Vibration table iterative learning control method, storage medium and electronic device thereof

Abstract

The present invention discloses a vibration table iterative learning control method and a storage medium and electronic device thereof, and relates to the technical field of earthquake resistance test of building structures. The steps of the method include: S1: obtaining the physical parameters of the substitute specimen model according to the modal parameters of the test specimen and the bottom shear time history of the test specimen under the action of seismic waves, and determining the substitute specimen model according to the physical parameters of the substitute specimen model; S2: carrying out vibration table iterative learning according to the substitute specimen model to obtain the vibration table loading command; S3: carrying out the vibration table test on the test specimen according to the vibration table loading command as the system input.

Description

Technical Field

[0001] The invention relates to the technical field of earthquake-resistant testing of building structures, and in particular to an iterative learning control method for a vibration table, a storage medium and an electronic device thereof. Background Art

[0002] The earthquake simulation shaking table is an important test equipment for studying the seismic performance of scaled structures and large-scale substructures. The accurate reproduction of the expected earthquake waveform on the shaking table surface is a prerequisite for ensuring accurate and reliable test results. Due to the nonlinearity and uncertainty of the loading system and the coupling characteristics of the shaking table specimen, it is difficult to obtain the ideal table acceleration reproduction accuracy by directly conducting the shaking table test without correcting the shaking table command through iterative learning. Therefore, iterative learning control of the shaking table is widely used.

[0003] There are generally two ways to iterate learning on a vibration table:

[0004] (1) The real vibration table test is carried out with the vibration table command obtained by no-load iterative learning, that is, there is no test specimen on the vibration table during iterative learning, and the test specimen is placed only during the real vibration table test. However, since the test specimen will interact with the vibration table when placed on the vibration table, the vibration table command obtained by iterative learning without the test specimen is not accurate enough, which leads to low test accuracy when carrying out the real vibration table test.

[0005] (2) The test specimen is placed on the vibration table, and the vibration table command is obtained by iterative learning with a small amplitude excitation, and then a real vibration table test is carried out. However, during the iterative learning process of the test specimen on the vibration table, the performance of the test specimen will change due to the interaction with the vibration table, and in serious cases, the test specimen may be damaged; therefore, the test data obtained by carrying out a real vibration table test based on the test specimen with changed or damaged performance lacks reliability. Summary of the invention

[0006] In view of the defects existing in the prior art, the technical problem solved by the present invention is: how to improve the test accuracy when carrying out a real vibration table test by adopting an iterative learning control method.

[0007] To achieve the above objectives, the present invention provides an iterative learning control method for a vibration table, comprising the following steps:

[0008] S1: obtaining the physical parameters of the substitute specimen model according to the modal parameters of the test specimen and the bottom shear time history of the test specimen under the action of seismic waves, and determining the substitute specimen model according to the physical parameters of the substitute specimen model;

[0009] S2: Perform iterative learning of the vibration table according to the alternative specimen model to obtain the vibration table loading command;

[0010] S3: Conduct a shaking table test on the test specimen based on the shaking table loading command as system input.

[0011] Based on the above scheme, the process of solving the physical parameters of the alternative specimen model described in S1 includes:

[0012] S101a: Simplify the test specimen into a spring-mass model with n degrees of freedom, according to the frequency formula and vibration mode equation Calculate the i-th order natural circular frequency ω of the test specimen i and vibration mode i=1,2,...,n; K represents the stiffness matrix of the test specimen, and M represents the mass matrix of the test specimen;

[0013] S101b: Using the absolute value of the relative vibration mode displacement of the degree of freedom as a reference, sort the n degrees of freedom in descending order, select the first s degrees of freedom as the main degrees of freedom, 0<s<n; take out the relative displacement of each main degree of freedom as the vibration mode of the s main degrees of freedom to replace the specimen model The first s order frequencies are the frequencies ω of the alternative specimen model a , a=1,2,...,s;

[0014] S101c: Replace the vibration mode of the specimen model according to s master degrees of freedom For the orthogonality of the mass matrix of the alternative specimen model, the diagonal mass matrix M of the alternative specimen model is obtained t , in M t Determine the ratio of the mass of each principal degree of freedom of the alternative specimen model;

[0015] S101d: According to M t ,ω a and Calculate the overall stiffness matrix K of the alternative specimen model t , the calculation formula is K t The stiffness coefficient in is converted into the stiffness between each layer to obtain the ratio of the stiffness between each layer of the alternative specimen model;

[0016] S101e: among all the master degrees of freedom, obtain the mass parameter of any preliminarily given master degree of freedom, calculate the correction coefficient of the mass parameter of the given degree of freedom, and correct the mass parameter of the given degree of freedom according to the correction coefficient;

[0017] S101f: Calculate the mass and interlayer stiffness of other main degrees of freedom according to the degree of freedom mass parameter corrected in S101e, the ratio of the masses of the main degrees of freedom described in S101c, and the ratio of the interlayer stiffness described in S101d.

[0018] Based on the above solution, the specific process of S101c includes: a,b=1,2,...,s, and a≠b, solve the simultaneous equations to determine M t The ratio of the mass of each principal degree of freedom of the alternative specimen model.

