Variational bayesian based interactive multiple model adaptive vibration active control method

Abstract

The application discloses a method for interactive multi-model adaptive vibration active control based on variational Bayes, and relates to the technical field of vibration control, comprising the following steps: a system model set containing multiple potential dynamic modes is established, and initialization setting is performed on each model; in each control sampling period, variational Bayes iteration is performed on each model; the above process is repeated for each channel to obtain optimal state estimation of each channel; covariance cross fusion method is used to fuse the state estimation results of multiple channels to calculate global optimal state estimation; the global optimal state estimation is convolved with a reference signal filtered by a secondary channel model to generate a reverse control signal, the reverse control signal is driven by a power amplifier to drive an actuator to generate a secondary force to offset the original vibration, and vibration suppression is realized. The application realizes high-precision and high-robustness vibration suppression by fusing variational Bayes adaptive Kalman filtering and interactive multi-model estimation.

Description

Technical Field

[0001] This invention relates to the field of vibration control technology, specifically to an adaptive active vibration control (AVC) method for unsteady excitation, and in particular, an interactive multi-model adaptive active vibration control method based on variational Bayes. Background Technology

[0002] Active Vibration Control (AVC), as a core technology for suppressing harmful vibrations in power machinery structures and improving system stability and reliability, has gained widespread attention and application in aerospace, shipbuilding, and high-end manufacturing. Its basic idea is to monitor the vibration response of the structure in real time and then use a controller to drive an actuator to generate a reverse control force, thereby effectively canceling out the target vibration. Compared to traditional passive vibration isolation or damping methods, AVC demonstrates significant advantages in dealing with low-frequency, time-varying, and complex multimodal vibrations.

[0003] In marine propulsion systems, core equipment such as diesel engines, gas turbines, and propulsion shafts often exhibit highly complex and time-varying operating conditions. Particularly during dynamic processes like startup, shutdown, speed changes, and even sudden load shifts, the excitation source displays typical non-stationary characteristics, including rapid frequency jumps, drastic amplitude fluctuations, and instantaneous reconstruction of spectral components. These non-stationary disturbances place extremely high demands on the real-time tracking and adaptive performance of the control system.

[0004] Currently, the feedforward / feedback structure based on filters is still the mainstream implementation method of AVC systems. Among them, the adaptive filtering method based on the Filtered-x Least Mean Square (FxLMS) algorithm has been widely used in engineering due to its simple structure and moderate computational cost. However, this algorithm and its variants are essentially dependent on the iterative mechanism of gradient descent, and their convergence performance is highly dependent on the correlation characteristics of the input signal and the selection of the step size parameter. Faced with the common non-steady-state excitation in marine power machinery, such as the rapid change in the eigenvalue distribution of the autocorrelation matrix of the reference signal caused by frequency change, the traditional FxLMS algorithm often faces the following key technical bottlenecks: (1) Slow convergence speed: After the frequency or amplitude changes abruptly, the algorithm needs a long adjustment time to reconverge to the steady state, which cannot meet the rapidly changing control requirements, resulting in instantaneous failure of vibration suppression or increase in residual.

[0005] (2) Insufficient robustness: Unsteady excitation can easily cause filter weights to oscillate or even diverge. Especially when there are modeling errors or time-varying characteristics in the secondary channel, the system stability decreases significantly, and in severe cases, it may induce closed-loop instability and aggravate structural vibration. Summary of the Invention

[0006] To overcome the aforementioned problems in the existing technology, this invention proposes an interactive multi-model adaptive active vibration control method based on variational Bayes.

