Method for controlling and reproducing random power spectrum of vibration table and system thereof

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

TECHNICAL FIELD

[0001] The present disclosure relates to the technical field of the vibration table control, and in particular to a method for controlling and reproducing a random power spectrum of a vibration table. BACKGROUND

[0002] The vibration table is mainly used to simulate the vibration tests on the specimens and test the performances of the specimens in a vibration environment. The vibrations that specimens are subjected to are mostly the random vibrations in an operating environment. Since the feature is mainly described by the statistical characteristics such as the acceleration power spectrum density, it is required to reproduce the measured power spectrum density on the vibration table to simulate the vibration. The traditional method for controlling and reproducing the power spectrum mainly have the following disadvantages.

[0003] 1. In the iterative process, the frequency response function estimated at the beginning of the test is mainly utilized, and the frequency response function is not corrected, which results in a decrease in the accuracy of the frequency response function as the number of the iterations increases.

[0004] 2. Although the frequency response function is corrected in the power spectrum reproduction control method provided in parts of public technical materials, the accuracy of the frequency response function is not be quantitatively evaluated, the historical information of the frequency response function are not be considered in the directly correction or in the correction process.

[0005] 3. The same iteration step size is adopted to all the frequency points during the iteration process, which cannot cope with the impact of the fluctuations of the frequency response function, and moreover, the selection of the iteration step size is not be quantified, so that it is difficult to guarantee the convergence and the convergence speed of the iterative algorithm. SUMMARY

[0006] Technical objectives: the objectives of the present disclosure are to provide a method for controlling and reproducing a random power spectrum of a vibration table and a system, which improves the an estimation accuracy and eliminates the problem of the fluctuation of the frequency response function.

[0007] Technical solutions: provided is a method for controlling and reproducing a random power spectrum of a vibration table. The method includes the following steps.

[0008] In Step 1, a frequency response function Ho( / ) of a vibration table system is estimated, steps for the estimating specifically includes following steps. A reference spectrum reproduced by the vibration table is set as (), times of () is taken as an input of the vibration table system, a drive signal 0( (0 is generated after a frequency domain randomization and a time domain randomization to input the drive signal p.o (t) into the vibration table system, and a response signal yo(t) of the vibration table is collected under an excitation by the drive signal / zo(t), and the frequency response function Ho( / ) of the vibration table system is estimated by utilizing a frequency response function estimation method according to the drive signal / zo(t) and the response signal yo(t).

[0009] In Step 2, an initial drive spectrum t / 1( / ), an initial frequency response function H1( / ) and an initial response spectrum 1^( / ) are calculated according to the reference spectrum R( / ) and the frequency response function Ho( / ) reproduced by the vibration table.

[0010] In Step 3, whether a precision for reproducing a power spectrum is reached is determined according to the initial response spectrum 1^( / ), when the precision is reached, an experiment is terminated, otherwise a subsequent step 4 is proceeded.

[0011] In Step 4, an error spectrum ( ) is calculated according to a response signal ( ) of the vibration table.

[0012] In Step 5, a corrected frequency response function ((f) and an iteration step size are calculated, and steps for calculating the corrected frequency response function ((f) are as follows.

[0013] A current iteration is a n-th iteration, where n is valued in a range of n > 1, and n is an integer. A corrected frequency response function at an i-th iteration is expressed as H[(f), where i is valued as 1, 2, — n, then a corrected frequency response function at the current iteration is expressed as Hn(f), and a formula for calculating the _        _      (H i(Z) Hn(f) is Hn(f= = 1^   * Hi(f) =1 , where ( ) n >2, and n is an integer denotes a frequency response function at an i-th iteration, * denotes a Hadamard product of a matrix, and indicates a multiplication of corresponding elements in the matrix, denotes a corrected frequency point correction coefficient for Hi (f), and ? 1 — [%, fi2, — ^im\, where ff^ denotes a corrected frequency point correction coefficient for an estimation value for a j-th frequency point of Hi (f), j is valued as 1,2, —, m, and m denotes a number of frequency points of Hi (f).

[0014] For the iteration step size , an iteration step size at the i-th iteration is expressed as a— = [a^, (%i,2, ,aim], where atJ denotes an iteration step size of the j-th frequency point at the i-th iteration, and a current iteration step size is expressed as n — [®n,l> ®n,2 , an,m] •

[0015] In Step 6, a drive spectrum is iteratively corrected, an iterative correction “l formula for the drive spectrum is U(f) — U(f+ + a[H( / )] E(0, where U(f) denotes a corrected drive spectrum, ( ) denotes a drive spectrum utilized in a previous iteration, and [HU)] i                  — denotes an inversion of ( ).

[0016] In Step 7, the vibration table is excited by taking the corrected drive spectrum U(f) as the drive spectrum, a corrected response spectrum Y(f) and a corrected frequency response function U(f) are calculated.

[0017] In Step 8, whether a precision for reproducing a power spectrum is reached is determined according to the corrected response spectrum ( ), when the precision is reached, the experiment is terminated, otherwise Steps 4 to 7 are repeated.

