A mapping-based MIMO vibration test zero-response control method and system

Abstract

This invention relates to a mapping-based MIMO vibration testing zero-response control method and system, belonging to the field of vibration testing technology. It includes: acquiring the frequency response matrix, response degrees of freedom, current response vector, and driving spectrum vector of the vibration testing system; constructing an unmapped error vector based on the difference between the current response vector and a preset target response vector; determining the active degrees of freedom and zero degrees of freedom based on the response degrees of freedom; determining a zero-mapping operator by combining the active and zero degrees of freedom; obtaining an effective error vector by combining the zero-mapping operator and the unmapped error vector; and iteratively updating the driving spectrum vector by combining the effective error vector and the frequency response matrix. This invention improves system stability, reduces sensitivity to noise, and minimizes unnecessary actuator output.

Description

Technical Field

[0001] This invention relates to the field of vibration testing technology, and in particular to a mapping-based MIMO vibration testing zero-response control method and system. Background Technology

[0002] Vibration testing is a mechanical test that applies controlled vibration to a product, structure, or test piece and measures its response to verify its strength, reliability, vibration resistance, lifespan, and to simulate real transportation / use environments.

[0003] Currently, multiple-input multiple-output (MIMO) vibration testing systems typically employ inverse or pseudo-inverse matrix techniques of the frequency response function (FRF) to calculate the driving signal, thereby minimizing response errors across multiple control channels. In practical testing scenarios such as multi-axis excitation tests, slide table tests, or six-degree-of-freedom systems, it is often necessary to excite vibrations in one or more primary degrees of freedom while minimizing or suppressing vibrations in other non-primary degrees of freedom. This suppression is achieved by setting the target response of the undesired degrees of freedom to zero.

[0004] When the target response of the undesired degrees of freedom is set to zero to achieve suppression, it is still affected by noise and errors from sensors or systems. Noise-dominated or weakly coupled channels will inject error-based correction energy into the inverse matrix calculation, resulting in system instability and excessive actuator load. Summary of the Invention

[0005] To improve system stability, reduce sensitivity to noise, and minimize unnecessary actuator output, this invention provides a mapping-based MIMO vibration testing zero-response control method and system.

[0006] In a first aspect, the present invention provides a mapping-based zero-response control method for MIMO vibration testing, employing the following technical solution:

[0007] A mapping-based zero-response control method for MIMO vibration testing includes:

[0008] Collect the frequency response matrix, response degrees of freedom, current response vector, and driving spectrum vector of the vibration testing system;

[0009] Construct an unmapped error vector based on the difference between the current response vector and the preset target response vector;

[0010] Determine the active degrees of freedom and zero degrees of freedom based on the response degrees of freedom;

[0011] The zero-mapping operator is determined by combining the active degrees of freedom and the zero degrees of freedom;

[0012] The effective error vector is obtained by combining the zero-mapping operator and the unmapped error vector.

[0013] The driving spectral vector is iteratively updated by combining the effective error vector and the frequency response matrix.

[0014] By adopting the above technical solution, the frequency response matrix, response degrees of freedom, current response vector, and driving spectrum vector are collected. First, an unmapped error vector is constructed. Then, based on the response degrees of freedom, active and zero degrees of freedom are divided and a zero-mapping operator is determined. The unmapped error vector is processed by the zero-mapping operator to obtain an effective error vector. Finally, the driving spectrum vector is iteratively updated by combining the effective error vector and the frequency response matrix. The error influence of zero degrees of freedom is eliminated from the source of the correction subspace, and only the correction information of the active degrees of freedom is retained for the update of the driving spectrum vector. This achieves accurate vibration suppression of zero degrees of freedom and accurate control of active degrees of freedom in MIMO vibration testing. It effectively avoids problems such as system instability and invalid actuator load caused by zero degrees of freedom participating in correction calculation, improves system stability, reduces sensitivity to noise, and reduces unnecessary actuator output.

[0015] Optionally, the methods for acquiring the frequency response matrix include:

[0016] Acquire time-domain data of drive and response signals;

[0017] Convert time-domain data to frequency-domain data;

[0018] Based on frequency domain data, estimate the driving power spectrum matrix and the cross power spectrum matrix between the driving force and the response for each frequency point.

