WO2025213643A1 - 一种振动台随机功率谱复现控制方法及系统 - Google Patents

一种振动台随机功率谱复现控制方法及系统

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Publication number
WO2025213643A1
WO2025213643A1 PCT/CN2024/109750 CN2024109750W WO2025213643A1 WO 2025213643 A1 WO2025213643 A1 WO 2025213643A1 CN 2024109750 W CN2024109750 W CN 2024109750W WO 2025213643 A1 WO2025213643 A1 WO 2025213643A1
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Prior art keywords
spectrum
response function
vibration table
frequency
frequency point
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PCT/CN2024/109750
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English (en)
French (fr)
Inventor
汤裕
叶腾波
府晓宏
沈刚
孟光
李鸿光
朱真才
卢昊
陈朋朋
刘显波
彭玉兴
常向东
常进
孙伟
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China University of Mining and Technology CUMT
China University of Mining and Technology Beijing CUMTB
Suzhou Dongling Vibration Test Instrument Co Ltd
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China University of Mining and Technology CUMT
China University of Mining and Technology Beijing CUMTB
Suzhou Dongling Vibration Test Instrument Co Ltd
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Application filed by China University of Mining and Technology CUMT, China University of Mining and Technology Beijing CUMTB, Suzhou Dongling Vibration Test Instrument Co Ltd filed Critical China University of Mining and Technology CUMT
Priority to AU2024287280A priority Critical patent/AU2024287280A1/en
Publication of WO2025213643A1 publication Critical patent/WO2025213643A1/zh
Pending legal-status Critical Current
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M7/00—Vibration-testing of structures; Shock-testing of structures
    • G01M7/02—Vibration-testing by means of a shake table
    • G01M7/022—Vibration control arrangements, e.g. for generating random vibrations

