A method for identifying infrastructure damage based on an improved MCMC method

Abstract

The application relates to a method and system for identifying infrastructure damage based on an improved MCMC method. The method comprises the following steps: acquiring a mode of a test cantilever beam; forming a population according to a Markov chain obtained from a standard MH algorithm according to the measured mode; iteratively including a normal period with only differential evolution and a competition period with competition after the normal period; obtaining two groups of correction vectors after mutation, crossover and selection in each iteration in the competition period, combining the two groups of correction vectors with correction vectors in the normal period, and recording two groups of complete iteration Markov chain parameter optimization schemes as Y W and Y L ; calculating the average value of the corrected parameters after convergence as Y W and Y L , learning Y W from the winner and Y L from the loser, and taking Y W as the optimal correction scheme according to comparison with the existing measured mode. By adopting the scheme, the calculation efficiency is high, the precision is higher, and the robustness of the system is stronger.

Description

Technical Field

[0001] This invention relates to the field of structural monitoring technology, and in particular to a method for identifying structural damage based on an improved MCMC method. Background Technology

[0002] Due to my country's vast territory and development needs, numerous civil infrastructure projects, such as bridges, buildings, towers, pipelines, tunnels, dams, and other structures, have been constructed over the past few decades. Today, these structures suffer cumulative damage and degradation over time. For civil structures, the safety maintenance and health monitoring of actual engineering structures are crucial to national economic and public safety; therefore, early identification of structural damage is extremely important and necessary. Structural health monitoring plays a vital role in providing performance information throughout a structure's lifespan. However, directly using information extracted from monitoring data to determine structural health is often subject to numerous uncertainties and is insufficient for investigating structural service conditions. Furthermore, regardless of the complexity of computer modeling, errors are inevitable. These errors can be broadly categorized into three types based on their origin: first, mathematical modeling errors resulting from simplifying complex actual structural behavior, including simplifications of boundary conditions, connections, and geometry; second, model order errors caused by discretizing continuous systems into finite element models; and third, physical parameter errors caused by incorrect assignment of various model parameters. Finite element model correction is a recognized and reliable method to ensure effective damage identification. Therefore, model correction is performed by obtaining effective structural responses, and the accuracy of the corrected model plays a crucial role in subsequent damage identification.

[0003] Among numerous finite element model correction methods, Bayesian correction procedures are widely used to reduce the impact of uncertainties in structural parameters and vibration measurements, and have a good effect on improving the correlation between the test structure and its related finite element models. The method combining Bayesian methods with Markov Chain Monte Carlo (MCMC) has matured in recent years and has become an important method for correcting structural finite element models and solving uncertainties. Currently, the Metropolis-Hastings algorithm (MH) is widely used to solve calculations involving complex posterior distributions or even non-explicit integrals in Bayesian theory. Its idea is to use random sampling from a probability distribution to replace computation. However, the MH-MCMC algorithm still has many drawbacks. For example, the sampling rejection mechanism of the MH algorithm often leads to stagnation in sample iteration; it suffers from low sampling efficiency and poor sample convergence when dealing with high-dimensional complex integrals of large civil structures; and it has poor robustness to noise interference. Therefore, it is extremely important to study a method that can consider the impact of uncertainties, has high correction accuracy and efficiency, and possesses good robustness.

[0004] To address the shortcomings of the MH-MCMC algorithm, particularly the poor efficiency in correcting high-dimensional parameter models, a Differential Evolution (DE) algorithm is introduced. DE is a simple genetic algorithm for numerical optimization in real-parameter space, used to overcome the stagnation problem in the correction process of high-dimensional parameter models. Based on this, a Competition-Based (CB) algorithm is proposed. In this algorithm, a Markov chain population undergoes mutation and crossover using the standard DE algorithm, accompanied by competition. In this competition, samples that are rejected during mutation and crossover learn from the winners, attempting to learn their advantages and narrow the gap with the objective function. The winners then randomly select existing optimization schemes from the Markov chain population for comparison and optimization, further improving the accuracy of model correction. However, existing algorithms suffer from low efficiency and poor optimization results, primarily due to slow convergence and insufficient intermediate correction capabilities, making it difficult to correct initial random errors. Summary of the Invention