[0018] Further provided is a system for reproducing a random power spectrum of a vibration table. The system includes an industrial computer, an acquisition board card, a drive board card, a communication network card and a signal conditioning device. The acquisition board card, the drive board card, and the communication network card are arranged inside the industrial computer. The signal conditioning device is in connection with the drive board card. The acquisition board card is configured to acquire sensor signals of a displacement and an acceleration during an operation of the vibration table in real time. The drive board card is configured to convert a real-time control signal obtained by computing to an actual drive signal. The signal conditioning device is configured to transform signals between the acquisition board card and a vibration sensor, and signals between the drive board card and a vibration drive unit, and the communication network card is configured to communicate between a power spectrum reproduction control system and a vibration table host computer display unit in real time.

[0019] Further, steps for calculating the initial drive spectrum Ux ( / ) and the initial frequency response function ^ / ( / ) and the initial response spectrum Y-JJ} specifically include as follows. The initial drive spectrum t / 1( / ) is calculated, and a formula for calculating the initial drive spectrum t / 1( / ) is u i(n = R^H^nr1, where [Ho^)]-1 denotes an inversion of Ho( / ). A drive signal / z1(t) is generated after the frequency domain randomization and the time domain randomization to input the drive signal p.1 (t) into the vibration table system, and a response signal y1(t) of the vibration table is collected under an excitation by the drive signal 1( (t).

[0020] The initial response function 7 / ,( / ) of the vibration table system is estimated by utilizing the frequency response function estimation method, according to the drive signal ^(t) and the response signal y1(t).

[0021] The initial response spectrum ^1( / ) is obtained by utilizing a power spectrum estimation method, according to the response signal y1 (t).

[0022] Further, steps for calculating the error spectrum ( ) specifically include as follows. A response spectrum ( ) is obtained by utilizing the power spectrum estimation method, according to the collected the response signal ( ) of the vibration table, and the error spectrum ( ) =   ( ) - ( ) is obtained through subtracting the reference spectrum ( ) reproduced by the vibration table from the response spectrum ( ).

[0023] Further, in Step 7, after the frequency domain randomization and the time domain randomization are performed on the corrected drive spectrum U(f), a drive signal g(t) is generated to be input into the vibration table system, and a response signal y(t) of the vibration table is collected under an excitation by the drive signal ■ "1^ ■ U (t). The corrected frequency response function U(f) of the vibration table system is calculated by utilizing the frequency response function estimation method according to the drive signal p.(t) and the response signal y(t), and the corrected response spectrum ( ) is calculated by utilizing the power spectrum estimation method according to the response signal y(t).

[0024] Further, the steps for calculating the corrected frequency point correction coefficient Pi of are as follows.

[0025] In Step 51, an uncorrected frequency point correction coefficient is set as Pi = [Pu,Pl,2,-Pun], Pl denotes a value for the corrected frequency point correction coefficient / ?|, and let the uncorrected frequency point correction coefficient faj in / ?, satisfy following conditions: ^^ =      (i=12,-,m — 1) P i^^+u (h = 1,2,-,71-1) * Pn,j = U (n > 2 and n is an integer, 7] raTiges from 0.6 to 0.8); n-1 £ f ij = 1 — 7]    (n> 2 and n is an integer)

[0026] In Step 52, gi(t) and yi(t) are respectively recorded as the drive signal and |SuyCf)|2 the response signal at the i-th iteration. A coherence function Cff) = s 1 (^ J^) at the i-th iteration is calculated according to the drive signal m (t) and the response signal yi(t), where 5^.( / ) denotes an auto-power spectrum of the g|(t), 5^.( / ) denotes a cross-power spectrum of the gi^t) and the yi(t), and Sy.y.(f) denotes an auto-power spectrum of the yi (t).

[0027] In Step 53, a discriminant matrix rc 1(H] c 2( / ) Lc n(f) (C1,1  c12 C2,1   ^2,2 cn,1   Cn,2 C^n C2,m is formed according to a C1 ( / ), C2 ( / ), ,Cn(H. An nxm element C[j in C denotes a coherence function value for the j-th frequency point of the coherence function Cj( / ) at the i-th iteration. An accuracy of the estimation value for the j-th frequency point of the frequency response function Ht(J') is characterized by the element C[j in the discriminant matrix C. A threshold of an accuracy of the frequency response function is set as , whether element values for elements in one single column in the discriminant matrix are all greater than or equal to is determined, and column numbers of the columns whose element values in one single column are all greater than or equal to in the discriminant matrix are counted, the column numbers are recorded as p 1,p2,— ,p^ in an ascending order, and the column numbers of m-k remaining columns in the discriminant matrix are recorded as q 1,Q2,^, qm-k in an ascending order. A corrected frequency point correction coefficient Pip of an estimation value for a ps -th frequency point of the frequency response function Hi (f), a corrected frequency point correction coefficient Pa $ of an estimation value for a qr-th frequency point of a frequency response function Haur( / ), and a corrected frequency point correction coefficient $ of an estimation value for the qr -th frequency point of a frequency response function Hbpr( / ) are respectively calculated.

