A multi-channel active vibration damping method based on diffusion filtering

Abstract

The present invention relates to a multi-channel active vibration damping method based on diffusion filtering. The method includes the following steps: S1. Establish an FIR filter model of the secondary path of each channel itself offline; S2. Construct a node topology graph and calculate a combination matrix based on the degree of nodes; S3. Set the algorithm update step size of each channel; S4. Obtain the estimated intermediate weight vector of each channel at the current moment; S5. Re-fuse through the combination matrix to form the actual weight vectors of each channel at the current moment; S6. Apply secondary forces according to the actual weight vectors of each channel at the current moment. Compared with the prior art, the present invention achieves the minimum global error in a multi-channel active vibration isolation system, and only uses the information of each channel itself and neighbor information to reduce the calculation amount, and the step size of each channel can be calculated, eliminating the cost of continuous trial and error.

Description

Technical Field

[0001] The present invention relates to the technical field of active vibration isolation control, and in particular to a multi-channel active vibration reduction method based on diffusion filtering. Background Art

[0002] Active vibration isolation control technology is the main method to solve low-frequency vibration, and vibration reduction is achieved by applying a secondary force with the opposite direction and the same magnitude as the primary vibration direction. Multi-channel active vibration isolation control can achieve vibration reduction effects for large-scale systems.

[0003] Traditional multi-channel active vibration isolation control algorithms adopt the centralized filtering x-least mean square algorithm (FxLMS) or the decentralized FxLMS algorithm. The former has problems such as large computational complexity and a large number of secondary channels to be modeled, and the latter has problems such as system instability caused by channel crosstalk. Summary of the Invention

[0004] The purpose of the present invention is to provide a multi-channel active vibration reduction method based on diffusion filtering to overcome the defects of the above-mentioned existing technologies, achieving the minimum global error in a multi-channel active vibration isolation system and only using the information of each channel itself and neighbor information to reduce the computational complexity.

[0005] The purpose of the present invention can be achieved through the following technical solutions:

[0006] A multi-channel active vibration reduction method based on diffusion filtering, the method comprising the following steps:

[0007] S1. Establish a multi-channel active vibration isolation system model. The system model includes multiple channels and secondary paths. The secondary paths are divided into the secondary paths of each channel itself and the secondary paths between two channels. Each channel is provided with an original input signal and an error signal. Each channel is regarded as a node, and an FIR filter model of the secondary path of each channel is established offline. In the FIR filter model, the secondary path between the i-th channel and the j-th channel is described as H ij (z). The original input signal becomes the filtered input signal of the i-th channel after passing through the secondary path of the i-th channel itself, and the original input signal becomes the filtered signal passing through the channel after passing through the secondary path between two channels;

[0008] S2. Construct a node topology graph between channels, calculate the degree of nodes based on the node topology graph, adopt the metropolis method, calculate the combination matrix based on the degree of nodes, and when the value of the element in the i-th row and the j-th column of the combination matrix is greater than 0, it indicates that the distance between node i and node j is less than the neighbor threshold, then channel i and channel j are neighbors;

[0009] S3. Set the algorithm update step size of each channel;

[0010] S4. Based on the FIR filter model, obtain the filtered input signals and error signals of each channel at the current time, execute the FxLMS algorithm for each channel separately, and obtain the estimated intermediate weight vector of the next moment of each channel based on the filtered input signal, error signal, algorithm update step size, and the estimated intermediate weight vector at the current moment;

[0011] S5. Based on the intermediate weight vectors updated separately for each channel, fuse them through a combination matrix to form the actual weight vectors of each channel at the next moment;

[0012] S6. Apply secondary forces according to the actual weight vectors of each channel at the next moment for vibration reduction. If the current moment reaches the threshold of the update moment or the obtained current error signal is less than the threshold of the error, stop the iteration. Otherwise, return to S4 until the condition for stopping the iteration is satisfied.

[0013] Further, the expression of the elements of the combination matrix is:

[0014]

[0015] where a ij is the element in the i-th row and j-th column of the combination matrix, η i represents the degree of the i-th channel in the graph, N i is the neighbor set of the i-th channel, and the neighbor set of the i-th channel includes the i node itself. N i \{i} represents the neighbor set of the i-th channel after removing the i node itself, and m represents the loop parameter.