[0019] Based on the above scheme, K in S101d t Specifically include:

[0020]

[0021] The stiffness coefficient k ab (i,j=1,2,...,s) refers to the reaction force generated at the bth mass due to the unit displacement of the ath mass; interlayer stiffness k c (c=1,2,...,s) refers to the sum of the shear forces in all vertical components of the c-th layer caused by the unit inter-layer lateral displacement of the mass of the c-th layer.

[0022] Based on the above scheme, the calculation formula of the correction coefficient described in S101e is: Where V xj and V yj are the bottom shear forces of the alternative specimen model and the test specimen at the jth moment, respectively, and N is the total number of time steps.

[0023] Based on the above scheme, the process of solving the physical parameters of the alternative specimen model described in S1 includes:

[0024] S102a: Define a set of physical parameters (m a ,k a ) is an individual in the population, m a is the mass of the ath degree of freedom of the surrogate specimen model, k a is the interlayer stiffness of the ath layer of the surrogate specimen model; the single physical parameter is the gene on the individual chromosome; defines the correlation coefficient of the bottom shear time history of the test specimen and the surrogate specimen model under the action of seismic waves The normalized root mean square J of the difference is the dual optimization objective; where V x is the bottom shear force time history curve of the alternative specimen model, V y is the bottom shear force time history curve of the test specimen, Cov(V x ,V y ) is V x and V y The covariance of x ) is V x The variance of D(V y ) is V y The variance of

[0025] The dual optimization objective ρ xy and J as the dual objective function of the degree of freedom mass m and interlayer stiffness k:

[0026]

[0027] Where s is the number of degrees of freedom of the alternative specimen model. The smaller the normalized root mean square J is, the higher the correlation coefficient ρ is. xy The bigger;

[0028] Set the random value range of the degree of freedom mass m and interlayer stiffness parameter k of the alternative specimen model, define the initial population size, the crossover ratio and mutation probability of the offspring, set the maximum number of iterations and the normalized root mean square and correlation coefficient expected value of the exit iteration, and initialize the first generation population;

[0029] S102b: Calculate the objective function of all individuals in the first generation population and perform roulette wheel selection, multi-point crossover and multi-point mutation operations to obtain offspring;

[0030] S102c: After merging and sorting the first generation population and the offspring, the objective function value of the optimal individual is obtained;

[0031] S102d: Obtain the physical parameters of the alternative specimen model according to the objective function value of the optimal individual.

[0032] On the basis of the above scheme, the specific process of S102d includes: judging whether the objective function value of the optimal individual reaches the expected value, if so, outputting the physical parameters of the alternative specimen model represented by the individual corresponding to the objective function value as the optimal scheme; otherwise, selecting individuals with larger fitness and the same size as the initial population as the parent population for the next round of iteration, and taking the parent population as the first generation population in S102b and then transferring to S102b.

[0033] Based on the above solution, the process of S2 specifically includes:

[0034] The alternative specimen model in S1 is installed on the vibration table to carry out vibration table iterative learning. For the kth iteration process, the following steps are included:

[0035] S201: According to the input command u k (t) and the measured table output response y k The system transfer function h is identified by the Fourier spectrum of (t) k (f);

[0036] S202: Calculate the known expected trajectory y d (t) and y k The difference Δy of (t) k (t);

[0037] S203: According to Δy k(t) and h k (f) Calculate the input increment Δu in the time domain k (t), the calculation formula is: Δu k (f) = Δy k (f) / h k (f), Δy k (f) By Δy k (t) is transformed by Fourier to obtain, Δu k (f) By Δu k (t) is obtained by inverse Fourier transform;

[0038] S204: Δu k (t) Same as the last input command u k After superposition, the modified shaking table loading command u is obtained k+1 (t),u k+1 (t) = Δu k (t)+u k (t).

[0039] The storage medium provided by the present invention stores a computer program, which is characterized in that the computer program implements the above method when executed by a processor.

[0040] The electronic device provided by the present invention comprises a memory and a processor, wherein the memory stores a computer program running on the processor, and is characterized in that the above method is implemented when the processor executes the computer program.

[0041] Compared with the prior art, the advantages of the present invention are:

[0042] The present invention can construct a substitute specimen model according to the modal parameters of the test specimen and the bottom shear time history of the test specimen under the action of seismic waves. After testing, it is found that the substitute specimen model constructed by the present invention and the actual test specimen to be tested have similar forces on the table surface under the same vibration table command input, that is, the substitute specimen model and the test specimen have similar influences on the control of the vibration table.

[0043] Therefore, compared with the no-load iterative learning in the prior art, the present invention can use the substitute specimen model with similar performance to the test specimen to carry out iterative learning. The interaction between the specimen and the vibration table is taken into account during the learning process, and the obtained vibration table loading command is relatively accurate. Compared with the prior art that directly conducts iterative learning on the test specimen and then conducts a real vibration table test, the present invention first uses the substitute specimen model for iterative learning to obtain an accurate vibration table loading command, and then conducts a real vibration table test on the test specimen according to the vibration table loading command, effectively avoiding damage to the test specimen during the iterative loading process, thereby significantly improving the test accuracy.