[0019] The frequency response matrix is ​​estimated based on the cross-power spectrum matrix and the driving self-power spectrum matrix.

[0020] By adopting the above technical solution, the time-domain data of the driving signal and response signal are collected and converted to the frequency domain. The driving self-power spectrum matrix and cross-power spectrum matrix are estimated at each frequency point. Then, the frequency response matrix is ​​estimated based on these two types of matrices. The frequency response matrix obtained by frequency domain spectrum estimation can accurately characterize the dynamic transmission characteristics of the driving and response of the vibration test system at different frequency points. Moreover, the derivation based on the measured time-domain signal is close to the actual working state of the system, providing an accurate and reliable basis for the subsequent iterative update of the driving spectrum vector, and improving the estimation accuracy and effectiveness of the frequency response matrix.

[0021] Optionally, the methods for acquiring the current response vector include:

[0022] The current response vector is obtained by calculating the driving spectral vector, cross-power spectral matrix, and driving self-power spectral matrix based on a preset response vector calculation formula. The response vector calculation formula is: Y corr (f)=S yx (f)*(Sxx (f) -1 )*X(f);

[0023] Among them, Y corr (f) is the current response vector;

[0024] S yx (f) is the cross-power spectrum matrix;

[0025] S xx (f) is the driving power spectrum matrix;

[0026] X(f) is the driving spectral vector.

[0027] By adopting the above technical solution, the current response vector is calculated by combining the driving spectrum vector, cross power spectrum matrix, and driving self power spectrum matrix through a preset response vector calculation formula. This method eliminates the influence of sensor noise and unrelated disturbances on the response signal. The obtained current response vector is a true representation of the driving-related response, which can accurately reflect the actual response state of the system under the excitation of the current driving spectrum vector. It provides accurate basic data for the subsequent construction of unmapped error vectors, effectively avoids error deviations introduced by noise, and improves the accuracy of error calculation.

[0028] Optional methods for constructing the unmapped error vector include:

[0029] The unmapped error vector is obtained by analyzing and calculating the current response vector and the preset target response vector based on a preset unmapped error construction formula. The unmapped error construction formula is as follows:

[0030] e(f) = Y target (f)-Y corr (f);

[0031] Where e(f) is the unmapped error vector;

[0032] Y target (f) is the preset target response vector.

[0033] By adopting the above technical solution, the unmapped error vector is calculated by the difference between the target response vector and the current response vector. This can directly and accurately characterize the degree of deviation between the current system response and the preset target response, providing a clear and accurate error basis for the subsequent construction of effective error vectors, and making the error characterization more in line with actual control requirements.

[0034] Optional methods for determining active degrees of freedom and zero degrees of freedom include:

[0035] Determine whether the response degrees of freedom are consistent with the preset degrees of freedom for suppressing vibration;

[0036] If so, the response degrees of freedom are defined as zero.

[0037] If not, then the response degrees of freedom are defined as active degrees of freedom.

[0038] By adopting the above technical solution, and by judging whether the response degree of freedom is consistent with the preset vibration suppression degree of freedom, the active degree of freedom and zero degree of freedom are clearly and explicitly defined, thus realizing the accurate classification of the response degree of freedom. It can determine the active degree of freedom to be controlled and the zero degree of freedom to be suppressed according to the actual needs of vibration testing, and provide an accurate basis for the determination of the subsequent zero mapping operator.

[0039] Optionally, methods for determining the zero-mapping operator include:

[0040] The zero-mapping operator is obtained by analyzing and calculating the active degrees of freedom and zero degrees of freedom based on the preset zero-mapping determination formula. The zero-mapping determination formula is as follows:

[0041] P null (f)=diag(p1(f),p2(f),…,p N (f));

[0042] Among them, P null (f) is the zero-mapping operator;

[0043] Regarding the degrees of freedom of active response, p i (f)=1;

[0044] For zero-response degrees of freedom, p i (f)=0.

[0045] By adopting the above technical solution, and by assigning a value of 1 to the active degree of freedom and a value of 0 to the zero degree of freedom, the unmapped error vector can be accurately screened. This allows the zero-mapping operator to selectively mask the error information of the zero degree of freedom and retain the error information of the active degree of freedom, providing a precise mapping basis for the construction of effective error vectors and ensuring that the zero degree of freedom can be explicitly removed from the correction subspace.

