050] The present invention provides a multi-objective optimization and efficiency-enhanced orthotropic steel bridge deck damage acoustic emission positioning method, comprising the following steps:

[0051] Step 1. The experimental equipment used is a multi-channel acoustic emission data acquisition system. The acoustic emission sensor is a WD model sensor with a frequency range of 100-1000kHz. The acoustic emission sensor is installed on the high-strength bolt connection node using a magnetic clamp and coupling agent, and then connected to the data acquisition board through a preamplifier for acoustic emission data acquisition. The amplification factor is set to 40dB and the sampling rate is set to 5MS / s. In order to filter out possible noise, a 100-1000kHz bandpass filter is set.

[0052] Step 2 Figure 2 Figure 1 is a schematic diagram of the geometric structure of a typical orthotropic steel bridge deck with ribbed surface. The acoustic emission signal transmits energy in the plate structure in the most effective path, that is, the shortest path, which is called the geodesic distance. The orthotropic steel bridge deck is a thin-walled spatial structure composed of a panel and a U-rib welded together. The longitudinal direction of the orthotropic steel bridge deck is along the extension direction of the U-rib, and the transverse direction is along the cross-sectional direction of the U-rib opening. It has multiple acoustic emission signal propagation paths. These acoustic emission signals are not only propagated through the panel, but also through the U-rib. The geodesic distance is related to the path of the initial arrival component of the acoustic emission signal. The length of the orthotropic steel bridge deck is l, the width is w, the width of the U-rib opening is w1, the bottom width is u1, the depth is h, the length of the U-rib cross section is u, and there are two dividing lines on the U-rib that satisfy the following formula:

[0053]

[0054] Among them, w2 is the distance from the weld on the panel to the acoustic emission sensor in the transverse direction, u2 is the distance from the dividing line on the U rib to the bottom of the U rib in the transverse direction, and is the distance from the dividing line to the weld in the transverse direction. Based on the above two dividing lines and welds, the steel bridge deck is divided into four areas. The U rib is unfolded into a plane, and two sub-domains D1 and D2 of the optimized search of the orthogonal anisotropic steel bridge deck are obtained. The sub-domain D1 corresponds to the panel, and the sub-domain D2 corresponds to the U rib. The coordinate system is established with the center of the panel as the coordinate origin. The expressions of the two sub-domains are as follows:

[0055]

[0056] The coordinate system of the subdomain D1 is represented by x f and f , the coordinate system of the subdomain D2 is represented by x u and u The formula for the shortest path from the damage source to the four acoustic emission sensors is derived as follows:

[0057]

[0058] Among them, d1, d2, d3, and d4 are the geodesic paths of the potential damage sources at different locations propagating to the four acoustic emission sensors. The dimensions of the steel bridge deck specimen in this embodiment are as follows: Figure 3 As shown, the steel plate is made of Q345 steel with a yield strength of 345MPa and an ultimate strength of 490MPa. The length and width of the panel are both 1500mm, and the thickness is 20mm. The U-rib section is 300×200×245mm (opening width×bottom width×depth), and the thickness is 8mm. The test area on the panel is 800mm wide and 1200mm long. 20 test points were selected to simulate the damage source using the lead breaking experiment. Figure 4 Schematic diagram of test point distribution. Figure 5 Schematic diagram of the artificial lead breaking test setup for steel bridge deck specimens;

[0059] According to the geometric structure of the steel bridge deck, substituting into formula (17), we get u1, u2, u3 are 200, 50, 200 mm respectively, and w1, w2 are 300, 250 mm respectively. Substituting into formulas (18)-(22), we get the following formula:

[0060]

[0061]

[0062] The shortest path from the damage source to the sensor in the steel bridge deck of the embodiment can be calculated by equations (24)-(27), which is the actual propagation distance of the acoustic emission signal.

[0063] Step 3: For the collected acoustic emission signals, the arrival time of the first arrival mode is extracted using the Akaike information criterion. The result is as follows: Figure 6 According to the material properties and thickness of the steel bridge deck, the schematic diagram of the theoretical dispersion curve of Lamb waves of 20mm thick Q345 steel plate is shown in Figure 7 As shown. Through fast Fourier transform, we can get Figure 8 The typical acoustic emission signal spectrum is shown in Figure 2. Figure 8 It can be seen that the acoustic emission signal has almost no energy distribution below 100kHz. For frequencies above 100kHz, the group velocity of the S0 mode is less than 4600m / s. Therefore, the initial mode obtained is no longer the S0 mode. The energy in the frequency domain is mainly distributed around 130kHz and 200kHz, corresponding to the A0 mode and the S1 mode. A waveform with 200 sampling points before and after the arrival time of the first arrival mode is selected, and the following is obtained by fast Fourier transform: Fig. 9 The frequency domain characteristics are shown in Figure 10, and the first arrival mode is found to be the S1 mode near 200kHz. Then, the fastest wave velocity of the S1 mode is found in the dispersion curve to be 4933m / s at 211kHz. The A0 mode arrival time is extracted using wavelet transform and is shown in Figure 10, a schematic diagram of the A0 mode arrival time determination.

