A method for generating a driving signal for multiple-input multiple-output vibration environmental testing
By reconstructing the delay and introducing the inverse state-space model with Tikhonov regularization, the matrix ill-conditioning problem in multi-input multi-output vibration environment tests is solved, achieving high-precision driving signal generation, which is suitable for online real-time reproduction of complex vibration environments.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- NANJING UNIV OF SCI & TECH
- Filing Date
- 2026-06-15
- Publication Date
- 2026-07-14
AI Technical Summary
In existing multi-input multi-output vibration environment tests, the frequency domain inversion method is prone to matrix ill-conditioning, which leads to unreasonable spikes, oscillations or amplitude abnormalities in the driving signal, especially when the structure resonates, reverses, or the channel coupling is strong, the error is significantly amplified.
By reconstructing the delay, the noncausal inverse dynamics is approximated as a causal finite memory mapping, rewritten as a shift register state space model, and online recursive calculation is performed using the inverse state space model to generate continuous multi-input driving signals. A Tikhonov regularization term is introduced to suppress noise and matrix ill-conditioning.
It effectively avoids the risk of ill-conditioned matrix inversion, reduces error amplification, improves the reproduction accuracy of complex vibration environments, has online real-time implementation capability, and is suitable for short-time and long-time-term multi-input multi-output vibration environment tests.
Smart Images
Figure CN122385115A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the fields of mechanical vibration environment testing, dynamic load inversion and signal processing technology, and in particular, a method for generating drive signals for multi-input multi-output vibration environment testing. Background Technology
[0002] Vibration environment testing is a crucial technical means for equipment reliability verification, structural dynamic performance evaluation, and reproduction of complex service environments. For spacecraft, aircraft, vehicles, ships, precision instruments, and large flexible structures, their actual service environment is typically not a single input excitation, but a coupled vibration environment formed by the combined effects of multiple mounting points, multiple directions, and multiple frequency bands. Therefore, in the laboratory, it is necessary to use multiple vibration tables, multiple hydraulic or electric actuators, and a multi-input multi-output vibration control system to collaboratively generate multi-channel drive signals, so that the response at key measurement points of the test object can reproduce the target vibration environment as accurately as possible.
[0003] Among existing methods for reproducing vibration environments, a common approach is to construct the frequency response function matrix between the driving input and the structural response, and then solve for the driving signal through frequency domain inverse or pseudo-inverse operations. This method has a clear theoretical framework and is widely used in engineering, but it is prone to matrix ill-conditioning in multi-input multi-output systems. Especially when the structure is in a resonant or anti-resonant state, or when channel coupling is strong and sensor noise is not negligible, the frequency response matrix inversion process can significantly amplify errors, leading to unreasonable spikes, oscillations, or abnormally large amplitude increases in the driving signal. Summary of the Invention
[0004] The purpose of this invention is to address the problems of ill-conditioned frequency domain inversion and poor control performance in existing drive generation methods for multi-input multi-output (MIMO) vibration environment tests. This invention provides a drive signal generation method for MIMO vibration environment tests. It approximates non-causal inverse dynamics as a causal finite memory mapping by reconstructing a delay, and then rewrites the identified inverse finite impulse response filter as a shift register state-space model. Applying this idea to the drive generation modification of MIMO vibration environment tests can form a recursively stable drive generation technology with online implementation capabilities.
[0005] The technical solution for achieving the objective of this invention is: a method for generating drive signals for multi-input multi-output vibration environment tests, the method comprising:
[0006] Step 1: Obtain low-level drive training data and corresponding response training data for the vibration test system;
[0007] Step 2: Set the order of the inverse filter and the reconstruction delay length;
[0008] Step 3: Based on the response training data, driving training data, order, and reconstruction delay length, construct the response training data regression matrix and the corresponding driving-response training data matrix;
[0009] Step 4: Based on the response training data regression matrix and the driver-response training data matrix, a regularization term is introduced to solve for the coefficient matrix of the inverse filter;
[0010] Step 5: Construct the inverse state-space model based on the solved coefficient matrix;
[0011] Step 6: Input the target reference signal of the experiment into the inverse state space model for online recursive calculation to generate continuous multi-input driving signals.
