Random power spectrum reproduction control method and system for vibration shaker

Abstract

A random power spectrum reproduction control method and system for a vibration shaker. The method comprises the following steps: 1, estimating a frequency response function of a vibration shaker; 2, calculating an initial drive spectrum, an initial frequency response function and an initial response spectrum; 3, on the basis of the initial response spectrum, determining whether power spectrum reproduction precision is achieved; 4, calculating an error spectrum; 5, calculating a corrected frequency response function and an iteration step size; 6, performing iterative correction on a drive spectrum; 7, calculating a response spectrum and a frequency response function; and 8, determining whether the power spectrum reproduction precision is achieved. The system comprises an industrial personal computer, an acquisition board, a drive board and a signal conditioning apparatus. During iteration, quantitative evaluation and dynamic correction are performed on each frequency point on the basis of historical data information, and the accuracy of a corrected frequency response function at each frequency point is used to quantitatively optimize an iteration step size, thereby overcoming the impact of frequency response function fluctuations on the power spectrum reproduction precision, and thus improving the random power reproduction control precision for vibration shakers.

Description

A vibration table random power spectrum replication control method and system TECHNICAL FIELD

[0001] The present application relates to the field of vibration table control, in particular to a vibration table random power spectrum replication control method and system. BACKGROUND

[0002] The vibration table is mainly used for simulating vibration test of test pieces, testing the performance of test pieces in vibration environment, and the vibration of test pieces in working environment is mostly random vibration. Since the characteristics are mainly described by acceleration power spectrum density and other statistical characteristics, it is necessary to replicate the measured power spectrum density on the vibration table to simulate such vibration. The main shortcomings of the traditional power spectrum replication control method are:

[0003] 1. In the iteration process, the frequency response function estimated at the beginning of the test is mainly used, and the accuracy of the frequency response function decreases with the increase of the iteration number due to the lack of correction of the frequency response function.

[0004] 2. Although the power spectrum replication control method proposed in some public technical materials corrects the frequency response function, it does not quantitatively evaluate the accuracy of the frequency response function, and directly corrects or does not consider the historical information of the frequency response function in the correction process.

[0005] 3. In the iteration process, the same iteration step is used for all frequency points, which cannot cope with the influence of frequency response function fluctuation, and the selection of iteration step is not quantified, and the convergence and convergence speed of iteration algorithm are also difficult to guarantee.

[0006] SUMMARY

[0007] The purpose of the present application is to provide a vibration table random power spectrum replication control method and system which improves the estimation accuracy and overcomes the problem of frequency response function characteristic fluctuation.

[0008] Technical scheme: A vibration table random power spectrum replication control method, comprising the following steps:

[0009] (1) estimating the frequency response function H0(f) of the vibration table system, the specific steps are as follows: taking the reference spectrum R(f) replicated by the vibration table as the input of the vibration table system, generating the driving signal u0(t) after frequency domain randomization and time domain randomization, inputting the driving signal u0(t) into the vibration table system and collecting the vibration table response signal y0(t) under the excitation of the driving signal u0(t), and estimating the frequency response function H0(f) of the vibration table system by using frequency response function estimation method according to the driving signal u0(t) and the response signal y0(t);

[0010] (2) Calculate initial driving spectrum U1(f), initial frequency response function H1(f) and initial response spectrum Y1(f) according to the reference spectrum R(f) and the frequency response function H0(f) reproduced by the vibration table;

[0011] (3) Determine whether the accuracy of power spectrum reproduction is reached according to the initial response spectrum Y1(f), and if the accuracy is reached, the experiment is ended, otherwise, go to step (4);

[0012] (4) Calculate error spectrum E(f) according to the response signal y(t) of the vibration table;

[0013] (5) Calculate the modified frequency response function and the iteration step size a; the specific calculation steps of the modified frequency response function are as follows:

[0014] The current iteration is the nth time, wherein: n is greater than or equal to 1 and is an integer, and the modified frequency response function at the ith iteration is denoted as i takes values of 1, 2, …, n; the current iteration modified frequency response function is denoted as The calculation formula of the modified frequency response function is wherein: H i (f) represents the frequency response function at the ith iteration; * is the Hadamard product of the matrix, which means that the corresponding elements of the matrix are multiplied; represents the corrected frequency point correction coefficient of H i (f), wherein, represents the corrected frequency point correction coefficient of the jth frequency point estimate value of H i (f), j takes values of 1, 2, …, m, and m is the number of frequency points of H i (f);