[0046] Optional methods for determining the effective error vector include:

[0047] The effective error vector is obtained by analyzing and calculating the zero-mapping operator and the unmapped error vector based on a preset effective error construction formula. The effective error construction formula is as follows:

[0048] E eff (f)=P null (f)*e(f);

[0049] Among them, E eff (f) is the effective error vector.

[0050] By adopting the above technical solution, the effective error vector is obtained by multiplying the zero-mapping operator with the unmapped error vector. Through the filtering effect of the zero-mapping operator, the error component with zero degrees of freedom in the unmapped error vector is effectively eliminated, and only the error information of the active degrees of freedom is retained. This allows the subsequent iterative update of the driving spectral vector to be corrected only based on the deviation of the active degrees of freedom, completely avoiding the injection of correction energy into the driving update by the error of zero degrees of freedom, and improving the pertinence and accuracy of the driving correction.

[0051] Optional methods for iteratively updating the driving spectral vector include:

[0052] Loop gain is obtained based on the driving spectrum vector;

[0053] The pseudo-inverse of the response matrix is ​​obtained by performing a regularized pseudo-inverse on the frequency response matrix.

[0054] Based on a preset iterative update formula, the loop gain, effective error vector, and pseudo-inverse of the response matrix are analyzed and calculated to obtain the updated driving spectrum vector.

[0055] The iterative update formula is as follows:

[0056] X {k+1} (f)=X k (f)+μ(f)*H†(f)*E eff (f);

[0057] Among them, X {k+1} (f) is the driving spectrum vector for the (k+1)th iteration;

[0058] X k (f) is the driving spectrum vector for the k-th iteration;

[0059] μ(f) is the loop gain;

[0060] H†(f) is the pseudo-inverse of the response matrix.

[0061] By adopting the above technical solution, the frequency response matrix is ​​normalized and pseudo-inverse is obtained by adjusting the loop gain. Then, the driving spectrum vector is iteratively updated based on the preset iterative update formula. The update amount of the driving spectrum vector is determined only by the effective error vector, the pseudo-inverse of the response matrix, and the loop gain. The correction energy only acts on the active degree of freedom subspace. This achieves accurate and dynamic iterative optimization of the driving spectrum vector. The introduction of the loop gain can also flexibly control the convergence speed and update stability of the driving spectrum vector, ensuring that the system converges quickly and remains stable during the iteration process, avoiding problems such as slow convergence or system oscillation.

[0062] Optional methods for determining the pseudoinverse of the response matrix include:

[0063] The regularization parameter, Hermitian conjugate transpose, and identity matrix are retrieved based on the frequency response matrix.

[0064] Based on a pre-defined regularization pseudo-inverse formula, the regularization parameter, Hermitian conjugate transpose, and identity matrix are analyzed and calculated to obtain the pseudo-inverse of the response matrix. The regularization pseudo-inverse formula is as follows:

[0065] H†(f)=(H H (f)*H(f)+λ(f)*I) -1 *H H (f);

[0066] Where H(f) is the frequency response matrix;

[0067] H H (f) is the Hermitian conjugate transpose;

[0068] λ(f) is the regularization parameter;

[0069] I is the identity matrix.

[0070] By adopting the above technical solution, based on the preset regularized pseudo-inverse formula, the pseudo-inverse of the response matrix is ​​calculated by combining the Hermitian conjugate transpose of the frequency response matrix, the regularization parameter, and the identity matrix. The introduction of the regularization parameter effectively avoids the matrix singularity problem that may occur when directly inverting the frequency response matrix, thus improving the stability and feasibility of matrix inversion.

[0071] Secondly, the present invention provides a mapping-based MIMO vibration test zero-response control system, which adopts the following technical solution:

[0072] A mapping-based MIMO vibration test zero-response control system includes:

[0073] The acquisition module is used to acquire the frequency response matrix, response degrees of freedom, current response vector, driving spectrum vector, and time domain data.

[0074] The memory stores a program for implementing a mapping-based MIMO vibration test zero-response control method as described in any one of the first aspects;

[0075] The processor loads and executes programs stored in memory.