[0005] This invention aims to provide a solution to any of the aforementioned problems. Specifically, this invention provides an identification method for solving any of the aforementioned problems. More specifically, this invention provides a basic structure damage identification method based on an improved MCMC method, wherein the basic structure includes cantilever beams, simply supported beams, continuous beams, bridge piers, buildings, towers, pipelines, tunnels, dams, etc. The method includes the following steps:

[0006] 1. Test the modal data acquisition of the cantilever beam, specifically including setting up several acceleration sensors on the cantilever beam and applying a vertical single-point pulse on the cantilever beam through an excitation device; the acceleration sensors collect response signal data, and the signal data is processed to obtain the modal information of the cantilever beam;

[0007] 2. Based on the measured modes, the Markov chain is obtained using the standard MH algorithm. The test is repeated multiple times to obtain multiple Markov chains to form a backup population.

[0008] 3. Iteration includes a normal phase consisting only of differential evolution and a competitive phase following the normal phase. When the iteration is in the normal phase:

[0009] 3.1 Randomly select a Markov chain Y from the Markov chain population t s Y is obtained based on mutations in differential evolution. t sp ;

[0010] 3.2 Based on the crossover in differential evolution, the mutation vector is... With native vectors Crossover yields the correction vector

[0011] 3.3 Calculate the normal period corrected acceptance probability r1,

[0012] 3.4 Based on the selection strategy in differential evolution, select the correction vector Y. t su ,in

[0013] 4. During the iteration phase, when there is competition:

[0014] 4.1 Randomly select a Markov chain from the Markov chain population, denoted as Y. t g (g≠s,a,b), and identify the winner (W). t s ) and losers (L t s );

[0015] 4.2 If the loser is obtained (L) t s ),but

[0016] a. Obtain L s t The mutation vector L t sp (s≠c,d);

[0017]

[0018] In the formula: L represents the loser; γ' is the mutation scaling factor, the larger the value, the higher the degree of mutation, generally taken as [0.5, 1.0], for the scheme of this invention, it is more preferably between [0, 0.6]. Experiments have found that unreasonable selection will affect the convergence process and indirectly affect the accuracy; the superscripts c and d are the indices of the Markov chain; e is the normal distribution N(0,k). d The extracted vector group, where d modifies the dimension of the vector, and k is typically chosen to be 10. -6 .

[0019] b. The mutation vector L will be obtained. t sp Each mutation value L in (s≠c,d) t (s,w)p With the winner W t s W at each corresponding position t (s,w) The crossover yields the correction vector L. t suCross value L corresponding to positions 1 to w t (s,w)u ;

[0020]

[0021] c. Obtain the corrected vector L of the loser after learning from the winner. t su Compared to the original L t s The acceptance probability is r2.

[0022]

[0023] d. Select the optimized L t s .

[0024]

[0025] 4.3. If the winner is W t s ,but

[0026] a. Obtain W t s The mutation vector W t sp (s≠e,f):

[0027]

[0028] b. The mutation vector W will be obtained. t sp Each mutation value W in (s≠e,f) t (s,w)p With the winner W t s W at the corresponding position t (s,w) The correction vector W obtained by the following crossover is... t su The cross value W corresponds to positions 1 to w. t (s,w)u :

[0029]

[0030] c. Obtain the winner's correction vector W t su Compared to the original W t s Acceptance probability r3:

[0031]

[0032] d. Select W after optimization in step 8). t s .

[0033]

[0034] 5. During the competition period, after each iteration involving mutation, crossover, and selection, two sets of correction vectors W are obtained. t s and L t s (At this point, t = m ~ T), and the correction vector Y of the normal period, respectively. t su Combining these (where t = 1 to m), we obtain two complete sets of Markov chain parameter optimization schemes after iteration (where t = 1 to T), denoted as Y. W and Y L ;

[0035] Where: T is the total number of iterations; m is the starting step number for entering the competition period;

[0036] 6. Based on the winner Y W Y, which is obtained by the losers learning from the winners. L The average value of the corrected parameters after convergence is denoted as . and And based on comparison with existing measured modes and The option with the smallest difference is selected as the optimal correction scheme.