[0012] Furthermore, the vibration test system described in step 1 includes m drive inputs and n response outputs; the drive training data is constructed. and the response training data All finite lengths are N, represented as:
[0013]
[0014] In the formula, This represents the training data vector for the k-th response. This represents the k-th driving training data vector.
[0015] Furthermore, the inverse filter mentioned in step 2 is a delayed inverse finite impulse response filter, with its order set to L and reconstruction delay length set to d.
[0016] Furthermore, step 3 specifically includes:
[0017] The historical vector of the response training data is constructed according to the following formula. :
[0018]
[0019] In the formula, the superscript T denotes matrix transpose;
[0020] Construct the historical vector of the corresponding delay-driven training data according to the following formula. :
[0021]
[0022] In the formula, This represents the driving training data with a delay length of d.
[0023] Furthermore, in step 3, the historical vector is used. and Construct a matrix, where:
[0024] The response training data regression matrix Represented as:
[0025]
[0026] In the formula, Indicates the kth i Historical vector data, ;
[0027] The driver-response training data matrix Represented as:
[0028]
[0029] In the formula, Indicates the kth i There are training data with a delay length of d.
[0030] Furthermore, in step 4, the system input-output relationship for constructing the inverse filter is as follows:
[0031]
[0032] in, Let be the coefficient matrix of the inverse filter to be solved. E is the error matrix; In response to the regression matrix of the training data, This is the driver-response training data matrix.
[0033] Furthermore, in step 4, by introducing the Tikhonov regularization term, the coefficient solution is transformed into the following ridge regularized least squares problem:
[0034]
[0035] In the formula, λ is the regularization parameter. This represents the Frobenius norm.
[0036] Furthermore, in step 4, the inverse filter coefficient matrix is processed... Taking the derivative and setting the gradient to zero, the closed-form solution of the inverse filter coefficient matrix is obtained as follows:
[0037]
[0038] In the formula, I is the identity matrix.
[0039] Furthermore, step 5 specifically includes:
[0040] The inverse filter coefficient matrix to be solved Divided into the following sub-block matrix:
[0041]
[0042] In the formula, Let j be the vector of finite impact response coefficients. ;
[0043] Define the inverse state vector using the shift register principle:
[0044]
[0045] In the formula, is the k-th inverse state vector of the inverse state-space model;
[0046] Construct the state transition matrix of the inverse state space model Input matrix Output matrix and direct feedthrough matrix They are respectively:
[0047]
[0048]
[0049] In the formula, It is an n×n identity matrix;
[0050] Therefore, the inverse state-space model is constructed as follows:
[0051]
[0052] In the formula, This is the inverse state vector at step k+1; This is the output vector with a delay length of d.
[0053] Furthermore, step 6 specifically includes: generating a multi-channel continuous reference signal using the target reference spectrum of the experiment, and using this reference signal as the response input. Substituting the input into the inverse state-space model, online recursive calculations are performed, and continuous multi-input driving signals are output in real time. The reconstructed excitation input drive signal is obtained through time alignment.
[0054] Compared with the prior art, the significant advantages of this invention are:
[0055] (1) This invention transforms the inverse dynamics problem into a time-domain model for solution, avoiding the operation of directly inverting the frequency response function matrix or the feedthrough matrix in traditional methods. This effectively overcomes the matrix ill-conditioning problem that is prone to occur in structural resonance, anti-resonance and strong channel coupling scenarios, reduces the risk of ill-conditioning inversion, and prevents error amplification.