Definitions

  • the present invention relates to the technical field of vibration table control, and in particular to a vibration table random power spectrum reproduction control method and system.
  • the vibration table is mainly used to simulate vibration tests on specimens to test their performance in a vibration environment.
  • the vibrations that specimens experience in a working environment are mostly random vibrations. Since this characteristic is mainly described by statistical characteristics such as acceleration power spectrum density, to simulate this vibration, it is necessary to reproduce the measured power spectrum density on the vibration table.
  • the main shortcomings of traditional power spectrum reproduction control methods are:
  • the frequency response function estimated at the beginning of the test is mainly used. No correction is made to the frequency response function, resulting in a decrease in the accuracy of the frequency response function as the number of iterations increases;
  • the purpose of the present invention is to provide a method and system for controlling the random power spectrum reproduction of a vibration table, which can improve the estimation accuracy and overcome the problem of fluctuation in the frequency response function characteristics.
  • a vibration table random power spectrum recurrence control method comprising the following steps:
  • step (3) Determine whether the accuracy of power spectrum reproduction is achieved based on the initial response spectrum Y 1 (f). If the accuracy is achieved, the experiment ends; otherwise, proceed to step (4).
  • the current iteration number is the nth, where n is an integer and n is equal to or greater than 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 Plan
  • the calculation formula is Where: 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; represents the corrected frequency point correction coefficient of Hi (f), in, The corrected frequency point correction coefficient of the j-th frequency point estimate of Hi (f), where j is 1, 2, ..., m, and m is the number of frequency points of Hi (f);
  • 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
  • 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
  • a vibration table random power spectrum reproduction 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.
  • the initial response spectrum Y 1 (f) is obtained by using the power spectrum estimation method according to the response signal y 1 (t).
  • 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.
  • ui (t) and yi (t) be the driving signal and response signal, respectively, at the i-th iteration.
  • the coherence function at the i-th iteration is obtained based on the driving signal ui (t) and the response signal yi (t). and are the autopower spectrum of u i (t), the cross-power spectrum of u i (t) and y i (t), and the autopower spectrum of y i (t);
  • the discriminant matrix is formed.
  • 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; the element C i,j in the discriminant matrix C is used to represent the accuracy of the estimated value of the j-th frequency point of the frequency response function H i (f); the frequency response function accuracy threshold ⁇ is set to determine whether all the element values of each column of the discriminant matrix C are greater than or equal to ⁇ , and the number of columns in the discriminant matrix C where all the element values of each column are greater than or equal to ⁇ is counted, and they are recorded as p 1 , p 2 , ..., p k in ascending order of the number of columns, and the remaining mk columns of the discriminant matrix C are recorded as q 1 , q 2 , ..., q mk in descending order
  • p 1 , p 2 , ..., p k , k represents the number of columns of the discriminant matrix C that satisfy that all values of the elements in each column are greater than or equal to ⁇
  • the value of k is 1 ⁇ k ⁇ m and k is an integer
  • p s represents the p s-th column in the discriminant matrix C
  • the value of s is 1, 2, ..., k
  • the values of the elements in the p s-th column of the discriminant matrix C are all greater than or equal to ⁇
  • the estimated value of the p s- th frequency point of the frequency response function H i (f) has high accuracy
  • the corrected frequency point correction coefficient of the estimated value of the p s- th frequency point of the frequency response function H i (f) is
  • the value of s is 1, 2,..., k.
  • q r represents the q rth column in the discriminant matrix C, and the value of r is 1, 2, ..., mk; the remaining mk columns do not satisfy that all element values are greater than or equal to ⁇ , and the row number of the discriminant matrix C where the element value of the q rth column of the discriminant matrix C is less than ⁇ is determined and recorded, and recorded in descending order as
  • l r is the number of elements in the q rth column whose value is less than ⁇
  • l r takes the value of 1 ⁇ l r ⁇ n and l is an integer
  • a u,r represents the a u, rth row of the discriminant matrix C, and u takes the value of 1, 2, ..., l r ;
  • the element value of the a u,rth row and q rth column of the discriminant matrix C is For the frequency response function
  • the values of the remaining nl r elements in the q rth column of the discriminant matrix C are greater than or equal to ⁇ , and the rows of the discriminant matrix C where the remaining nl r elements are located are recorded in descending order as
  • b v,r represents the b v,rth row of the discriminant matrix C
  • v takes the value of 1, 2, ..., nl r
  • the element value of the b v,rth row and q rth column of the discriminant matrix C For the frequency response function
  • the q rth frequency point the estimated value is accurate, the frequency response function
  • the estimated value of the q rth frequency point is corrected by the frequency point correction coefficient: in: Represents the correction coefficient of the uncorrected frequency point, where v is 1, 2, ..., nl r and r is 1, 2, ..., mk.
  • the coherence function value C i,j and the uncorrected frequency point correction coefficient ⁇ i,j can be used to calculate the corrected frequency response function at the nth iteration.
  • the average coherence function value at each frequency point The calculation formula is Where: j takes the value of 1, 2, ..., m; the element ⁇ n, j in the iteration step ⁇ n is calculated as follows: Where ⁇ is the proportional coefficient; if This indicates that the frequency response function at this frequency point has high accuracy, and the value of ⁇ is ⁇ 1 ; if This indicates that the accuracy of the frequency response function at this frequency point is low, and the value of ⁇ is ⁇ 2 .
  • the present invention has the following significant effects: 1. Compared with the traditional power spectrum reproduction control method, the power spectrum reproduction control method proposed by the present invention corrects the frequency response function and uses the historical information of the frequency response function to correct all frequency points of the frequency response function, thereby improving the accuracy of the frequency response function estimation;
  • the power spectrum reproduction control method proposed in the present invention quantitatively evaluates the accuracy of each frequency point of the frequency response function by calculating the coherence function
  • the power spectrum reproduction control method proposed in the present invention eliminates low-precision frequency response function values according to accuracy during the frequency response function correction process, thus overcoming the problem of fluctuation in frequency response function characteristics;
  • the power spectrum reproduction control method proposed in the present invention adopts different iteration step sizes for different frequency points, and quantitatively calculates the iteration step size based on the accuracy of each frequency point of the corrected frequency response function, thereby improving the convergence of the iterative algorithm and ensuring a faster convergence speed.
