A method for identifying excitation loads under incomplete transfer function matrix conditions of vibration systems

Abstract

The present invention discloses a method for identifying an excitation load under the condition of incomplete transfer function matrix information of a vibration system, which belongs to the technical field of mechanical vibration system identification and excitation load identification test, and can solve the problem that the excitation load cannot be directly identified by inverse matrix solution due to the lack of some elements of the transfer function matrix obtained due to the limitation of measurement environment conditions. The main technical feature of the present invention is that, based on the vibration response data obtained by measurement and the transfer function matrix data with some elements missing, a multi-input and multi-output linear system mathematical model is established, and the information grouping recursive calculation mode is designed and adopted, and the matrix singular value decomposition and generalized inverse matrix solution method are combined to calculate and obtain the system input excitation load, so as to realize the identification of the excitation load under the condition of incomplete transfer function matrix information of the vibration system. The method for identifying an excitation load under the condition of incomplete transfer function matrix information of a vibration system disclosed by the present invention can effectively realize the accurate identification of the excitation load under the condition of incomplete transfer function matrix information, and meet the application requirements of mechanical vibration system identification engineering.

Description

Technical Field

[0001] The invention belongs to the technical field of mechanical vibration system identification and excitation load identification test. Background Art

[0002] When a mechanical system is in operation, it generates excitation loads on its mounting structure and other connection systems. These excitation loads cause the corresponding structural vibration response, which is a typical multi-input multi-output system characteristic. Obtaining the input excitation load, system transfer function matrix and output vibration response through experiments is an important technical means to master the vibration characteristics of the mechanical system, support the design and control of vibration performance, and evaluate the vibration state and control effect. Under actual engineering environment conditions, it is difficult to directly measure and obtain the system excitation load. Generally, based on the multi-input multi-output system model, the transfer function matrix and vibration response are obtained by measurement to realize the identification of the excitation load, which belongs to the solution of the inverse problem of system identification. However, due to the limitations of the measurement environment conditions, if some elements of the transfer function matrix cannot be directly obtained, the information of the transfer function matrix is ​​incomplete at this time, and the excitation load identification cannot be realized directly through the inverse matrix solution. Therefore, it is necessary to establish a method for accurately identifying the excitation load under the condition of incomplete information of the transfer function matrix of the vibration system to meet the engineering application requirements of mechanical vibration system identification. Summary of the invention

[0003] The purpose of the present invention is to propose an excitation load identification method under the condition of incomplete transfer function matrix information of a vibration system, in order to solve the problem that some elements of the transfer function matrix obtained due to measurement environment conditions are missing and the excitation load identification cannot be realized directly through inverse matrix solution. The method can accurately identify the input excitation load and system transfer function of the mechanical vibration system and meet the application requirements of mechanical vibration system identification engineering.

[0004] To achieve the above-mentioned purpose of the present invention, the core of the present invention is to establish a mathematical model of a multi-input and multi-output linear system based on the measurement of vibration response data and transfer function matrix data with some elements missing, design and adopt an information grouping recursive calculation mode, combine matrix singular value decomposition and generalized inverse matrix solution method, calculate and obtain the system input excitation load, and realize the identification of excitation load under the condition of incomplete information of the vibration system transfer function matrix.

[0005] A vibration system transfer function matrix information incomplete condition excitation load identification method of the present invention comprises the following contents:

[0006] (I) Vibration response and transfer function data acquisition method

[0007] Accelerometers are used to measure the vibration response of the vibration system. The installation position and direction of the measuring point are consistent with the position and direction of the excitation load. In addition, 2-6 accelerometers are installed at other positions of the system as vibration response reference points. The measurement frequency range and accuracy must meet the measurement requirements, or the measurement frequency range is 5Hz-1kHz, the measurement accuracy is not less than 16 bits, and the sampling rate is not less than 2.56 times the maximum measurement frequency. The vibration response measurement points realize synchronous data acquisition, and the synchronization error is better than 3×10 -9 s. During measurement, the mechanical vibration system operates in a steady state, and the acceleration time domain signals of all vibration response measurement points are collected synchronously. Then, the time domain signals are Fourier transformed, and the transformed frequency domain signals are in the form of a combination of real and imaginary parts. The frequency domain signals of all measurement points form a vibration response vector:

[0008] X=[X1,X2,…,X N ] T (1)

[0009] Where X is the vibration response vector, X i (i=1, 2, ..., N) is the frequency domain signal of the vibration response measurement point, and N is the number of the vibration response measurement points.