[0037] In one implementation, the method for determining the number of iterations m between the normal period and the competition period is as follows: m is selected as the number of iterations that is 8-15% greater than the convergence threshold of the Markov chain, more preferably 10%. Studies have found that if m is too small, it will affect the convergence of the algorithm; if the value is too large, exceeding the convergence threshold by too much, it will eliminate the competition effect, resulting in more normal periods and affecting the correction accuracy and efficiency. The method for determining the number of iterations proposed in this application can improve efficiency and ensure accuracy, and its effect is significantly better than the general methods in the prior art.

[0038] In one implementation, the number of Markov chains forming the backup population is 4-10, more preferably 7. The applicant's research found that beyond 7 chains, especially beyond 10, the improvement in accuracy is limited. The research also found that using the method of this invention, a quantity of 7 chains is just sufficient for one complete damage identification. Since the Markov chains used for crossover and mutation are all different and not reused, before 7 chains, each additional chain significantly improves accuracy. After 7 chains, the increased population diversity also improves accuracy, but the computational cost-effectiveness is not as good as the increase from the first 7 chains.

[0039] In one implementation scheme, Y is obtained based on mutations in differential evolution. t sp The formula is as follows:

[0040]

[0041] In the formula: Y is the Markov chain; superscripts s, a, b are the indices of the Markov chain; superscript p represents the mutation vector; subscript t is the current iteration step; γ is the mutation scaling factor, the larger the value, the higher the mutation degree, generally taken as [0.4, 1.0]; e is the mutation vector from the normal distribution N(0,k). d The extracted vector group, where d modifies the dimension of the vector, and k is typically chosen to be 10. -6 .

[0042] In one implementation, the crossover yields a correction vector Y. t su =(Y t (s,1)u ,Y t (s,2)u ,Y t (s,3)u ,...,Y t (s,D)u The formula for ) is:

[0043]

[0044] In the formula: Y is an element in a set of correction vectors of the Markov chain; the superscript s is the index of the Markov chain; the superscript u represents the correction vector; the superscript w is the index of the correction parameters included in each Markov chain at the current iteration step t, w = 1, 2, 3, ..., D; D is the number of parameters to be corrected in each Markov chain; CR is the crossover probability with a value range of [0.0, 1.0]; w rand Let t be a random number in the range [1, D]; the subscript t represents the current iteration step.

[0045] In one implementation, the suspended portion of the steel beam is divided into multiple units, with the installation location at the node of each cantilever steel beam unit.

[0046] In one implementation, applying a vertical single-point pulse to the cantilever beam via an excitation device means applying a vertical single-point pulse to the cantilever beam at its furthest point from the wall.

[0047] The present invention also provides a basic structure damage identification system based on an improved MCMC method, including an acceleration sensor, an excitation device, and a processor. The system is characterized in that: multiple acceleration sensors are arranged on the cantilever steel beam to detect the vertical acceleration of the cantilever steel beam; the excitation device is used to apply vertical single-point pulse excitation to the steel beam.

[0048] The processor is used to detect damage to the cantilever steel beam according to the method described in any of the preceding embodiments.

[0049] The solution adopted in this application has the following effects:

[0050] 1) High computational efficiency, because candidates only participate in the competition once, and the losers try to get closer to the winners. Therefore, during the competition period, half of the elements (correction vectors) of each Markov chain win through the competition, and the other half of the elements (correction vectors) will converge in the direction of convergence of the winning half of the elements.

[0051] 2) The optimization effect is better because the addition of the difference algorithm means that the winner and loser only have a temporary lead. The three operations of mutation, crossover and selection in the difference algorithm enable the winner to find the best solution, and the loser can still surpass the winner by quickly learning from the winner.