  • FIG1 is a flow chart of a control method of the present invention.
  • FIG2 is a comparison diagram of random power reproduction waveforms in an electrodynamic vibration table according to the present invention.
  • FIG3 is a comparison diagram of random power reproduction waveforms in an electro-hydraulic vibration table according to the present invention.
  • the present invention provides a method for controlling the random power spectrum reproduction of a vibration table, comprising the following steps:
  • Step 1 Estimate the frequency response function H 0 (f) of the vibration table system.
  • the specific steps are as follows: assume that the reference spectrum reproduced by the vibration table is R(f), and the frequency response function R(f) is estimated using the frequency response function estimation method. Take ⁇ times R(f) as the input of the vibration table system, where ⁇ is 0 ⁇ 1. After frequency domain randomization and time domain randomization, generate a driving signal u 0 (t) and input it into the vibration table system. Collect the vibration table response signal y 0 (t) under the excitation of the driving signal u 0 (t). Use the H1 estimation method to estimate the frequency response function H 0 (f) of the vibration table system based on the driving signal u 0 (t) and the response signal y 0 (t).
  • Step 2 Calculate the initial driving spectrum U 1 (f), the estimated value of the initial frequency response function H 1 (f), and the initial response spectrum Y 1 (f).
  • Step 3 Determine whether the power spectrum reproduction accuracy is achieved based on the initial response spectrum Y 1 (f) in step 2. If the accuracy is achieved, the experiment ends; otherwise, proceed to the next step.
  • Step 4 Calculate the error spectrum E(f).
  • Step 5 Calculate the corrected frequency response function and the iteration step size ⁇ .
  • Step 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.
  • Step 7 Calculate The response spectrum obtained by exciting the vibration table as the driving spectrum Sum frequency response function
  • the specific steps are: 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 Calculating the Frequency Response Function of a Shaking Table System Using the H1 Estimation Method According to the response signal
  • the response spectrum is calculated using the Blackman-Tukey spectral estimation method
  • Step 8 Based on the response spectrum in step 7 Determine whether the accuracy of power spectrum reproduction is achieved. If the accuracy is achieved, the experiment ends; otherwise, repeat steps 4 to 7.
  • the current iteration number is the nth, where n is an integer and n is equal to or greater than 1.
  • the corrected frequency response function at the i-th iteration is: Where: i takes the value of 1, 2, ..., n.
  • the frequency response function after the current iteration correction can be recorded as The calculation formula is Where: H i (f) represents the frequency response function of the i-th iteration; * is the Hadamard product of the matrix, which means the multiplication of the corresponding elements of the matrix;
  • the corrected frequency point coefficient of Hi (f) is number, The expression is in, Elements in The corrected frequency point correction coefficient of the j-th frequency point estimate of Hi (f), where i is 1, 2, ..., n, j is 1, 2, ..., m, and m is the number of frequency points of Hi (f).
  • ⁇ i the correction coefficient for the corrected frequency point.
  • Step 52 Let ui (t) and yi (t) be the driving signal and the response signal, respectively, at the i-th iteration, and calculate the coherence function at the i-th iteration based on the driving signal ui (t) and the response signal yi (t).
  • i takes the value of 1, 2, ..., n, and are the autopower spectrum of u i (t), the cross-power spectrum of u i (t) and y i (t), and the autopower spectrum of y i (t);
  • Step 53 Construct a discriminant matrix based on C 1 (f), C 2 (f), ..., Cn ( f ) , the element Ci ,j in C represents the coherence function value of the j-th frequency point of the coherence function Ci (f) at the i-th iteration, where: i takes the value of 1, 2, ..., n, and j takes the value of 1, 2, ..., m; the element Ci ,j in the discriminant matrix C is used to represent the accuracy of the estimated value of the j-th frequency point of the frequency response function Hi (f); the frequency response function accuracy threshold ⁇ is set to 0.90-0.98, if Ci ,j ⁇ , it indicates that the accuracy of the estimated value of the j-th frequency point of Hi (f) is high; if Ci ,j ⁇ , it indicates that the accuracy of the estimated value of the j-th frequency point of Hi (f) is low;
  • the correction coefficients of the uncorrected frequency points in three different cases are To perform the calculation, first determine whether all the element values in each column of the discriminant matrix C are greater than or equal to ⁇ , and count the number of columns in the discriminant matrix C where all the element values in each column are greater than or equal to ⁇ .
  • k represents the number of columns in the discriminant matrix C that satisfy all the element values in each column are greater than or equal to ⁇
  • the value of k is 1 ⁇ k ⁇ m and k is an integer
  • p s represents the p s-th column in the discriminant matrix C
  • the value of s is 1, 2, ..., k; therefore, the element values in the p s-th column of the discriminant matrix C are all greater than or equal to ⁇ , so the estimated value of the p s- th frequency point of the frequency response function H i (f) is highly accurate, and the corrected frequency point correction coefficient of the estimated value of the p s- th frequency point of the frequency response function H i (f) is Where: i is 1, 2, ..., n, s is 1, 2, ..., k;
  • the remaining mk columns of the discriminant matrix C are recorded as q 1 , q 2 , ..., q mk from small to large, where q r represents the q rth column in the discriminant matrix C, and the value of r is 1, 2, ..., mk; the remaining mk columns do not satisfy the element All values are greater than or equal to ⁇ ; Based on the above content, determine and record the row number of the discriminant matrix C where the element value of the q r column of the discriminant matrix C is less than ⁇ , and record it in order from small to large as
  • l r is the number of elements in the q rth column whose value is less than ⁇
  • l r takes the value of 1 ⁇ l r ⁇ n and l is an integer
  • a u,r represents the a u, rth row of the discriminant matrix C
  • u takes the value of 1, 2, ..., l r ; therefore, the element value of the a u,
  • the current iteration number is denoted as n, where n is n ⁇ 1 and k is an integer.
  • the current iteration step size can be expressed as ⁇ n [ ⁇ n, 1 , ⁇ n , 2 , ..., ⁇ n , m ].
  • the corrected frequency response function at the n-th iteration is calculated.
  • the average coherence function value at each frequency point The calculation formula is Where: j takes the value of 1, 2, ..., m; the calculation formula for the element ⁇ n,j in the iteration step ⁇ n is Where ⁇ is the proportional coefficient; if This indicates that the frequency response function at this frequency point has high accuracy, and the value of ⁇ is 0.96 ⁇ 1; if This indicates that the accuracy of the frequency response function at this frequency point is low, and the value of ⁇ is 0.90 ⁇ 0.95.
  • the present invention also provides a vibration table random power spectrum reproduction system that can be applied to an electric vibration table or an electro-hydraulic vibration table.
  • the system mainly includes an industrial computer, an acquisition board, a drive board, 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 vibration table host computer display unit.
  • Figures 2 and 3 are waveform diagrams of random power spectrum reproduction in an electrodynamic vibration table and an electro-hydraulic vibration table using the present invention. 2 and 3 , it can be concluded that the random power spectrum reproduction control method for the vibration table provided by the present invention effectively improves the power spectrum reproduction accuracy.