[0010] The impact excitation method is used to measure and obtain the transfer function between the input excitation load of the vibration system and the vibration response position. The impact excitation position and direction are consistent with the vibration response position and direction. Except for the position where the impact excitation cannot be performed (such as the corresponding position of a certain input excitation load of the vibration system), the corresponding positions of the vibration response measurement points are impacted and excited respectively. The transfer function between the input excitation load of the vibration system and the vibration response position is obtained by synchronously measuring the impact excitation load and the vibration response data. The measurement frequency range and accuracy requirements are consistent with the vibration response measurement requirements. The frequency domain signal of the transfer function is a combination of the real part and the imaginary part. All the transfer functions obtained by measurement are combined into the vibration system transfer function matrix:

[0011]

[0012] Where H is the N×M order transfer function matrix, H ij (i=1, 2, ..., N; j=1, 2, ..., M) are elements of the transfer function matrix, M is the number of system input excitation loads (M<N), and an element of a column of the transfer function matrix is ​​missing.

[0013] (II) Calculation method of excitation load

[0014] Based on the vibration response and transfer function matrix data of the vibration system obtained by measurement, a multi-input and multi-output linear system model X=HF is established, that is:

[0015]

[0016] Where, F=[F1,F2,…,F M ] T Enter the excitation load vector for the system to be identified, F j (j=1, 2, ..., M) is the excitation load frequency domain signal. According to the reciprocity principle of linear systems, the missing column element of the transfer function matrix is ​​equal to its symmetrical row element, thereby obtaining other cross-point transfer functions except the missing origin transfer function.

[0017] Let H kk (1≤k≤M) is the missing origin transfer function, and the extracted H does not contain H kk The row vector and column vector of the elements form the transfer function matrix H1. At the same time, the corresponding position elements in the vibration response vector and the excitation load vector are removed, and the initial group excitation load identification model is established according to formula (4):

[0018] X1=H1F1 (4)

[0019] Where X1=[X1,…,X k-1 ,X k+1 ,…,X N ] T , F1=[F1,…,F k-1 ,F k+1 ,…,F M ] T , H1 is a (N-1)×(M-1) order transfer function matrix.

[0020] According to formula (5), the transfer function matrix H1 is subjected to singular value decomposition:

[0021]

[0022] Where U1 is a (N-1)×(N-1)-order unitary matrix, S1=diag(s1, s2, …, s M-1 ) is a (N-1)×(M-1)-order non-negative real diagonal matrix, and V1 is a (M-1)×(M-1)-order unitary matrix.

[0023] Calculate the generalized inverse matrix of matrix H1 according to formula (6):

[0024]

[0025] In the formula, is a (M-1)×(N-1) order non-negative real diagonal matrix.

[0026] Let X1 = [X1, ..., X k-1 ,X k+1 ,…,X N ] T, F1=[F1,…,F k-1 ,F k+1 ,…,F M ] T , calculate the initial excitation load F1 according to formula (7):

[0027]

[0028] Extract the minimum amplitude element in the initial excitation load vector F1, and set it as F l (1≤l≤M), subtract the load action from the vibration response vector, and calculate the vibration response vector X2 according to formula (8):

[0029] X2=X1-H1[0,…,0,F l , 0, …, 0] T (8)

[0030] Extraction, does not contain F l The element composition excitation load vector F2 = [F1, ..., F l-1 ,F l+1 ,…,F M ] T , extract H does not contain H kk The row vector of elements does not contain H ll The column vectors of the elements form the transfer function matrix H2, and the second group excitation load identification model is established according to formula (9):

[0031] X2=H2F2 (9)

[0032] Where H2 is a (N-1)×(M-1) order transfer function matrix.