[0015] For the iteration step size a, the iteration step size at the ith iteration is represented as a i =[a i,1 , a i，2 , …, a i，m ], and a i,j represents the jth frequency point iteration step size at the ith iteration, and the current iteration step size is represented as a n =[a n，1 , a n，2 , …, a n，m ];

[0016] (6) Iteratively correct the driving spectrum, and the iterative correction formula of the driving spectrum is , wherein represents the corrected driving spectrum, and U(f) represents the driving spectrum used in the last iteration, the inverse of

[0017] (7) the modified driving spectrum excite the vibration table with the modified driving spectrum, calculate the modified response spectrum and the modified frequency response function

[0018] (8) determine whether the accuracy of power spectrum replication is reached according to the modified response spectrum if the accuracy is reached, the experiment is ended; otherwise, repeat steps (4) to (7).

[0019] A vibration table random power spectrum replication system, comprising an industrial computer, a collection board card, a driving board card, a communication network card and a signal conditioning device, the collection board card, the driving board card and the communication network card are arranged in the industrial computer, the signal conditioning device is connected with the driving board card, the collection board card is used for collecting displacement and acceleration sensor signals in the running process of the vibration table in real time, the driving board card is used for converting the calculated real-time control signal into an actual driving signal, the signal conditioning device is used for signal transformation between the collection board card and the vibration table sensor and between the driving board card and the vibration table driving unit, and the communication network card is used for real-time communication between the power spectrum replication control system and the vibration table host computer display unit.

[0020] Further, the initial driving spectrum U1(f), the initial frequency response function H1(f) and the initial response spectrum Y1(f) calculation method has the following specific steps: calculating the initial driving spectrum U1(f), and the expression is U1(f)=R(f)[H0(f)] -1 , wherein [H0(f)] -1 represents the inverse of H0(f), after frequency domain randomization and time domain randomization, the driving signal u1(t) is generated and input into the vibration table system, and the vibration table response signal y1(t) under the excitation of the driving signal u1(t) is collected;

[0021] According to the driving signal u1(t) and the response signal y1(t), the initial frequency response function H1(f) of the vibration table system is estimated by using the frequency response function estimation method;

[0022] According to the response signal y1(t), the initial response spectrum Y1(f) is obtained by using the power spectrum estimation method.

[0023] Further, the error spectrum E(f) calculation method has the following specific steps: according to the collected vibration table response signal y(t), the response spectrum Y(f) is obtained by using the power spectrum estimation method, and the error spectrum E(f) is obtained by subtracting the response spectrum Y(f) from the reference spectrum R(f) of the vibration table replication.

[0024] ​Furthermore, in step (7), the modified driving spectrum After frequency domain randomization and time domain randomization processing, the driving signal is generated Input the vibration table system and collect the driving signal Vibration table response signal under excitation According to the driving signal and response signals Calculate the corrected frequency response function of the shaking table system using the frequency response function estimation method According to the response signal The corrected response spectrum is calculated using the power spectrum estimation method.

[0025] Furthermore, the corrected frequency point correction coefficient The calculation steps are as follows:

[0026] (51) Set the uncorrected frequency point correction coefficient β i =β i，1 , β i，2 ,…,β i，m ], β i It is used to correct the frequency point coefficient after calibration Let β i The correction coefficient β of the uncorrected frequency point in i，j The following conditions are met: The value range of η is 0.6 to 0.8;

[0027] (52) Let u be the value at the i-th iteration. i (t) and y i (t) are driving signal and response signal respectively, according to the driving signal u i (t) and the response signal y i (t) Find the coherence function at the i-th iteration and u i (t)’s autopower spectrum, u i (t) and y i The cross power spectrum of (t) and y i The autopower spectrum of (t);