[0044] It can be seen that the present invention is of great significance for improving the accuracy of the shaking table in reproducing seismic waves and enhancing the reliability and accuracy of the shaking table test results. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0046] Figure 1 It is a schematic flow chart of an iterative learning control method for a vibration platform in an embodiment of the present invention;

[0047] Figure 2 It is a schematic diagram of a process of solving the model parameters of the substitute specimen based on the modal parameters of the specimen in an embodiment of the present invention;

[0048] Figure 3 It is a schematic diagram of a process of solving the parameters of the alternative specimen model based on the genetic algorithm in an embodiment of the present invention;

[0049] Figure 4 It is a comparison diagram of the bottom shear force time history of the replacement specimen model and the test specimen under the initial given mass in the embodiment of the present invention;

[0050] Figure 5 It is a comparison diagram of the bottom shear force time history of the replacement specimen model and the test specimen after the given mass is corrected in the embodiment of the present invention;

[0051] Figure 6 It is a comparison diagram of the bottom shear force time history of the bilinear specimen and the linear replacement specimen model in the embodiment of the present invention;

[0052] Figure 7 It is a comparison diagram of the bottom shear force time history of the bilinear specimen and the linear replacement specimen model with damper in the embodiment of the present invention. DETAILED DESCRIPTION

[0053] In order to make the purpose, technical solution and advantages of the embodiments of the present application clearer, the technical solution in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of this application.

[0054] The flowcharts shown in the accompanying drawings are only examples and do not necessarily include all the contents and operations / steps, nor must they be executed in the order described. For example, some operations / steps may also be decomposed, combined or partially merged, so the actual execution order may change according to actual conditions.

[0055] See also Figure 1 As shown, the iterative learning control method of the vibration table in the embodiment of the present invention includes the following steps:

[0056] S1: According to the modal parameters of the test specimen and the bottom shear time history of the test specimen under the action of seismic waves, the physical parameters of the substitute specimen model are obtained, and the substitute specimen model is determined according to the physical parameters of the substitute specimen model.

[0057] S2: Perform iterative learning of the vibration table based on the alternative specimen model obtained in S1 to obtain the vibration table loading command that can make the table output waveform reproduce the expected input trajectory.

[0058] S3: Carry out a real vibration table test according to the vibration table loading command and the test specimen; that is, remove the substitute specimen model from the vibration table, replace it with the test specimen to be tested, and carry out a real vibration table test according to the vibration table loading command obtained in S2 as the system input.

[0059] The present invention can construct a substitute specimen model according to the modal parameters of the test specimen and the bottom shear time history of the test specimen under the action of seismic waves. After testing, it is found that the substitute specimen model constructed by the present invention and the actual test specimen to be tested have similar forces on the table surface under the same vibration table command input, that is, the substitute specimen model and the test specimen have similar influences on the control of the vibration table.

[0060] Therefore, compared with the no-load iterative learning in the prior art, the present invention can use the substitute specimen model with similar performance to the test specimen to carry out iterative learning, and the interaction between the specimen and the vibration table is taken into account during the learning process, so the obtained vibration table loading command is relatively accurate. Compared with the prior art that directly uses the test specimen for iterative learning and then continues to carry out the real vibration table test, the present invention first uses the substitute specimen model for iterative learning to obtain an accurate vibration table loading command, and then carries out a real vibration table test on the test specimen according to the vibration table loading command, which effectively avoids damage to the test specimen during the iterative loading process, thereby significantly improving the test accuracy.

[0061] It can be seen that the present invention is of great significance for improving the accuracy of the shaking table in reproducing seismic waves and enhancing the reliability and accuracy of the shaking table test results.

[0062] Preferably, the process for solving the physical parameters of the alternative specimen model of S1 can be any one of the following two methods, specifically including:

[0063] (1) See Figure 2 As shown in the figure, the inverse solution based on the modal parameters of the specimen is obtained. The specific process includes the following steps:

[0064] S101a: Simplify the test specimen into a spring-mass model with n degrees of freedom, according to the frequency formula and vibration mode equation Calculate the i-th order natural circular frequency ω of the test specimen i and vibration mode i=1,2,...,n; K represents the stiffness matrix of the test specimen, and M represents the mass matrix of the test specimen.

[0065] S101b: With the absolute value of the relative modal displacement of the degree of freedom as a reference, sort the n degrees of freedom in descending order, and select the first s (0<s<n) degrees of freedom (the degrees of freedom with larger modal displacement and uniform distribution) as the main degrees of freedom; take out the relative displacement of each main degree of freedom as the modal displacement of the s main degrees of freedom to replace the specimen model The first s order frequencies are the frequencies ω of the alternative specimen model a , a=1,2,...,s.

[0066] S101c: Replace the vibration mode of the specimen model according to s master degrees of freedom For the orthogonality of the mass matrix of the surrogate specimen model, the ratio of the mass of each principal degree of freedom of the surrogate specimen model is obtained. The specific process includes:

[0067] Lian Li a,b=1,2,...,s, and a≠b, M t is the diagonal mass matrix of the surrogate specimen model, and the simultaneous equations are solved to determine M t The ratio of the mass of each principal degree of freedom of the alternative specimen model.