[0033] Replace H1, X1 and F1 in equations (5), (6) and (7) with H2, X2 and F2 respectively, and calculate the second excitation load vector F2. Calculate the missing origin transfer function H according to equation (10): kk :

[0034]

[0035] In the formula, F l is the initial excitation load identification result, F i With F k Identify the results for the second excitation load.

[0036] The origin transfer function H is calculated kk Substitute the corresponding element positions of the transfer function matrix H, and then replace H1, X1, and F1 in Equations (5), (6), and (7) with H, X, and F respectively, and calculate the excitation load vector F, thereby realizing the identification of the input excitation load of the vibration system.

[0037] The advantages of the present invention are that, by using tests to obtain the transfer function and vibration response data information of the vibration system, and adopting the information grouping recursive load calculation method, the accurate identification of the excitation load under the condition of incomplete transfer function matrix information can be effectively realized, thus meeting the application requirements of mechanical vibration system identification engineering. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 Schematic diagram of the arrangement of measurement points for typical vibration system, vibration response and transfer function measurement in the present invention.

[0039] Figure 2 The excitation load identification result is input at the first position of the installation base of the typical vibration system in the present invention.

[0040] Figure 3 The excitation load identification result is input at the second position of the installation base of the typical vibration system in the present invention.

[0041] Figure 4 The excitation load identification result is input at the third position of the installation base of the typical vibration system in the present invention.

[0042] Figure 5 The excitation load identification result is input at the fourth position of the installation base of the typical vibration system in the present invention. DETAILED DESCRIPTION

[0043] In conjunction with the embodiments, a vibration system transfer function matrix information incomplete condition excitation load identification method of the present invention is described in detail. In this embodiment, the typical vibration system consists of a vibration source and a mounting base. To verify the effectiveness of the excitation source identification method, the vibration source is vertically fixed to the mounting base through four force sensors, and the four input excitation loads of the mounting base are the excitation loads to be identified.

[0044] In combination with the embodiments, Figure 1 As shown, the specific implementation of the present invention is as follows:

[0045] (1) Use an accelerometer to measure the vibration response of the mounting base. Install accelerometers at the corresponding positions of the force sensors. The installation direction is consistent with the direction of the excitation load. At the same time, install an accelerometer near the force sensor as a vibration response reference point. The vibration response measurement frequency range and accuracy must meet the measurement requirements, or the measurement frequency range is 5Hz-1kHz, the measurement accuracy is not less than 16 bits, the sampling rate is not less than 2.56 times the maximum measurement frequency, and the vibration response measurement points achieve synchronous data acquisition, and the synchronization error is better than 3×10 -9 The acceleration time domain signals of all vibration response measurement points are collected, and then the time domain signals are Fourier transformed. The transformed frequency domain signals are in the form of a combination of real and imaginary parts, and the vibration response vector is formed according to formula (1).

[0046] (2) The impact excitation method is used to measure and obtain the transfer function between the input excitation load of the mounting base and the vibration response position. The impact excitation position and direction are consistent with the vibration response position and direction. Except for the position where the impact excitation cannot be performed (such as the corresponding position of a force sensor on the mounting base), the corresponding positions of the vibration response measurement points are impact-excited respectively. The transfer function between the input excitation load of the mounting base and the vibration response position is obtained by synchronously measuring the impact excitation load and the vibration response data. The measurement frequency range and accuracy requirements are consistent with the vibration response measurement requirements. The transfer function frequency domain signal is a combination of the real part and the imaginary part, and the transfer function matrix is ​​formed according to formula (2).

[0047] (3) Based on the measured vibration response of the mounting base and the transfer function matrix data, a multi-input and multi-output linear system model is established according to formula (3). According to the reciprocity principle of linear systems, the missing column element of the transfer function matrix is ​​equal to its symmetrical row element, thereby obtaining the other cross-point transfer functions except the missing origin transfer function.