[0052] 3) The method is more robust to noise because it uses a multi-chain approach to build the Markov chain population, resulting in higher utilization of test information compared to existing methods. Attached Figure Description

[0053] Figure 1 This is a flowchart of the method of the present invention;

[0054] Figure 2 This is a schematic diagram of the cantilever steel beam unit division structure of the present invention;

[0055] Figure 3 The mean value of the first order frequency and the mean value of the first four normalized vibration modes were obtained from actual measurements of the cantilever steel beam.

[0056] Figure 4 The diagram shows the correction process of the existing MCMC algorithm and the algorithm of this invention;

[0057] Figure 5 The above are histograms of the frequency of damage identification for parameter θ1 in the existing MCMC algorithm and the algorithm of this invention. Detailed Implementation

[0058] To make the technical solutions and advantages of the present invention clearer, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. Some technical terms and expressions used herein have the same meaning as understood by those skilled in the art to which this application pertains.

[0059] See Figure 1 This application discloses a structural damage identification method based on an improved MCMC method, comprising the following steps:

[0060] 1. Test the modal data acquisition of the cantilever beam, specifically including setting up several acceleration sensors on the cantilever beam and applying a vertical single-point pulse on the cantilever beam through an excitation device; the acceleration sensors collect response signal data, and the signal data is processed to obtain the modal information of the cantilever beam;

[0061] 2. Based on the measured modes, the Markov chains are obtained using the standard MH algorithm (Metropolis–Hastings algorithm, MH). The tests are repeated multiple times to obtain multiple Markov chains to form a backup population.

[0062] 3. Iteration includes a normal phase consisting only of differential evolution and a competitive phase following the normal phase. When the iteration is in the normal phase:

[0063] 3.1 Randomly select a Markov chain Y from the Markov chain population t s Y is obtained based on mutations in differential evolution. t sp ;

[0064] 3.2 Based on the crossover in differential evolution, the mutation vector is... With the original vector Y t s =(Y t (s,1) ,Y t (s,2) ,Y t (s,3) ,...,Y t (s,D) The crossover yields the correction vector.

[0065] Y t su =(Y t (s，1)u Y t (s，2)u Y t (s，3)u , ..., Y t (s，D)u ),

[0066] 3.3 Calculate the normal period corrected acceptance probability r1,

[0067] In the formula: F is the difference between the calculated value and the test value, set as the objective function;

[0068] 3.4 Based on the selection strategy in differential evolution, select the correction vector Y. t su ,in

[0069] 4. During the iteration phase, when there is competition:

[0070] 4.1 Randomly select a Markov chain from the Markov chain population, denoted as Y. t g (g≠s,a,b), and identify the winner (W). t s ) and losers (L t s );

[0071] 4.2 If the loser is obtained (L) t s ),but

[0072] a. Obtain L s t The mutation vector L t sp (s≠c,d);

[0073]

[0074] In the formula: c and d are the indices of the Markov chain in the population;

[0075] b. The mutation vector L will be obtained. t sp Each mutation value L in (s≠c,d) t (s,w)p With the winner W t s W at each corresponding position t (s,w) The crossover yields the correction vector L. t su Cross value L corresponding to positions 1 to w t (s,w)u ;

[0076]

[0077] c. Obtain the corrected vector L of the loser after learning from the winner. t su Compared to the original L t s Acceptance probability r2

[0078]

[0079] d. Select the optimized L t s .

[0080]

[0081] 4.3. If the loser W is obtained. t s ,but

[0082] a. Obtain W t s The mutation vector W t sp (s≠e,f):

[0083]

[0084] In the formula: e, f are the indices of the Markov chain in the population;

[0085] b. The mutation vector W will be obtained. t sp Each mutation value W in (s≠e,f) t (s,w)p With the winner W t s W at the corresponding position t (s,w) The correction vector W obtained by the following crossover is... t su The cross value W corresponds to positions 1 to w. t (s,w)u :

[0086]

[0087] c. Obtain the winner's correction vector W t su Compared to the original W t s Acceptance probability r3:

[0088]

[0089] d. Select W after optimization in step 8). t s .