[0068] S101d: According to the ratio of the mass of each principal degree of freedom of the alternative specimen model, ω a and Calculate the overall stiffness matrix K of the alternative specimen model t , the calculation formula is K t The stiffness coefficient in is converted into the stiffness between each layer to obtain the ratio of the stiffness between each layer of the alternative specimen model.

[0069]

[0070] The stiffness coefficient k ab (i,j=1,2,...,s) refers to the reaction force generated at the bth mass due to the unit displacement of the ath mass; interlayer stiffness k c(c=1,2,...,s) refers to the sum of the shear forces in all vertical components of the c-th layer caused by the unit inter-layer displacement of the mass. It can be seen from the vibration mode decomposition method that for the test specimen and the substitute specimen model with the same modal parameters, the relative acceleration time history under the same seismic excitation is the same. Ignoring the interaction between the degrees of freedom, the force exerted by the substitute specimen model on the vibration table surface is the bottom shear force under seismic excitation, that is, the sum of the inertia forces of each layer. Therefore, the bottom shear time history of the substitute specimen model obtained by taking different given mass parameters is linearly related to the test specimen.

[0071] In order to obtain the surrogate specimen model parameters close to the shear time history at the bottom of the test specimen, the present invention adopts a strategy of preliminarily giving a degree of freedom mass parameter and then correcting it.

[0072] The steps to correct this are:

[0073] S101e: among all the master degrees of freedom, obtain the mass parameter of any preliminarily given master degree of freedom, calculate the correction coefficient of the mass parameter of the given degree of freedom, and correct the mass parameter of the given degree of freedom according to the correction coefficient, that is, multiply the mass parameter of the given degree of freedom by the correction coefficient.

[0074] The calculation principle of the correction coefficient in S101e is: first, the masses of other degrees of freedom are solved according to the preliminary given degree of freedom mass parameters and the ratio relationship of each degree of freedom, and then the correction coefficient is calculated according to the mass of all degrees of freedom, ω a and Solve the stiffness between each layer to obtain the substitute specimen model under the condition of the initial given degree of freedom mass parameter, then solve the bottom shear time history of the substitute specimen model and the test specimen under the same seismic wave, and then use the least squares method to obtain the average amplitude ratio of the two curve time histories, which is the correction coefficient d of the given degree of freedom mass parameter;

[0075] On this basis, the calculation formula of the correction coefficient d is: Where V xj and V yj are the bottom shear forces of the alternative specimen model and the test specimen at the jth moment, respectively, and N is the total number of time steps.

[0076] S101f: According to the modified degree of freedom mass parameter in S101e, the ratio of the masses of each main degree of freedom in S101c, and the calculation method of the interlayer stiffness of each main degree of freedom in S101d, the mass and interlayer stiffness of other main degrees of freedom are calculated to obtain the physical parameters of the s degree of freedom alternative specimen model.

[0077] In order to verify the similarity between the substitute specimen model obtained in S1 and the test specimen, this embodiment uses the normalized root mean square of the difference in bottom shear time history between the test specimen and the substitute specimen model as an evaluation index of the similarity between the two:

[0078]

[0079] Where V xj and V yj are the bottom shear forces of the alternative specimen model and the test specimen at the jth moment, respectively, and N is the total number of time steps.

[0080] According to the specific results, it can be seen that the seismic response of the alternative specimen model proposed in the present invention and the experimental specimen under the same excitation is very similar, and specific data will be explained below.

[0081] (2) See Figure 3 As shown in the figure, the physical parameters of the alternative specimen model are solved based on the genetic algorithm. The specific process includes the following steps:

[0082] S102a: Define a set of physical parameters (m a ,k a ) is an individual in the population, m a is the mass of the ath degree of freedom of the surrogate specimen model, k a is the interlayer stiffness of the ath layer of the surrogate specimen model; the single physical parameter is the gene on the individual chromosome; defines the correlation coefficient of the bottom shear time history of the test specimen and the surrogate specimen model under the action of seismic waves The normalized root mean square J of the difference is the dual optimization objective; where V x is the bottom shear force time history curve of the alternative specimen model, V y is the bottom shear force time history curve of the test specimen, Cov(V x ,V y ) is V x and V y The covariance of x ) is V x The variance of D(V y ) is V y The variance of .

[0083] Since V x It is related to the mass of each layer and the interlayer stiffness, so the dual objective ρ xy and J are functions of the degree of freedom mass m and the interlayer stiffness k, that is, the dual objective function is:

[0084]

[0085] Where s is the number of degrees of freedom of the alternative specimen model. The smaller the normalized root mean square J is, the higher the correlation coefficient ρ is.xy The larger it is, the closer the bottom shear time history of the alternative specimen model is to the original test specimen, that is, the greater the fitness of the individual, and the better the individual.

[0086] Set the random value range of the degree of freedom mass m and interlayer stiffness parameter k of the alternative specimen model, define the initial population size, the crossover ratio and mutation probability of the offspring, set the maximum number of iterations and the normalized root mean square and correlation coefficient expected value of the exit iteration, and initialize the first generation population.