[0028] (53) According to C1(f), C2(f), ..., C n (f) Forming the discriminant matrix Element C in C i，j represents the coherence function C at the i-th iteration i (f) The coherence function value of the jth frequency point; use the element C in the discriminant matrix C i，jCharacterizing the frequency response function H i (f) The accuracy of the estimated value of the jth frequency point; set the frequency response function accuracy threshold γ, judge whether the values ​​of each column element of the discriminant matrix C are all greater than or equal to γ, and count the number of columns in the discriminant matrix C where the values ​​of each column element are all greater than or equal to γ, and record them as p1, p2, ..., p according to the number of columns from small to large. k , the remaining mk columns of the discriminant matrix C are recorded as q1, q2, ..., q m-k , calculate the frequency response function H respectively i (f) p s The correction factor of the corrected frequency point estimate is: Frequency Response Function The qth r The correction factor of the corrected frequency point estimate is: Harmony function The qth r The correction coefficient of the frequency point after the estimated value of the frequency point is corrected is:

[0029] Furthermore, p1, p2, ..., p k Where k represents the number of columns of the discriminant matrix C that satisfy the requirement that all column element values ​​are greater than or equal to γ, and the value of k is 1≤k≤m and k is an integer, p s Represents the pth in the discriminant matrix C s The value of s is 1, 2, ..., k; the pth column of the discriminant matrix C s The element values ​​of the column are all greater than or equal to γ, and the frequency response function H i (f) p s The estimated value of each frequency point is highly accurate, and the frequency response function H i (f) p s The correction factor of the corrected frequency point estimate is: The value of s is 1, 2,…, k.

[0030] Furthermore, the q1, q2, ..., q m-k Middle Q r Represents the qth in the discriminant matrix C r Column, r takes the value of 1, 2, ..., mk; the remaining mk columns do not satisfy that all element values ​​are greater than or equal to, judge and record the qth discriminant matrix C r The number of rows of the discriminant matrix C where the column element value is less than γ is recorded from small to large as Among them: r For the qth r The number of elements whose column values ​​are less than γ, l r The value is 1≤l r≤n and l is an integer, a u，r represents the ath of the discriminant matrix C u，r row, u takes values ​​of 1, 2, ..., l r ; The ath of the discriminant matrix C u，r Row q r Column element value For the frequency response function The qth r The accuracy of the estimated value of each frequency point is low, and the frequency response function The qth r The correction factor of the corrected frequency point estimate is: Where: u takes the value of 1, 2, ..., l r , the value of r is 1, 2,…, mk.

[0031] Furthermore, the discriminant matrix Cq r Column remaining nl r The element value of elements is greater than or equal to γ, and the remaining nl r The number of rows in the discriminant matrix C where the element is located is recorded from small to large as Where: b v，r represents the bth discriminant matrix C v，r row, v takes values ​​of 1, 2, ..., nl r ; The bth discriminant matrix C v,r Row q r Column element value For the frequency response function The qth r frequency points, the estimated value is accurate, and the frequency response function The qth r The correction coefficient of the frequency point after the estimated value of the frequency point is corrected is: in: Indicates the correction coefficient of the uncorrected frequency point, v takes the value of 1, 2, ..., nl r , the value of r is 1, 2,…, mk.

[0032] Furthermore, the coherence function value C i，j and the correction coefficient β of the uncorrected frequency point i，j The corrected frequency response function can be calculated at the nth iteration The average coherence function value at each frequency point The calculation formula is Where: j is 1, 2, ..., m; the iteration step length is α n The element α in n，j The calculation formula is Where λ is the proportional coefficient; if It is shown that the frequency point on the frequency response function accuracy is high, and the value of lambda is lambda1; if It is shown that the frequency point on the frequency response function accuracy is low, and the value of lambda is lambda2.