[0007] The technical solution adopted by this invention to solve its technical problem is: an interactive multi-model adaptive active vibration control method based on variational Bayes, comprising the following steps: Step 1: Identify the secondary channels between each actuator and error sensor in the multi-channel system, and use an adaptive algorithm to identify a finite-length impulse response filter as the estimation model for the secondary channels; Step 2: Establish a system model set containing multiple potential dynamic modes to describe the state equations and measurement equations under different vibration sources or different system operating conditions, and initialize each model. Step 3: For each model in the system model set in Step 2, use the variational Bayesian framework to perform online joint estimation and optimization of its process noise covariance matrix and / or measurement noise covariance matrix; Step 4: Perform interactive multi-model state estimation within each control sampling period; Step 5: For each channel of the multi-channel system, execute steps 2-4 to obtain the optimal state estimate of each channel. Use the covariance cross-fusion method to fuse the state estimates of multiple channels and calculate the global optimal state estimate. Step 6: Convolve the global optimal state estimate with the reference signal filtered by the secondary channel model to generate an anti-noise signal, which is then converted from digital to analog and driven by a power amplifier to output the actuator. Step 7: Feed the newly acquired error sensor signal back to the controller for algorithm iteration and update at the next sampling time.

[0008] The interactive multi-model adaptive vibration active control method based on variational Bayes described above, specifically the initialization in step 2, involves: setting initial state estimates, state estimation error covariance matrices, model prior probabilities, and Markov transition probability matrices between models for each model; and initializing the hyperparameters required for variational Bayes inference.

[0009] In the aforementioned interactive multi-model adaptive active vibration control method based on variational Bayes, step 3 specifically comprises: Step 3.1: Construct a hierarchical probabilistic graphical model of latent variables, assuming that the variational posterior distribution is decomposable using mean-field theory; A Markov evolution model of the prediction error covariance matrix based on the beta-Bartlett distribution is introduced to utilize historical estimation information; Step 3.3: By maximizing the variational lower bound, the posterior distribution of the state and the posterior distribution of the noise parameters are alternately optimized to achieve decoupled joint estimation of the state and noise parameters.

[0010] In the aforementioned interactive multi-model adaptive active vibration control method based on variational Bayes, step 4 specifically comprises: Step 4.1: Based on the probabilities of each model and the transition probabilities between models at the previous time step, calculate the initial mixing state and covariance of each filter at the current time step. Step 4.2: Starting with its mixed initial value, each sub-filter uses an adaptive Kalman filter with noise parameters optimized online by variational Bayes to perform independent state prediction and measurement update in parallel, thereby obtaining its own conditional state estimate and covariance. Step 4.3: Calculate the innovation likelihood function of each sub-filter and update the matching probability of each model with the current real system mode accordingly; Step 4.4: Using the updated model probabilities as weights, perform weighted fusion of the state estimates of all sub-filters to obtain the global optimal state estimate and its covariance based on IMM at the current time.

[0011] The interactive multi-model adaptive vibration active control method based on variational Bayes described above, specifically step 4.2, involves: using the model equations of each model to perform a one-step prediction of the state and covariance; based on the prediction results and new measurements, performing variational Bayes iteration: fixing the variational distribution of the state and updating the variational posterior distribution of the noise parameters; fixing the noise parameter distribution and updating the variational posterior distribution of the state, i.e., performing an adaptive Kalman filter update with time-varying noise parameters to obtain the conditional state estimate and covariance of the model, as well as the innovation covariance.

[0012] In the aforementioned interactive multi-model adaptive active vibration control method based on variational Bayes, step 4.3 introduces a correction factor based on the likelihood function value to perform real-time correction on the fixed transition probability matrix.

[0013] The beneficial effects of the present invention are: (1) stronger model adaptability: through the interactive multi-model framework, the algorithm can effectively cover a variety of dynamic modes that may occur in the system under non-steady-state excitation, and achieve smooth switching through probability weighting, thus overcoming the problem of insufficient description capability of a single model.

[0014] (2) Higher estimation accuracy and robustness: The integrated variational Bayesian adaptive Kalman filter can estimate the state and time-varying noise statistics online and jointly, which significantly reduces the risk of model mismatch and improves the state estimation accuracy and algorithm robustness in non-steady and uncertain environments.