[0076] In summary, the present invention has at least one of the following beneficial technical effects:

[0077] 1. By acquiring the frequency response matrix, response degrees of freedom, current response vector, and driving spectrum vector, an unmapped error vector is first constructed. Then, based on the response degrees of freedom, active and zero degrees of freedom are divided and a zero-mapping operator is determined. The unmapped error vector is processed by the zero-mapping operator to obtain an effective error vector. Finally, the driving spectrum vector is iteratively updated by combining the effective error vector with the frequency response matrix. The error influence of zero degrees of freedom is eliminated from the source of the correction subspace, and only the correction information of the active degrees of freedom is retained for updating the driving spectrum vector. This achieves accurate vibration suppression of zero degrees of freedom and accurate control of active degrees of freedom in MIMO vibration testing. It effectively avoids problems such as system instability and invalid actuator load caused by zero degrees of freedom participating in correction calculation, improves system stability, reduces sensitivity to noise, and reduces unnecessary actuator output.

[0078] 2. By acquiring time-domain data of driving and response signals and converting them to the frequency domain, the driving self-power spectrum matrix and cross-power spectrum matrix are estimated at each frequency point. Then, the frequency response matrix is ​​estimated based on these two types of matrices. The frequency response matrix obtained by frequency domain spectrum estimation can accurately characterize the dynamic transmission characteristics of the driving and response of the vibration test system at different frequency points. Moreover, the derivation based on the measured time-domain signal is consistent with the actual working state of the system, providing an accurate and reliable basis for the subsequent iterative update of the driving spectrum vector, thus improving the estimation accuracy and effectiveness of the frequency response matrix.

[0079] 3. By assigning a value of 1 to the active degree of freedom and a value of 0 to the zero degree of freedom, the unmapped error vector can be accurately filtered and processed. This allows the zero-mapping operator to selectively mask the error information of the zero degree of freedom and retain the error information of the active degree of freedom, providing a precise mapping basis for the construction of effective error vectors and ensuring that the zero degree of freedom can be explicitly removed from the correction subspace. Attached Figure Description

[0080] Figure 1 This is a flowchart of a mapping-based method for zero-response control in MIMO vibration testing. Detailed Implementation

[0081] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments.

[0082] A mapping-based zero-response control method for MIMO vibration testing.

[0083] Reference Figure 1 This invention discloses a mapping-based zero-response control method for MIMO vibration testing, comprising:

[0084] S1: Collect the frequency response matrix, response degrees of freedom, current response vector, and driving spectrum vector of the vibration test system.

[0085] The frequency response matrix refers to the matrix that characterizes the dynamic transmission characteristics between the driving signal input and the structural response output of the vibration test system at different frequency points.

[0086] The response degree of freedom refers to the independent motion dimension that characterizes the vibration response state of the tested structure in vibration testing. The response degree of freedom is collected after being predefined and input by the actual needs of vibration testing, the structural characteristics of the tested structure, and the vibration testing objectives.

[0087] The current response vector refers to the vector composed of the drive-related response components induced by the drive signal under the current drive spectrum vector excitation of the structure under test.

[0088] The drive spectrum vector refers to the vector representing the complex amplitude at each frequency point, formed by converting the time-domain drive signal of each drive channel in a MIMO vibration testing system to the frequency domain. The drive spectrum vector is obtained by generating the initial time-domain drive signal of each drive channel according to the test type (random / sinusoidal vibration, etc.) in the initial stage of testing, converting it to the frequency domain using Discrete Fourier Transform, and then using this initial drive spectrum vector for subsequent use.

[0089] The method for acquiring the frequency response matrix includes the following steps:

[0090] S11: Acquire time-domain data of drive and response signals.

[0091] In this context, the driving signal refers to the signal output by the vibration actuator in the vibration testing system, used to apply vibration excitation to the structure under test. The response signal refers to the vibration feedback signal generated by the structure under test under the vibration excitation of the driving signal. Time-domain data refers to the numerical representation of the driving signal and response signal in the time dimension, recording physical quantities such as the amplitude and intensity of the signal at different time points.

