A diffusion multi-channel vibration active control method based on adaptive fusion matrix

Abstract

The application discloses a diffusion multi-channel vibration active control method based on an adaptive fusion matrix, and comprises the following steps: establishing a multi-channel vibration active control system model considering crosstalk; deriving an adaptive distributed FXLMS algorithm suitable for the present scene based on a diffusion structure, wherein the scene is a multi-channel strong coupling mechanical vibration active control scene, the algorithm is a distributed vibration active control method based on the diffusion structure, and the fusion matrix in the algorithm is in a form capable of adaptively learning and adjusting weight coefficients; initializing parameters, continuously iterating a filter weight vector according to the algorithm, and realizing active vibration isolation by applying a secondary force through an actuator. Compared with the prior art, the application proposes a clearer and more complete adaptive fusion matrix design method, which can further reduce a global mean square error index while ensuring a lower calculation amount, and the proposed fusion matrix iteration formula is a time-varying and adaptive method, can learn unknown parameters and cope with non-stationary environments, and has good robustness.

Description

Technical Field

[0001] This invention relates to the field of multi-channel distributed active vibration control, and in particular to a diffusion multi-channel active vibration control method based on an adaptive fusion matrix. Background Technology

[0002] Mechanical equipment generates vibrations during operation, which can adversely affect the performance of instruments and meters, and even cause structural damage. Traditional passive vibration isolation techniques have limitations, necessitating the use of active vibration control technology to address low-frequency vibrations.

[0003] Currently, distributed active vibration control technology is mainly based on a distributed strategy of diffusion and cooperation. Compared with decentralized control, this strategy adds a fusion step. By using fusion coefficients to weightedly sum the updated information of the controlled variables of each node, the result is used as the controlled variable for the next time step, thereby achieving information interaction and ultimately global control. This method improves the impact of the coupling relationship between control nodes on system stability in decentralized control.

[0004] Existing distributed active vibration control technologies based on diffusion structures mainly fall into two categories. One type constructs a global controlled variable at each node, encompassing all controlled variables of all nodes, to replace the controlled variables of each node in the diffusion algorithm. Then, a diffusion strategy is used to exchange information between the global controlled variables at each node. However, in the multi-core single controller used in this scenario, this distributed technology does not significantly improve computational efficiency compared to centralized control. The other type of technology retains the controlled variable structure of the diffusion algorithm, treating the coupling relationship between nodes as crosstalk from neighboring nodes to the current node. It analyzes this based on the assumption that the crosstalk from neighboring nodes to the control node is weakly correlated with the filter input vector of the control node. However, this assumption is also not applicable to this scenario. Furthermore, existing distributed active vibration control technologies based on diffusion strategies often use classic distributed linear consensus protocols when selecting the fusion matrix in the diffusion structure. These protocols aim to solve the distributed linear consensus problem, which differs somewhat from the active vibration control problem. Some other technologies first identify quantities potentially related to the fusion matrix and then set an appropriate fusion matrix based on experience.

[0005] Therefore, neither of the two existing types of distributed active vibration control technologies based on diffusion structures is entirely suitable for this scenario. The first type of technology, when using a multi-core single controller, does not significantly improve computational efficiency compared to centralized control. The second type of technology, based on the assumption that crosstalk generated by neighboring nodes to the control node is weakly correlated with the filtered input vector of the control node, also deviates from the actual scenario. Furthermore, existing distributed active vibration control technologies based on diffusion strategies lack a clear and complete explanation of how to select the fusion matrix. Summary of the Invention

[0006] The purpose of this invention is to propose a diffusion-based FXLMS algorithm suitable for strongly coupled vibration reduction scenarios, along with a design method for its adaptive fusion matrix, to reduce computational complexity. Through formula derivation, a method is obtained that can further improve the global mean square error (MSE). network An adaptive fusion matrix design method.

[0007] To achieve the above objectives, this invention proposes a diffusion multi-channel vibration active control method based on an adaptive fusion matrix, comprising the following steps:

[0008] Step 1: Establish a model for a multi-channel distributed active vibration control system. The error signal model considering crosstalk is established as follows:

[0009]

[0010] In the formula, i represents the sampling time, and when i appears in subscript form, the corresponding term is a vector; otherwise, the corresponding term is a scalar. The subscript k refers to the term corresponding to control node k, and e k (i) represents residual vibration, d k (i) is the vibration to be reduced caused by the vibration source. It is the filtered input signal, w l (i) is the neighbor node filter weight vector, and N is the total number of control nodes;

[0011] Step 2: Derive the adaptive diffusion FXLMS algorithm and the adaptive fusion matrix iteration formula applicable to this scenario, and analyze its steady-state mean square performance. Based on this, derive the fusion matrix iteration update formula for adaptive learning of unknown parameters.