[0015] (3) Excellent unsteady-state response performance: Combining the multi-model fast switching capability of IMM and the online parameter adaptation capability of variational Bayes, the algorithm can still make an effective response in a very short time (such as within 1 second) during strong unsteady-state processes such as sudden changes in excitation frequency and amplitude or start-up and shutdown of power machinery, and has a fast convergence speed.

[0016] (4) Applicable to complex multi-channel systems: By using the covariance cross-fusion method, multi-channel information can be effectively fused to obtain better global state estimation, thereby improving the overall control effect of complex systems with multiple vibration sources coupled together.

[0017] (5) Low dependence on reference signal: Thanks to the strong adaptive capability of the hybrid control structure and algorithm, even when the reference signal is inaccurate or completely missing (replaced by noise), it can still maintain a certain vibration control effect, thus broadening the application scenarios. Attached Figure Description

[0018] Figure 1 This is a schematic diagram illustrating the overall principle of the method of the present invention; Figure 2 This is a schematic diagram of a parameter decoupling probabilistic graphical model based on variational Bayes. Figure 3 This is a schematic diagram of the interactive multi-model algorithm flow. Figure 4 A schematic diagram illustrating the implementation of dual-channel information fusion and vibration control; Figure 5 The graphs show the power spectral density (PSD) of various algorithms for unsteady excitation of power machinery as a function of time at 30 Hz on one channel. Among them, (a) is the AVC OFF algorithm (turning off the active vibration control system), (b) is the FxLMS algorithm, (c) is the Exponentially Weighted Recursive Least Squares (EWRLS) algorithm, and (d) is the Interacting Multiple Model Variational Bayesian Kalman Filter (IMMVBKF, i.e., the algorithm in this embodiment). Figure 6The graphs show the power spectral density (PSD) of various algorithms for unsteady excitation of power machinery at 30 Hz in the two channels as a function of time. Among them, (a) is the AVC OFF algorithm (turning off the active vibration control system), (b) is the FxLMS algorithm, (c) is the Exponentially Weighted Recursive Least Squares (EWRLS) algorithm, and (d) is the Interacting Multiple Model Variational Bayesian Kalman Filter (IMMVBKF, i.e., the algorithm in this embodiment). Detailed Implementation

[0019] To enable those skilled in the art to better understand the technical solution of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0020] This invention provides an interactive multi-model adaptive active vibration control method based on variational Bayes, the overall implementation process of which is as follows: Figure 1 As shown, the primary vibration source signal is acquired by vibration acceleration and transmitted to an ADC (analog-to-digital converter with embedded digital filter). The filtered signal is then transmitted to an embedded digital signal processing system. Using an interactive multi-model adaptive vibration active control algorithm based on variational Bayes proposed in this invention, a signal opposite to that of the primary vibration source is generated. This signal is then transmitted to a secondary vibration source via a DAC (digital-to-analog converter) and a power amplifier to suppress vibration. Specifically, the process includes the following steps: Step 1: Offline identification of secondary channels.

[0021] Before implementing active control, the physical transmission path (secondary channel) between the actuator and the error sensor is first identified. A broadband excitation signal (such as white noise) drives the actuator, while the error sensor signal is acquired simultaneously. An adaptive algorithm (such as the LMS algorithm) is used to identify a finite-length impulse response filter as the estimation model for the secondary channel. This identification must be performed for each actuator-sensor pair in the multi-channel system.

[0022] Step 2: System initialization.

[0023] Define an interactive multi-model set M, which may contain multiple state-space models corresponding to different typical frequencies or dynamic characteristics. Initialize the initial state estimates, estimation error covariance matrix, and model prior probabilities for each model j. Define the inter-model transition probability matrix. Initialize the hyperparameters required for variational Bayesian inference, such as the degrees of freedom and scale matrix of the inverse Wissaud distribution.

[0024] Step 3: Online vibration active control cycle.

[0025] At each sampling time k, execute the following loop: 1. Signal Acquisition: Acquire reference sensor signals and error sensor signals. If the reference signal is missing or inaccurate, the reference signal input is set to Gaussian white noise, and the algorithm performance is maintained by the estimation capabilities of the hybrid structure (feedforward + feedback) and the variable structure interactive multi-model.