[0033] Compared with the prior art, the present application has the following remarkable effects: 1. The power spectrum reproduction control method proposed by the present application modifies the frequency response function compared with the traditional power spectrum reproduction control method, and modifies all frequency points of the frequency response function using historical information of the frequency response function, thereby improving the accuracy of the frequency response function estimation;

[0034] 2. The power spectrum reproduction control method proposed by the present application quantitatively evaluates the accuracy of each frequency point of the frequency response function by calculating the coherence function;

[0035] 3. In the frequency response function modification process of the power spectrum reproduction control method proposed by the present application, the frequency response function value with low accuracy is removed according to the accuracy, thereby overcoming the problem of fluctuation of the frequency response function characteristics;

[0036] 4. The power spectrum reproduction control method proposed by the present application uses different iteration steps for different frequency points, and quantitatively calculates the iteration step according to the accuracy of each frequency point of the modified frequency response function, thereby improving the convergence of the iteration algorithm and ensuring a faster convergence speed. BRIEF DESCRIPTION OF DRAWINGS

[0037] Fig. 1 is a flow chart of the control method of the present application;

[0038] Fig. 2 is a comparison diagram of random power reproduction waveforms in an electric vibration table according to the present application;

[0039] Fig. 3 is a comparison diagram of random power reproduction waveforms in an electro-hydraulic vibration table according to the present application; DETAILED DESCRIPTION

[0040] The present application will be further described in detail below in combination with the drawings and specific embodiments.

[0041] Referring to Fig. 1, the present application provides a vibration table random power spectrum reproduction control method, which comprises the following steps:

[0042] Step one, estimate the frequency response function H0(f) of the vibration table system, and the specific steps are as follows: set the reference spectrum reproduced by the vibration table as R(f), the estimation of the frequency response function R(f) uses the frequency response function estimation method, take ε times of R(f) as the input of the vibration table system, and ε takes 0<ε<1, after frequency domain randomization and time domain randomization, generate the driving signal u0(t) inputting the vibration table system and collect the vibration table response signal y0(t) under the excitation of the driving signal u0(t), and estimate the frequency response function H0(f) of the vibration table system using H1 estimation method according to the driving signal u0(t) and the response signal y0(t).

[0043] Step two, calculate the initial driving spectrum U1(f), the initial frequency response function estimate H1(f) and the initial response spectrum Y1(f), the specific steps are: first, according to the reference spectrum R(f) and the frequency response function H0(f) in (1) reproduced by the vibration table, calculate the initial driving spectrum U1(f), the expression is U1(f) = R(f) [H0(f)] -1 , where [H0(f)] -1 represents the inverse of H0(f), after frequency domain randomization and time domain randomization, the driving signal u1(t) is generated and input into the vibration table system, and the vibration table response signal y1(t) under the excitation of the driving signal u1(t) is collected, the vibration table system frequency response function H1(f) is estimated according to the driving signal u1(t) and the response signal y1(t) using H1 estimation method, and the initial response spectrum Y1(f) is obtained by using Blackman-Tukey spectrum estimation according to the response signal y1(t).

[0044] Step three, according to the initial response spectrum Y1(f) in step two, judge whether the accuracy of power spectrum reproduction is reached, if the accuracy is reached, the experiment is ended, otherwise, enter the next step.

[0045] Step four, calculate the error spectrum E(f), the specific steps are: according to the response signal y(t) of the vibration table, the response spectrum Y(f) is obtained by using Blackman-Tukey spectrum estimation method, and the error spectrum E(f) = R(f)-Y(f) is obtained by subtracting the reference spectrum R(f) reproduced by the vibration table from the response spectrum Y(f).

[0046] Step five, calculate the modified frequency response function and the iteration step α.

[0047] Step six, iterative correction of the driving spectrum, the iterative correction formula of the driving spectrum is , where represents the modified driving spectrum, U(f) represents the driving spectrum used in the last iteration, represents the inverse of .

[0048] Step seven, calculate the response spectrum and the frequency response function obtained by using the driving spectrum as the driving spectrum to excite the vibration table, the specific steps are: after the modified driving spectrum is processed by frequency domain randomization and time domain randomization, the driving signal is generated and input into the vibration table system, and the vibration table response signal under the excitation of the driving signal is collected, according to the driving signal and the response signal The H1 estimation method is used to calculate the frequency response function of the shaking table system According to the response signal The Blackman-Tukey spectrum estimation method is used to calculate the response spectrum

[0049] Step eight, according to the response spectrum in step seven It is judged whether the accuracy of the power spectrum replication is reached, and if the accuracy is reached, the experiment is ended, otherwise steps four to seven are repeated.