[0028] Further, k in the p 1,p2,— ,p^ denotes a number of the columns whose element values in one single column are all greater than or equal to the in the discriminant matrix C, k is valued in a range of 1 < k < m, and k is an integer, p s denotes a ps-th column in the discriminant matrix C, s is valued as 1, 2, — k. When the element values for the elements in the ps -th column of the discriminant matrix C are all greater than or equal to the y, an accuracy of the estimation value for the ps -th frequency point of the frequency response function H^J) is high, and a corrected frequency point correction coefficient of an estimation value for the ps-th frequency point of the frequency response function Hi^f) is / ? i^ = / ?i,Ps, and s is valued as 1, 2, -, k.

[0029] Further, qr in the qn q2, —, Qm-k denotes a qr -th column in the discriminant matrix C, r is valued as 1, 2, -, m-k, the remaining m-k columns do not satisfy that the element values for the elements in one single column are all greater than or equal to y, row numbers of the elements in the qr-th column of the discriminant matrix C whose element values are less than are determined, and the row numbers are sequentially recorded as ai r, a2r, — dir,r in an ascending order, where lr denotes a number of the elements in the qr-th column whose element values are less than the y, Ir is valued in a range of 1 < lr < n, and n is an integer, au>r denotes an ar-t-th row in the discriminant matrix C, q is valued as 1,2, —, lr. When an element value Caurtqr for an element in an au,r-th row and a qr-th column in the discriminant matrix C is less than y, an accuracy of the estimation value for the qr -th frequency point of the frequency response function Hanr( / ) is low, and a corrected frequency point correction coefficient Pa $ of the estimation value for the qr -th frequency point of the frequency response function Olclur(f') is Pa $ = 0, where q is valued as 1,2, — ,lr, and r is valued as 1, 2, —, m-k.

[0030] Further, element values for remaining n — lr elements in the qr -th column in the discriminant matrix C are greater than or equal to , and row numbers of the remaining n — lr elements in the discriminant matrix C are sequentially recorded as bi,r,b2,r, — ,bn-ir,r in an ascending order, where bvr denotes a bvr-th row in the discriminant matrix C, v is valued as 1,2, —,n — lr. When the element value Qpr,qr for the element in a bv-.-th row and a qr -th column in the discriminant matrix C is greater than or equal to y, an accuracy of an estimation value for the qr-th frequency point of the frequency response function Hbpr( / ) is high, and a corrected frequency point correction coefficient for an estimation value for the qr -th frequency point of the bn-lr,r __                       1-^       Pbvr, ^r frequency response function is 0bv,r,qr = ¢^+ +——n----, where bb^ denotes the uncorrected frequency point correction coefficient, is valued as 1,2, •”, n — lr, and r is valued as 1, 2, —, m-k. _

[0031] Further, an average coherence function value Cnj for each of the frequency points in a corrected frequency response function Hn(f) at the n-th iteration is calculated and obtained according to the coherence function value Cjj and the uncorrected frequency point corrected coefficient / j(J, and a formula for calculating Cn,j =1 , where j is valued as 1, 2, — m, n >2, and n is an integer and a formula for calculating an element an,j in the iteration step size an is anj = ACn,j, where A denotes a proportional coefficient, when Cnj > y, which indicates that the accuracy of frequency response function at the frequency point is high, is valued as Ai, and when Cnj < y, which indicates that an accuracy of frequency response function at the frequency point is low, A is valued as A2.

[0032] In comparison with the prior art, the present disclosure have the following significant effects.

[0033] 1. In comparison with the traditional power spectrum reproduction control method, the method for controlling and reproducing the power spectrum provided in the present disclosure corrects the frequency response function, corrects all frequency points of the frequency response function by utilizing the historical information of the frequency response function and improves the accuracy of the estimation of the frequency response function estimation.

[0034] 2. The method for controlling and reproducing the power spectrum provided in the present disclosure quantitatively evaluates the accuracy of each of the frequency points of the frequency response function by calculating the coherence function.

[0035] 3. The method for controlling and reproducing the power spectrum provided in the present disclosure removes the response function value with low precision according to the accuracy during the correction process of the frequency response function, which eliminates the problem of the fluctuation of the frequency response function characteristics.

[0036] 4. The method for controlling and reproducing the power spectrum provided in the present disclosure adopts different iteration step sizes for the different frequency points, and quantitatively calculates the iteration step size according to the accuracy of each of the frequency points of the corrected frequency response function, which improves the convergence of the iterative algorithm and ensures a rapider convergence speed. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] FIG. 1 illustrates a flow chart of a control method of the present disclosure.

[0038] FIG. 2 illustrates a comparison diagram of random power reproduction waveforms in an electric vibration table of the present disclosure.

[0039] FIG. 3 illustrates a comparison diagram of random power reproduction waveforms in an electro-hydraulic vibration table of the present disclosure. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0040] The present disclosure is further described in detail below with reference to the accompanying drawings and the specific embodiments of the description.

[0041] With reference to FIG. 1, a method for controlling and reproducing a random power spectrum of a vibration table is provide in the present disclosure. The method includes the following steps.

