CN110363275A - Immune Algorithms and Data Fusion for Structural Damage Identification - Google Patents

Abstract

An immune algorithm and data fusion for structural damage identification relate to the technical field of structural damage identification. The immune algorithm for structural damage identification is characterized in that it includes the following steps: randomly generating an initial population of antibodies of size N, setting various parameters in the algorithm; calculating the affinity of all antibodies, according to the proposed equilibrium distribution rule The antibodies are divided into m sub-populations, and each sub-population randomly selects τ non-autoantibodies from the memory bank to achieve inter-population interaction. After the above technical scheme is adopted, the beneficial effects of the present invention are as follows: the population size of a single calculation is reduced, the algorithm search space is greatly reduced, and factors such as the measurement error of a single sensor and the insufficient sensitivity of the sensor itself to damage are reduced to a certain extent. The impact on the recognition results improves the recognition accuracy.

Description

Immune Algorithms and Data Fusion for Structural Damage Identification

technical field

The invention relates to the technical field of structural damage identification, in particular to an immune algorithm and data fusion for structural damage identification.

Background technique

Infrastructure as the backing and necessary conditions for economic and social development has always been a key construction object in my country, and large structures such as bridges, as an important part of transportation infrastructure, have naturally become key support projects.

As the service life of structural engineering increases, different degrees of damage will inevitably occur. Intelligent algorithms are widely used due to their strong search ability and good adaptability. applied research. Chen Yuzhou et al. first used wavelet analysis to detect damaged structural units, and then used immune algorithm to identify the damage degree of damaged structural units. Guo.H.Y et al. performed Bayesian fusion processing of multiple sensor data to obtain more effective damage factors, and then used an immune algorithm to identify damage information, which improved the reliability of the identification results. In order to reduce the noise interference during damage detection, Guo.T et al. used the multi-scale space theory to search for damage features from multiple angles, and fused them to obtain accurate damage information. Liu Jian et al. used an immune algorithm based on forward selection to detect the abnormality of the wavelet energy spectrum, which improved the speed of damage identification.

At this stage, when identifying the damage of large-scale structures, there are mainly the following problems to be solved: the number of sensors in large-scale structures is large, and the amount of data processed is huge, which leads to a slow speed of identifying the damage state of the structure; due to the error in the measurement data of a single sensor, the sensor Its own recognition accuracy is insufficient, and it is difficult to make an accurate judgment on the structural damage state.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide an immune algorithm and data fusion for structural damage identification in view of the defects and deficiencies of the prior art, which reduces the population size of a single calculation, greatly reduces the algorithm search space, and improves the memory capacity. Antibody performance reduces the blindness of the algorithm in the search process, so that the algorithm can find the optimal solution faster when processing a large amount of sensor data, reducing the search time, thereby improving the speed of identification; using the D-S evidence theory for multi-sensor parameters The recognition results are fused to a certain extent, which reduces the influence of factors such as the measurement error of a single sensor and the insufficient sensitivity of the sensor itself to damage on the recognition results, and improves the recognition accuracy.

To achieve the above object, the present invention adopts the following technical solutions:

An immune algorithm for structural damage identification, which consists of the following steps:

Step 1. Randomly generate an initial population of antibodies with a scale of N, and set various parameters in the algorithm;

Step 2: Calculate the affinity of all antibodies, divide the antibodies into m sub-populations according to the proposed balanced distribution rule, and randomly select τ non-autoantibodies from the memory library for each sub-population to achieve inter-population interaction;

Step 3. Select the top δ% excellent antibodies of each sub-population for cloning. The number of clones is proportional to the affinity of the antibodies, that is, the better the antibody, the greater the proportion;

Step 4. Affinity mutation is performed on the cloned antibody. The probability of mutation is as follows:

In the formula, Fmax and Fmin are the maximum and minimum affinity values of the cloned antibody;

Step 5: Calculate the similarity of the cloned antibodies after mutation, and remove the antibodies with high similarity to ensure the diversity of the cloned population. The similarity is calculated as follows:

Step 6. Recalculate the affinity of the cloned antibody, compare the antibody with the best affinity with the parent antibody, if it is better than the parent, replace the parent antibody with the excellent antibody;

Step 7. Select excellent antibodies in each subpopulation and add them to the memory bank, and then update the memory bank antibodies using the affinity threshold A _tv and the concentration threshold C _tv , and eliminate the antibodies with poor affinity and high concentration to ensure that the memory bank changes with time. As the overall superiority of the population changes, the antibody concentration is derived from the antibody similarity:

In the formula, n is the number of antibodies in the current population;

Step 8: Judging whether the specified maximum number of iterations is reached, if so, stop the search and output the results in the memory library, if not, go to Step 2 to continue.