[0026] 2. Iteration of the IMMVBKF algorithm: (1) Online optimization of adaptive Kalman filter parameters based on variational Bayes For each sub-model, a variational Bayesian framework is used to perform online joint estimation and optimization of its process noise covariance matrix and / or measurement noise covariance matrix, specifically including: A hierarchical probabilistic graphical model is constructed, which includes latent variables such as state vectors and prediction error covariance matrix (PECM). The mean-field theory is used to assume that the variational posterior distribution is decomposable.

[0027] A PECM Markov evolution model based on the Beta-Bartlett distribution is introduced to utilize historical estimation information.

[0028] By maximizing the variational lower bound and alternately optimizing the posterior distributions of the state and noise parameters, decoupled joint estimation of the state and noise parameters is achieved. This process can adaptively track changes in the statistical characteristics of system noise under unsteady excitation, avoiding the degradation of filtering performance caused by improper setting of fixed noise parameters.

[0029] The variational Bayesian optimization process is achieved by iteratively solving the following variational distribution: The variational posterior distribution of the state vector follows a Gaussian distribution, and its mean and covariance are given by the Kalman filter equation that takes into account the current noise parameter estimation.

[0030] The variational posterior distribution of the prediction error covariance matrix follows an inverse Wissaud distribution, and its parameters are determined by historical estimates and current information.

[0031] Figure 2A schematic diagram of a parameter-decoupled probabilistic graphical model based on variational Bayesian theory is disclosed. First, a hierarchical probabilistic graphical model is presented, jointly estimating the target state, the Predicted Error Covariance Matrix (PECM), and the Measurement Noise Covariance Matrix. This model employs indirect variational inference and incorporates an evolutionary model of the PECM. Second, a solution method for multi-parameter iterative optimization is given using variational Bayesian (VB) theory. (Figure...) For state variables; This is the state transition matrix; For measurement matrix; Here is the state variable covariance matrix; Process noise covariance matrix; For measurement; The measurement noise covariance matrix; for New information vector; for New information covariance matrix; for New information vector; for The new information covariance matrix; Predicted degrees of freedom parameters; Scale matrix.

[0032] (2) Interactive multi-model state estimation Within each control sampling period, the following interactive multi-model process is executed: Input interaction: Based on the probabilities of each model and the transition probabilities between models at the previous time step, calculate the initial mixing state and covariance of each filter at the current time step.

[0033] Model conditional filtering: Each sub-filter starts with its mixed initial value and uses an adaptive Kalman filter with noise parameters optimized online by variational Bayes to perform independent state prediction and measurement update in parallel, thereby obtaining its own conditional state estimate and covariance.

[0034] Model probability update: Calculate the innovation likelihood function of each sub-filter and update the matching probability of each model with the current real system mode accordingly. Optionally, a correction factor based on the likelihood function value is introduced to adjust the fixed transition probability matrix in real time to accelerate model switching and improve the response speed to sudden stimuli. The correction factor used in the model probability update is related to the ratio of the model likelihood function values ​​at adjacent time points; when the model matching degree improves, its transition probability increases accordingly.

[0035] Output interaction: Using the updated model probabilities as weights, the state estimates of all sub-filters are weighted and fused to obtain the global optimal state estimate and its covariance based on IMM at the current time.

[0036] Figure 3 The interactive multi-model algorithm flowchart is presented. Input interaction is a process of obtaining the initial state value of the filter at the current time using the state estimates of each sub-filter from the previous time step. This process is achieved through the interaction between the state estimates of the sub-filters. After obtaining the input values ​​of the state estimates and state covariance of each sub-filter through the first step of input interaction, each sub-filter needs to independently update its filter using its own filter input value, system model, and measurement information. This process is described using Kalman filtering as an example. The model probability represents the degree of matching between each sub-model and the current system model; therefore, model probability updating is a crucial process. The model probability can be calculated from the likelihood function corresponding to each sub-model. Output interaction uses the probability of each sub-model matching the current system model under the current measurement information, obtained from the model probability update process, as the weight of the estimation results of each sub-filter. A weighted average is then performed on the estimated values ​​of each sub-filter to obtain the final estimate of the IMM filter at the current time step. In the figure, "1~r" represents the filter index; k-1 and k represent time steps. Let be the likelihood function.