[0042] In Step 1, a frequency response function H0 ( / ) of the vibration table system is estimated, which is specifically as follows. A reference spectrum reproduced by the vibration table is set as T?( / ), the frequency response function H0( / ) is estimated by a frequency response function estimation method, times of ( ) is taken as an input of the vibration table system, where 0 < £ < 1, a drive signal / z0(t) is generated after a frequency domain randomization and a time domain randomization to input the drive signal / z0(t) into the vibration table system, and a response signal y0(t) of the vibration table under is collected under an excitation by the drive signal i0(t), the frequency response function Ho( / ) of the vibration table system is estimated by utilizing an H1 estimation method according to the drive signal / r0(t) and the response signal yo(O-

[0043] In Step 2, an initial drive spectrum U^f) and an initial frequency response function estimation value H-JJ) and an initial response spectrum K1( / ) are specifically calculated as follows. Firstly, the initial drive spectrum t / 1( / ) is calculated according to the reference spectrum R(f) and the frequency response function Ho( / ) reproduced by the vibration table in Step 1, and a formula for calculating t / 1( / ) is u 1( / ) = ^) ^) ' , where [^1 denotes an inversion of Ho( / ), a drive signal / z1(t) is generated after the frequency domain randomization and the time domain randomization to input the drive signal 1( (t) into the vibration table system and a response signal y1(t) of vibration table is collected under excitation by the drive signal i 1(t), the frequency response function H^f) of the vibration table system is estimated by utilizing the H1 estimation method according to the drive signal 1(()) and the response signal y1(t), and the initial response spectrum Y^f) is estimated and obtained by utilizing a Blackman-Tukey spectrum according to the response signal y 1(0

[0044] In Step 3, whether a precision for reproducing a power spectrum is reached is determined according to the initial response spectrum Y^f) obtained in Step 2, when the precision is reached, the experiment is terminated, otherwise the subsequent step is proceeded.

[0045] In Step 4, an error spectrum ( ) is calculated, which is specifically as follows. A response spectrum ( ) is obtained by utilizing the Blackman-Tukey spectrum estimation method, according to a response signal ( ), and an error spectrum ()=  ()- () is obtained by subtracting the reference spectrum ( ) reproduced by the vibration table from the response spectrum ( ).

[0046] In Step 5, a corrected frequency response function H(f) and an iteration step size are calculated.

[0047] In Step 6, the drive spectrum is iteratively corrected. The iterative correction ~                      I--    -1 — i                 ~ formula for the drive spectrum is Y(f) = U( / + + a[H( / )] E(f), where Y(f) denotes a corrected drive spectrum, ( ) denotes a drive spectrum utilized in the previous iteration, and [H(Z>] i                  — denotes an inversion of ( ).

[0048] In Step 7, the steps for calculating a response spectrum ( ) and a frequency response function ( ) obtained through a means of exciting the vibration table by taking Y (f) as the drive spectrum specifically include as follows. After the frequency domain randomization and the time domain randomization are performed on the corrected drive spectrum U(f), a drive signal .(L) is generated to be input into the vibration table system, and a response signal y(t) of the vibration table is collected under an excitation by the drive signal p.(t) . The frequency response function H(f) of the vibration table system is calculated by utilizing the H1 estimation method according to the drive signal p.(t) and the response signal y(t), and the response spectrum K( / ) is calculated by utilizing the Blackman-Tukey spectrum estimation method according to the response signal y(t).

[0049] In Step 8, whether a precision for reproducing a power spectrum is reached is determined according to the corrected response spectrum Y(f), when the precision is reached, the experiment is terminated, otherwise Steps 4 to 7 are repeated.

[0050] The specific steps for calculating the frequency response function H^f) in Step 5 are as follows.

[0051] A current iteration is the n-th iteration, where n is valued as n > 1, and n is an integer. The corrected frequency response function at the i-th iteration is expressed as Ht(f), where i is valued as 1, 2, — n. According to the above principle, a corrected frequency response function at the current iteration is expressed as Hn( / ), and a formula for calculating the Hn( / ) is Hn(J= = ^ H i(f)          n = 1 £ 0. *        n > 2 , where Hi^ denotes a frequency response at the i-th iteration, * denotes a Hadamard product of a matrix, which indicates a multiplication of the corresponding elements in the matrix, Pi denotes a corrected frequency point correction coefficient for the Hj( / ), and the (f is expressed as 01 = ^1,1, / 1,2,- / ^] , where an element / , j in the Pi denotes a corrected frequency point correction coefficient of an estimation value for the j-th frequency point of T / j ( / ), where i is valued as 1, 2, —, n, j is valued as 1, 2, —, m, and m denotes a number of the frequency points of 7 / ,( / ).

[0052]

[0053] The specific steps for calculating Pi in the above step are as follows. In Step 51, the uncorrected frequency point correction coefficient is set as PI = [Pu,Pl,2,-Pun], Pl denotes a value for the corrected frequency point correction coefficient / ?,, where i is valued as 1, 2, —, n, and let the element / ?|,j in / ?, satisfy the following conditions.