[0092] By recording the physical quantities of the excitation signals output by the actuator at different time points in real time according to a preset sampling frequency, the time-domain data of the drive signal is formed. The time-domain data of the response signal requires that, according to the vibration test target, sensors (such as acceleration sensors and displacement sensors) be placed at the specified response positions of the structure under test. The sensors convert the physical vibration of the structure under test into an acquireable electrical signal. Then, the signal acquisition and processing subsystem acquires the electrical signal at the same sampling frequency, records the signal values ​​at each time point, and obtains the time-domain data of the response signal.

[0093] S12: Convert time-domain data to frequency-domain data.

[0094] Frequency domain data refers to the numerical representation of time domain data in the frequency dimension after mathematical transformation.

[0095] First, the acquired time-domain data of the drive / response signal is preprocessed (such as windowing to suppress spectral leakage and removing DC components to eliminate baseline offset). Then, the preprocessed time-domain data sequence is input into the FFT algorithm for operation, thereby converting the one-dimensional numerical sequence in the time dimension into a complex-valued sequence in the frequency dimension. This complex-valued sequence is the frequency domain data, and each element corresponds to a frequency point, containing the amplitude and phase information of the signal at that frequency.

[0096] S13: Estimate the self-power spectrum matrix of the driver and the cross-power spectrum matrix between the driver and the response for each frequency point based on frequency domain data.

[0097] The self-power spectrum matrix of the driving channel refers to the matrix characterizing the frequency domain energy distribution of each driving channel in the MIMO vibration test system, as well as the signal correlation and coupling characteristics between different driving channels. The cross-power spectrum matrix refers to the matrix characterizing the frequency domain signal energy coupling, phase relationship, and correlation between the driving channel and the response channel.

[0098] For each frequency point in the vibration test, the complex-valued data of all driving channels at that frequency are first extracted from the frequency domain data and integrated into a driving spectrum vector. Simultaneously, the complex-valued data of all response channels at that frequency are extracted and integrated into a response spectrum vector. The driving spectrum vector at that frequency point is then multiplied by its Hermitian conjugate transpose and the original driving spectrum vector. The expected value of the calculated results from multiple samplings is then statistically analyzed to suppress noise interference, ultimately yielding the driving self-power spectrum matrix for that frequency point. Finally, the response spectrum vector at that frequency point is multiplied by its Hermitian conjugate transpose and the driving spectrum vector. This process is then repeated through averaging of multiple sampling data segments to obtain the cross-power spectrum matrix between the driving and response at that frequency point.

[0099] S14: Estimate the frequency response matrix based on the cross power spectrum matrix and the driving self power spectrum matrix.

[0100] Specifically, by employing the cross-spectral method, the frequency response matrix is ​​independently estimated for each frequency point. This involves extracting the estimated cross-power spectrum matrix and the driving self-power spectrum matrix at that frequency point, first inverting the driving self-power spectrum matrix, and then performing matrix multiplication between the cross-power spectrum matrix and the inverted driving self-power spectrum matrix. The result of this operation is the frequency response matrix at that frequency point.

[0101] The method for obtaining the current response vector includes the following steps:

[0102] S15: Calculate the driving spectrum vector, cross power spectrum matrix, and driving self power spectrum matrix based on the preset response vector calculation formula to obtain the current response vector.

[0103] The formula for calculating the response vector is: Y corr (f)=S yx (f)*(Sxx (f) -1 )*X(f). Y corr (f) is the current response vector; S yx (f) is the cross-power spectrum matrix; S xx X(f) is the driving power spectrum matrix; X(f) is the driving spectrum vector.

[0104] S2: Construct an unmapped error vector based on the difference between the current response vector and the preset target response vector.

[0105] The target response vector refers to the vector, pre-defined based on the control requirements of vibration testing, industry testing standards, or pre-set experimental objectives, that characterizes the expected vibration response state of the tested structure at each frequency point. The unmapped error vector refers to the degree of deviation in vibration response at each degree of freedom of response at each frequency point.

[0106] The unmapped error vector can be constructed in the following ways:

[0107] The unmapped error vector is obtained by analyzing and calculating the current response vector and the preset target response vector based on the preset unmapped error construction formula.

[0108] The formula for constructing the unmapped error is: e(f) = Y target (f)-Y corr (f).

[0109] e(f) is the unmapped error vector; Y target (f) is the preset target response vector.

[0110] S3: Determine the active degree of freedom and zero degree of freedom based on the response degree of freedom.