The first step is specifically: assuming an antibody population X={x1,x2,x3,...,xN} with a scale of N, the affinity between the antibody and the antigen is represented by A(xi), and each antibody is carried out. Calculate the affinity with the antigen to obtain the affinity of the population A={A1,A2,A3,...,AN}, arrange all the antibodies in order of affinity, and then use the affinity as the standard to divide the population It is divided into n classes, and then randomly selects an antibody from each class and adds it to a small population. After n×m operations, the population is divided into m small populations with balanced affinity.

The second step is as follows: each small population must use other populations to continuously adjust its own search direction during its evolution, so as to avoid its own search direction deviating from the overall direction. Since the memory bank collects excellent antibodies of each subpopulation. , so this paper uses the memory bank as an intermediate carrier to realize the interaction between populations. Assuming that the size of the antibodies in the memory bank is ι, for each small population, the antibodies belonging to its own population are first eliminated, and then randomly selected from the remaining antibodies τ antibodies are replicated, and the τ antibodies with the smallest affinity in this population are replaced with replicated antibodies, and this operation is performed on all small populations, that is, a population interaction is completed.

The calculation of the affinity threshold value A _tv in the seventh step is:

A _tv =k _A ×A _max

First, rank all antibody affinities in the population from large to small, where the maximum affinity is recorded as Amax, and a ratio of kA is taken;

The concentration threshold C _tv is calculated as:

C _tv =k _C ×C _min

Select the antibodies with affinity in the range of (Atv, Amax) in the population, and then arrange the antibodies according to the concentration index from large to small, where the minimum concentration is recorded as Cmin, take a ratio of kc, and set (Cmin, Ctv ) The antibodies in this range are retained, and others are removed to form a memory bank.

Data fusion for structural damage identification, which consists of the following steps:

Use DS evidence theory to fuse the damage identification results of acceleration and displacement parameters and the damage identification results of stress parameters, and use the following method to determine the basic probability assignment function m(A) in DS evidence theory, using the vector Indicates that the damage degree of position j is α%. Assuming that the identification result of damage index i is ri, and the result of damage index i identifying position j is rij, the reliability of position j identified by index i is expressed as follows:

Use the following formula to determine the mi(A) of index i for damage state A:

The combination rules of D-S evidence theory are as follows:

where k is called the inconsistency factor, which is calculated as follows:

The damage identification results of the acceleration and displacement parameters: the natural frequency and mode shape of the structure can be combined to obtain more accurate structural damage information. The natural frequency and mode shape of the structure can be obtained by acceleration and displacement sensors, and α is assumed to be stiffness damage. Coefficient, the difference between the natural frequency and mode shape calculated by α and the measured natural frequency and mode shape after damage is taken as the objective function, and then α is continuously adjusted to make the objective function tend to 0, and finally each damage can be obtained. α value to determine the location and extent of damage. The objective function is expressed as follows:

In the formula, Cω and Cφ are the weight coefficients; ωci and ωt i are the calculated and measured values of the natural frequency after the i-th order damage; value and measured value.

The damage identification results of the stress parameters: the strain modal change of each node after damage can be obtained by the stress sensor, and the damage position and degree of the structure can also be identified. Curvature mode ρ(i), as follows:

where △ is the distance between adjacent nodes,

Then, the strain modal quantity is calculated by the nodal curvature and the height of the structure, and the nodal mode shape can be calculated by the stiffness damage coefficient α, so the strain modal difference of the structure can also be expressed as the objective function of α, as shown below:

In the formula, εc ij and εt ij are the calculated and measured strain modal values after the i-th damage of the j-th node, respectively.