[0054]

[0055] (0i,Ji=0i,Ji+1   ( / 1 = 1,2, — ,m — 1) / h,j<Pii+1,j   d1 = 1,2, — ,n—1 / = 1,2, —,m) ' / n,j =    (n — 2 and n is an integer,— = 1,2, — ,m, g ranges from 0.6 to 0.8); n-1 ^ [fj = l — g   (n — 2 and n is an integer j = 1,2, — ,m ) x i=1   ' In Step 52, g। (t) and y|(t) are respectively recorded as the drive signal and 1^1^1(^)1 the response signal at the i-th iteration, a coherence function C । (j ) =----—-----—• JUiUi(J )Jy,y,( / ) at the i-th iteration is calculated according to the drive signal / / , (t) and the response signal yi(t), where i is valued as 1, 2, —, n, $^.^( / ) denotes an auto-power spectrum of the / / , (t), 5 / ^,,( / ) denotes a cross-power spectrum of the / t। (t) and the y|(t), and -^^( / ) denotes an auto-power spectrum of the y। (t).

[0056] In Step 53, rc1( / )1 () a discriminant matrix =          = K n(Di (c 1,1 C 2,1 Cn,i 1,2 ■ • r. c 1,m C2,2 ”  C 2,m Cn,2   • .. c _ u n,m is formed acc ording to C1 ( / ), C2 (f), —, Cn ( / ), an nxm element CtJ in C denotes a coherence function value for the j-th frequency point of the coherence function Ci ( / ) at the i-th iteration, where i is valued as 1, 2, — n, j is valued as 1, 2, — m. An accuracy of an estimation value for the j-th frequency point of the frequency response function Ht(J) is characterized by the element C[j in the discriminant matrix C, a threshold of the accuracy of the frequency response function is set as y = 0.90~0.98, when Cj j > y, it indicates that the accuracy of the estimation value for the j-th frequency point is high, when Ci,j < y, it indicates that the accuracy of the estimation value for the j-th frequency point is low.

[0057] Subsequently, the uncorrected frequency point correction coefficients Px are calculated in the three different conditions. Firstly, whether the element values for the elements in one single column in the discriminant matrix C are all greater than or equal to is determined, and the column numbers of the columns whose elements values in one single column are all greater than or equal to in the discriminant matrix C are counted, and the column numbers are recorded as p1,p2, — >Pk in an ascending order, where k denotes the number of the columns whose element values in single column are all greater than or equal to y in the discriminant matrix, k is valued as 1 < k < m, and k is an integer, ps denotes the ps -th column in the discriminant matrix C, s is valued as 1, 2, — k, so that the element values for the elements in the ps-th column of the discriminant matrix C are all greater than or equal to the , the accuracy of the estimation value for the ps -th frequency point of the frequency response function Hj(f) is high, and the corrected frequency point correction coefficient fHi p of the estimation value for the ps -th frequency point of the frequency response function Hi ( / ) is / ?.   = Ws Pi,Ps, where i is valued as 1, 2, — n, and s is valued as 1,2, —, k.

[0058] The column numbers of the remaining m-k columns in the discriminant matrix C are recorded as q 1, q2, — ,qm-^ in an ascending order, where qr denotes the qr-th column in the discriminant matrix C, r is valued as 1, 2, —, m-k, and the remaining m-k columns do not satisfy that the element values for the elements in single column are all greater than or equal to . According to the above contents, the row number of the elements in the qr-th column of the discriminant matrix C whose element values are less than y is determined, which are sequentially recorded as a 1r, a2 r, — ai r in an ascending order, where lr denotes the number of the elements in the q--th column whose element values are less than the y, lr is valued as 1 < lr < n, and n is an integer, au>r denotes the au-t -th row in the discriminant matrix C, yc is valued as 1,2, — ,lr, so that the element value CauqiClr for the element in the au,r-th row and qr-th column of the discriminant matrix C is less than , and the accuracy of the estimation value for the qr-th frequency point of the frequency response function HCur( / ) is low, and the corrected frequency point correction coefficient Pa $ of the estimation value for the qr-th frequency point of the frequency response function Ha ( / ) is P = u,r             au,r,qr 0, where / / is valued as 1,2, — ,lr, r is valued as 1, 2, —, m-k. After determination through the above steps, the element values for the remaining n — lr elements in the qr-th column of the discriminant matrix C are greater than or equal to y, and the row numbers of the remaining n — lr elements in the discriminant matrix C are sequentially recorded as bir,b2,r, —, bn-ir,r in an ascending order, where bv>r denotes the bv-t-th row in the discriminant matrix C, v is valued as 1,2, —, n — lr, so that the element value Cbvr,qr for the element in the bvr-th row and qr -th column of the discriminant matrix C is greater than or equal to y, and the accuracy of the estimation value for the qr -th frequency point of the frequency response function Hbpr( / ) is high, and the corrected frequency point correction coefficient / 3 / $ of the estimation value for the q- -th frequency point of the frequency response function H^X / ) is @bVq,qr = ^,r,qr + —, b ■ Dv ,r~Dl,r__________ n~lr where / bpr,qr denotes the uncorrected frequency point correction coefficient, v is valued as 1,2, —, lr, and r is valued as 1, 2, —, m-k.