[0111] Among them, active degrees of freedom refer to the response dimensions that need to be controlled to a non-zero target response value according to the vibration test control requirements, as separated from the response degrees of freedom. Zero degrees of freedom refer to the response dimensions that need to be suppressed or minimized from the response degrees of freedom.

[0112] The method for determining active degrees of freedom and zero degrees of freedom includes the following steps:

[0113] S31: Determine whether the response degree of freedom is consistent with the preset degree of freedom for suppressing vibration. If yes, proceed to S32; if no, proceed to S33.

[0114] Among them, the vibration suppression degree of freedom refers to the set of response degrees of freedom that need to be suppressed or minimized based on the vibration suppression requirements, test objectives and test requirements of the structure under test in MIMO vibration testing.

[0115] By judging whether the response degree of freedom is consistent with the preset degree of freedom to suppress vibration, the active degree of freedom and zero degree of freedom are distinguished.

[0116] S32: Define the response degree of freedom as zero.

[0117] When the response degree of freedom is consistent with the preset suppression vibration degree of freedom, it means that the vibration response needs to be suppressed or minimized, so the response degree of freedom is defined as zero degree of freedom.

[0118] S33: Define the response degree of freedom as the active degree of freedom.

[0119] When the response degree of freedom is inconsistent with the preset suppression vibration degree of freedom, it means that there is no need to suppress or minimize its vibration response. Therefore, the response degree of freedom is defined as the active degree of freedom.

[0120] S4: Determine the zero mapping operator by combining the active degrees of freedom and the zero degrees of freedom.

[0121] Among them, the zero-mapping operator refers to the diagonal matrix constructed based on the partitioning result of active degrees of freedom and zero degrees of freedom.

[0122] The method for determining the zero-mapping operator includes the following steps:

[0123] The zero-mapping operator is obtained by analyzing and calculating the active degrees of freedom and zero degrees of freedom based on the preset zero-mapping determination formula, whereby the zero-mapping determination formula is: P null (f)=diag(p1(f),p2(f),…,p N (f)). P null (f) is the zero-mapping operator; for the active response degrees of freedom, p i (f)=1; for zero-response degrees of freedom, p i (f)=0.

[0124] S5: Combine the zero-mapping operator with the unmapped error vector to obtain the effective error vector.

[0125] The effective error vector refers to the error vector obtained by performing matrix operations on the zero-mapping operator and the unmapped error vector, which retains only the error information of the active degrees of freedom.

[0126] The method for determining the effective error vector includes the following steps:

[0127] The effective error vector is obtained by analyzing and calculating the zero-mapping operator and the unmapped error vector based on the preset effective error construction formula.

[0128] The effective error is constructed as follows: E eff (f)=P null(f)*e(f). E eff (f) is the effective error vector.

[0129] S6: Iteratively update the driving spectral vector by combining the effective error vector and the frequency response matrix.

[0130] By combining the analysis of the effective error vector and the frequency response matrix, the driving spectrum vector is iteratively updated, achieving precise vibration suppression of zero degrees of freedom and precise control of active degrees of freedom in MIMO vibration testing. This effectively avoids system instability and invalid actuator load caused by zero degrees of freedom participating in correction calculations, thus significantly improving stability even in the presence of noise-dominant channels, reducing unnecessary actuator driving energy, and achieving faster and more robust convergence. It is compatible with existing control architectures based on inverse FRF. Furthermore, it is applicable to MIMO random vibration control, MIMO sinusoidal vibration control, time-domain waveform reproduction (TWR / ITWR), hydraulic and electric excitation systems, etc.

[0131] The iterative update method for driving spectral vectors includes the following steps:

[0132] S61: Loop gain is obtained based on the driving spectrum vector.

[0133] Among them, loop gain refers to the control parameter that varies with frequency.

[0134] Before vibration testing, based on the dynamic characteristics of the MIMO vibration testing system, the load capacity of the vibration drive actuator, and the convergence requirements of vibration control, a suitable loop gain value is pre-set for each frequency point of the test, forming a mapping table of frequency points and loop gain values, and this table is stored in the memory of the vibration control system. When retrieving the loop gain based on the drive spectrum vector, the specific frequency point to which the drive spectrum vector to be iterated belongs is used as an index to perform a one-to-one precise match in the pre-set mapping table, directly retrieving the pre-set loop gain value at that frequency point, providing matching control parameters for subsequent iterative calculations of the drive spectrum vector.