[0016] Further, the algorithm update step size of S3 is selected based on the compensation condition for ensuring average convergence. The compensation condition for ensuring average convergence is obtained through the analysis of the average convergence of the diffusion algorithm in the presence of crosstalk. For the i-th channel, the expression of the algorithm update step size is:

[0017]

[0018] where μ i is the algorithm update step size of the i-th channel, is the expectation of the autocorrelation matrix, λ max is the maximum eigenvalue, is the filtered input signal of the i-th channel at the current moment.

[0019] Further, for the i-th channel, the expression of the estimated intermediate weight vector of the next moment is:

[0020]

[0021] where ψ i(n + 1) is the estimated intermediate weight vector of the i-th channel at the next moment, is the filtered input signal of the i-th channel at the current moment, ψ i (n) is the estimated intermediate weight vector of the i-th channel at the current moment, μ i is the algorithm update step size of the i-th channel, e i (n) is the error of the i-th channel at the current moment.

[0022] Further, the filtered input signal of the i-th channel at the current moment has the same order as the estimated intermediate weight vector and the actual weight vector, and the order is the order of the FIR filter.

[0023] Further, for the i-th channel, the expression of the actual weight vector at the next moment is:

[0024]

[0025] where, ψ j (n + 1) is the estimated intermediate weight vector of the j-th channel at the next moment, N i is the neighbor set of the i-th channel, w i (n + 1) is the actual weight vector of the i-th channel at the next moment.

[0026] Further, for the i-th channel, the expression of the error signal at the current moment is:

[0027]

[0028] where, d i (n) is the original vibration of the i-th channel, is the filtered signal of the input signal x(n) passing through the secondary channel H ji (z), H ji (z) is the secondary path between the j-th channel and the i-th channel, and k is the total number of channels.

[0029] Further, for the i-th channel, the expression of the original vibration is:

[0030] d i (n) = x(n) * p i (n)

[0031] where, p i (n) is the impulse response of the forward channel P i (z), and x(n) is the original input signal.

[0032] Further, the combination matrix satisfies A1 T = 1 T, where A is a combined matrix, and 1 represents a row vector with all elements being 1.

[0033] Further, the FIR filter model is established by the least mean square algorithm.

[0034] Compared with the prior art, the present invention has the following advantages:

[0035] (1) The present invention adopts a distributed algorithm. By using the combined matrix, the amount of calculation and the number of secondary channels to be modeled are greatly reduced compared with the centralized algorithm.

[0036] (2) On the basis of reducing the amount of calculation, the present invention realizes the effect of minimizing the global error similar to that of the centralized algorithm through the mutual cooperation between channels and neighbors.

[0037] (3) The present invention adopts a distributed algorithm, selects an appropriate step size in the presence of channel crosstalk in a multi-channel scenario, ensures the convergence of the distributed algorithm, and can also stably reduce vibration in the presence of channel crosstalk. Description of the Drawings

[0038] Figure 1 is a flowchart of the present invention;

[0039] Figure 2 is a model diagram of a multi-channel active vibration isolation system of the present invention;

[0040] Figure 3 is a node modeling diagram of a six-channel active vibration isolation system of the present invention;

[0041] Figure 4 is an error curve diagram of a six-channel active vibration isolation system. Detailed Embodiments

[0042] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, rather than all, of the embodiments of the present invention. Usually, the components of the embodiments of the present invention described and illustrated herein can be arranged and designed in various different configurations.

[0043] Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed present invention, but merely represents selected embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts fall within the scope of protection of the present invention.

[0044] Embodiment 1

[0045] The present invention proposes a multi-channel active vibration damping method based on diffusion filtering. The flowchart of the method is as shown in Figure 1 and is as follows:

[0046] S1. Offline establish the FIR filter form H ij (z) of the secondary path of each channel itself.

[0047] S2. Construct the node topology graph between channels and calculate the combination matrix using the metropolis method.

[0048] S3. Set the update step size of the algorithm for each channel.

[0049] S4. Obtain the filtered input signal of the i-th channel at the current time and the error signal e i (n), and separately execute the FxLMS algorithm for each channel to estimate the intermediate weight vector.

[0050] S5. The intermediate weight vectors separately updated for each channel are fused through the combination matrix to form the actual weight vector at the current moment.