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  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Measurement Of Mechanical Vibrations Or Ultrasonic Waves (AREA)
  • Feedback Control In General (AREA)

Abstract

一种振动台随机功率谱复现控制方法及系统，所述方法包括以下步骤：1、估计振动台频响函数；2、计算初始驱动谱、初始频响函数和初始响应谱；3、根据初始响应谱判断是否达到功率谱复现精度；4、计算误差谱；5、计算修正后频响函数和迭代步长；6、对驱动谱进行迭代修正；7、计算响应谱和频响函数；8、判断是否达到功率谱复现的精度。所述系统包括工控机、采集板卡、驱动板卡和信号调理装置。通过迭代过程中结合历史数据信息对每个频率点进行定量评价和动态修正，利用修正后每个频率点频响函数准确度对迭代步长进行定量优化，克服了频响函数波动对功率谱复现精度的影响，提高了振动台随机功率复现控制精度。

Description

一种振动台随机功率谱复现控制方法及系统 技术领域
本发明涉及振动台控制技术领域，尤其涉及一种振动台随机功率谱复现控制方法及系统。
背景技术
振动台主要是用于对试件进行模拟振动试验，测试试件在振动环境下的性能，试件的在工作环境中所受的振动大多为随机振动，由于该特征主要是用加速度功率谱密度等统计特性的描述，因此要模拟这种振动就需要在振动台上复现出实测的功率谱密度。传统的功率谱复现控制方法的不足主要有：
1、在迭代过程中主要采用试验开始时估计的频响函数，没有对频响函数进行修正导致随着迭代次数的增加频响函数的准确度下降；
2、部分公开技术资料中提出的功率谱复现控制方法虽然对频响函数进行了修正，但没有对频响函数的准确度进行定量评估，直接进行修正或修正过程中没有考虑频响函数的历史信息；
3、在迭代过程中对于所有频率点采用相同的迭代步长无法应对频响函波动的影响，而且没有对迭代步长的选择进行量化，对迭代算法的收敛性和的收敛速度也难以保证。
发明内容
发明目的：本发明的目的是提供一种提升估计准确度和克服频响函数特性波动问题的振动台随机功率谱复现控制方法及系统。
技术方案：一种振动台随机功率谱复现控制方法，包括以下步骤：
(1)估计振动台系统的频响函数H0(f)，具体步骤如下：设振动台复现的参考谱为R(f)，取R(f)的ε倍为振动台系统输入，经过频域随机化和时域随机化后，生成驱动信号u0(t)，输入振动台系统并采集在驱动信号u0(t)激励下的振动台响应信号y0(t)，根据驱动信号u0(t)和响应信号y0(t)使用频响函数估计法估计振动台系统频响函数H0(f)；
(2)根据振动台复现的参考谱R(f)和频响函数H0(f)，计算初始驱动谱U1(f)、初始频响函数H1(f)和初始响应谱Y1(f)；
(3)根据初始响应谱Y1(f)判断是否达到功率谱复现的精度，若达到精度则实验结束，否则进入步骤(4)；
(4)根据振动台的响应信号y(t)，计算误差谱E(f)；
(5)计算修正后的频响函数和迭代步长α；对于修正后的频响函数的具体计算步骤如下：
当前迭代次数为第n次，其中：n取值为n≥1且n为整数，记第i次迭代时修正后的频响函数为i取值为1，2，…，n；则当前迭代修正后的频响函数记为所述的计 算公式为其中：Hi(f)表示第i次迭代时的频响函数；*为矩阵的Hadamard积，表示矩阵对应元素相乘；表示Hi(f)的校正后频率点修正系数，其中，表示Hi(f)的第j个频率点估计值的校正后频率点修正系数，j取值为1，2，…，m，m为Hi(f)的频率点个数；
对于迭代步长α，第i次迭代时迭代步长表示为αi＝[αi,1，αi，2，…，αi，m],αi,j表示第i次迭代时第j个频率点迭代步长，则当前迭代步长表示为αn＝[αn，1，αn，2，…，αn，m]；
(6)对驱动谱进行迭代修正，驱动谱的迭代修正公式为，其中表示修正后的驱动谱，U(f)表示上一次迭代中使用的驱动谱，表示的逆；
(7)由修正后驱动谱作为驱动谱激励振动台，计算修正后响应谱和修正后频响函数
(8)根据修正后响应谱判断是否达到功率谱复现的精度，若达到精度则实验结束；否则，重复步骤(4)至步骤(7)。
一种振动台随机功率谱复现系统，包括工控机、采集板卡、驱动板卡、通讯网卡和信号调理装置，所述采集板卡、驱动板卡和通讯网卡设置于工控机内部，所述信号调理装置与驱动板卡连接，所述采集板卡用于实时采集振动台运行过程中的位移和加速度传感器信号，所述驱动板卡用于将计算得到的实时控制信号转化为实际驱动信号，所述信号调理装置用于采集板卡与振动台传感器、驱动板卡与振动台驱动单元间信号的变换，所述通讯网卡用于功率谱复现控制系统与振动台上位机显示单元间的实时通讯。
进一步地，所述初始驱动谱U1(f)、初始频响函数H1(f)和初始响应谱Y1(f)计算方法，具体步骤如下：计算初始驱动谱U1(f)，其表达式为U1(f)＝R(f)[H0(f)]-1，其中[H0(f)]-1表示H0(f)的逆，经过频域随机化和时域随机化后，生成驱动信号u1(t)输入振动台系统并采集在驱动信号u1(t)激励下的振动台响应信号y1(t)；
根据驱动信号u1(t)和响应信号y1(t)使用频响函数估计法估计振动台系统初始频响函数H1(f)；
根据响应信号y1(t)采用功率谱估计方法得到初始响应谱Y1(f)。
进一步地，所述误差谱E(f)的计算方法，具体步骤如下：根据采集的振动台的响应信号y(t)，采用功率谱估计方法得到响应谱Y(f)，将振动台复现的参考谱R(f)与响应谱Y(f)作差得到误差谱E(f)＝R(f)-Y(f)。
进一步地，步骤(7)中，将修正后的驱动谱进行频域随机化和时域随机化处理后，生成驱动信号输入振动台系统并采集在驱动信号激励下的振动台响应信号根据驱动信号和响应信号使用频响函数估计法计算振动台系统修正后的频响函数根据响应信号采用功率谱估计方法计算得到修正后的响应谱