[0064] Step 4: Use the shortest path derived in step 2 and the multi-mode arrival time and wave velocity parameters determined in step 3 to establish a multi-objective optimization model for damage location of orthotropic steel bridge decks.

[0065]

[0066] Among them, E(x f ,y f ,x u ,y u ) and E'(x f ,y f ,x u ,y u ) are the first-level objective function and the second-level objective function of the multi-objective optimization model respectively; Δt ij is the arrival time of the first arrival mode of the acoustic emission signal collected by the i-th sensor and the j-th sensor; d i and d j are the geodesic distances from the damage source to the i-th sensor and the j-th sensor respectively; v s is the wave velocity of the first arrival mode of the acoustic emission signal; in the second level objective function of the multi-objective optimization model, d i,M is the propagation distance of the acoustic emission signal calculated using formula (29):

[0067] d i,M =(t i,A -t i,S )×v S ×v A / (v S -v A ) (29)

[0068] In formula (29), t i,S and t i,A are the arrival times of the acoustic emission signal in the first arrival mode and A0 mode, respectively, and v A is the wave velocity of the acoustic emission signal A0 mode. Substituting the steel bridge deck parameters of the embodiment into the multi-objective optimization model:

[0069]

[0070] Step 5: Use the hierarchical sequence method to solve the multi-objective optimization model. First, search for the optimal solution set of the first-layer function of the multi-objective model in the four areas of the steel bridge deck. If the optimal solution is unique, the output is the damage location. If the optimal solution of the first-layer function is not unique, the second-layer function is solved on the solution set, and then the unique damage location is output. Finally, the positioning error of the multi-objective optimization and efficiency-enhanced orthogonal anisotropic steel bridge deck damage acoustic emission positioning method proposed in this patent at 20 test points is: average error 49mm, standard deviation 56mm, see for details Fig.11Verification results of a multi-objective optimization and efficiency-enhanced orthogonal anisotropic steel bridge deck damage acoustic emission location method. In order to highlight that the multi-objective optimization and efficiency-enhanced orthogonal anisotropic steel bridge deck damage acoustic emission location method proposed in this patent has a high damage location accuracy, it is compared with the traditional optimization-based acoustic emission location method. The error of the traditional optimization-based acoustic emission location method is: average error 94mm, standard deviation 84mm, the results are shown in detail. Fig.12 Verification results of traditional optimization-based positioning methods. By comparison, it is found that the positioning accuracy of the multi-objective optimization and efficiency-enhanced orthogonal anisotropic steel bridge deck damage acoustic emission positioning method proposed in this patent is improved by 1.9 times.

[0071] It is to be understood that the present invention is described by some embodiments, and it is known to those skilled in the art that various changes or equivalent substitutions may be made to these features and embodiments without departing from the spirit and scope of the present invention. In addition, under the teachings of the present invention, these features and embodiments may be modified to adapt to specific circumstances and materials without departing from the spirit and scope of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the scope of protection of the present invention.

Claims

1. A multi-objective optimization and efficiency-enhanced orthotropic steel bridge deck damage acoustic emission positioning method, characterized in that: The steps include: Step S1, collecting acoustic emission signals of the orthotropic steel bridge deck in a working state through acoustic emission sensors at four vertices of the rectangular area to be measured; Step S2, according to the complex spatial thin-wall geometric structure of the orthotropic steel bridge deck, deriving the shortest path formula for the acoustic emission signal propagating from the potential damage sources at different positions to the acoustic emission sensor; Step S3, using the Akaike information criterion to extract the arrival time of the first arrival mode of the acoustic emission signal, obtaining the dispersion curve of the acoustic emission signal through the lamb wave dispersion theory, determining the characteristic frequency and wave velocity of the first arrival mode and the A0 mode respectively, and determining the arrival time of the A0 mode of the acoustic emission signal by wavelet transform; Step S4, establishing a multi-objective optimization model for orthotropic steel bridge deck damage location using the shortest path derived in step S2 and the multi-mode arrival time and wave velocity parameters determined in step S3; S5. Taking the first layer of the multi-objective optimization model as the important objective function, the multi-objective optimization model is solved by the hierarchical sequence method to evaluate the location of the acoustic emission source, that is, the location of the damage.