[0037] 3. Multi-channel fusion: The final state estimation results of each channel obtained in step 2 are fused using the covariance cross-fusion algorithm to calculate the global optimal state estimate.

[0038] Figure 4This paper presents the implementation process of dual-channel information fusion and vibration control. The initialization steps include: initializing the state estimate of each model; initializing the covariance matrix of each model; initializing the weighting values ​​of each model; and initializing the transition probabilities (transition probabilities between models). Measurement matrices are used in the algorithm iteration, with the measurement matrix serving as the reference signal for each channel to determine the corresponding control order. The estimates from each model are mixed based on the transition probabilities, serving as the initial conditions for the current prediction. For each model, the state at the next time step is estimated using the prediction step of a Kalman filter; the predicted state and covariance matrix of each model are calculated. Parameters such as process noise covariance are estimated online. The state estimate of each model is updated using observation data; the Kalman gain, updated state estimate, and covariance matrix of each model are calculated. The estimates of all models are weighted and fused based on the prior probability and prediction error of each model; the posterior probability (weight) of each model is calculated; a weighted average is performed to obtain the final state estimate. The weighted final state estimates for each channel are output. The weights of different models are adjusted according to the transition probabilities between models; model switching is performed based on the transition probabilities. Consistency between estimates from different channels is ensured. Based on the state estimation results obtained from channels 1 and 2, the optimal weights are selected for fusion to obtain the final state estimation value.

[0039] 4. Control signal generation and output: The global optimal state estimate (usually used as the weight coefficient vector of the control filter) is convolved with the processed reference signal (filtered by the secondary channel model) to generate an anti-noise signal, which is then converted from digital to analog and driven by the power amplifier to output the actuator.

[0040] 5. Feedback Iteration: The newly acquired error sensor signal is fed back to the controller for algorithm iteration and update at the next sampling time.

[0041] Based on the above method, taking the vibration control during the start-up and shutdown process of the power machinery in a certain type of double-layer structure as an example, an exciter is arranged in the lower layer to simulate an unsteady vibration source, and two actuators and two error sensors are arranged in the upper layer to form a dual-channel control system. The sampling frequency is set to 2000Hz. Using the interactive multi-model adaptive active vibration control method based on variational Bayes proposed in this invention, the following results are obtained.

[0042] Test data such as Figure 5 (One-channel vibration reduction effect) Figure 6 (The vibration reduction effect of the two channels is shown). In the one-channel control mode ( Figure 5The original unsteady-state excitation peak vibration acceleration level was 113.12 dB. Traditional control algorithms FxLMS and EWRLS only achieved weak suppression of 0.11 dB (113.01 dB) and 0.19 dB (112.93 dB) respectively, indicating significant control lag under dynamic excitation. In contrast, the IMMVBKF algorithm (the algorithm in this embodiment) effectively reduced the peak value to 107.59 dB, a reduction of 5.53 dB, and exhibited fast response characteristics (convergence time < 1 s) during the time-varying excitation signal. Further analysis of the two-channel control effect... Figure 6 The IMMVBKF algorithm (the algorithm in this embodiment) achieves a vibration reduction of 3.83 dB, while the FxLMS and EWRLS algorithms show no significant vibration suppression effect. Experiments show that the effective response time of the IMMVBKF algorithm under unsteady excitation is significantly improved compared with traditional methods, and it can still maintain algorithm stability (residual fluctuation < ±0.7 dB) under dual-channel collaborative control, verifying the strong robustness of the IMMVBKF algorithm (the algorithm in this embodiment) to complex working conditions.