[0048] (4)H 11 For the missing origin transfer function, the extracted transfer function matrix H does not contain H 11 The row vector and column vector of form the transfer function matrix H1, and remove the corresponding position elements in the vibration response vector and the excitation load vector, and establish the initial group excitation load identification model according to formula (4). Perform singular value decomposition on the transfer function matrix H1 according to formula (5), and calculate the generalized inverse matrix of matrix H1 according to formula (6): Calculate the initial excitation load F1 according to formula (7).

[0049] (5) Extract the element F3 with the minimum amplitude in the initial excitation load vector F1, subtract the load action from the vibration response vector, and calculate the vibration response vector X2 according to formula (8). Extract the element F that does not contain F3 to form the excitation load vector F2, and extract the element H that does not contain H 11 The row vectors of 33 The column vectors of the elements form the transfer function matrix H2, and the second group excitation load identification model is established according to formula (9). The transfer function matrix H2 is subjected to singular value decomposition according to formula (5), and the generalized inverse matrix of the matrix H2 is calculated according to formula (6): Calculate the excitation load F2 according to formula (7).

[0050] (6) Calculate the missing origin transfer function H according to formula (10): 11 , H 11 Substitute the corresponding element position of the transfer function matrix H, perform singular value decomposition on the transfer function matrix H according to formula (5), and calculate the generalized inverse matrix H of the matrix H according to formula (6): +, the excitation load F is calculated according to formula (7), thereby realizing the identification of the input excitation load of the mounting base.

[0051] According to a vibration system transfer function matrix information incomplete condition excitation load identification method of the present invention, the typical vibration system input excitation load identification result of this embodiment is given, and the input excitation load of each position measured by the force sensor is also given, such as Figure 2-Figure 5 According to the excitation load identification results, it is shown that the excitation load identification method of the vibration system transfer function matrix under incomplete information conditions according to the present invention can realize accurate identification of the excitation load under the condition of missing some elements of the transfer function matrix, and meet the application requirements of mechanical vibration system identification engineering.

[0052] Finally, it should be noted that the above embodiments are only used to illustrate the general process of the technical implementation of the present invention and are not intended to limit it. Although the present invention has been described in detail, it should be understood by those skilled in the art that any modification or equivalent replacement of the technical solution of the present invention does not depart from the spirit and scope of the technical solution of the present invention, and is included in the scope of the claims of the present invention.

Claims

1. A method for identifying excitation loads under incomplete transfer function matrix information of a vibration system, characterized in that: Based on the vibration response data obtained by measurement and the transfer function matrix data with some elements missing, a mathematical model of a multi-input and multi-output linear system is established. The design adopts an information grouping recursive calculation mode, combined with the matrix singular value decomposition and generalized inverse matrix solution method, to calculate the system input excitation load and realize the excitation load identification under the condition of incomplete information of the transfer function matrix of the vibration system.