[0056] (2) In solving the inverse filter coefficient matrix, this invention innovatively introduces a Tikhonov regularization term (i.e., ridge regularized least squares method), which can effectively suppress the influence of measurement noise and ill-conditioned matrix characteristics on the inverse filter coefficients. By adjusting the regularization parameter, a good balance can be achieved between the accuracy of training data fitting and the smoothness and robustness of coefficient noise resistance.
[0057] (3) By reasonably setting and utilizing the “reconstruction delay”, the present invention successfully approximates non-causal inverse dynamics as causal finite memory mapping, which significantly improves the feasibility and reproducibility of non-minimum phase systems or non-concurrent (sensor and exciter are not in the same position) systems in complex vibration environment tests.
[0058] (4) The inverse state space model reconstructed in this invention has a state transition matrix composed of a null-power shift matrix. This special matrix construction naturally ensures the absolute theoretical stability of the system at the mathematical structure level, and can effectively avoid unreasonable spikes, oscillations or excessive amplitudes in the driving signal.
[0059] (5) The recursive implementation method using the shift register state space model has the characteristics of high computational efficiency and low latency, and has excellent online real-time implementation capability. This method is not only suitable for short-term tests, but can also effectively meet the test requirements of long-term, random, transient and continuous multi-input multi-output complex vibration environments.
[0060] The present invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description
[0061] Figure 1 This is a flowchart of the method for generating drive signals for multi-input multi-output vibration environment tests according to the present invention.
[0062] Figure 2 This is a schematic diagram of the test site in one embodiment.
[0063] Figure 3 A reference spectrum for a vibration test setup in one embodiment.
[0064] Figure 4 This is a schematic diagram illustrating the generation of a two-channel drive signal segment using a delayed inverse state-space model in one embodiment, wherein... Figure 4 (a) and (b) in the figure are two-channel drive signal segments, respectively. Detailed Implementation
[0065] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.
[0066] It should be noted that if the embodiments of the present invention involve directional indicators (such as up, down, left, right, front, back, etc.), the directional indicators are only used to explain the relative positional relationship and movement of the components in a certain specific posture (as shown in the figure). If the specific posture changes, the directional indicators will also change accordingly.
[0067] Furthermore, if the embodiments of this invention involve descriptions such as "first" or "second," these descriptions are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined with "first" or "second" may explicitly or implicitly include at least one of those features. Additionally, the technical solutions of the various embodiments can be combined with each other, but this must be based on the ability of those skilled in the art to implement them. If the combination of technical solutions is contradictory or impossible to implement, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by this invention.
[0068] In one embodiment, combined Figure 1 A method for generating drive signals for multi-input multi-output vibration environment tests is provided, the method comprising:
[0069] Step 1: Obtain low-level drive training data and corresponding response training data for the vibration test system;
[0070] Step 2: Set the order of the inverse filter and the reconstruction delay length;
[0071] Step 3: Based on the response training data, driving training data, order, and reconstruction delay length, construct the response training data regression matrix and the corresponding driving-response training data matrix;
[0072] Step 4: Based on the response training data regression matrix and the driver-response training data matrix, a regularization term is introduced to solve for the coefficient matrix of the inverse filter;
[0073] Step 5: Construct the inverse state-space model based on the solved coefficient matrix;
[0074] Step 6: Input the target reference signal of the experiment into the inverse state space model for online recursive calculation to generate continuous multi-input driving signals.
[0075] Furthermore, in one embodiment, the vibration test system described in step 1 includes m drive inputs and n response outputs; constructing the drive training data and the response training data All finite lengths are N, represented as:
[0076]
[0077] In the formula, This represents the training data vector for the k-th response. This represents the k-th driving training data vector.
[0078] Furthermore, in one embodiment, the inverse filter in step 2 is a delayed inverse finite impulse response filter, with its order set to L and reconstruction delay length set to d.