[0059] The steps for calculating the iteration step size in Step 5 are specifically as follows.

[0060] The current iteration number is set as the n-th, where n is valued as n > 1, and n is an integer. The iteration step size at the i-th iteration is expressed as a= = [an a.1,2, —, ^i,m], where i is valued as 1, 2, —, n, and the element at ] in the at denotes an iteration step size of the j-th frequency point at the i-th iteration, i is valued as 1, 2, —, n, and j is valued as 1, 2, —, m. According to the above principle, the current iteration step size can be expressed as an = [an,1, an2, —, ^n,m] • The coherence function mean value Cnj for each of the frequency points in the corrected frequency response function Hn( / ) at the n-th iteration is obtained according to the coherence function value Cjj and the uncorrected frequency point corrected coefficient , and a formula for calculating Cnj _    (Qj is Cn-j  y^Aj =1 n >2 , where j is valued as 1, 2, ••• m. A formula for calculating the element anj in the iteration step size an is an,j = ACn,j, where A denotes a proportional coefficient. When Cnj > y, it indicates that the accuracy of frequency response function at the frequency point is high, is valued in a range from 0.96 to 1, and when Cnj < y, it indicates that the accuracy of frequency response function at the frequency point is low, is valued in a range from 0.90 to 0.95.

[0061] A system for reproducing a random power spectrum of a vibration table that is applicable to an electric vibration table or an electro-hydraulic vibration table is further provided in the present disclosure. The system main includes an industrial computer, an acquisition board card, a drive board card, and a signal conditioning device. The acquisition board card, the drive board card, and a communication network card are arranged inside the industrial computer. The signal conditioning device is in connection with the drive board card. The acquisition board card is configured to acquire the sensor signals of the displacement and the acceleration during the operation of the vibration table in real time. The drive board card is configured to convert a real-time control signal obtained by computing to an actual drive signal. The signal conditioning device is configured to transform the signals between the acquisition board card and the vibration sensor, and signals between the drive board card and the vibration drive unit, and the communication network card is configured to communicate between the power spectrum reproduction control system and the vibration table host computer display unit in real time.

[0062] The waveform comparison diagrams of the random power spectrum reproduced by the present disclosure in the electric vibration table and the electro-hydraulic vibration table are illustrated in FIG. 2 and FIG. 3. From FIG. 2 and FIG.3, it can be concluded that the method for controlling and reproducing the random power spectrum of the vibration table provided in the present disclosure effectively improves the reproduction accuracy of the power spectrum.

[0063] The above is merely a preferred embodiment of the present disclosure. It should be pointed out that a plurality of improvements and modifications can be made for those ordinary skilled person in the art without departing from the principle of the present disclosure, and these improvements and the modifications should also be within the protection scope of the present disclosure.