进一步地，所述校正后频率点修正系数的计算步骤如下：
(51)设置未校正频率点修正系数βi＝βi，1，βi，2，…，βi，m]，βi是用于对校正后频率点修正系数的取值，令βi中的未修正频率点修正系数βi，j满足以下条件： 所述η的取值范围为0.6～0.8；
(52)记在第i次迭代时ui(t)和yi(t)分别为驱动信号和响应信号，根据驱动信号ui(t)和响应信号yi(t)求出第i次迭代时的相干函数 和分别为ui(t)的自功率谱、ui(t)和yi(t)的互功率谱和yi(t)的自功率谱；
(53)根据C1(f)、C2(f)、…、Cn(f)组成判别矩阵C中元素Ci，j表示第i次迭代时相干函数Ci(f)的第j个频率点的相干函数值；用判别矩阵C中的元素Ci，j表征频响函数Hi(f)的第j个频率点估计值的准确度；设置频响函数准确度阈值γ，判断判别矩阵C的每一列元素值是否全部大于等于γ，并统计满足每一列元素值全部大于等于γ的列所在判别矩阵C的列数，根据列数从小到大分别记为p1、p2、…、pk，将判别矩阵C剩余的m-k列从小到大分别记为q1、q2、…、qm-k，分别计算频响函数Hi(f)的第ps个频率点估计值的校正后频率点修正系数为频响函数的第qr个频率点估计值的校正后频率点修正系数为和响函数的第qr个频率点的估计值校正后频率点修正系数为
进一步地，所述，p1、p2、…、pk中k表示满足每一列元素值全部大于等于γ的判别矩阵C的列的个数，k的取值为1≤k≤m且k为整数，ps表示判别矩阵C中的第ps列，s的取值为1，2，…，k；判别矩阵C的第ps列的元素值全部大于等于γ，频响函数Hi(f)的第ps个频率点的估计值准确度高，频响函数Hi(f)的第ps个频率点估计值的校正后频率点修正系数为s的取值为1，2，…，k。
进一步地，所述q1、q2、…、qm-k中qr表示判别矩阵C中的第qr列，r的取值为1，2，…，m-k；剩余的m-k列不满足元素值全部大于等于，判断并记录判别矩阵C第qr列元素值小于γ的元素所在判别矩阵C的行数，从小到大依次记为其中：lr为第qr列元素值小于γ的元素的个数，lr取值为1≤lr≤n且l为整数，au，r表示判别矩阵C的第au，r行，u取值为1，2，…，lr；判别矩阵C的第au，r行第qr列的元素值对于频响函数的第qr个频率点估计值的准确度低，频响函数的第qr个频率点估计值的 校正后频率点修正系数为其中：u取值为1，2，…，lr，r的取值为1，2，…，m-k。
进一步地，所述判别矩阵C第qr列剩余的n-lr个元素的元素值大于等于γ，将剩余的n-lr个元素所在判别矩阵C行数从小到大依次记为其中：bv，r表示判别矩阵C的第bv，r行，v取值为1，2，…，n-lr；判别矩阵C的第bv,r行第qr列的元素值对于频响函数的第qr个频率点，估计值的准确度高，频响函数的第qr个频率点的估计值校正后频率点修正系数为其中：表示未校正频率点修正系数，v取值为1，2，…，n-lr，r的取值为1，2，…，m-k。
进一步地，所述相干函数值Ci，j和未修正频率点修正系数βi，j能计算得到第n次迭代时修正后的频响函数每个频率点的平均相干函数值的计算公式为其中：j取值为1，2，…,m；迭代步长αn中的元素αn，j计算公式为式中λ为比例系数；若表明该频率点上频响函数准确度高，λ取值为λ1；若表明该频率点上频响函数准确度低，λ取值为λ2。
本发明与现有技术相比，其显著效果如下：1、本发明提出的功率谱复现控制方法与传统的功率谱复现控制方法相比，对频响函数进行了修正，采用频响函数的历史信息对频响函数的所有频率点进行修正，提高了频响函数估计的准确度；
2、本发明提出的功率谱复现控制方法通过计算相干函数对频响函数的每个频率点准确度进行了定量评估；
3、本发明提出的功率谱复现控制方法在频响函数修正过程中，根据准确度剔除了精度低的频响函数值，克服了频响函数特性的波动的问题；
4、本发明提出的功率谱复现控制方法对不同频率点采用不同迭代步长，并根据修正后频响函数每个频率点的准确度，对迭代步长进行了定量计算，提高了迭代算法的收敛性，保证了较快的收敛速度。
附图说明
图1为本发明的控制方法流程图；
图2为本发明于电动振动台中随机功率复现波形对比图；
图3为本发明于电液振动台中随机功率复现波形对比图；
具体实施方式
下面结合说明书附图和具体实施方式对本发明做进一步详细描述。
参考图1，本发明提供了一种振动台随机功率谱复现控制方法，包括以下步骤：
步骤一，估计振动台系统的频响函数H0(f)，具体步骤为：设振动台复现的参考谱为R(f)，频响函数R(f)的估计采用频响函数估计法，取R(f)的ε倍为振动台系统输入，ε取0<ε＜1，经过频域随机化和时域随机化后，生成驱动信号u0(t)输入振动台系统并采集在驱动信号u0(t)激励下的振动台响应信号y0(t)，根据驱动信号u0(t)和响应信号y0(t)使用H1估计法估计振动台系统频响函数H0(f)。
步骤二，计算初始驱动谱U1(f)、初始频响函数估计值H1(f)和初始响应谱Y1(f)，具体步骤为：首先根据(1)中的振动台复现的参考谱R(f)和频响函数H0(f)计算初始驱动谱U1(f)，其表达式为U1(f)＝R(f)[H0(f)]-1，其中[H0(f)]-1表示H0(f)的逆，经过频域随机化和时域随机化后，生成驱动信号u1(t)输入振动台系统并采集在驱动信号u1(t)激励下的振动台响应信号y1(t)，根据驱动信号u1(t)和响应信号y1(t)使用H1估计法估计振动台系统频响函数H1(f)，根据响应信号y1(t)采用Blackman-Tukey谱估计得到初始响应谱Y1(f)。
步骤三，根据步骤二中的初始响应谱Y1(f)判断是否达到功率谱复现的精度，若达到精度则实验结束，否则进入下一步。
步骤四，计算误差谱E(f)，具体步骤为：根据振动台的响应信号y(t)，采用Blackman-Tukey谱估计法得到响应谱Y(f)，将振动台复现的参考谱R(f)与响应谱Y(f)作差得到误差谱E(f)＝R(f)-Y(f)。
步骤五，计算修正后的频响函数和迭代步长α。
步骤六，对驱动谱进行迭代修正，驱动谱的迭代修正公式为其中表示修正后的驱动谱，U(f)表示上一次迭代中使用的驱动谱，表示的逆。