[0043] The above embodiments are merely exemplary embodiments of the present invention and are not intended to limit the present invention. Those skilled in the art can make various modifications or equivalent substitutions to the present invention within its scope and spirit, and such modifications or equivalent substitutions should also be considered to fall within the scope of protection of the present invention.

Claims

1. An interactive multi-model adaptive active vibration control method based on variational Bayes, characterized in that, Includes the following steps: Step 1: Identify the secondary channels between each actuator and error sensor in the multi-channel system, and use an adaptive algorithm to identify a finite-length impulse response filter as the estimation model for the secondary channels; Step 2: Establish a system model set containing multiple potential dynamic modes to describe the state equations and measurement equations under different vibration sources or different system operating conditions, and initialize each model. Step 3: For each model in the system model set in Step 2, use the variational Bayesian framework to perform online joint estimation and optimization of its process noise covariance matrix and / or measurement noise covariance matrix; Step 4: Perform variational Bayes iteration on each model within each control sampling period; Step 5: For each channel of the multi-channel system, execute steps 2-4 to obtain the optimal state estimate of each channel. Use the covariance cross-fusion method to fuse the state estimates of multiple channels and calculate the global optimal state estimate. Step 6: Convolve the global optimal state estimate with the reference signal filtered by the secondary channel model to generate an anti-noise signal, which is then converted from digital to analog and driven by a power amplifier to output the actuator. Step 7: Feed the newly acquired error sensor signal back to the controller for algorithm iteration and update at the next sampling time.

2. The interactive multi-model adaptive active vibration control method based on variational Bayes as described in claim 1, characterized in that, The initialization in step 2 specifically involves: setting initial state estimates, state estimation error covariance matrices, model prior probabilities, and Markov transition probability matrices between models for each model; and initializing the hyperparameters required for variational Bayesian inference.

3. The interactive multi-model adaptive active vibration control method based on variational Bayes as described in claim 1, characterized in that, Step 3 specifically involves: Step 3.1: Construct a hierarchical probabilistic graphical model of latent variables, assuming that the variational posterior distribution is decomposable using mean-field theory; Step 3.2 introduces a Markov evolution model of the prediction error covariance matrix based on the beta-Bartlett distribution to utilize historical estimation information; Step 3.3: By maximizing the variational lower bound, the posterior distribution of the state and the posterior distribution of the noise parameters are alternately optimized to achieve decoupled joint estimation of the state and noise parameters.

4. The interactive multi-model adaptive active vibration control method based on variational Bayes as described in claim 1, characterized in that, Step 4 specifically involves: Step 4.1: Based on the probabilities of each model and the transition probabilities between models at the previous time step, calculate the initial mixing state and covariance of each filter at the current time step. Step 4.2: Starting with its mixed initial value, each sub-filter uses an adaptive Kalman filter with noise parameters optimized online by variational Bayes to perform independent state prediction and measurement update in parallel, thereby obtaining its own conditional state estimate and covariance. Step 4.3: Calculate the innovation likelihood function of each sub-filter and update the matching probability of each model with the current real system mode accordingly; Step 4.4: Using the updated model probabilities as weights, perform weighted fusion of the state estimates of all sub-filters to obtain the global optimal state estimate and its covariance based on IMM at the current time.

5. The interactive multi-model adaptive active vibration control method based on variational Bayes as described in claim 4, characterized in that, Step 4.2 specifically involves: using the model equations of each model to perform a one-step prediction of the state and covariance; based on the prediction results and new measurements, performing variational Bayesian iteration: fixing the variational distribution of the state and updating the variational posterior distribution of the noise parameters; fixing the noise parameter distribution and updating the variational posterior distribution of the state, i.e., performing an adaptive Kalman filter update with time-varying noise parameters to obtain the conditional state estimate and covariance of the model, as well as the innovation covariance.

6. The interactive multi-model adaptive active vibration control method based on variational Bayes as described in claim 4, characterized in that, In step 4.3, a correction factor based on the likelihood function value is introduced to correct the fixed transition probability matrix in real time.

Images