[0135] S62: Obtain the pseudo-inverse of the response matrix by performing regularization on the frequency response matrix.

[0136] The pseudo-inverse of the response matrix refers to the pseudo-inverse matrix obtained by performing regularization on the frequency response matrix.

[0137] The method for determining the pseudoinverse of the response matrix includes the following steps:

[0138] S621: Retrieves regularization parameters, Hermitian conjugate transpose, and identity matrix based on the frequency response matrix.

[0139] The regularization parameter refers to a numerical adjustment parameter that varies with frequency. The Hermitian conjugate transpose is a specialized transpose operation for frequency-domain complex-valued matrices; it involves first transposing the frequency response matrix and then taking the complex conjugate of each complex element. The identity matrix is ​​a square matrix with 1s on the main diagonal and 0s elsewhere, with the same dimensions as the square matrix formed by multiplying the frequency response matrix itself.

[0140] Hermitian conjugate transpose is obtained by performing mathematical operations on the frequency response matrix at the current frequency point; the identity matrix is ​​automatically constructed according to the size of the frequency response matrix; the regularization parameters are preset and stored according to the frequency point before the test, and are retrieved by matching with the frequency corresponding to the frequency response matrix.

[0141] S622: Based on the preset regularization pseudo-inverse formula, the regularization parameter, Hermitian conjugate transpose and identity matrix are analyzed and calculated to obtain the pseudo-inverse of the response matrix.

[0142] The regularized pseudo-inverse formula is: H†(f) = (H H (f)*H(f)+λ(f)*I) -1 *H H H(f) is the frequency response matrix; H H (f) is the Hermitian conjugate transpose; λ(f) is the regularization parameter; I is the identity matrix.

[0143] S63: Based on the preset iterative update formula, the loop gain, effective error vector and pseudo-inverse of the response matrix are analyzed and calculated to obtain the updated driving spectrum vector.

[0144] The iterative update formula is: X {k+1} (f)=X k (f)+μ(f)*H†(f)*E eff (f).

[0145] Among them, X {k+1} (f) is the driving spectrum vector for the (k+1)th iteration; X k (f) is the driving spectrum vector of the k-th iteration; μ(f) is the loop gain; H†(f) is the pseudo-inverse of the response matrix.

[0146] Based on the same inventive concept, embodiments of the present invention provide a mapping-based MIMO vibration testing zero-response control system, comprising:

[0147] The acquisition module is used to acquire the frequency response matrix, response degrees of freedom, current response vector, driving spectrum vector, and time domain data.

[0148] The memory stores a program for implementing a mapping-based zero-response control method for MIMO vibration testing as described above.

[0149] The processor loads and executes programs stored in memory.

[0150] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional modules is used as an example. In practical applications, the above functions can be assigned to different functional modules as needed, that is, the internal structure of the device can be divided into different functional modules to complete all or part of the functions described above. The specific working process of the system, device, and unit described above can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0151] The above description is merely a preferred embodiment of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should also be considered within the scope of protection of the present invention.

Claims

1. A mapping-based zero-response control method for MIMO vibration testing, characterized in that, include: Collect the frequency response matrix, response degrees of freedom, current response vector, and driving spectrum vector of the vibration testing system; Construct an unmapped error vector based on the difference between the current response vector and the preset target response vector; Determine the active degrees of freedom and zero degrees of freedom based on the response degrees of freedom; The zero-mapping operator is determined by combining the active degrees of freedom and the zero degrees of freedom; The effective error vector is obtained by combining the zero-mapping operator and the unmapped error vector. The driving spectral vector is iteratively updated by combining the effective error vector and the frequency response matrix.

2. The mapping-based MIMO vibration test zero-response control method according to claim 1, characterized in that, Methods for acquiring the frequency response matrix include: Acquire time-domain data of drive and response signals; Convert time-domain data to frequency-domain data; Based on frequency domain data, estimate the driving power spectrum matrix and the cross power spectrum matrix between the driving force and the response for each frequency point. The frequency response matrix is ​​estimated based on the cross-power spectrum matrix and the driving self-power spectrum matrix.