步骤七，计算由作为驱动谱激励振动台得到的响应谱和频响函数具体步骤为：将修正后的驱动谱进行频域随机化和时域随机化处理后，生成驱动信号输入振动台系统并采集在驱动信号激励下的振动台响应信号根据驱动信号和响应信号使用H1估计法计算振动台系统频响函数根据响应信号采用Blackman-Tukey谱估计法计算得到响应谱
步骤八，根据步骤七中的响应谱判断是否达到功率谱复现的精度，若达到精度则实验结束，否则重复步骤四至步骤七。
其中，针对步骤五中的频响函数其具体计算步骤如下：
当前迭代次数为第n次，其中：n取值为n≥1且n为整数，记第i次迭代时修正后的频响函数为其中：i取值为1，2，…，n，根据以上原则，当前迭代修正后的频响函数可记为的计算公式为其中：Hi(f)表示第i次迭代时频响函数；*为矩阵的Hadamard积，表示矩阵对应元素相乘；表示Hi(f)的校正后频率点修正系 数，的表达式为其中，中的元素表示Hi(f)的第j个频率点估计值的校正后频率点修正系数，其中：i取值为1，2，…，n，j取值为1，2，…，m，m为Hi(f)的频率点个数。
对于上述步骤中的具体计算步骤如下：
步骤51，设置未校正频率点修正系数βi＝[βi,1，βi，2，…，βi，m]，βi是用于对校正后频率点修正系数的取值，其中：i取值为1，2，…，n，令βi中的元素βi，j满足以下条件：
步骤52，记在第i次迭代时ui(t)和yi(t)分别为驱动信号和响应信号，根据驱动信号ui(t)和响应信号yi(t)求出第i次迭代时的相干函数其中：i取值为1，2，…，n，和分别为ui(t)的自功率谱、ui(t)和yi(t)的互功率谱和yi(t)的自功率谱；
步骤53，根据C1(f)、C2(f)、…、Cn(f)组成判别矩阵，C中元素Ci，j表示第i次迭代时相干函数Ci(f)的第j个频率点的相干函数值，其中：i取值为1，2，…，n，j取值为1，2，…，m；用判别矩阵C中的元素Ci，j表征频响函数Hi(f)的第j个频率点估计值的准确度；设置频响函数准确度阈值γ＝0.90～0.98，若Ci，j≥γ，则表明Hi(f)的第j个频率点估计值的准确度高；若Ci，j＜γ，则表明Hi(f)的第j个频率点估计值的准确度低；
然后对三种不同情况下的未校正频率点修正系数进行计算，首先判断判别矩阵C的每一列元素值是否全部大于等于γ，并统计满足每一列元素值全部大于等于γ的列所在判别矩阵C的列数，根据列数从小到大分别记为p1、p2、…、pk，其中：k表示满足每一列元素值全部大于等于γ的判别矩阵C的列的个数，k的取值为1≤k≤m且k为整数，ps表示判别矩阵C中的第ps列，s的取值为1，2，…，k；因此，判别矩阵C的第ps列的元素值全部大于等于γ，所以频响函数Hi(f)的第ps个频率点的估计值准确度高，频响函数Hi(f)的第ps个频率点估计值的校正后频率点修正系数为其中：i取值为1，2，…，n，s的取值为1，2，…，k；
将判别矩阵C剩余的m-k列所在判别矩阵C的列数从小到大分别记为q1、q2、…、qm-k，其中：qr表示判别矩阵C中的第qr列，r的取值为1，2，…，m-k；剩余的m-k列不满足元素 值全部大于等于γ；依据上述内容，判断并记录判别矩阵C第qr列元素值小于γ的元素所在判别矩阵C的行数，从小到大依次记为其中：lr为第qr列元素值小于γ的元素的个数，lr取值为1≤lr≤n且l为整数，au，r表示判别矩阵C的第au，r行，u取值为1，2，…，lr；因此，判别矩阵C的第au,r行第qr列的元素值所以对于频响函数的第qr个频率点估计值的准确度低，频响函数的第qr个频率点估计值的校正后频率点修正系数为其中：u取值为1，2，…，lr，r的取值为1，2，…，m-k；经过上述步骤的判断，判别矩阵C第qr列剩余的n-lr个元素的元素值大于等于γ，将剩余的n-lr个元素所在判别矩阵C行数从小到大依次记为其中：bv，r表示判别矩阵C的第bv，r行，v取值为1，2，…，n-lr；因此，判别矩阵C的第bv，r行第qr列的元素值所以对于频响函数的第qr个频率点估计值的准确度高，频响函数的第qr个频率点的估计值校正后频率点修正系数为其中：表示未校正频率点修正系数，v取值为1，2，…，n-lr，r的取值为1，2，…，m-k。
其中，针对步骤五中的迭代步长α，其具体计算步骤如下：
记当前迭代次数为第n次，其中：n取值为n≥1且k为整数，第i次迭代时迭代步长表示为αi＝[αi，1，αi,2，…，αi,m]，其中：i取值为1，2，…，n，αi的元素αi，j表示第i次迭代时第j个频率点迭代步长，i取值为1，2，…，n，j取值为1，2，…，m；根据以上原则，当前迭代步长可表示为αn[αn，1，αn，2，…，αn，m]；根据相干函数值Ci，j和未修正频率点修正系数βi,j，计算得到第n次迭代时修正后的频响函数每个频率点的平均相干函数值的计算公式为其中：j取值为1，2，…，m；迭代步长αn中的元素αn,j计算公式为式中λ为比例系数；若则表明该频率点上频响函数准确度高，λ取值为0.96～1；若则表明该频率点上频响函数准确度低，λ取值为0.90～0.95。
本发明还提供了一种可应用于电动振动台或电液振动台的振动台随机功率谱复现系统，主要包括工控机、采集板卡、驱动板卡、信号调理装置，采集板卡、驱动板卡和通讯网卡设置于工控机内部，信号调理装置与驱动板卡连接，采集板卡用于实时采集振动台运行过程中的位移和加速度传感器信号，驱动板卡用于将计算得到的实时控制信号转化为实际驱动信号，信号调理装置用于采集板卡与振动台传感器、驱动板卡与振动台驱动单元间信号的变换，通讯网卡用于功率谱复现控制系统与振动台上位机显示单元间的实时通讯。
图2和图3是应用本发明在电动振动台和电液振动台中进行随机功率谱复现的波 形对比图，通过图2和图3可以得出本发明提供的振动台随机功率谱复现控制方法，有效提升功率谱复现精度。
以上所述仅是本发明的优选实施方式，应当指出：对于本技术领域的普通技术人员来说，在不脱离本发明原理的前提下，还可以做出若干改进和润饰，这些改进和润饰也应该为本发明的保护范围。