2. The multi-objective optimization and efficiency-enhanced orthotropic steel bridge deck damage acoustic emission positioning method according to claim 1 is characterized in that: In step S2, the acoustic emission signal transmits energy in the plate structure in the most effective path, that is, the shortest path, which is called the geodesic distance; the orthotropic steel bridge deck is a thin-walled space structure composed of a panel and a U-rib welded together, the longitudinal direction of the orthotropic steel bridge deck is along the extension direction of the U-rib, and the transverse direction is along the cross-sectional direction of the U-rib opening, and has multiple acoustic emission signal propagation paths; the acoustic emission signal propagates through the panel and the U-rib; the geodesic distance is related to the path of the initial arrival component of the acoustic emission signal; the orthotropic steel bridge deck is l long and w wide, the U-rib opening width is w1, the bottom width is u1, the depth is h, the U-rib cross-section length is u, and there are two dividing lines on the U-rib defined by the following formula: Among them, w2 is the distance from the weld on the panel to the acoustic emission sensor in the transverse direction, u2 is the distance from the dividing line on the U rib to the bottom of the U rib in the transverse direction, and u3 is the distance from the dividing line on the U rib to the weld in the transverse direction. Based on the two dividing lines and the weld, the steel bridge deck is divided into four areas. The U rib is unfolded into a plane to obtain two sub-domains D1 and D2 of the optimized search of the orthogonal anisotropic steel bridge deck. The sub-domain D1 corresponds to the panel, and the sub-domain D2 corresponds to the U rib. The coordinate system is established with the center of the panel as the coordinate origin. The expressions of the two sub-domains are as follows: The coordinate system of the subdomain D1 is represented by x f and f , the coordinate system of the subdomain D2 is represented by x u and u .

3. The multi-objective optimization and efficiency-enhanced orthotropic steel bridge deck damage acoustic emission positioning method according to claim 2 is characterized in that: In step S2, the formula for the shortest path from the damage source to the four acoustic emission sensors is derived as follows: Among them, d1, d2, d3, and d4 are the geodesic paths of the potential damage sources at different locations to reach the four acoustic emission sensors. The shortest path from the source to the sensor calculated by formulas (3)-(6) is considered to be the actual propagation distance of the acoustic emission signal.

4. The multi-objective optimization and efficiency-enhanced orthotropic steel bridge deck damage acoustic emission positioning method according to claim 3 is characterized in that: In step S4, the proposed multi-objective optimization model expression is: Among them, E(x f ,y f ,x u ,y u ) and E'(x f ,y f ,x u ,y u ) are the first-level objective function and the second-level objective function of the multi-objective optimization model respectively; Δt ij is the arrival time of the first arrival mode of the acoustic emission signal collected by the i-th sensor and the j-th sensor; d i and d j are the geodesic distances from the damage source to the i-th sensor and the j-th sensor respectively; v s is the wave velocity of the first arrival mode of the acoustic emission signal; in the second level objective function of the multi-objective optimization model, d i,M is the propagation distance of the acoustic emission signal calculated using formula (8): d i,M =(t i,A -t i,S )×v S ×v A / (v S -v A ) (8) In formula (9), t i,S and t i,A are the arrival times of the acoustic emission signal in the first arrival mode and A0 mode, respectively, and v A is the wave velocity of the A0 mode of the acoustic emission signal.

5. The multi-objective optimization and efficiency-enhanced orthotropic steel bridge deck damage acoustic emission positioning method according to claim 4 is characterized in that: In step S5, the steps of solving the multi-objective optimization model using the hierarchical sequence method are: Step S5.1, set E(x f ,y f ,x u ,y u ) is an important objective function of the multi-objective optimization model, E'(x f ,y f ,x u ,y u ) is the secondary important objective function; Step S5.2: Genetic algorithm is used to calculate the function E(x f ,y f ,x u ,y u ) to optimize and find its optimal solution set Ω; Step S5.3: If Ω is unique, then output the damage location. If Ω is not unique, then search for the next most important objective function E'(x f ,y f ,x u ,y u ) obtains the coordinates of the minimum value and outputs the location of the acoustic emission source, that is, the location of the damage.

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