[0079] Furthermore, in one embodiment, step 3 specifically includes:
[0080] The historical vector of the response training data is constructed according to the following formula. :
[0081]
[0082] In the formula, the superscript T denotes matrix transpose;
[0083] Construct the historical vector of the corresponding delay-driven training data according to the following formula. :
[0084]
[0085] In the formula, This represents the driving training data with a delay length of d.
[0086] Furthermore, in one embodiment, in step 3, the historical vector is utilized. and Construct a matrix, where:
[0087] The response training data regression matrix Represented as:
[0088]
[0089] In the formula, Indicates the kth i Historical vector data, ;
[0090] The driver-response training data matrix Represented as:
[0091]
[0092] In the formula, Indicates the kth i There are training data with a delay length of d.
[0093] Furthermore, in one embodiment, in step 4, the system input-output relationship for constructing the inverse filter is as follows:
[0094]
[0095] in, Let be the coefficient matrix of the inverse filter to be solved. E is the error matrix; In response to the regression matrix of the training data, This is the driver-response training data matrix.
[0096] Furthermore, in one embodiment, in step 4, by introducing a Tikhonov regularization term, the coefficient solution is transformed into the following ridge-regularized least squares problem:
[0097]
[0098] In the formula, λ is the regularization parameter. This represents the Frobenius norm.
[0099] Preferably, in some embodiments, the regularization parameter λ is determined by any one or more combinations of L-curves, cross-validation, generalized cross-validation, target response reproduction error, or engineering experience.
[0100] Furthermore, in one embodiment, step 4 involves adjusting the inverse filter coefficient matrix. Taking the derivative and setting the gradient to zero, the closed-form solution of the inverse filter coefficient matrix is obtained as follows:
[0101]
[0102] In the formula, I is the identity matrix.
[0103] Furthermore, in one embodiment, step 5 specifically includes:
[0104] The inverse filter coefficient matrix to be solved Divided into the following sub-block matrix:
[0105]
[0106] In the formula, Let j be the vector of finite impact response coefficients. ;
[0107] Define the inverse state vector using the shift register principle:
[0108]
[0109] In the formula, is the k-th inverse state vector of the inverse state-space model;
[0110] Construct the state transition matrix of the inverse state space model Input matrix Output matrix and direct feedthrough matrix They are respectively:
[0111]
[0112]
[0113] In the formula, It is an n×n identity matrix;
[0114] Therefore, the inverse state-space model is constructed as follows:
[0115]
[0116] In the formula, This is the inverse state vector at step k+1; This is the output vector with a delay length of d.
[0117] Furthermore, in one embodiment, step 6 specifically includes: generating a multi-channel continuous reference signal using the target reference spectrum of the experiment, and using the reference signal as a response input. Substituting the input into the inverse state-space model, online recursive calculations are performed, and continuous multi-input driving signals are output in real time. The reconstructed excitation input drive signal is obtained through time alignment.
[0118] In one embodiment, a drive signal generation system for multi-input multi-output vibration environment testing is provided, the system comprising:
[0119] The first module is used to: acquire low-level drive training data of the vibration test system and the corresponding response training data;
[0120] The second module is used to set the order of the inverse filter and the reconstruction delay length.
[0121] The third module is used to: construct a response training data regression matrix and a corresponding driver-response training data matrix based on the response training data, driver training data, order, and reconstruction delay length;
[0122] The fourth module is used to: solve the coefficient matrix of the inverse filter by introducing a regularization term based on the regression matrix of the response training data and the driver-response training data matrix;
[0123] The fifth module is used to construct the inverse state-space model based on the solved coefficient matrix;
[0124] The sixth module is used to: input the target reference signal of the experiment into the inverse state space model for online recursive calculation to generate continuous multi-input driving signals.
[0125] Specific limitations regarding the drive signal generation system for multi-input multi-output (MIMO) vibration environment testing can be found in the limitations regarding the drive signal generation method for MIMO vibration environment testing described above, and will not be repeated here. Each module in the aforementioned drive signal generation system for MIMO vibration environment testing can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in hardware or independently of the processor in a computer device, or stored in software in the memory of a computer device, so that the processor can call and execute the corresponding operations of each module.