Claims (10)

  1. 一种振动台随机功率谱复现控制方法，其特征在于，包括以下步骤：
    (1)估计振动台系统的频响函数H0(f)，具体步骤如下：设振动台复现的参考谱为R(f)，取R(f)的ε倍为振动台系统输入，经过频域随机化和时域随机化后，生成驱动信号u0(t)，输入振动台系统并采集在驱动信号u0(t)激励下的振动台响应信号y0(t)，根据驱动信号u0(t)和响应信号y0(t)使用频响函数估计法估计振动台系统频响函数H0(f)；
    (2)根据振动台复现的参考谱R(f)和频响函数H0(f)，计算初始驱动谱U1(f)、初始频响函数H1(f)和初始响应谱Y1(f)；
    (3)根据初始响应谱Y1(f)判断是否达到功率谱复现的精度，若达到精度则实验结束，否则进入步骤(4)；
    (4)根据振动台的响应信号y(t)，计算误差谱E(f)；
    (5)计算修正后的频响函数和迭代步长α；对于修正后的频响函数的具体计算步骤如下：
    当前迭代次数为第n次，其中：n取值为n≥1且n为整数，记第i次迭代时修正后的频响函数为i取值为1,2,…,n；则当前迭代修正后的频响函数记为所述的计算公式为其中：Hi(f)表示第i次迭代时的频响函数；*为矩阵的Hadamard积，表示矩阵对应元素相乘；表示Hi(f)的校正后频率点修正系数，其中，表示Hi(f)的第j个频率点估计值的校正后频率点修正系数，j取值为1，2，…，m，m为Hi(f)的频率点个数；
    对于迭代步长α，第i次迭代时迭代步长表示为αi＝[αi，1，αi，2，…，αi，m]，αi,j表示第i次迭代时第j个频率点迭代步长，则当前迭代步长表示为αn＝[αn,1,αn,2,…,αn,m]；
    (6)对驱动谱进行迭代修正，驱动谱的迭代修正公式为其中表示修正后的驱动谱，U(f)表示上一次迭代中使用的驱动谱，表示的逆；
    (7)由修正后驱动谱作为驱动谱激励振动台，计算修正后响应谱和修正后频响函数
    (8)根据修正后响应谱判断是否达到功率谱复现的精度，若达到精度则实验结束；否则，重复步骤(4)至步骤(7)。
  2. 根据权利要求1所述的振动台随机功率谱复现控制方法，其特征在于，所述初始驱动谱U1(f)、初始频响函数H1(f)和初始响应谱Y1(f)计算方法，具体步骤如下：计算初始驱动谱U1(f)，其表达式为U1(f)＝R(f)[H0(f)]-1，其中[H0(f)]-1表示H0(f)的逆，经过频域随机化和时域随机化后，生成驱动信号u1(t)输入振动台系统并采集在驱动信号u1(t)激励下的振动台响应信号y1(t)；
    根据驱动信号u1(t)和响应信号y1(t)使用频响函数估计法估计振动台系统初始频响函数H1(f)；
    根据响应信号y1(t)采用功率谱估计方法得到初始响应谱Y1(f)。
  3. 根据权利要求1所述的振动台随机功率谱复现控制方法，其特征在于，所述误差谱 E(f)的计算方法，具体步骤如下：根据采集的振动台的响应信号y(t)，采用功率谱估计方法得到响应谱Y(f)，将振动台复现的参考谱R(f)与响应谱Y(f)作差得到误差谱E(f)＝R(f)-Y(f)。
  4. 根据权利要求1所述的振动台随机功率谱复现控制方法，其特征在于，步骤(7)中，将修正后的驱动谱进行频域随机化和时域随机化处理后，生成驱动信号输入振动台系统并采集在驱动信号激励下的振动台响应信号根据驱动信号和响应信号使用频响函数估计法计算振动台系统修正后的频响函数根据响应信号采用功率谱估计方法计算得到修正后的响应谱
  5. 根据权利要求1所述的振动台随机功率谱复现控制方法，其特征在于，
    所述校正后频率点修正系数的计算步骤如下：
    (51)设置未校正频率点修正系数βi＝[βi，1，βi，2，…，βi，m]，βi是用于对校正后频率点修正系数的取值，令βi中的未修正频率点修正系数βi，j满足以下条件：
    所述η的取值范围为0.6～0.8；
    (52)记在第i次迭代时ui(t)和yi(t)分别为驱动信号和响应信号，根据驱动信号ui(t)和响应信号yi(t)求出第i次迭代时的相干函数和分别为ui(t)的自功率谱、ui(t)和yi(t)的互功率谱和yi(t)的自功率谱；
    (53)根据C1(f)、C2(f)、…、Cn(f)组成判别矩阵C中元素Ci，j表示第i次迭代时相干函数Ci(f)的第j个频率点的相干函数值；用判别矩阵C中的元素Ci，j表征频响函数Hi(f)的第j个频率点估计值的准确度；设置频响函数准确度阈值γ，判断判别矩阵C的每一列元素值是否全部大于等于γ，并统计满足每一列元素值全部大于等于γ的列所在判别矩阵C的列数，根据列数从小到大分别记为p1、p2、…、pk，将判别矩阵C剩余的m-k列从小到大分别记为q1、q2、…、qm-k，分别计算频响函数Hi(f)的第ps个频率点估计值的校正后频率点修正系数为频响函数的第qr个频率点估计值的校正后频率点修正系数为和响函数的第qr个频率点的估计值校正后频率点修正系数为
  6. 根据权利要求5所述的振动台随机功率谱复现控制方法，其特征在于，所述 p1、p2、…、pk中k表示满足每一列元素值全部大于等于γ的判别矩阵C的列的个数，k的取值为1≤k≤m且k为整数，ps表示判别矩阵C中的第ps列，s的取值为1，2，…，k；判别矩阵C的第ps列的元素值全部大于等于γ，频响函数Hi(f)的第ps个频率点的估计值准确度高，频响函数Hi(f)的第ps个频率点估计值的校正后频率点修正系数为s的取值为1，2，...，k。
  7. 根据权利要求5所述的振动台随机功率谱复现控制方法，其特征在于，所述q1、q2、...、qm-k中qr表示判别矩阵C中的第qr列，r的取值为1，2，...，m-k；剩余的m-k列不满足元素值全部大于等于，判断并记录判别矩阵C第qr列元素值小于γ的元素所在判别矩阵C的行数，从小到大依次记为其中：lr为第qr列元素值小于γ的元素的个数，lr取值为1≤lr≤n且l为整数，au，r表示判别矩阵C的第au，r行，u取值为1，2，…，lr；判别矩阵C的第au，r行第qr列的元素值对于频响函数的第qr个频率点估计值的准确度低，频响函数的第qr个频率点估计值的校正后频率点修正系数为其中：u取值为1,2,…,lr，r的取值为1,2,…,m-k。
  8. 根据权利要求7所述的振动台随机功率谱复现控制方法，其特征在于，所述判别矩阵C第qr列剩余的n-lr个元素的元素值大于等于γ，将剩余的n-lr个元素所在判别矩阵C行数从小到大依次记为其中：bv，r表示判别矩阵C的第bv，r行，v取值为1，2…，n-lr；判别矩阵C的第bv,r行第qr列的元素值对于频响函数的第qr个频率点，估计值的准确度高，频响函数的第qr个频率点的估计值校正后频率点修正系数为其中：表示未校正频率点修正系数，v取值为1,2,…,n-lr，r的取值为1,2,…,m-k。
  9. 根据权利要求5所述的振动台随机功率谱复现控制方法，其特征在于，所述相干函数值Ci,j和未修正频率点修正系数βi,j能计算得到第n次迭代时修正后的频响函数每个频率点的平均相干函数值的计算公式为其中：j取值为1,2,…,m；迭代步长αn中的元素αn,j计算公式为式中λ为比例系数；若表明该频率点上频响函数准确度高，λ取值为λ1；若表明该频率点上频响函数准确度低，λ取值为λ2。
  10. 一种振动台随机功率谱复现系统，用于实现如权利要求1-9任一项所述的方法，其特征在于，包括工控机、采集板卡、驱动板卡、通讯网卡和信号调理装置，所述采集板卡、驱动板卡和通讯网卡设置于工控机内部，所述信号调理装置与驱动板卡连接，所述采集板卡用于实时采集振动台运行过程中的位移和加速度传感器信号，所述驱动板卡用于将计算得到的实时控制信号转化为实际驱动信号，所述信号调理装置用于采集板卡与振动台传感 器、驱动板卡与振动台驱动单元间信号的变换，所述通讯网卡用于功率谱复现控制系统与振动台上位机显示单元间的实时通讯。
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Publication number Priority date Publication date Assignee Title
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Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20100305886A1 (en) * 2009-06-01 2010-12-02 Bruel & Kjaer, Sound & Vibration Measurement A/S Kurtosis Regulating Vibration Controller Apparatus and Method
CN107449577A (zh) * 2017-06-14 2017-12-08 西安交通大学 复合信号的电动振动台复现方法及振动复现系统
CN108469849A (zh) * 2017-12-15 2018-08-31 中国航空工业集团公司北京长城计量测试技术研究所 一种随机角振动控制方法
CN110672290A (zh) * 2019-09-24 2020-01-10 浙江大学 一种考虑滞后时间的地震模拟振动台迭代控制方法
CN118032253A (zh) * 2024-04-12 2024-05-14 苏州东菱振动试验仪器有限公司 一种振动台随机功率谱复现控制方法及系统