[0087] S102b: Calculate the objective function of all individuals in the first generation population and perform roulette wheel selection, multi-point crossover and multi-point mutation operations to obtain offspring.

[0088] S102c: After merging and sorting the first generation population and the offspring, the objective function value of the optimal individual is obtained.

[0089] S102d: Determine whether the objective function value of the optimal individual reaches the expected value. If so, output the physical parameters of the alternative specimen model represented by the individual corresponding to the objective function value as the optimal solution; otherwise, select individuals with larger fitness and the same size as the initial population as the parent population for the next round of iteration until an individual that meets the requirements is found to obtain all the physical parameters of the alternative specimen model.

[0090] It should be noted that: when the objective function value of the optimal individual does not reach the expected value, but has reached the set number of iterations, the physical parameters of the alternative specimen model represented by the individual corresponding to the objective function value are still output as the optimal solution.

[0091] The S2 process specifically includes:

[0092] The substitute specimen model in S1 is installed and fixed on the shaking table to carry out shaking table iterative learning. The system input is the expected earthquake acceleration signal. On the basis of the inner loop PID servo controller or three-parameter controller, an outer loop iterative learning control is added. The actual output acceleration of the shaking table surface is collected by the sensor, and the shaking table loading command is further corrected after comparison with the expected acceleration signal.

[0093] The specific process of the k-th iteration process in S2 includes:

[0094] S201: According to the input command u k (t) and the measured table output response y k The system transfer function h is identified by the Fourier spectrum of (t) k (f);

[0095] S202: Calculate the known expected trajectory y d (t) and y k The difference Δy of (t) k (t).

[0096] S203: According to Δy k (t) and h k (f) Calculate the input increment Δu in the time domain k (t), the calculation formula is: Δu k (f) = Δy k (f) / h k (f), Δy k (f) By Δy k (t) is transformed by Fourier to obtain, Δu k (f) By Δu k (t) is obtained by inverse Fourier transform.

[0097] S204: Δu k (t) Same as the last input command u k After superposition, the modified shaking table loading command u is obtained k+1 (t),u k+1 (t) = Δu k (t)+u k (t).

[0098] The method of the present invention is specifically described below by means of two embodiments.

[0099] Embodiment 1:

[0100] The control strategy is based on dual-loop control of outer loop iterative control and inner loop servo control. The inner loop servo control can be implemented in a variety of ways, such as three-parameter control, PID control, etc. In this embodiment, a three-parameter controller is used as the inner loop servo control module, and the outer loop iterative learning control adopts a modified iteration method.

[0101] Take a six-DOF linear shear spring mass specimen as an example. The mass of the first to fifth layers is 600kg, and the stiffness between each layer is 800kN / m; the mass of the sixth layer is 400kg, and the stiffness between layers is 650kN / m; the damping ratio is 0.05, and Rayleigh damping is used;

[0102] S1: Solve the physical parameters of the alternative specimen model. There are two specific processes.

[0103] (1) Using the frequency formula and vibration mode equation The frequency and vibration mode of the specimen are obtained, where K and M are the stiffness matrix and mass matrix of the test specimen, respectively, and ω i and is the i-th order natural circular frequency and mode shape of the test specimen, i = 1, 2, ..., 6. The first three order frequencies and mode shapes of the example six degrees of freedom are shown in Table 1;

[0104] The number of degrees of freedom of the substitute specimen model is s = 3. The 2nd, 4th, and 6th degrees of freedom with large relative displacements and uniform distribution in the first three vibration modes of the test specimen are taken as the main degrees of freedom, and the relative displacements of each main degree of freedom are taken as the vibration modes of the three-degree-of-freedom substitute specimen model. The first s-order frequency of the test specimen is the frequency of each order of the alternative specimen model ω a , a=1,2,3, as shown in the fourth column of Table 1;

[0105] Table 1. The first three frequencies and vibration modes of the six degrees of freedom

[0106]

[0107] Orthogonality of the mass matrix using the vibration modes of the surrogate specimen model Find the ratio of the mass of each degree of freedom, where

[0108] a, b = 1, 2, 3, and a ≠ b;

[0109] Substituting the ratio relationship into the vibration mode equation of multi-degree-of-freedom free vibration The interlayer stiffness of the alternative specimen model is obtained as:

[0110]

[0111] in, k ab is the stiffness coefficient, which is the reaction force generated at the bth mass due to the unit displacement of the ath mass; k a is the interlayer stiffness of the ath layer.

[0112] A degree of freedom mass parameter m1=600kg is preliminarily given, and other parameters are calculated to obtain the alternative specimen model.

[0113] Input the El-Centro seismic wave with a duration of 50s, a sampling step of 0.005s, and an acceleration peak of 250gal. The time history of the bottom shear force of the substitute specimen model and the specimen is compared. Figure 4 As shown, the correlation coefficient between the two is 0.9985, which is highly linearly correlated.

[0114] Calculate the correction factor for a given quality parameter

[0115] Where V xj and V yj are the bottom shear forces of the alternative specimen model and the test specimen at the jth moment respectively, and N is the total number of time steps. In this example, N = 10000.