After the above technical solution is adopted, the beneficial effects of the present invention are as follows: the population size of a single calculation is reduced, the search space of the algorithm is greatly reduced, the antibody performance of the memory bank is improved, and the blindness of the algorithm in the search process is reduced, so that the When processing a large amount of sensor data, the algorithm can find the optimal solution faster, reduce the search time, and thus improve the speed of recognition; the D-S evidence theory is used to fuse the recognition results of multi-sensor parameters, which reduces the measurement of a single sensor to a certain extent. The influence of factors such as errors and the lack of sensitivity of the sensor itself to damage on the recognition results improves the recognition accuracy.

Description of drawings

In order to explain the embodiments of the present invention or the technical solutions in the prior art more clearly, the following briefly introduces the accompanying drawings that need to be used in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only These are some embodiments of the present invention, and for those of ordinary skill in the art, other drawings can also be obtained from these drawings without any creative effort.

Fig. 1 is the schematic flow chart block diagram of immune algorithm in the present invention;

Fig. 2 is the structural representation of the main bridge model of the cable-stayed bridge in the present invention;

Fig. 3 is the natural frequency diagram of the first 10 orders after damage in the present invention;

Fig. 4 is the relevant parameter diagram of the improved immune algorithm in the present invention;

Fig. 5 is the function mean value change diagram of two kinds of algorithm search objective function 1 in the present invention;

Fig. 6 is the function mean value change diagram of two kinds of algorithms searching objective function 2 in the present invention;

Fig. 7 is the relevant statistical value diagram of two kinds of algorithm searches in the present invention;

FIG. 8 is a comparison diagram of three kinds of identification results and actual values in the present invention.

Detailed ways

1-8, the technical solution adopted in this specific embodiment is: an immune algorithm for structural damage identification, which includes the following steps:

Step 1. Randomly generate an initial population of antibodies with a scale of N, and set various parameters in the algorithm;

Step 2: Calculate the affinity of all antibodies, divide the antibodies into m sub-populations according to the proposed balanced distribution rule, and randomly select τ non-autoantibodies from the memory library for each sub-population to achieve inter-population interaction;

Step 3. Select the top δ% excellent antibodies of each sub-population for cloning. The number of clones is proportional to the affinity of the antibodies, that is, the better the antibody, the greater the proportion;

Step 4. Affinity mutation is performed on the cloned antibody. The probability of mutation is as follows:

In the formula, Fmax and Fmin are the maximum and minimum affinity values of the cloned antibody;

Step 5: Calculate the similarity of the cloned antibodies after mutation, and remove the antibodies with high similarity to ensure the diversity of the cloned population. The similarity is calculated as follows:

Step 6. Recalculate the affinity of the cloned antibody, compare the antibody with the best affinity with the parent antibody, if it is better than the parent, replace the parent antibody with the excellent antibody;

Step 7. Select excellent antibodies in each subpopulation and add them to the memory bank, and then update the memory bank antibodies using the affinity threshold A _tv and the concentration threshold C _tv , and eliminate the antibodies with poor affinity and high concentration to ensure that the memory bank changes with time. As the overall superiority of the population changes, the antibody concentration is derived from the antibody similarity:

In the formula, n is the number of antibodies in the current population;

Step 8: Judging whether the specified maximum number of iterations is reached, if so, stop the search and output the results in the memory library, if not, go to Step 2 to continue.

The first step is specifically: assuming an antibody population X={x1,x2,x3,...,xN} with a scale of N, the affinity between the antibody and the antigen is represented by A(xi), and each antibody is carried out. Calculate the affinity with the antigen to obtain the affinity of the population A={A1,A2,A3,...,AN}, arrange all the antibodies in order of affinity, and then use the affinity as the standard to divide the population It is divided into n classes, and then randomly selects an antibody from each class and adds it to a small population. After n×m operations, the population is divided into m small populations with balanced affinity.

The second step is as follows: each small population must use other populations to continuously adjust its own search direction during its evolution, so as to avoid its own search direction deviating from the overall direction. Since the memory bank collects excellent antibodies of each subpopulation. , so this paper uses the memory bank as an intermediate carrier to realize the interaction between populations. Assuming that the size of the antibodies in the memory bank is ι, for each small population, the antibodies belonging to its own population are first eliminated, and then randomly selected from the remaining antibodies τ antibodies are replicated, and the τ antibodies with the smallest affinity in this population are replaced with replicated antibodies, and this operation is performed on all small populations, that is, a population interaction is completed.