Claims

2024287280   18 Jun 20261. A method for controlling and reproducing a random power spectrum of a vibration table, comprising following steps:Step 1, estimating a frequency response function Ho( / ) of a vibration table system, wherein steps for the estimating specifically include:setting a reference spectrum reproduced by the vibration table as (); taking times of () as an input of the vibration table system;generating, after a frequency domain randomization and a time domain randomization, a drive signal / zo(t) to input the drive signal ^o(t) into the vibration table system, and collecting, under an excitation by the drive signal o(t), a response signal yo(t) of the vibration table; andestimating, by utilizing a frequency response function estimation method, the frequency response function Ho( / ) of the vibration table system according to the drive signal / xo(t) and the response signal yo(t);Step 2, calculating, according to the reference spectrum () and the frequency response function Ho( / ) reproduced by the vibration table, an initial drive spectrum U1( / ), an initial frequency response function and an initial response spectrum y 1( / );Step 3, determining, according to the initial response spectrum K1( / ), whether a precision for reproducing a power spectrum is reached, wherein when the precision is reached, an experiment is terminated, otherwise a subsequent step 4 is proceeded;Step 4, calculating, according to a response signal ( ) of the vibration table, an error spectrum ( );2024287280   18 Jun 2026Step 5, calculating, a corrected frequency response function ((f) and an iteration step size a, wherein steps for calculating the corrected frequency response function ((f) are that:a current iteration number is a n-th iteration, where n is valued in a range of n > 1, and n is an integer, a corrected frequency response function at an i-th iteration is expressed as 7 / / ( / ), where i is valued as 1, 2, — n, then a corrected frequency response function at the current iteration is expressed as Hn( / ), and a formula for calculating Hn(f) isH ff)         n = 1n _2 P* * Hff) > 2, and n is an integer , j=iwhereH / (f) denotes a frequency response function at the i-th iteration,* denotes a Hadamard product of a matrix, and indicates a multiplication of corresponding elements in the matrix, / ? / denotes a corrected frequency point correction coefficient for Hff), andP i = Pj,l'^j,2'—^j,m], whereP / . denotes a corrected frequency point correction coefficient of an estimation value for a j-th frequency point of Hff).j is valued as 1, 2, — , , andH n(f) = f2024287280   18 Jun 2026m denotes a number of frequency points of Hj( / ); andfor the iteration step size a, an iteration step size at the z-th iteration is expressed as a i = [«i,i, ^,2,-, ai,m\, whereaij denotes an iteration step size of the j-th frequency point at the z-th iteration, anda current iteration step size is expressed as an = [an,i, an2, —, an,m\wherein steps for calculating the corrected frequency point correction coefficient Ptinclude:Step 5.1, setting an uncorrected frequency point correction coefficient as P= = [Pi,i, Pi,2, -Pi,m\, where Pi denotes a value for the corrected frequency pointcorrection coefficient Pt, and letting the uncorrected frequency point correctioncoefficient Pjj in P\_ satisfy following conditions:(P i,J1=Pi,J1+i   (ji = 1,2,-,m — 1)Pii,j<Pii+i,j   (h = 1,2,-, n -1)< Pnj=V (n>2 and n is an integer), g ranges from 0.6 to 0.8); n-i£ P^j = 1 — g   (n>2 and n is an integer)i=iStep 5.2, respectively recording   (t) and yi(t) as the drive signal and theresponse signal at the z-th iteration;calculating, according to the drive signal / / i (t) and the response signal yi(t), a|su-y (Z)|2coherence function C,(f) =—- at the z-th iteration, tJ     sUiUi6nsyiyi(n                       ’2024287280   18 Jun 2026whereSUlUl(f) denotes an auto-power spectrum of   (t),SUlyl(f') denotes a cross-power spectrum of / / i (t) and yj(t), andyiySf) denotes an auto-power spectrum of ) / / ( / ,); andStep 5.3, forming, according to C}(f), C2(f), —, Cn(f) a discriminant matrixrc i(f) / C i,i   Ci,2 c = C 2(f) = | ^2,1   ^2,2 c Vn,i  Cn,2whereCi,mC2,mnxman element Cjj in C denotes a coherence function value for the j-thfrequency point of the coherence function Ci ( / ) at the z-th iteration, andan accuracy of the estimation value for the j-th frequency point of the frequency response function Hi^f) is characterized by the element Cjj in the discriminant matrix C;setting a threshold of an accuracy of the frequency response function as ;counting column numbers of the columns whose element values in one single column are all greater than or equal to in the discriminant matrix , and recording the column numbers as plt p2, • ,pk in an ascending order;recording the columns numbers of m-k remaining columns in the discriminantmatrix C as qn q2, — ,qm-k in an ascending order;2024287280   18 Jun 2026determining and recording row numbers of the elements in a qr -th column of the discriminant matrix C whose element values are less than y as arx, a2,r, -0,^ in an ascending order;recording row numbers of remaining n — lr elements in the qr -th column of the discriminant matrix C whose element values in the discriminant matrix C are greater than or equal to y as b1>r, b2r, •••, bn-ir,r in an ascending order;respectively calculatinga corrected frequency point correction coefficient / ?ip of an estimation value for a ps -th frequency point of the frequency response function H t(H,a corrected frequency point correction coefficient P a $ of an estimation value for a qr -th frequency point of a frequency response function Hau,r(H, anda corrected frequency point correction coefficient bb $ of an estimationvalue for the qr -th frequency point of a frequency response functionH bvr(f)Step 6, iteratively-correcting a drive spectrum, wherein an iterative correction formula for~                     I     -1 “1                ~the drive spectrum is U(f) = U(f+ + a[H( / )] E(f), where U(f) denotes a correcteddrive spectrum, ( ) denotes a drive spectrum utilized in a previous iteration, andI--    1 “1                                    --[H(H\   denotes an inversion of ( );2024287280   18 Jun 2026Step 7, exciting, by taking the corrected drive spectrum U( / ) as the drive spectrum, the vibration table, and calculating a corrected response spectrum ( ) and a corrected frequency response function U(f); andStep 8, determining, according to the corrected response spectrum ( ), whether a precision for reproducing a power spectrum is reached, wherein when the precision is reached, the experiment is terminated, otherwise Steps 4 to 7 are repeated.

2. The method for controlling and reproducing the random power spectrum of the vibration table according to claim 1, wherein steps for calculating the initial drive spectrum t / 1( / ) and the initial frequency response function         and the initialresponse spectrum ^( / ) specifically include:calculating the initial drive spectrum t / 1( / ), wherein a formula for calculating the initial drive spectrum t / 1( / ) is t / 1( / ) = T?( / )[H0( / )]-1, where [Ho( / )]-1 denotes an inversion of Ho( / ); generating, after the frequency domain randomization and the time domain randomization, a drive signal / z1(t) to input the drive signal 1(()) into the vibration table system, and collecting a response signal y1(t) of the vibration table under an excitation by the drive signal 1 1 (t);estimating, by utilizing the frequency response function estimation method, the initial response function / / ( / ) of the vibration table system, according to the drive signal / z 1(t) and the response signal y 1(t); andobtaining, by utilizing a power spectrum estimation method, the initial response spectrum K 1( / ) according to the response signal y 1(t).