[0050] Among them, the frequency response function in step five The specific calculation steps are as follows:

[0051] The current iteration number is the nth time, wherein: n takes the value of n≥1 and n is an integer, and the modified frequency response function at the ith iteration is denoted as Wherein: i takes the value of 1, 2, …, n, according to the above principle, the current iteration modified frequency response function can be denoted as The calculation formula of Wherein: H i (f) represents the frequency response function at the ith iteration; * is the Hadamard product of the matrix, which means that the corresponding elements of the matrix are multiplied; The correction factor of the frequency point of H i (f) is denoted as The expression of Wherein, The element in The correction factor of the jth frequency point estimate of H i (f) is denoted as, wherein: i takes the value of 1, 2, …, n, j takes the value of 1, 2, …, m, and m is the number of frequency points of H i (f).

[0052] The specific calculation steps of in the above steps are as follows:

[0053] Step 51, set the uncorrected frequency point correction factor β i =[β i,1 ,β i，2 , …, β i，m ], β i is the value of the corrected frequency point correction factor , wherein: i takes the value of 1, 2, …, n, and the element β i，j in β i satisfies the following conditions:

[0054] Step 52, record u i(t) and y i (t) are driving signal and response signal respectively, the driving signal u i (t) and response signal y i (t) is the coherence function at the i-th iteration Wherein: i takes 1, 2, …, n, And The self-power spectrum of u i (t), the cross-power spectrum of u i (t) and y i (t), and the self-power spectrum of y i (t) ;

[0055] Step 53, according to C1(f), C2(f), …, Cn( f ) to form a discriminant matrix , the element C i，j in C represents the coherence function value of the j-th frequency point of the coherence function C i (f) at the i-th iteration, wherein: i takes 1, 2, …, n, j takes 1, 2, …, m; the element C i，j in the discriminant matrix C represents the accuracy of the j-th frequency point estimate of the frequency response function H i (f) ; Set the frequency response function accuracy threshold γ = 0.90-0.98, if C i，j ≥ γ, it indicates that the accuracy of the j-th frequency point estimate of H i (f) is high; if C i，j < γ, it indicates that the accuracy of the j-th frequency point estimate of H i (f) is low;

[0056] Then the uncorrected frequency point correction coefficient is calculated, first determine whether the element value of each column of the discriminant matrix C is greater than or equal to γ, and count the column number of the discriminant matrix C that satisfies that the element value of each column is greater than or equal to γ, and according to the column number from small to large, respectively recorded as p1, p2, …, p k , wherein: k represents the number of columns of the discriminant matrix C that satisfies that the element value of each column is greater than or equal to γ, k takes 1 ≤ k ≤ m and k is an integer, p s represents the p s th column in the discriminant matrix C, s takes 1, 2, …, k; Therefore, the element value of the p s th column of the discriminant matrix C is greater than or equal to γ, so the accuracy of the p i th frequency point estimate of the frequency response function H s (f) is high, and the accuracy of the p i th frequency point estimate of the frequency response function H sThe correction factor of the corrected frequency point estimate is: Where: i is 1, 2, ..., n, s is 1, 2, ..., k;

[0057] The remaining mk columns of the discriminant matrix C are marked as q1, q2, ..., q from small to large. m-k , where: q r Represents the qth in the discriminant matrix C r Column, r takes the value of 1, 2, ..., mk; the remaining mk columns do not satisfy that all element values ​​are greater than or equal to γ; Based on the above content, judge and record the qth discriminant matrix C r The number of rows of the discriminant matrix C where the column element value is less than γ is recorded from small to large as Among them: r For the qth r The number of elements whose column values ​​are less than γ, l r The value is 1≤l r ≤n and l is an integer, a u，r represents the ath of the discriminant matrix C u，r row, u takes values ​​of 1, 2, ..., l r ; Therefore, the a-th discriminant matrix C u,r Row q r Column element value So for the frequency response function The qth r The accuracy of the estimated value of each frequency point is low, and the frequency response function The qth r The correction factor of the corrected frequency point estimate is: Where: u takes the value of 1, 2, ..., l r , r takes the value of 1, 2, ..., mk; after the above steps, the discriminant matrix C q r Column remaining nl r The element value of elements is greater than or equal to γ, and the remaining nl r The number of rows in the discriminant matrix C where the element is located is recorded from small to large as Where: b v，r represents the bth discriminant matrix C v，r row, v takes values ​​of 1, 2, ..., nl r ; Therefore, the bth discriminant matrix C v，r Row q r Column element value So for the frequency response function The qth r The accuracy of the estimated value of each frequency point is high, and the frequency response function The qth rThe corrected frequency point correction coefficient of each frequency point is Wherein: The uncorrected frequency point correction coefficient is represented by β , and v takes the value of 1, 2, …, n-l r , and r takes the value of 1, 2, …, m-k.