[0116] The correction coefficient 1.9933 is multiplied by the given degree of freedom mass to complete the correction. The physical parameters of the corrected alternative specimen model are [m1, m2, m3] = [1196, 1353, 663] kg, [k1, k2, k3] = [423, 430, 363] kN / m. At this time, the bottom shear time history comparison of the two is as follows: Figure 5 shown.

[0117] The normalized root mean square of the difference in the bottom shear force time history between the specimen and the replacement specimen model is calculated as an evaluation index of the degree of proximity between the two:

[0118]

[0119] In this case, J = 0.0552, achieving a very good substitution effect;

[0120] (2) Solving the parameters of the alternative specimen model based on the intelligent optimization algorithm can be achieved using a variety of solutions, such as genetic algorithm, particle swarm algorithm, etc. This example uses the genetic algorithm to solve the problem. The specific steps are as follows:

[0121] The normalized root mean square of the bottom shear time difference and the correlation coefficient of the six-degree-of-freedom specimen and the three-degree-of-freedom substitute specimen model under the action of El-Centro wave with a duration of 50s, a sampling step of 0.005s, and an acceleration peak of 250gal are used as the dual optimization objective function:

[0122]

[0123] The three mass parameters of the alternative specimen model and the three interlayer stiffnesses are used as optimization design variables, and the value ranges are set to 100≤m≤2000kg, 100≤k≤1000kN / m respectively;

[0124] The population size of the genetic algorithm is set to 30, the crossover ratio of the offspring is 0.8, the mutation probability is 0.1, the normalized root mean square expectation is 0.0552, the expected value of the correlation coefficient is 0.9985, and the maximum number of iterations is 100;

[0125] Initialize the parameters of the first generation population, calculate the objective function of all individuals in the first generation population, and perform roulette wheel selection, multi-point crossover and multi-point mutation operations to obtain the first generation of offspring.

[0126] The first generation population and the offspring after selection, crossover and mutation are merged and sorted to determine whether the objective function value of the optimal individual reaches the expected value. If so, the parameters of the alternative specimen model represented by the individual corresponding to the objective function value are output as the optimal solution; if the expected value requirements are not met, individuals with larger fitness and the same size as the initial population are selected as the parent population for the next round of iteration until individuals that meet the requirements are found, and all the physical parameters of the alternative specimen model can be obtained.

[0127] The results of five calculations using the genetic algorithm in this example are shown in Table 2, which shows the results of solving the model parameters of the alternative specimen based on the genetic algorithm. It can be seen that when the normalized root mean square and correlation coefficient corresponding to the model parameters of the alternative specimen solved by method 1 are used as the expected value reference, the solution based on the genetic algorithm can obtain better results.

[0128] The empirical calculation, the solution based on the modal parameters of the specimen and the method of using genetic algorithm to solve the model parameters of the alternative specimen have good generalization ability; the model parameters are not affected by the type of seismic waves and the change of peak value, and have strong adaptability.

[0129] Table 2. Results of genetic algorithm calculations for 5 times

[0130]

[0131] S2: Construct a substitute specimen model based on the parameters obtained in S1, and perform iterative learning on the vibration table to obtain a modified vibration table loading command. The specific steps include:

[0132] For the kth iteration, according to the given input command u k (t) and the measured table output response y k The transfer function h of the system is identified by the Fourier spectrum of (t) k (f); Obtain the expected trajectory y d (t) and the current response y k (t), combined with the system transfer function h k (f) Obtain the input increment Δu in the time domain k (t); superimpose the previous input u k (t) Then the modified vibration table loading command u is obtained k+1 (t) = u k (t)+Δu k (t).

[0133] S3: Carry out a real vibration table test based on the vibration table loading command obtained in S2 and the original specimen.

[0134] Embodiment 2:

[0135] The six-degree-of-freedom shear spring mass specimen in Example 1 is changed to a bilinear model, the mass and stiffness of each layer remain unchanged, the yield displacement of each layer is set to 0.01m, and the stiffness after yield is 0.5 times the original stiffness.

[0136] Since the mechanical properties of the specimen change after yielding, the substitution effect of the alternative specimen model is solved based on the specimen modal parameters. Figure 6As shown, it is difficult to achieve a good substitution effect. The following are the steps for solving the substitution model parameters of nonlinear specimens using genetic algorithms:

[0137] The parameters of the genetic algorithm in Example 1 remain unchanged, three damper parameters are added as optimization design parameters, the value range is set to 1≤c≤2000, no expected value is set, 100 population iterations are performed each time, and the solution results are shown in Table 3.

[0138] Table 3. Genetic algorithm solution results of the alternative specimen model parameters including damper parameters

[0139]

[0140] The comparison of the alternative specimen model and the shear force time history curve at the bottom of the specimen in the first calculation result in Table 3 is shown in Figure 7 As shown, the normalized root mean square is 0.4076, which is 8.2% lower than the modal inverse solution method, and the correlation coefficient is 0.9257, which is 2.97% higher. This shows that the substitute specimen model with damper parameters has a better substitution effect than the linear substitute specimen model.