3. The method for controlling and reproducing the random power spectrum of the vibration table according to claim 1, wherein steps for calculating the error spectrum ( ) specifically include:2024287280   18 Jun 2026obtaining, by utilizing the power spectrum estimation method, a response spectrum ( ) according to the collected response signal ( ) of the vibration table; and obtaining, through subtracting the reference spectrum ( ) reproduced by the vibration table from the response spectrum ( ), the error spectrum ( ) = ( ) - ( ).

4. The method for controlling and reproducing the random power spectrum of thevibration table according to claim 1, wherein in Step 7, after the frequency domainrandomization and the time domain randomization are performed on the corrected drive spectrum U(f), a drive signal q(t) is generated to be input into the vibration table system, and a response signal y(t) of the vibration table is collected under an excitation by the drive signal q(t), the corrected frequency response function U(f) of the vibration table system is calculated by utilizing the frequency response functionestimation method according to the drive signal p.(t) and the response signal y(t), and the corrected response spectrum ( ) is calculated by utilizing the power spectrum estimation method according to the response signal y(t).

5. The method for controlling and reproducing the random power spectrum of the vibration table according to claim 1, wherein in Step 5.3, k in pi,p2, — >Pk denotes a number of the columns whose element values in one single column are all greater than or equal to y in the discriminant matrix C, k is valued in a range of 1 < k < m, and k is an integer, ps denotes a ps-th column in the discriminant matrix C, s is valued as 1, 2, — k, the element values for the elements in the ps -th column of the discriminant matrix C are all greater than or equal to y, an accuracy of the estimation value for the ps-th frequency point of the frequency response function 7 / / ( / ) is high, and a corrected frequency point correction coefficient of an estimation value for the ps-th frequency point of the frequency response function H,(J') is / ?ip = / ?j,Ps, and s is valued as 1, 2, —, k.

6. The method for controlling and reproducing the random power spectrum of the vibration table according to claim 1, wherein in Step 5.3, qr in q1, q2, —, qm-k denotes2024287280   18 Jun 2026a qr-th column in the discriminant matrix C, r is valued as 1, 2, —, m-k, the remaining m-k columns do not satisfy that the element values for the elements in one single column are all greater than or equal to y, lr denotes a number of the elements in the qr-th column whose element values are less than the y, lr is valued in a range of 1 < lr < n, and n is an integer, arr denotes an aur -th row in the discriminant matrix C, q is valued as 1, 2, —, lr, when an element value Cauqqr for an element in an au,r-th row and a qr -th column of the discriminant matrix C is less than y, an accuracy of the estimation value for the qr -th frequency point of the frequency response function hauyn is low, and the corrected frequency point correction coefficient Pa $ of the estimation value for the qr -th frequency point of the frequency response function H a^D is Pa $ = 0, where q is valued as 1, 2, —, Zr, and r is valued as 1, 2, —, m-k.

7. The method for controlling and reproducing the random power spectrum of the vibration table according to claim 1, wherein in Step 5.3, bv>r denotes a bv-t-th row in the discriminant matrix C, v is valued as 1,2, — ,n — lr, the element value Qpr,qr for the element in a bv-r -th row and a qr -th column in the discriminant matrix C is greater than or equal to y, an accuracy of the estimation value for the qr -th frequency point of the frequency response function Hbpr( / ) is high, and a corrected frequency point correction coefficient for an estimation value for the qr -th frequency point of the ^n—lr,r__                        1^ ?^ Pbv,r, qr frequency response function H^t)} is p^,$r = pbv$rir + —^^^-----, wherePbvr,qr denotes the uncorrected frequency point correction coefficient, v is valued as 1,2, —, n — lr, and r is valued as 1, 2, —, m-k.

8. The method for controlling and reproducing the random power spectrum of the vibration table according to claim 1, wherein an average coherence function value C;|J for each of the frequency points in a corrected frequency response function Hn( / ) at the n-th iteration is calculated and obtained according to the coherence function value2024287280   18 Jun 2026Cjj and the uncorrected frequency point corrected coefficient fit,, and a formula for(cU         n = 1calculating C»J is ^=^,^    n>2, and nis an integer ’ where j lsI i=ivalued as 1, 2, — m, and a formula for calculating an element anj in the iteration step size an is anj = ACn,j, where A denotes a proportional coefficient, when Cnj > y, which indicates that the accuracy of frequency response function at the frequency point is high, X is valued as A,, and when Cn,j < y, which indicates that an accuracy of frequency response function at the frequency point is low, X is valued as A2.

9. A system for reproducing a random power spectrum of a vibration table, utilized to implement the method according to any one of claims 1 to 8, comprising an industrial computer, an acquisition board card, a drive board card, a communication network card and a signal conditioning device, wherein the acquisition board card, the drive board card, and the communication network card are arranged inside the industrial computer, the signal conditioning device is in connection with the drive board card, the acquisition board card is configured to acquire sensor signals of a displacement and an acceleration during an operation of the vibration table in real time, the drive board card is configured to convert a real-time control signal obtained by computing to an actual drive signal, the signal conditioning device is configured to transform signals between the acquisition board card and a vibration sensor, and signals between the drive board card and a vibration drive unit, and the communication network card is configured to communicate between a power spectrum reproduction control system and a vibration table host computer display unit in real time.

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