The calculation of the affinity threshold value A _tv in the seventh step is:

A _tv =k _A ×A _max

First, rank all antibody affinities in the population from large to small, where the maximum affinity is recorded as Amax, and a ratio of kA is taken;

The concentration threshold C _tv is calculated as:

C _tv =k _C ×C _min

Select the antibodies with affinity in the range of (Atv, Amax) in the population, and then arrange the antibodies according to the concentration index from large to small, where the minimum concentration is recorded as Cmin, take a ratio of kc, and set (Cmin, Ctv ) The antibodies in this range are retained, and others are removed to form a memory bank. Assuming that the concentration of the antibody in the population is represented by C(xi), and the affinity between the antibody and the antigen is represented by A(xi), a staged threshold division method is used to obtain the memory bank, so that the memory The antibodies in the library are always composed of the antibody that is closest to the optimal solution, and the concentration index is used to ensure the difference between the antibodies, so that the memory library can be adjusted in real time according to the superiority of the population antibodies.

Data fusion for structural damage identification, which consists of the following steps:

Use DS evidence theory to fuse the damage identification results of acceleration and displacement parameters and the damage identification results of stress parameters, and use the following method to determine the basic probability assignment function m(A) in DS evidence theory, using the vector Indicates that the damage degree of position j is α%. Assuming that the identification result of damage index i is ri, and the result of damage index i identifying position j is rij, the reliability of position j identified by index i is expressed as follows:

Use the following formula to determine the mi(A) of index i for damage state A:

The combination rules of D-S evidence theory are as follows:

where k is called the inconsistency factor, which is calculated as follows:

The damage identification results of the acceleration and displacement parameters: the natural frequency and mode shape of the structure can be combined to obtain more accurate structural damage information. The natural frequency and mode shape of the structure can be obtained by acceleration and displacement sensors, and α is assumed to be stiffness damage. Coefficient, the difference between the natural frequency and mode shape calculated by α and the measured natural frequency and mode shape after damage is taken as the objective function, and then α is continuously adjusted to make the objective function tend to 0, and finally each damage can be obtained. α value to determine the location and extent of damage. The objective function is expressed as follows:

In the formula, Cω and Cφ are the weight coefficients; ωci and ωt i are the calculated and measured values of the natural frequency after the i-th order damage; value and measured value. Damage to a part of the structure will change the stiffness and other parameters of the structure, resulting in the change of the overall natural frequency of the structure and the mode shape of each node. The natural frequency reflects the overall characteristics of the structure, but the damage information contained is not accurate. Mode shapes are more sensitive to local changes in the structure and contain more damage information.

The damage identification results of the stress parameters: the strain modal change of each node after damage can be obtained by the stress sensor, and the damage position and degree of the structure can also be identified. Curvature mode ρ(i), as follows:

where △ is the distance between adjacent nodes,

Then, the strain modal quantity is calculated by the nodal curvature and the height of the structure, and the nodal mode shape can be calculated by the stiffness damage coefficient α, so the strain modal difference of the structure can also be expressed as the objective function of α, as shown below:

In the formula, εc ij and εt ij are the calculated and measured strain modal values after the i-th damage of the j-th node, respectively. The stiffness change when the structure is damaged will also cause the stress at the damaged location to change, so the strain mode of each node also changes.

Taking an extra-large bridge as the research object, the bridge has a total length of 2478 meters, of which the main bridge is a three-span double-tower double-cable-plane cable-stayed bridge. It is divided into 109 sections, using C50 concrete material, the relevant parameters are: V=0.2, E=325Gpa, ρ=2600kg/m3. The overall structure is divided into multiple areas for damage identification. In this paper, the damage of the 20 sections from 30# to 50# is analyzed, and the finite element model of the structure is established by ANSYS software, and the selected 20 sections are divided into 300 structures. Elements, reduce the stiffness of the five elements 40, 100, 150, 210, 270 by 30%, 50%, 75%, 45%, 20%, respectively. The modal analysis is performed on the damaged structure, and the first 10 natural frequencies of the structure and the first 3 vibration modes and strain modes of each node are taken out as the measured data values in the objective function.