[0141] It can be seen that the present invention uses a substitute specimen model to carry out iterative learning of the vibration table, which effectively avoids damage to the original specimen during the iterative loading process, thereby changing the mechanical properties of the specimen; and compared with the traditional iterative learning with no load, the present invention uses a substitute model similar to the dynamic characteristics of the specimen to complete iterative learning, which can provide a vibration table loading command with better control effect, which is of great significance for improving the accuracy of the vibration table in reproducing seismic waves and enhancing the reliability and accuracy of the vibration table test results. In addition, the substitute model is made into a reusable standardized module, which can be quickly assembled according to specific test requirements without the need for design and production processes. There is no need to arrange too many sensors in the substitute model test, so the time spent on instrument selection, sensor installation, data acquisition and other links can be greatly reduced.

[0142] The embodiment of the present invention further provides a storage medium, on which a computer program is stored, and when the computer program is executed by a processor, the above-mentioned vibration table iterative learning control method is implemented. It should be noted that the storage medium includes various media that can store program codes, such as a USB flash drive, a mobile hard disk, a ROM (Read-Only Memory), a RAM (Random Access Memory), a magnetic disk or an optical disk.

[0143] An embodiment of the present invention further provides an electronic device, including a memory and a processor, wherein the memory stores a computer program that runs on the processor, and the processor implements the above-mentioned vibration table iterative learning control method when executing the computer program.

[0144] It will be appreciated by those skilled in the art that all or some of the steps, systems, and functional modules / units in the methods disclosed above may be implemented as software, firmware, hardware, and appropriate combinations thereof. In a hardware implementation, the division between the functional modules / units mentioned in the above description does not necessarily correspond to the division of physical components; for example, a physical component may have multiple functions, or a function or step may be performed by several physical components in cooperation. Some or all physical components may be implemented as software executed by a processor, such as a central processing unit, a digital signal processor, or a microprocessor, or may be implemented as hardware, or may be implemented as an integrated circuit, such as an application-specific integrated circuit. Such software may be distributed on a computer-readable storage medium, which may include a computer-readable storage medium (or a non-transitory medium) and a communication medium (or a temporary medium).

[0145] As is known to those of ordinary skill in the art, the term computer-readable storage media includes volatile and nonvolatile, removable and non-removable media implemented in any method or technology for storing information (such as computer-readable instructions, data structures, program modules or other data). Computer-readable storage media include, but are not limited to, RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, digital versatile disk (DVD) or other optical disk storage, magnetic cassettes, magnetic tapes, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to store the desired information and can be accessed by a computer. In addition, it is known to those of ordinary skill in the art that communication media typically contain computer-readable instructions, data structures, program modules or other data in a modulated data signal such as a carrier wave or other transmission mechanism, and may include any information delivery medium.

[0146] Exemplarily, the computer-readable storage medium may be an internal storage unit of the electronic device of the aforementioned embodiment, such as a hard disk or memory of the electronic device. The computer-readable storage medium may also be an external storage device of the electronic device, such as a plug-in hard disk, a smart memory card (Smart Media Card, SMC), a secure digital (SecureDigital, SD) card, a flash card (Flash Card), etc. equipped on the electronic device.

[0147] The above are only specific implementations of the embodiments of the present invention, but the protection scope of the embodiments of the present invention is not limited thereto. Any technician familiar with the technical field can easily think of various equivalent modifications or replacements within the technical scope disclosed in the embodiments of the present invention, and these modifications or replacements should be included in the protection scope of the embodiments of the present invention. Therefore, the protection scope of the embodiments of the present invention shall be based on the protection scope of the claims.