[0058] Wherein, the specific calculation steps of the iteration step size α in step five are as follows:

[0059] Let the current iteration number be the n th time, wherein: n takes the value of n≥1 and k is an integer, and the iteration step size at the i th iteration is represented by α i i，1 i,2 i,m , wherein: i takes the value of 1, 2, …, n, and the element α i of α i，j represents the j th frequency point iteration step size at the i th iteration, i takes the value of 1, 2, …, n, and j takes the value of 1, 2, …, m; according to the above principle, the current iteration step size can be represented as α n n，1 n，2 n，m ; according to the coherence function value C i，j and the uncorrected frequency point correction coefficient β i,j , the corrected frequency response function at the n th iteration is calculated as The calculation formula of the average coherence function value of each frequency point is Wherein: j takes the value of 1, 2, …, m; the element α n in the iteration step size α n,j has the calculation formula In the formula, λ is a proportionality coefficient; if , it indicates that the accuracy of the frequency response function at this frequency point is high, and λ takes the value of 0.96-1; if , it indicates that the accuracy of the frequency response function at this frequency point is low, and λ takes the value of 0.90-0.95.

[0060] ​​​​​​The application further provides a vibration table random power spectrum replication system applicable to an electric vibration table or an electro-hydraulic vibration table, mainly comprising an industrial computer, an acquisition board, a drive board, and a signal conditioning device; the acquisition board, the drive board and a communication network card are arranged in the industrial computer; the signal conditioning device is connected with the drive board; the acquisition board is used for collecting displacement and acceleration sensor signals in real time during vibration table operation; the drive board is used for converting the calculated real-time control signals into actual driving signals; the signal conditioning device is used for signal conversion between the acquisition board and the vibration table sensor and between the drive board and the vibration table driving unit; and the communication network card is used for real-time communication between the power spectrum replication control system and the vibration table host computer display unit.

[0061] FIGS. 2 and 3 are waveform comparison diagrams of random power spectrum replication in the electric vibration table and the electro-hydraulic vibration table according to the application; it can be concluded from FIGS. 2 and 3 that the vibration table random power spectrum replication control method provided by the application effectively improves the power spectrum replication precision.

[0062] The above description is only the preferred embodiments of the application, and it should be pointed out that those skilled in the art can make several improvements and refinements without departing from the principles of the application, and these improvements and refinements should also be within the protection scope of the application.

Claims

1. A vibration table random power spectrum recurrence control method, characterized in that: The following steps are involved: (1) Estimate the frequency response function H0(f) of the vibration table system. The specific steps are as follows: let the reference spectrum reproduced by the vibration table be R(f), take ε times R(f) as the input of the vibration table system, generate the driving signal u0(t) after frequency domain randomization and time domain randomization, input it into the vibration table system and collect the vibration table response signal y0(t) under the excitation of the driving signal u0(t), and use the frequency response function estimation method to estimate the frequency response function H0(f) of the vibration table system based on the driving signal u0(t) and the response signal y0(t); (2) Based on the reference spectrum R(f) and frequency response function H0(f) reproduced by the vibration table, calculate the initial driving spectrum U1(f), initial frequency response function H1(f), and initial response spectrum Y1(f); (3) Determine whether the accuracy of power spectrum reproduction is achieved based on the initial response spectrum Y1(f). If the accuracy is achieved, the experiment ends; otherwise, proceed to step (4). (4) Calculate the error spectrum E(f) based on the response signal y(t) of the vibration table; (5) Calculate the corrected frequency response function and iteration step α; for the modified frequency response function The specific calculation steps are as follows: The current iteration number is the nth, where n is an integer and n is n≥1. The corrected frequency response function at the i-th iteration is: The value of i is 1, 2, ..., n; then the frequency response function after the current iteration is recorded as described The calculation formula is Among them: H i (f) represents the frequency response function at the i-th iteration; * is the Hadamard product of the matrix, which means the multiplication of the corresponding elements of the matrix; Indicates H i (f) is the correction factor of the corrected frequency point, in, Indicates H i (f) is the correction coefficient of the j-th frequency point estimate after correction, j is 1, 2, ..., m, m is H i (f) the number of frequency points; For the iteration step α, the iteration step at the i-th iteration is expressed as α i =[α i，1 , α i，2 ,…,α i，m ], α i, j represents the iteration step of the jth frequency point in the i-th iteration, and the current iteration step is expressed as α n =[α n,1 ,α n,2 ,…,α n,m ]; (6) Iteratively correct the driving spectrum. The iterative correction formula of the driving spectrum is: in represents the modified driving spectrum, U(f) represents the driving spectrum used in the previous iteration, express The inverse of (7) The corrected driving spectrum Use the driving spectrum to excite the vibration table and calculate the corrected response spectrum and the corrected frequency response function (8) According to the corrected response spectrum Determine whether the accuracy of power spectrum reproduction is achieved. If the accuracy is achieved, the experiment ends; otherwise, repeat steps (4) to (7).