[0051] S6. Apply the secondary force according to the actual weight vectors of each channel at the current moment, and re-execute steps S4 - S5 until the time ends or the ideal vibration damping effect is achieved to realize vibration damping control.

[0052] In the present invention, let n be the current moment and n + 1 be the next moment.

[0053] In S1, use the traditional least mean square algorithm to offline identify the secondary path H ij (z) between the i-th channel and the j-th channel.

[0054] The system model includes multiple channels and secondary paths. The secondary paths are divided into the secondary path of each channel itself and the secondary path between two channels. Each channel is provided with an original input signal and an error signal. Each channel is regarded as a node, and the FIR filter model of the secondary path of each channel is established offline. In the FIR filter model, the secondary path between the i-th channel and the j-th channel is described as H ij (z). The original input signal becomes the filtered input signal of the i-th channel after passing through the secondary path of the i-th channel itself, and the original input signal becomes the filtered signal passing through the channel after passing through the secondary path between two channels. The model diagram of the multi-channel active vibration isolation system is as shown in Figure 2 and is as follows.

[0055] H ij (z) is modeled in the form of an FIR filter, expressed as H ij (z) = h 0 +h 1 z-1 +h 2 z -2 +…+h L-1 z -(L-1) , where L is the filter order. The input signal of the least mean square algorithm is the open-loop pulse excitation applied at the input sensor of the i-th channel. At this time, the error of the j-th channel detected at the j-th channel corresponds to H ij (z). The total error of the j-th channel is the sum of the errors of the corresponding j-th channel obtained separately at the j-th channel after applying the open-loop pulse excitation to each channel. This sum is the error of the j-th channel. Based on this error, the weight vector of the j-th channel is calculated, and the weight vector updated using the algorithm is the coefficient h ij in H 0 ~h L-1 . The same applies to the i-th channel. After applying the open-loop pulse excitation to each channel, the errors of the corresponding i-th channel are obtained separately, and the errors of all the i-th channels are summed. This sum is the error of the i-th channel. Based on this error, the weight vector of the i-th channel is calculated, and the weight vector updated using the algorithm is the coefficient in H ji (z).

[0056] In S2, a node topology graph between channels is constructed, and the combination matrix A = [a ij is calculated using the metropolis method. The node topology graph is usually assumed to be an undirected graph. Each channel of the multi-channel system is regarded as a node, and the neighbors of the node are selected using distance. Generally, the closer the distance, the greater the crosstalk between nodes. The degree η i of the node represents the number of edges associated with the node. The degree of each node is calculated, and the combination matrix A is calculated based on this. The calculation method of the combination matrix A adopts the metropolis method, that is:

[0057]

[0058] where η i represents the degree of the i-th channel in the graph, N i is the neighbor set of the i-th channel, and N i \{i} represents the neighbor set of the i-th channel after removing the i node itself, and m is the loop parameter.

[0059] The selection of the combination matrix A can be adjusted by μ without affecting the convergence, but it must satisfy the condition A1 T = 1 T , where 1 represents a row vector with all elements being 1.

[0060] The neighbors of each channel node in S2 can be simply described by distance. For example, taking this channel as the center and a certain distance as the radius to draw a circle, other channels within the circle are regarded as the neighbors of this channel. When the value of the element in the i-th row and j-th column of the combination matrix is greater than 0, it indicates that the distance between node i and node j is less than the neighbor threshold, that is, i and j are neighbors.

[0061] In S3, set the algorithm update step size μ for each channel i The specific steps are as follows: Through the analysis of the average convergence of the diffusion algorithm in the presence of crosstalk, obtain the compensation condition to ensure average convergence:

[0062]

[0063] Therefore, in actual execution, we can select the step size through the following formula, that is, by measuring the input signal of each channel and then calculating:

[0064]

[0065] Here is the filtered input signal of the i-th channel at the current moment, and λ max (·) represents the maximum eigenvalue represents the expectation of the autocorrelation matrix, which can be approximated as:

[0066]

[0067] In S4, execute the diffusion FxLMS algorithm to update the optimal weight vector w i (n) at the current moment of each channel. At the n-th moment, the signal detected by the input signal sensor of each channel, that is, the original input signal of each channel is x(n). Therefore, the filtered input signal matrix is:

[0068]

[0069]

[0070]

[0071] Therefore, the estimated intermediate weight vector at the next moment is:

[0072]

[0073] The input signal at each moment n in step S3 and step S4 represents the input signal filtered by the secondary channel, and its order is the same as that of ψ i (n) and w i (n), both of which are L, and L is the filter order.