[0090]

[0091] 5. During the competition period, after each iteration involving mutation, crossover, and selection, two sets of correction vectors W are obtained. t s and L t s (At this point, t = m ~ T), and the correction vector Y of the normal period, respectively. t su Combining these (where t = 1 to m), we obtain two complete sets of Markov chain parameter optimization schemes after iteration (where t = 1 to T), denoted as Y. W and YL ;

[0092] 6. Based on the winner Y W Y, which is obtained by the losers learning from the winners. L The average value of the corrected parameters after convergence is denoted as . and And based on comparison with existing measured modes and The option with the smallest difference is selected as the optimal correction scheme.

[0093] In this scheme, during the competition phase, two candidates (two Markov chains) compete based on the objective function value. The candidate with the smaller objective function value (the optimization problem is a minimization problem) wins. The winner updates its position based on standard mutations and crossovers, while the loser updates its position based on the winner's position. Finally, the optimal correction scheme is selected by comparing it with the objective. Compared to existing methods or other competitive approaches, the proposed method has the following advantages: 1) High computational efficiency: because candidates only participate in one competition, and losers try to get closer to the winners, half of the elements (correction vectors) of each Markov chain win through the competition during the competition period, while the other half of the elements (correction vectors) converge towards the convergence direction of the winning half; 2) Better optimization effect: because the addition of the difference algorithm makes the advantage of the winners and losers only temporary. The mutation, crossover, and selection operations in the difference algorithm allow the winners to continue to break through and find better solutions, and the losers can still surpass the winners by quickly learning from them; 3) Stronger noise resistance (good robustness): because the Markov chain population is built in a multi-chain form, it has a higher utilization rate of test information compared to existing methods.

[0094] In one implementation, the number of times the boundary between the normal period and the competition period is determined manually. For example, t is the current iteration number, m is the boundary number, and T is the final total number of iterations. The normal period is when t = 1 - m, and the competition period is when t = mT.

[0095] In one implementation, m is determined by selecting an iteration number greater than 10% of the Markov chain convergence threshold. This is because if m is too small, it will be within the Markov chain convergence threshold and will affect the convergence of the algorithm; if the value is too large, it will exceed the convergence threshold by too much and will eliminate the competition effect, resulting in more normalization periods and affecting the correction accuracy and efficiency.

[0096] In one implementation, the number of Markov chains forming the backup population is 4-10, preferably 7. Theoretically, a larger number results in more accurate corrections; however, in practice, when N≥7, especially when greater than 10, further increases have only a minor effect on accuracy. Where N is the number of Markov chains in the Markov chain population.

[0097] In one implementation scheme, Y is obtained based on mutations in differential evolution. t sp The formula is as follows:

[0098]

[0099] In one implementation, the cross yields a correction vector. The formula is:

[0100]

[0101] In one implementation scheme, the winner (W) is distinguished using the following formula. t s ) and losers (L t s ):

[0102]

[0103]

[0104] In one implementation, a monitoring system is also included, which performs preliminary dynamic testing on the structure under test to obtain the natural frequencies and mode shapes of the structure. The locations of the sensors are then selected based on the characteristics of the monitored mode shapes.

[0105] Specifically, in practice, the number of sensors and the arrangement of measuring points need to be selected based on the effectiveness and purpose of the vibration monitoring system. The first step is to conduct preliminary dynamic testing on the structure to be monitored. The purpose is to determine the natural frequencies and mode shapes of the structure and to assess the amplitude level caused by the current environment. At this stage, the sensors are temporarily fixed. The second step is to determine the design scheme of the monitoring system based on the preliminary tests, including the type, number, and location of the sensors. During planning, the sensor positions should avoid modal nodes (locations where the mode shape value is zero) based on the characteristics of the mode shapes. In actual operation, the decision to fully implement the system depends on the situation. For simple structures where the modal vibration characteristics are known, the sensors can be arranged directly based on structural dynamics knowledge.