Family Cites Families (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO1997011344A1 (fr) * 1995-09-18 1997-03-27 Hitachi, Ltd. Ensemble table vibrante et procede de commande associe
CN101968405B (zh) * 2010-08-27 2012-05-30 北京工业大学 一种测试结合面动态特性装置及方法
CN113155385B (zh) * 2021-06-09 2022-06-28 南京航空航天大学 一种用于多振动台冲击加随机振动试验的系统及方法
CN113204255B (zh) * 2021-06-21 2021-12-21 北京博科测试系统股份有限公司 一种多自由度振动台功率谱加载控制方法
CN115950610A (zh) * 2022-06-30 2023-04-11 南京航空航天大学 一种多振动台正弦加随机振动试验系统及控制方法

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20100305886A1 (en) * 2009-06-01 2010-12-02 Bruel & Kjaer, Sound & Vibration Measurement A/S Kurtosis Regulating Vibration Controller Apparatus and Method
CN107449577A (zh) * 2017-06-14 2017-12-08 西安交通大学 复合信号的电动振动台复现方法及振动复现系统
CN108469849A (zh) * 2017-12-15 2018-08-31 中国航空工业集团公司北京长城计量测试技术研究所 一种随机角振动控制方法
CN110672290A (zh) * 2019-09-24 2020-01-10 浙江大学 一种考虑滞后时间的地震模拟振动台迭代控制方法
CN118032253A (zh) * 2024-04-12 2024-05-14 苏州东菱振动试验仪器有限公司 一种振动台随机功率谱复现控制方法及系统

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
GAUN GUANGFENG, CONG DACHENG, HAN JUNWEI, LI HONGREN: "Research on replicate iterative algorithm for power spectral density of random vibration", EARTHQUAKE ENGINEERING AND ENGINEERING VIBRATION, vol. 26, no. 6, 30 December 2006 (2006-12-30), pages 71 - 76, XP093363227, ISSN: 1000-1301, DOI: 10.13197/j.eeev.2006.06.012 *
XU JINCHENG, XIE YONG, CHEN LI, HAO LIANKUI: "Power Spectral Density Control Algorithm of Random Vibration Based on Hv Estimator", JOURNAL OF YANGZHOU UNIVERSITY (NATURAL SCIENCE EDITION), vol. 18, no. 01, 28 February 2015 (2015-02-28), pages 13 - 15 + 56, XP009565165, ISSN: 1007-824X *

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