Claims

1. A vibration table iterative learning control method, characterized in that: The method comprises the following steps: S1: obtaining the physical parameters of the substitute specimen model according to the modal parameters of the test specimen and the bottom shear time history of the test specimen under the action of seismic waves, and determining the substitute specimen model according to the physical parameters of the substitute specimen model; S2: Perform iterative learning of the vibration table according to the alternative specimen model to obtain the vibration table loading command; S3: Conduct a shaking table test on the test specimen according to the shaking table loading command as system input; The process of solving the physical parameters of the alternative specimen model described in S1 includes solving based on the inverse solution method of the specimen modal parameters or solving based on the genetic algorithm; The process of inverse solution based on the specimen modal parameters includes: S101a: Simplify the test specimen into a spring-mass model with n degrees of freedom, according to the frequency formula and vibration mode equation Calculate the i-th order natural circular frequency ω of the test specimen i and vibration mode i=1,2,...,n; K represents the stiffness matrix of the test specimen, and M represents the mass matrix of the test specimen; S101b: Using the absolute value of the relative vibration mode displacement of the degree of freedom as a reference, sort the n degrees of freedom in descending order, select the first s degrees of freedom as the main degrees of freedom, 0<s<n; take out the relative displacement of each main degree of freedom as the vibration mode of the s main degrees of freedom to replace the specimen model The first s order frequencies are the frequencies ω of the alternative specimen model a , a=1,2,...,s; S101c: Replace the vibration mode of the specimen model according to s master degrees of freedom For the orthogonality of the mass matrix of the alternative specimen model, the diagonal mass matrix M of the alternative specimen model is obtained t , in M t Determine the ratio of the mass of each principal degree of freedom of the alternative specimen model; S101d: According to M t ,ω a and Calculate the overall stiffness matrix K of the alternative specimen model t , the calculation formula is K t The stiffness coefficient in is converted into the stiffness between each layer to obtain the ratio of the stiffness between each layer of the alternative specimen model; S101e: among all the master degrees of freedom, obtain the mass parameter of any preliminarily given master degree of freedom, calculate the correction coefficient of the mass parameter of the given degree of freedom, and correct the mass parameter of the given degree of freedom according to the correction coefficient; S101f: Calculate the mass and interlayer stiffness of other main degrees of freedom according to the modified degree of freedom mass parameter in S101e, the ratio of the masses of the main degrees of freedom described in S101c, and the ratio of the interlayer stiffness described in S101d; The genetic algorithm-based solution process includes: S102a: Define a set of physical parameters (m a ,k a ) is an individual in the population, m a is the mass of the ath degree of freedom of the surrogate specimen model, k a is the interlayer stiffness of the ath layer of the surrogate specimen model; the single physical parameter is the gene on the individual chromosome; defines the correlation coefficient of the bottom shear time history of the test specimen and the surrogate specimen model under the action of seismic waves The normalized root mean square J of the difference is the dual optimization objective; where V x is the bottom shear force time history curve of the alternative specimen model, V y is the bottom shear force time history curve of the test specimen, Cov(V x ,V y ) is V x and V y The covariance of x ) is V x The variance of D(V y ) is V y The variance of V xj and V yj are the bottom shear forces of the surrogate specimen model and the test specimen at the jth moment, respectively, and N is the total number of time steps; The dual optimization objective ρ xy and J as the dual objective function of the degree of freedom mass m and interlayer stiffness k: Where s is the number of degrees of freedom of the alternative specimen model. The smaller the normalized root mean square J is, the higher the correlation coefficient ρ is. xy The bigger; Set the random value range of the degree of freedom mass m and interlayer stiffness parameter k of the alternative specimen model, define the initial population size, the crossover ratio and mutation probability of the offspring, set the maximum number of iterations and the normalized root mean square and correlation coefficient expected value of the exit iteration, and initialize the first generation population; S102b: Calculate the objective function of all individuals in the first generation population and perform roulette wheel selection, multi-point crossover and multi-point mutation operations to obtain offspring; S102c: After merging and sorting the first generation population and the offspring, the objective function value of the optimal individual is obtained; S102d: obtaining the physical parameters of the substitute specimen model according to the objective function value of the optimal individual; The S2 process specifically includes: The alternative specimen model in S1 is installed on the vibration table to carry out vibration table iterative learning. For the kth iteration process, the following steps are included: S201: According to the input command u k (t) and the measured table output response y k The system transfer function h is identified by the Fourier spectrum of (t) k (f); S202: Calculate the known expected trajectory y d (t) and y k The difference Δy of (t) k (t); S203: According to Δy k (t) and h k (f) Calculate the input increment Δu in the time domain k (t), the calculation formula is: Δu k (f) = Δy k (f) / h k (f), Δy k (f) By Δy k (t) is transformed by Fourier to obtain, Δu k (f) By Δu k (t) is obtained by inverse Fourier transform; S204: Δu k (t) Same as the last input command u k After superposition, the modified shaking table loading command u is obtained k+1 (t),u k+1 (t) = Δu k (t)+u k (t).

2. The iterative learning control method for a vibration table according to claim 1, characterized in that: The specific process of S101c includes: a,b=1,2,...,s, and a≠b, solve the simultaneous equations to determine M t The ratio of the mass of each principal degree of freedom of the alternative specimen model.

3. The iterative learning control method for a vibration table according to claim 1, characterized in that: S101d Medium K t Specifically include: The stiffness coefficient k ab (i,j=1,2,...,s) refers to the reaction force generated at the bth mass due to the unit displacement of the ath mass; interlayer stiffness k c (c=1,2,...,s) refers to the sum of the shear forces in all vertical components of the c-th layer caused by the unit inter-layer lateral displacement of the mass of the c-th layer.

4. The iterative learning control method for a vibration table according to claim 1, characterized in that: The calculation formula for the correction factor described in S101e is: Where V xj and V yj are the bottom shear forces of the alternative specimen model and the test specimen at the jth moment, respectively, and N is the total number of time steps.

5. The iterative learning control method for a vibration table according to claim 1, characterized in that: The specific process of S102d includes: judging whether the objective function value of the optimal individual reaches the expected value, if so, outputting the physical parameters of the alternative specimen model represented by the individual corresponding to the objective function value as the optimal solution; otherwise, selecting individuals with larger fitness and the same size as the initial population as the parent population for the next round of iteration, and taking the parent population as the first generation population in S102b and then transferring to S102b.

6. A storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method according to any one of claims 1 to 5 is implemented.

7. An electronic device comprising a memory and a processor, wherein the memory stores a computer program running on the processor, wherein: When a processor executes the computer program, the method according to any one of claims 1 to 5 is implemented.

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