[0106] For cantilever beams, the fixed end does not experience axial, vertical, or rotational displacement due to the fixed method. The unconstrained end can generate forces parallel and perpendicular to the axial direction, and can also produce axial and vertical displacements. However, due to the high strength and compressive strength of steel, the axial displacement is negligible. Therefore, the cantilever beam mainly experiences vertical displacement. Only an excitation device needs to be placed at the free end, and an acceleration sensor needs to be placed on the upper surface of the steel. Since actual structures are continuous elastic bodies with countless degrees of freedom and infinitely many corresponding mode shapes for natural frequencies, it is impossible to monitor every degree of freedom. Based on the vibration characteristics of the cantilever beam and the variation diagram of the first four mode shapes (e.g....), we can see... Figure 3 In one implementation, at least four acceleration sensors are required at the quarter-point, half-point, three-quarter-point, and free end. In a preferred embodiment, considering both economy and identification effectiveness, ten acceleration sensors are chosen, with the remaining six sensors positioned between the four points mentioned above. This allows damage to be localized to a smaller area, and compared to using interpolation algorithms to obtain modal shapes from only four required points, this approach is closer to reality. This is because modal shapes of damaged structures are often irregular, and even data interpolation cannot yield satisfactory results. In a preferred embodiment, at least one of the remaining six sensors is positioned near the root of the cantilever beam, for example, at position ① in the figure. For example, two sensors are used, one at position ① and one between positions ① and ②, preferably closer to the side closer to ①. Research has found that structures calculated using this approach are more accurate because the applicant has discovered that cantilever beam structures are prone to damage in this location during engineering applications.

[0107] In one implementation, the suspended portion of the steel beam is divided into multiple units, with the installation locations at the nodes of each cantilever steel beam unit. Each unit is 50-60mm long, preferably 55mm. For example, a 550mm cantilever steel beam with 10 units and 11 nodes, each unit being 55mm long, would have 10 acceleration sensors arranged at the nodes. Using the scheme of this application, as long as the structure is not extremely long, dividing it into 10 equal segments and arranging 10 sensors is sufficient. Evenly distributing 10 sensors is acceptable for beam structures. For extremely long structures, multi-segment inspection can be adopted, or the entire length can be measured to find the approximate damage location and gradually narrow down the inspection area.

[0108] In one implementation, applying a vertical single-point pulse to the cantilever beam via an excitation device means applying a vertical single-point pulse to the cantilever beam at its furthest point from the wall.

[0109] This application also provides a basic structure damage identification system based on an improved MCMC method, including an acceleration sensor, an excitation device, and a processor.

[0110] Among them, there are multiple acceleration sensors arranged on the cantilever steel beam to detect the vertical acceleration of the cantilever steel beam; the excitation device is used to apply vertical single-point pulse excitation to the steel beam.

[0111] The processor is used to detect damage to the cantilever steel beam using the method described above.

[0112] Example:

[0113] The method of the present invention will be described below with reference to specific embodiments, such as... Figure 2 A cantilever steel beam has a total length of 550mm + 20mm, with 550mm suspended and 20mm embedded in the wall. The suspended portion of the beam is divided into multiple units, with installation points at the nodes of each unit. Each unit is 55mm long, resulting in 11 nodes (10 units total). Ten accelerometers are placed at each node, with node ① being a modal node (no sensors are placed there as the modal value is zero). (The use of 10 sensors for the cantilever beam is not an absolute value, but rather a selection based on a trade-off between economy and effectiveness. For extremely long beams, multi-segment inspection or full-length measurement can be used to approximate damage locations and gradually narrow down the inspection area.)

[0114] Steel parameters are shown in Table 1.

[0115] Table 1

[0116]

[0117] The overall stiffness of the cantilever steel beam decreased to 90%, and the cantilever steel beam was damaged within one unit, with a stiffness loss of 75%. The damage to this cantilever steel beam needs to be identified.

[0118] Thirty measured data points were obtained through preprocessing by the signal acquisition device. The average measured damage frequencies of the first six orders are shown in the table below, and the measured values ​​for each order are as follows: Figure 3 (a) The measured mean values ​​of the first four normalized vibration modes are shown in the figure. Figure 3 (b) Standard deviation and coefficient of variation are both used to determine the degree of dispersion of data, enabling timely detection of problems in the test data.