3. The zero-response control method for MIMO vibration testing based on mapping according to claim 2, characterized in that, The current methods for acquiring response vectors include: The current response vector is obtained by calculating the driving spectral vector, cross-power spectral matrix, and driving self-power spectral matrix based on a preset response vector calculation formula. The response vector calculation formula is: Y corr (f)=S yx (f)*(S xx (f) -1 )*X(f); Among them, Y corr (f) is the current response vector; S yx (f) is the cross-power spectrum matrix; S xx (f) is the driving power spectrum matrix; X(f) is the driving spectral vector.

4. The zero-response control method for MIMO vibration testing based on mapping according to claim 1, characterized in that, The unmapped error vector can be constructed in the following ways: The unmapped error vector is obtained by analyzing and calculating the current response vector and the preset target response vector based on a preset unmapped error construction formula. The unmapped error construction formula is as follows: e(f)=Y target (f)-Y corr (f); Where e(f) is the unmapped error vector; Y target (f) is the preset target response vector.

5. The mapping-based MIMO vibration test zero-response control method according to claim 4, characterized in that, Methods for determining active degrees of freedom and zero degrees of freedom include: Determine whether the response degrees of freedom are consistent with the preset degrees of freedom for suppressing vibration; If so, the response degrees of freedom are defined as zero. If not, then the response degrees of freedom are defined as active degrees of freedom.

6. The zero-response control method for MIMO vibration testing based on mapping according to claim 5, characterized in that, Methods for determining zero-mapping operators include: The zero-mapping operator is obtained by analyzing and calculating the active degrees of freedom and zero degrees of freedom based on the preset zero-mapping determination formula, whereby the zero-mapping determination formula is: P null (f)=diag(p1(f),p2(f),…,p N (f)); Among them, P null (f) is the zero-mapping operator; Regarding the degrees of freedom of active response, p i (f)=1; For zero-response degrees of freedom, p i (f)=0.

7. The mapping-based MIMO vibration test zero-response control method according to claim 6, characterized in that, Methods for determining the effective error vector include: The effective error vector is obtained by analyzing and calculating the zero-mapping operator and the unmapped error vector based on a preset effective error construction formula. The effective error construction formula is as follows: E eff (f)=P null (f)*e(f); Among them, E eff (f) is the effective error vector.

8. The zero-response control method for MIMO vibration testing based on mapping according to claim 1, characterized in that, Iterative update methods for driving spectral vectors include: Loop gain is obtained based on the driving spectrum vector; The pseudo-inverse of the response matrix is ​​obtained by performing a regularized pseudo-inverse on the frequency response matrix. Based on a preset iterative update formula, the loop gain, effective error vector, and pseudo-inverse of the response matrix are analyzed and calculated to obtain the updated driving spectrum vector. The iterative update formula is as follows: X {k+1} (f)=X k (f)+μ(f)*H†(f)*E eff (f); Among them, X {k+1} (f) is the driving spectrum vector for the (k+1)th iteration; X k (f) is the driving spectrum vector for the k-th iteration; μ(f) is the loop gain; H†(f) is the pseudo-inverse of the response matrix.

9. The zero-response control method for MIMO vibration testing based on mapping according to claim 8, characterized in that, Methods for determining the pseudoinverse of the response matrix include: The regularization parameter, Hermitian conjugate transpose, and identity matrix are retrieved based on the frequency response matrix. Based on a pre-defined regularization pseudo-inverse formula, the regularization parameter, Hermitian conjugate transpose, and identity matrix are analyzed and calculated to obtain the pseudo-inverse of the response matrix. The regularization pseudo-inverse formula is as follows: H†(f)=(H H (f)*H(f)+λ(f)*I) -1 *H H (f); Where H(f) is the frequency response matrix; H H (f) is the Hermitian conjugate transpose; λ(f) is the regularization parameter; I is the identity matrix.

10. A mapping-based MIMO vibration test zero-response control system, characterized in that, include: The acquisition module is used to acquire the frequency response matrix, response degrees of freedom and current response vector, driving spectrum vector and time domain data; The memory stores a program for implementing a mapping-based MIMO vibration test zero-response control method as described in any one of claims 1 to 9; The processor loads and executes programs stored in memory.

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