[0074] In S5, after obtaining the intermediate weight vectors for each channel, the intermediate weight vectors between channels are recombined using the combination matrix to achieve information exchange between channels. The actual weight vector at the next moment is:

[0075]

[0076] In S6, the controller applies different secondary forces to each channel according to the calculated actual weight vector to achieve vibration reduction control. Update for the next moment. If the sensor detects that the error e(n) meets the requirements or reaches the upper limit of the iteration time, stop the update; otherwise, return to S4.

[0077] In S6, for channel i, the error e(n) at the current moment is:

[0078]

[0079] where d i (n) is the original vibration of the i-th channel, is the filtered signal of the input signal x(n) passing through the secondary channel H ji (z), H ji (z) is the secondary path between the j-th channel and the i-th channel, and k is the total number of channels.

[0080] The following is verified by simulation:

[0081] This simulation considers a six-channel single-task active vibration isolation system. Assuming the fundamental frequency f = 20Hz, the sampling rate fs = 1000, and the simulation time T = 10, the input sensor signal of each channel can be modeled as a sine signal, that is:

[0082]

[0083] ω = 2πf

[0084] Step S1, offline identification of the secondary channel.

[0085] In this simulation, in order to simulate the crosstalk between channels, the secondary paths of each channel itself and the secondary paths between channels are identified offline, and the secondary path matrix is 6×6. Thus, the crosstalk of channel i to channel j can be expressed as γ ij (n) = x(n) * H ij (n) * w i (n), * represents convolution.

[0086] Step S2, construct the node topology graph between channels. The node topology graph is as Figure 3 shown.

[0087] In this simulation, the neighbor distance threshold is set to 0.3 m, that is, nodes within a radius of 0.3 m are considered neighbors. After obtaining the connected node topology graph, the combination matrix can be calculated:

[0088]

[0089] Step S3: Set the step size of each channel:

[0090]

[0091] In this simulation, the calculated step size is:

[0092]

[0093] Step S4: Execute the diffusion FxLMS algorithm to estimate the intermediate weight vector of each channel.

[0094] In this simulation, the signal obtained by the input sensor of each channel is set to x(n), and the signal obtained by the error sensor is calculated as follows:

[0095]

[0096] where d i (n) = x(n) * p i (n) represents the original vibration, and p i (n) is the impulse response of the forward channel P i (z). In this way, the simulation verification can be carried out according to step S4.

[0097] Step S5: Execute the diffusion FxLMS algorithm to combine the intermediate weight vectors to obtain the optimal weight vector.

[0098] Step S6: The controller applies different secondary forces to each channel according to the calculated actual weight vector to achieve vibration reduction control. As Figure 4 shown is the real-time change curve of the error e i (n).

[0099] The preferred specific embodiments of the present invention have been described in detail above. It should be understood that those of ordinary skill in the art can make many modifications and variations based on the concept of the present invention without creative efforts. Therefore, all technical solutions that can be obtained by those skilled in the art in the technical field of the present invention based on the concept of the present invention through logical analysis, reasoning, or limited experiments on the basis of the existing technology should be within the protection scope determined by the claims.