2. The method according to claim 1, characterized in that: (1) Accelerometers are used to measure the vibration response of the vibration system. The installation position and direction of the measuring point are consistent with the position and direction of the excitation load. In addition, 2-6 accelerometers are installed at other locations in the system as vibration response reference points. The measurement frequency range and accuracy must meet the measurement requirements, or the measurement frequency range is 5Hz-1kHz, the measurement accuracy is not less than 16 bits, and the sampling rate is not less than 2.56 times the maximum measurement frequency. The vibration response measurement points realize synchronous data acquisition, and the synchronization error is better than 3×10 -9 s, the mechanical vibration system is running in a steady state during measurement, and the acceleration time domain signals of all vibration response measurement points are collected synchronously. Then, the time domain signals are Fourier transformed, and the transformed frequency domain signals are in the form of a combination of real and imaginary parts. The vibration response vector is formed according to formula (1): X=[X1,X2,...,X N ]T(1) Where X is the vibration response vector, X i (i=1, 2, ..., N) is the frequency domain signal of the vibration response measurement point, and N is the number of vibration response measurement points; (2) The impact excitation method is used to measure and obtain the transfer function between the input excitation load of the vibration system and the vibration response position. The impact excitation position and direction are consistent with the vibration response position and direction. Except for the position where the impact excitation cannot be performed (such as the corresponding position of a certain input excitation load of the vibration system), the corresponding positions of the vibration response measurement points are impacted and excited respectively. The transfer function between the input excitation load of the vibration system and the vibration response position is obtained by synchronously measuring the impact excitation load and the vibration response data. The measurement frequency range and accuracy requirements are consistent with the vibration response measurement requirements. The frequency domain signal of the transfer function is a combination of the real part and the imaginary part. All the transfer functions obtained by measurement are combined into a transfer function matrix according to formula (2): where H is an N×M transfer function matrix, and H ij (i = 1, 2, …, N; j = 1, 2, …, M) are the elements of the transfer function matrix, M is the number of system input excitation loads (M < N), and one column of elements of the transfer function matrix is missing; (3) Based on the measured system vibration response and transfer function matrix data, a multi-input multi-output linear system model is established according to formula (3): Where, F=[F1,F2,…,F M ] T Enter the excitation load vector for the system to be identified, F j (j=1, 2, ..., M) is the frequency domain signal of the excitation load. According to the reciprocity principle of linear systems, the missing column element of the transfer function matrix is ​​equal to its symmetrical row element, thereby obtaining other cross-point transfer functions except the missing origin transfer function; (4) Let H kk (1≤k≤M) is the missing origin transfer function, and the extracted H does not contain H kk The row vector and column vector of the elements form the transfer function matrix H1. At the same time, the corresponding position elements in the vibration response vector and the excitation load vector are removed, and the initial group excitation load identification model is established according to formula (4): X1=H1F1 (4) Where X1=[X1,…,X k-1 ,X k+1 ,…,X N ] T , F1=[F1,…,F k-1 ,F k+1 ,…,F M ] T , H1 is a (N-1)×(M-1) order transfer function matrix; (5) According to formula (5), the transfer function matrix H1 is subjected to singular value decomposition H1=U1S1V1 * (5) Where U1 is a (N-1)×(N-1)-order unitary matrix, S1=diag(s1, s2, …, s M-1 ) is a (N-1)×(M-1)-order non-negative real diagonal matrix, and V1 is a (M-1)×(M-1)-order unitary matrix; (6) Calculate the generalized inverse matrix of matrix H1 according to formula (6): In the formula, is a (M-1)×(N-1) order non-negative real diagonal matrix; (7) Let X1 = [X1, ..., X k-1 ,X k+1 ,…,X N ] T , F1=[F1,…,F k-1 ,F k+1 ,…,F M ] T , calculate the initial excitation load F1 according to formula (7) (8) Extract the element with the smallest amplitude in the initial excitation load vector F1, which can be set as F l (1≤l≤M), subtract the load action from the vibration response vector, and calculate the vibration response vector X2 according to formula (8): X2=X1-H1[0,…,0,F l ,0,…,0] T (8) (9) Extract F does not contain F l The element composition excitation load vector F2 = [F1, ..., F l-1 ,F l+1 ,…,F M ] T , extract H does not contain H kk The row vector of elements does not contain H ll The column vectors of the elements form the transfer function matrix H2, and the second group excitation load identification model is established according to formula (9): X2=H2F2 (9) Where H2 is a (N-1)×(M-1) order transfer function matrix; (10) Replace H1, X1 and F1 in equations (5), (6) and (7) with H2, X2 and F2 respectively, and calculate the second excitation load vector F2. Calculate the missing origin transfer function H according to equation (10): kk In the formula, F l is the initial excitation load identification result, F i With F k This is the result of the second excitation load identification; (11) The calculated origin transfer function H kk Substitute the corresponding element positions of the transfer function matrix H, and then replace H1, X1, and F1 in Equations (5), (6), and (7) with H, X, and F respectively, and calculate the excitation load vector F, thereby realizing the identification of the input excitation load of the vibration system.

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