[0126] In one embodiment, a computer device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements:
[0127] Step 1: Obtain low-level drive training data and corresponding response training data for the vibration test system;
[0128] Step 2: Set the order of the inverse filter and the reconstruction delay length;
[0129] Step 3: Based on the response training data, driving training data, order, and reconstruction delay length, construct the response training data regression matrix and the corresponding driving-response training data matrix;
[0130] Step 4: Based on the response training data regression matrix and the driver-response training data matrix, a regularization term is introduced to solve for the coefficient matrix of the inverse filter;
[0131] Step 5: Construct the inverse state-space model based on the solved coefficient matrix;
[0132] Step 6: Input the target reference signal of the experiment into the inverse state space model for online recursive calculation to generate continuous multi-input driving signals.
[0133] For specific limitations on each step, please refer to the limitations on the drive signal generation method for multi-input multi-output vibration environment tests mentioned above, which will not be repeated here.
[0134] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, the computer program being implemented when executed by a processor:
[0135] Step 1: Obtain low-level drive training data and corresponding response training data for the vibration test system;
[0136] Step 2: Set the order of the inverse filter and the reconstruction delay length;
[0137] Step 3: Based on the response training data, driving training data, order, and reconstruction delay length, construct the response training data regression matrix and the corresponding driving-response training data matrix;
[0138] Step 4: Based on the response training data regression matrix and the driver-response training data matrix, a regularization term is introduced to solve for the coefficient matrix of the inverse filter;
[0139] Step 5: Construct the inverse state-space model based on the solved coefficient matrix;
[0140] Step 6: Input the target reference signal of the experiment into the inverse state space model for online recursive calculation to generate continuous multi-input driving signals.
[0141] For specific limitations on each step, please refer to the limitations on the drive signal generation method for multi-input multi-output vibration environment tests mentioned above, which will not be repeated here.
[0142] As a specific example, the invention will be further verified and illustrated in one embodiment.
[0143] In this embodiment, a cantilever beam vibration system is used, such as... Figure 2 As shown, one end of the beam is clamped, forming a cantilever boundary condition. Two electric exciters are installed to apply external excitation at two different locations on the beam, named excitation 1 and excitation 2, respectively. Correspondingly, two response measurement points are arranged on the beam, denoted as response 1 and response 2, respectively.
[0144] The experiment mainly consists of the following steps:
[0145] 1. A white noise signal is sent to the two exciters using a signal generator. The exciters start working, the cantilever beam begins to vibrate, and two acceleration sensors collect the vibration response signal.
[0146] 2. In the computer, the collected input and output signals are used to generate the historical vector of the training data and the corresponding delay-driven historical vector of the training data.
[0147] 3. Construct the regression matrix of the response training data and the corresponding driving response training data matrix.
[0148] 4. Estimate the coefficients of the delayed inverse finite impulse response filter and generate the state transition matrix, input matrix, output matrix and direct feedthrough matrix of the inverse state space model.
[0149] 5. Obtain the delayed inverse state-space model of the system.
[0150] 6. The vibration test reference spectral density of both channels is set as follows: Figure 3 As shown, a two-channel reference signal is generated using the reference spectral density.
[0151] 7. Generate a two-channel drive signal segment based on the reference signal and the obtained delayed inverse state-space model, such as... Figure 4 As shown.
[0152] This invention effectively overcomes the matrix ill-conditioning and signal divergence problems of traditional frequency domain inversion methods, and significantly improves the reproduction accuracy of complex inverse dynamic environments in multi-axis coupled vibration tests.
[0153] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention without departing from its spirit and scope should be included within the protection scope of the present invention.