2. The vibration table random power spectrum reproduction control method according to claim 1, characterized in that: The calculation method of the initial drive spectrum U1(f), the initial frequency response function H1(f) and the initial response spectrum Y1(f) is as follows: Calculate the initial drive spectrum U1(f), which is expressed as U1(f) = R(f)[H0(f)] -1 , where [H0(f)] -1 It represents the inverse of H0(f). After randomization in the frequency domain and time domain, it generates a driving signal u1(t) which is input into the vibration table system and collects the vibration table response signal y1(t) under the excitation of the driving signal u1(t). Estimate the initial frequency response function H1(f) of the vibration table system using the frequency response function estimation method based on the driving signal u1(t) and the response signal y1(t); The initial response spectrum Y1(f) is obtained by using the power spectrum estimation method based on the response signal y1(t).

3. The vibration table random power spectrum reproduction control method according to claim 1, characterized in that: The calculation method of the error spectrum E(f) comprises the following specific steps: according to the response signal y(t) of the collected vibration table, a power spectrum estimation method is used to obtain the response spectrum Y(f); the reference spectrum R(f) reproduced by the vibration table is subtracted from the response spectrum Y(f) to obtain the error spectrum E(f) = R(f) - Y(f).

4. The vibration table random power spectrum reproduction control method according to claim 1, characterized in that: In step (7), the modified driving spectrum After frequency domain randomization and time domain randomization processing, the driving signal is generated Input the vibration table system and collect the driving signal Vibration table response signal under excitation According to the driving signal and response signals Calculate the corrected frequency response function of the shaking table system using the frequency response function estimation method According to the response signal The corrected response spectrum is calculated using the power spectrum estimation method.

5. The vibration table random power spectrum reproduction control method according to claim 1, characterized in that: The corrected frequency point correction coefficient The calculation steps are as follows: (51) Set the uncorrected frequency point correction coefficient β i =[β i，1 , β i，2 ,…,β i，m ], β i It is used to correct the frequency point coefficient after calibration Let β i The correction coefficient β of the uncorrected frequency point in i，j The following conditions are met: The value range of η is 0.6 to 0.8; (52) Let u be the value at the i-th iteration. i (t) and y i (t) are driving signal and response signal respectively, according to the driving signal u i (t) and the response signal y i (t) Find the coherence function at the i-th iteration and u i (t)’s autopower spectrum, u i (t) and y i The cross power spectrum of (t) and y i The autopower spectrum of (t); (53) According to C1(f), C2(f), ..., C n (f) Forming the discriminant matrix Element C in C i，j represents the coherence function C at the i-th iteration i (f) The coherence function value of the jth frequency point; use the element C in the discriminant matrix C i，j Characterize the frequency response function H i (f) The accuracy of the estimated value of the jth frequency point; set the frequency response function accuracy threshold γ, judge whether the values ​​of each column element of the discriminant matrix C are all greater than or equal to γ, and count the number of columns in the discriminant matrix C where the values ​​of each column element are all greater than or equal to γ, and record them as p1, p2, ..., p according to the number of columns from small to large. k , the remaining mk columns of the discriminant matrix C are recorded as q1, q2, ..., q m-k , calculate the frequency response function H respectively i (f) p s The correction factor of the corrected frequency point estimate is: Frequency Response Function The qth r The correction factor of the corrected frequency point estimate is: Harmony function The qth r The correction coefficient of the frequency point after the estimated value of the frequency point is corrected is:

6. The vibration table random power spectrum reproduction control method according to claim 5, characterized in that: The p1, p2, ..., p k Where k represents the number of columns of the discriminant matrix C that satisfy the requirement that all column element values ​​are greater than or equal to γ, and the value of k is 1≤k≤m and k is an integer, p s Represents the pth in the discriminant matrix C s The value of s is 1, 2, ..., k; the pth column of the discriminant matrix C s The element values ​​of the column are all greater than or equal to γ, and the frequency response function H i (f) p s The estimated value of each frequency point is highly accurate, and the frequency response function H i (f) p s The correction factor of the corrected frequency point estimate is: The value of s is 1, 2, ..., k.

7. The vibration table random power spectrum reproduction control method according to claim 5, characterized in that: The q1, q2, ..., q m-k Middle Q r Represents the qth in the discriminant matrix C r Column, r takes the value of 1, 2, ..., mk; the remaining mk columns do not satisfy that all element values ​​are greater than or equal to, judge and record the qth discriminant matrix C r The number of rows of the discriminant matrix C where the column element value is less than γ is recorded from small to large as Among them: r For the qth r The number of elements whose column values ​​are less than γ, l r The value is 1≤l r ≤n and l is an integer, a u，r represents the ath of the discriminant matrix C u，r row, u takes values ​​of 1, 2, ..., l r ; The ath of the discriminant matrix C u，r Row q r Column element value For the frequency response function The qth r The accuracy of the estimated value of each frequency point is low, and the frequency response function The qth r The correction factor of the corrected frequency point estimate is: Where: u takes the value of 1, 2, ..., l r , the value of r is 1, 2,…, mk.

8. The vibration table random power spectrum reproduction control method according to claim 7, characterized in that: The discriminant matrix Cq r Column remaining nl r The element value of elements is greater than or equal to γ, and the remaining nl r The number of rows in the discriminant matrix C where the element is located is recorded from small to large as Where: b v，r represents the bth discriminant matrix C v，r row, v takes values ​​of 1, 2…, nl r ; The bth discriminant matrix C v,r Row q r Column element value For the frequency response function The qth r frequency points, the estimated value is accurate, and the frequency response function The qth r The correction coefficient of the frequency point after the estimated value of the frequency point is corrected is: in: Indicates the correction coefficient of the uncorrected frequency point, v takes the value of 1, 2, ..., nl r , the value of r is 1, 2,…, mk.

9. The vibration table random power spectrum reproduction control method according to claim 5, characterized in that: The coherence function value C i,j and the correction coefficient β of the uncorrected frequency point i,j The corrected frequency response function can be calculated at the nth iteration The average coherence function value at each frequency point The calculation formula is Where: j is 1, 2, ..., m; the iteration step length is α n The element α in n,j The calculation formula is Where λ is the proportional coefficient; if It shows that the frequency response function at this frequency point has high accuracy, and the value of λ is λ1; if This indicates that the accuracy of the frequency response function at this frequency point is low, and the value of λ is λ2.

10. A vibration table random power spectrum reproduction system, used to implement the method according to any one of claims 1 to 9, characterized in that: The system includes an industrial computer, an acquisition board, a drive board, a communication network card and a signal conditioning device. The acquisition board, the drive board and the communication network card are arranged inside the industrial computer. The signal conditioning device is connected to the drive board. The acquisition board is used to collect displacement and acceleration sensor signals during the operation of the vibration table in real time. The drive board is used to convert the calculated real-time control signal into an actual drive signal. The signal conditioning device is used to convert signals between the acquisition board and the vibration table sensor, and between the drive board and the vibration table drive unit. The communication network card is used for real-time communication between the power spectrum reproduction control system and the display unit of the vibration table host computer.

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