Claims

1. A multi-channel active vibration damping method based on diffusion filtering, characterized in that, the method comprises the following steps: S1. Establish a multi-channel active vibration isolation system model. The system model includes multiple channels and secondary paths. The secondary paths are divided into the secondary paths of each channel itself and the secondary paths between two channels. Each channel is provided with an original input signal and an error signal. Each channel is regarded as a node. Offline, establish the FIR filter model of the secondary path of each channel. In the FIR filter model, the secondary path between the i-th channel and the j-th channel is described as H ij (z). The original input signal becomes the filtered input signal of the i-th channel after passing through the secondary path of the i-th channel itself. The original input signal becomes the filtered signal passing through the channel after passing through the secondary path between two channels; S2. Construct a node topology graph between channels, calculate the degree of nodes based on the node topology graph, and adopt the metropolis method to calculate the combination matrix based on the degree of nodes. When the value of the element in the i-th row and j-th column of the combination matrix is greater than 0, it indicates that the distance between nodes i and j is less than the neighbor threshold, then channels i and j are neighbors; S3. Set the algorithm update step size for each channel; S4. Obtain the filtered input signal and error signal of each channel at the current time based on the FIR filter model, perform the FxLMS algorithm on each channel separately, and obtain the estimated intermediate weight vector of each channel at the next moment based on the filtered input signal, error signal, algorithm update step size, and the estimated intermediate weight vector at the current moment; S5. Based on the intermediate weight vectors updated separately for each channel, fuse them through the combination matrix to form the actual weight vectors of each channel at the next moment; S6. Apply secondary forces according to the actual weight vectors of each channel at the next moment for vibration damping. If the current moment reaches the threshold of the update moment or the obtained current error signal is less than the error threshold, stop the iteration. Otherwise, return to S4 until the condition for stopping the iteration is met.

2. The multi-channel active vibration damping method based on diffusion filtering according to claim 1, characterized in that, the expression of the elements of the combination matrix is: where a ij is the element at the \(i\)-th row and \(j\)-th column of the combined matrix, and \(\eta\) i represents the degree of the \(i\)-th channel in the graph, and \(N\) i is the neighbor set of the \(i\)-th channel. The neighbor set of the \(i\)-th channel includes the \(i\) node itself. \(N\) i \(\{i\}\) represents the neighbor set of the \(i\)-th channel after removing the \(i\) node itself, and \(m\) represents the loop parameter.

3. The multi-channel active vibration damping method based on diffusion filtering according to claim 1, characterized in that, the algorithm update step size in S3 is selected based on the compensation condition for ensuring average convergence, and the compensation condition for ensuring average convergence is obtained through the analysis of the average convergence of the diffusion algorithm in the presence of crosstalk. For the i-th channel, the expression of the algorithm update step size is: where μ i is the algorithm update step size of the i-th channel, is the expectation of the autocorrelation matrix, λ max is the maximum eigenvalue, is the filtered input signal of the i-th channel at the current moment.

4. The multi-channel active vibration damping method based on diffusion filtering according to claim 1, characterized in that, for the i-th channel, the expression of the estimated intermediate weight vector at the next moment is: Among them, ψ i (n + 1) is the estimated intermediate weight vector of the i-th channel at the next moment, is the filtered input signal of the i-th channel at the current moment, ψ i (n) is the estimated intermediate weight vector of the i-th channel at the current moment, μ i is the algorithm update step size of the i-th channel, e i (n) is the error of the i-th channel at the current moment.

5. The multi-channel active vibration damping method based on diffusion filtering according to claim 3 or 4, characterized in that, The filtered input signal of the i-th channel at the current moment The same as the order of the estimated intermediate weight vector and the actual weight vector, and the order is the order of the FIR filter.

6. The multi-channel active vibration damping method based on diffusion filtering according to claim 5, characterized in that, for the i-th channel, the expression of its actual weight vector at the next moment is: Among them, ψ j (n + 1) is the estimated intermediate weight vector of the j-th channel at the next moment, and N i is the neighbor set of the i-th channel, and w i (n + 1) is the actual weight vector of the i-th channel at the next moment.

7. The multi-channel active vibration damping method based on diffusion filtering according to claim 1, characterized in that, for the i-th channel, the expression of the error signal at the current moment is: where d i (n) is the original vibration of the i-th channel, is the filtered signal of the input signal x(n) passing through the secondary channel H ji (z), and H ji (z) is the secondary path between the j-th channel and the i-th channel, and k is the total number of channels.

8. The multi-channel active vibration damping method based on diffusion filtering according to claim 7, characterized in that, for the i-th channel, the expression of the original vibration is: d i (n) = x(n) * p i (n) where p i (n) is the impulse response of the forward channel P i (z), and x(n) is the original input signal.

9. The multi-channel active vibration damping method based on diffusion filtering according to claim 2, characterized in that, The combinatorial matrix satisfies A1 T = 1 T , where A is the combinatorial matrix and 1 represents a row vector with all elements being 1.

10. The multi-channel active vibration damping method based on diffusion filtering according to claim 1, characterized in that, the FIR filter model is established by the least mean square algorithm.

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