[0119] Table 2. Average measured frequency values ​​of the first 6 stages of cantilever steel beams

[0120]

[0121]

[0122] The cantilever steel beam is divided into 10 units and 11 nodes. An accelerometer is arranged at each node. Then, a vertical single-point pulse excitation is applied to the end of the cantilever beam away from the wall.

[0123] The signals received by the accelerometer are transmitted to the computer in real time, and the structural modes are obtained through FFT (Fast Fourier Transform); such as Figure 3 As shown, where

[0124] Based on the measured modes, the Markov chain is obtained using the standard MH algorithm. The test is repeated multiple times to obtain multiple Markov chains to form a backup population.

[0125] The optimal solution was then obtained by employing the method described in this application.

[0126] The parameter correction process of the method used in this application, compared with that of the MCMC method in the prior art, is shown in the diagram below. Figure 4 Among them, it is obvious that (a) shows a large number of iteration stagnation phenomena, resulting in low correction efficiency and low final convergence accuracy; (b) shows that the method of the present invention greatly improves the utilization rate of measurement information and greatly improves the efficiency of model correction through multi-chain differential competition.

[0127] Figure 5 As shown in Table 2, this method is superior to the existing MCMC method in identifying the degree and location of damage and judging the probability of damage. For example, the existing MCMC method misjudges the stiffness of regions 6 and 10 of the cantilever steel beam with a 90% probability of stiffness loss to about 85%, which has an absolute error of 5% compared with the actual state. However, the absolute error of misjudgment in each region of this invention is less than 3%, and the damage probability indicates that the probability of this damage occurring is less than 25%, with almost no misjudgment. θ1 here refers to the current relative stiffness value of element 1. Here, "relative" means relative to the intact state before damage. Therefore, θ1 here indicates that element 1 was detected as damaged by the MH-MCMC method and now has a stiffness of about 0.7-0.75.

[0128] The regional values ​​in Table 2 represent elements 1-10 of the cantilever steel beam. The correction values ​​refer to the relative elastic modulus values ​​of each element region obtained through different methods, following the same principle as the baseline values. The baseline value formula is:

[0129]

[0130] In the formula: E is the elastic model in the intact state; E0 is the true elastic model after damage; the dimensionless reference value refers to the ratio of the elastic modulus of the damaged state to that of the intact state.

[0131] The damage probability is calculated after obtaining the optimal correction scheme, taking H as the lower bound of the stiffness distribution with a confidence level of 95% (under the condition of structural integrity). The formula for the damage probability of the parameters is as follows:

[0132] P i =probability(-∞<θ)i ≤H)

[0133] In the formula: P is the damage probability; i is the unit number; probability is a function for calculating the cumulative distribution.

[0134] The absolute error is the error between the corrected result and the actual damage, and the formula is as follows:

[0135] Absolute error = Correction value - Reference value

[0136] Figure 5 θ1-θ 10 The stiffness of the corresponding elements 1-10 is also the correction value in region 1-10 of Table 2 for each iteration. A total of 3000 iterations were performed, but convergence was achieved after about 300 iterations. Figure 5 (Only the first 1000 steps are shown)

[0137] Table 2 Damage Identification

[0138]