In order to verify the superiority and feasibility of the improved immune algorithm, the traditional immune algorithm based on clone selection and the proposed improved immune algorithm were selected to search for two objective functions in MATLAB environment. In the experiment, the population size of the two algorithms is 100, the clone size is 60%, and the maximum number of iterations is specified as 400. The affinity is determined by the objective function value, and the smaller the function value, the higher the affinity of the antibody. For the convenience of expression, the function based on natural frequency and mode shape is denoted as objective function 1, and the strain modal function is denoted as objective function 2.

Both algorithms can reach the convergence state within the specified number of iterations, but the traditional algorithm has a large fluctuation range of the objective function value during the search process, and the search direction is prone to deviation, and there will be small fluctuations when it is about to converge at the end; the improved algorithm The fluctuation range is significantly smaller during the search process, and it can converge rapidly in the final stage. This shows that the search blindness of the improved algorithm is reduced compared with the traditional algorithm, and many unnecessary calculations are avoided.

Compared with the traditional algorithm, the improved algorithm can reach the convergence state faster, and the search time is less. This means that the search efficiency of the improved algorithm is higher, the search speed is faster, and the damage state of the structure can be quickly identified.

Use the improved immune algorithm to search for the objective function, and obtain the α value of each node to know the identification results of the two damage indicators.

The basic probability assignment function values of the two indicators for each damaged unit are constructed, and the two damage results are fused. In the identification results of the natural frequency and mode shape damage indicators, the preset five damaged units are consistent with the actual values, and the errors are all within 4%. Damage is identified; in the identification results of the strain modal damage index, although the identification error is small at the adjacent unit, the difference between the preset damage unit and the actual value is large. After using the D-S evidence theory to fuse the identification results of the two damage indicators, the damage is only larger in the preset five structural units, and the damage errors of the remaining positions are all within 5%. Compared with the two single damage indicators, not only in the damage The recognition results at the location are more accurate, and the recognition errors for adjacent units are also within a reasonable range, which indicates that the D-S evidence fusion process eliminates the recognition result errors of a single indicator to a certain extent, and complements their respective advantages, making the results higher. accuracy.

After adopting the above technical scheme, the beneficial effects of the present invention are as follows: the immune algorithm improves the damage identification speed of the structure, divides the antibody population into multiple small populations for parallel search, and enhances the guidance of the memory bank for the search process, so as to shorten the algorithm search time Afterwards, the D-S evidence theory is used to fuse the identification results of multiple sensors to eliminate the redundancy and errors between them, so as to achieve the purpose of accurately identifying the structural damage state.

The above is only used to illustrate the technical solution of the present invention and not to limit it. Other modifications or equivalent replacements made by those of ordinary skill in the art to the technical solution of the present invention, as long as they do not depart from the spirit and scope of the technical solution of the present invention, should be Included within the scope of the claims of the present invention.

Claims (7)