Claims
1. A method for generating drive signals for multi-input multi-output vibration environment testing, characterized in that, The method includes: Step 1: Obtain low-level drive training data and corresponding response training data for the vibration test system; Step 2: Set the order of the inverse filter and the reconstruction delay length; Step 3: Based on the response training data, driving training data, order, and reconstruction delay length, construct the response training data regression matrix and the corresponding driving-response training data matrix; Step 4: Based on the response training data regression matrix and the driver-response training data matrix, a regularization term is introduced to solve for the coefficient matrix of the inverse filter; Step 5: Construct the inverse state-space model based on the solved coefficient matrix; Step 6: Input the target reference signal of the experiment into the inverse state space model for online recursive calculation to generate continuous multi-input driving signals.
2. The method for generating drive signals for multi-input multi-output vibration environment testing according to claim 1, characterized in that, The vibration test system described in step 1 includes m drive inputs and n response outputs; construct the drive training data. and the response training data All finite lengths are N, represented as: In the formula, This represents the training data vector for the k-th response. This represents the k-th driving training data vector.
3. The method for generating drive signals for multi-input multi-output vibration environment testing according to claim 2, characterized in that, The inverse filter mentioned in step 2 is a delayed inverse finite impulse response filter, with its order set to L and reconstruction delay length set to d.
4. The method for generating drive signals for multi-input multi-output vibration environment testing according to claim 3, characterized in that, Step 3 specifically includes: The historical vector of the response training data is constructed according to the following formula. : In the formula, the superscript T denotes matrix transpose; Construct the historical vector of the corresponding delay-driven training data according to the following formula. : In the formula, This represents the driving training data with a delay length of d.
5. The method for generating drive signals for multi-input multi-output vibration environment testing according to claim 4, characterized in that, In step 3, the historical vector is used. and Construct a matrix, where: The response training data regression matrix Represented as: In the formula, Indicates the kth i Historical vector data, ; The driver-response training data matrix Represented as: In the formula, Indicates the kth i There are training data with a delay length of d.
6. The method for generating drive signals for multi-input multi-output vibration environment testing according to claim 1, characterized in that, In step 4, the system input-output relationship for constructing the inverse filter is as follows: in, Let be the coefficient matrix of the inverse filter to be solved. E is the error matrix; In response to the regression matrix of the training data, The training data matrix is for the driver-response model.
7. The method for generating drive signals for multi-input multi-output vibration environment testing according to claim 6, characterized in that, In step 4, by introducing the Tikhonov regularization term, the coefficient solution is transformed into the following ridge regularized least squares problem: In the formula, λ is the regularization parameter. This represents the Frobenius norm.
8. The method for generating drive signals for multi-input multi-output vibration environment testing according to claim 7, characterized in that, In step 4, the inverse filter coefficient matrix is processed. Taking the derivative and setting the gradient to zero, the closed-form solution of the inverse filter coefficient matrix is obtained as follows: In the formula, I is the identity matrix.
9. The method for generating drive signals for multi-input multi-output vibration environment testing according to claim 1, characterized in that, Step 5 specifically includes: The inverse filter coefficient matrix to be solved Divided into the following sub-block matrix: In the formula, Let j be the vector of finite impact response coefficients. ; Define the inverse state vector using the shift register principle: In the formula, is the k-th inverse state vector of the inverse state-space model; Construct the state transition matrix of the inverse state space model Input matrix Output matrix and direct feedthrough matrix They are respectively: In the formula, It is an n×n identity matrix; Therefore, the inverse state-space model is constructed as follows: In the formula, This is the inverse state vector at step k+1; This is the output vector with a delay length of d.
10. The method for generating drive signals for multi-input multi-output vibration environment testing according to claim 1, characterized in that, Step 6 specifically includes: generating a multi-channel continuous reference signal using the target reference spectrum of the experiment, and using this reference signal as the response input. Substituting the input into the inverse state-space model, online recursive calculations are performed, and continuous multi-input driving signals are output in real time. The reconstructed excitation input drive signal is obtained through time alignment.