[0139] It should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them; although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A method for identifying structural damage based on an improved MCMC method, comprising dividing the cantilever steel beam's suspended portion into multiple units, with the installation position at each cantilever steel beam unit node, and applying a vertical single-point pulse on the cantilever steel beam via an excitation device, wherein the vertical single-point pulse is applied at the furthest point of the cantilever steel beam from the wall, characterized in that: It also includes the following steps: 1) Test the modal data acquisition of the cantilever steel beam, specifically including setting up several acceleration sensors on the cantilever steel beam and applying a vertical single-point pulse on the cantilever steel beam through an excitation device; the acceleration sensors collect response signal data, and the signal data is processed to obtain the modal information of the cantilever steel beam; 2) Based on the measured modes, the Markov chain is obtained using the standard MH algorithm. The test is repeated multiple times to obtain multiple Markov chains to form a backup population. 3) Iterations include a normal period consisting only of differential evolution and a competitive period following the normal period. When the iteration is in the normal period: 3.1 Randomly select a Markov chain Y from the Markov chain population t s Y is obtained based on mutations in differential evolution. t sp ; 3.2 Based on the crossover in differential evolution, the mutation vector Y is... t sp =( Y t (s,1)p , Y t (s,2)p , Y t (s,3)p , ..., Y t (s, D)p ) and the original vector Y t s =( Y t (s, 1) , Y t (s, 2) , Y t (s, 3) , ..., Y t (s, D) The cross-section yields the correction vector Y. t su =( Y t (s,1)u , Y t (s ,2)u , Y t (s, 3)u , ..., Y t (s, D)u ); 3.3 Calculate the corrected acceptance probability during the normal period r 1, 3.4 Based on the selection strategy in differential evolution, select the correction vector Y. t su ,in ; 4) During the iteration in a competitive phase: 4.1 Randomly select a Markov chain from the Markov chain population, denoted as Y. t g ( g ≠s, a , b ), and distinguish the winner (W) t s ) and losers (L t s ); 4.2 If the loser is obtained (L) t s ),but a. Obtain L s t The mutation vector L t sp ( s ≠ c , d ); b. The mutation vector L will be obtained. t sp ( s ≠ c, d Each variability value in ) L t (s, w)p With the winner W t s Each corresponding position in W t (s, w) The crossover yields the correction vector L. t su Corresponding to 1~ w Position cross value L t (s, w)u ; c. Obtain the corrected vector L of the loser after learning from the winner. t su Compared to the original L t s Acceptance probability r 2 d. Select the optimized L t s ; 4.

3. If the winner is W t s ,but a. Obtain W t s Mutation vector : b. The mutation vector will be obtained. Each mutation value in W t (s, w)p With the winner W t s W at the corresponding position t (s , w) The correction vector W obtained by the following crossover is... t su Corresponding to 1~ w Position cross value W t (s, w)u : c. Obtain the winner's correction vector W t su Compared to the original W t s Acceptance probability r 3: d. Select W after optimization in step 8). t s 5) During the competition period, after each iteration involving mutation, crossover, and selection, two sets of correction vectors W are obtained. t s and L t s (at this time, t = m~ T), and the correction vector Y during the normal period, respectively. t su Combined (at this time, t =1 ~m This will yield two complete sets of Markov chain parameter optimization schemes after iteration (at this point, t =1 ~ T), denoted as Y W and Y L ; 6) Based on the obtained winner Y W Y, which is obtained by the losers learning from the winners. L The average value of the corrected parameters after convergence is denoted as . W and L And based on comparison with existing measured modes F ( W )and F ( L The option with the smallest difference is selected as the optimal correction scheme. The damage probability is determined after obtaining the optimal correction scheme, taking H as the lower bound of the stiffness distribution confidence level according to the normal distribution under the condition that the structure is intact, and the formula for the damage probability of the parameter is: In the formula: P is the damage probability; i is the unit number; probability is a function for calculating the cumulative distribution.

2. The structural damage identification method based on the improved MCMC method according to claim 1, characterized in that: The method for determining the number of iterations for the normal period and the competition period is as follows: select an iteration number that is 8-15% greater than the convergence boundary of the Markov chain as the number of iterations.

3. The structural damage identification method based on the improved MCMC method according to claim 1, characterized in that: The number of Markov chains forming a backup population is 4-7.

4. A method for identifying structural damage based on an improved MCMC method as described in claim 1. Its features are: Y is obtained based on mutations in differential evolution. t sp The formula is as follows: 。 5. A method for identifying structural damage based on an improved MCMC method according to claim 1. Its features are: The crossover yields the correction vector Y. t su =( Y t (s,1)u , Y t (s,2)u , Y t (s, 3)u , ..., Y t (s, D)u The formula for ) is: (2)。 6. A structural damage identification system based on an improved MCMC method, comprising an acceleration sensor, an excitation device, and a processor, characterized in that: Multiple accelerometers are arranged on the cantilever steel beam to detect the vertical acceleration of the cantilever steel beam; the excitation device is used to apply vertical single-point pulse excitation to the steel beam. The processor is used to detect damage to the cantilever steel beam according to any one of claims 1-5.

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