1. An immune algorithm for structural damage identification, characterized in that it comprises the following steps: Step 1. Randomly generate an initial population of antibodies with a scale of N, and set various parameters in the algorithm; Step 2: Calculate the affinity of all antibodies, divide the antibodies into m sub-populations according to the proposed balanced distribution rule, and randomly select τ non-autoantibodies from the memory library for each sub-population to achieve inter-population interaction; Step 3. Select the top δ% excellent antibodies of each sub-population for cloning. The number of clones is proportional to the affinity of the antibodies, that is, the better the antibody, the greater the proportion; Step 4. Affinity mutation is performed on the cloned antibody. The probability of mutation is as follows: In the formula, Fmax and Fmin are the maximum and minimum affinity values of the cloned antibody; Step 5: Calculate the similarity of the cloned antibodies after mutation, and remove the antibodies with high similarity to ensure the diversity of the cloned population. The similarity is calculated as follows: Step 6. Recalculate the affinity of the cloned antibody, compare the antibody with the best affinity with the parent antibody, if it is better than the parent, replace the parent antibody with the excellent antibody; Step 7. Select excellent antibodies in each subpopulation and add them to the memory bank, and then update the memory bank antibodies using the affinity threshold A _tv and the concentration threshold C _tv , and eliminate the antibodies with poor affinity and high concentration to ensure that the memory bank changes with time. As the overall superiority of the population changes, the antibody concentration is derived from the antibody similarity: In the formula, n is the number of antibodies in the current population; Step 8: Judging whether the specified maximum number of iterations is reached, if so, stop the search and output the results in the memory library, if not, go to Step 2 to continue. 2 . The immune algorithm for structural damage identification according to claim 1 , wherein the step 1 is specifically: assuming that an antibody population X = {x1, x2, x3, . . . , xN} with a scale of N, The affinity between the antibody and the antigen is represented by A(xi), and the affinity of each antibody with the antigen is calculated to obtain the affinity of the population A={A1,A2,A3,...,AN}, Arrange all the antibodies in sequence according to their affinity, and then divide the population into n classes based on the affinity, and then randomly select an antibody from each class and add it to a small population, after n×m times After the operation, the population is divided into m small populations with balanced affinity. 3. The immune algorithm for structural damage identification according to claim 1, wherein the step 2 is specifically: each small population must use other populations to continuously adjust its own search direction for its cross-intervention during evolution, In order to avoid the deviation of the search direction from the general direction, since the excellent antibodies of each subpopulation are collected in the memory bank, this paper uses the memory bank as an intermediate carrier to realize the interaction between the populations. For a small population, first remove the antibodies belonging to its own population, then randomly select τ antibodies from the remaining antibodies for replication, and replace the τ antibodies with the smallest affinity in this population with the replicated antibodies, and for all small populations Populations implement this operation, that is, a population interaction is completed. 4. The immune algorithm for structural damage identification according to claim 1, wherein the calculation of the affinity threshold A _tv in the step 7 is: A _tv =k _A ×A _max First, rank all antibody affinities in the population from large to small, where the maximum affinity is recorded as Amax, and a ratio of kA is taken; The concentration threshold C _tv is calculated as: C _tv =k _C ×C _min Select the antibodies with affinity in the range of (Atv, Amax) in the population, and then arrange the antibodies according to the concentration index from large to small, where the minimum concentration is recorded as Cmin, take a ratio of kc, and set (Cmin, Ctv ) The antibodies in this interval are retained, and others are removed to form a memory bank. 5. Data fusion for structural damage identification, characterized in that it comprises the following steps: Use DS evidence theory to fuse the damage identification results of acceleration and displacement parameters and the damage identification results of stress parameters, and use the following method to determine the basic probability assignment function m(A) in DS evidence theory, using the vector Indicates that the damage degree of position j is α%. Assuming that the identification result of damage index i is ri, and the result of damage index i identifying position j is rij, the reliability of position j identified by index i is expressed as follows: Use the following formula to determine the mi(A) of index i for damage state A: The combination rules of D-S evidence theory are as follows: where k is called the inconsistency factor, which is calculated as follows: 6. The data fusion for structural damage identification according to claim 5, characterized in that: the damage identification result of the acceleration and displacement parameters: a more accurate structure can be obtained by combining the natural frequency and mode shape of the structure Damage information, the natural frequency and mode shape of the structure can be obtained by acceleration and displacement sensors, assuming that α is the stiffness damage coefficient, and the difference between the natural frequency and mode shape calculated by α and the measured natural frequency and mode shape after damage as the target. function, and then continuously adjust α to make the objective function tend to 0, and finally each α value after damage can be obtained to determine the location and degree of damage. The objective function is expressed as follows: In the formula, Cω and Cφ are the weight coefficients; ωci and ωti are the calculated and measured values of the natural frequency after the i-th order damage; . 7. The data fusion for structural damage identification according to claim 5, characterized in that: the damage identification result of the stress parameter: obtaining the strain modal change of each node after damage through the stress sensor can also identify the structural damage. To determine the damage location and degree, first use the center difference method for the nodal mode shape φ(i) to obtain the nodal curvature mode ρ(i), as shown in the following formula: where △ is the distance between adjacent nodes, Then, the strain modal quantity is calculated by the nodal curvature and the height of the structure, and the nodal mode shape can be calculated by the stiffness damage coefficient α, so the strain modal difference of the structure can also be expressed as the objective function of α, as shown below: In the formula, εcij and εtij are the calculated and measured strain modal values of the j-th node after the ith-order damage, respectively.