[0012] Step 3: Initialize all parameters, including the filter weight vector w composed of the filter tap coefficients at each node. k,-1 The intermediate weight vector ψ represents the local filter vector. k,-1 γ, the estimated value of the product of variance lk 2 (-1), Fusion Matrix A i-1 Fixed step size μ k and v k Where l is a neighbor of node k, denoted as k = 1, 2, ..., N, step size μ k and v k It is a very small positive number;

[0013] Step 4: Update the intermediate weight vector:

[0014]

[0015] Step 5: Update the fusion matrix based on the topology and variance product estimate:

[0016]

[0017] Step 6: Update the filter weight vector based on the fusion matrix:

[0018]

[0019] Step 7: Iterate and update the intermediate weight vector, the fusion matrix, and the filter weight vector until the residual vibration of each control node converges to a small range.

[0020] Furthermore, in step 2, based on the system model with crosstalk, and combining the idea of ​​using neighbor communication to control all nodes through a diffusion structure, the local cost function and global cost function of the node are written out. Based on the global cost function and the cost function of the neighbor node, the cost function of each control node is modified so that it can approximate the global cost function.

[0021] Furthermore, the specific steps include:

[0022] Step 2.1: Propose the global cost function and the local cost function;

[0023] The local cost function is:

[0024] J k =E{e k 2 (i)};

[0025] The global cost function is:

[0026]

[0027] Step 2.2: Correct the local cost function;

[0028] Based on the local cost function and the global cost function, the local cost function is modified as follows:

[0029]

[0030] Where b lk These are weighting coefficients, and are subject to the following constraints:

[0031] b lk ≥0, And when time b lk =0;

[0032] In the local cost function This represents the neighbor set of control node k, excluding the node itself; Step 2.3: Design the filter update formula;

[0033] Based on the modified local cost function and using the gradient descent method, a filter update formula suitable for multi-channel strongly coupled active vibration control systems is obtained.

[0034] Step 2.4: Analyze steady-state second-order performance;

[0035] After controlling a multi-channel strongly coupled system using the aforementioned active control method for diffused vibration, the second-order global performance index at steady state is analyzed:

[0036]

[0037] Step 2.5: Design the fusion matrix coefficients;

[0038] The update expressions for the control filters at each node are as follows:

[0039]

[0040]

[0041] Furthermore, in step 1, before the system model is established, the secondary channel transfer function of the multi-channel mechanical vibration system is obtained to characterize the vibration transmission relationship of each control node.

[0042] The transfer function includes both error channel information caused by the D / A converter and power amplifier stages, and coupling channel information.

[0043] Furthermore, the method for obtaining the secondary channel transfer function includes: isolating the vibration source, performing open-loop excitation on the target control node, and then obtaining the vibration transfer function of the target control node to all control nodes through the LMS algorithm.

[0044] Furthermore, step 7 includes the following steps:

[0045] Step 7.1: Obtain the vibration transfer function of each control node actuator to all control node acceleration sensors, including the node itself;

[0046] Step 7.2: Based on the secondary channel transfer function, the actuation intensity of the control node is continuously updated using the provided adaptive diffusion FXLMS algorithm. The actuation intensity of the control node includes the intermediate weight vector, the fusion matrix, and the filter weight vector.

[0047] Step 7.3: Stop updating the actuation intensity of all control nodes when the mean square value of the acceleration sensor data of the control nodes converges to a fixed range.

[0048] Furthermore, in step 7, based on the continuous iterative updating of the intermediate weight vector, the fusion matrix, and the filter weight vector, the mean square values ​​of the acceleration sensor data of the control node are all converged to a fixed range, thereby applying the adaptive diffusion FXLMS algorithm to reduce mechanical vibration.

[0049] Compared with the prior art, the advantages of the present invention are:

[0050] 1. This invention proposes an adaptive fusion matrix design method, which has a clearer and more complete derivation process than general fusion matrix selection methods, and is more suitable for this scenario than classical fusion matrix methods, thus further improving MSE. network Performance metrics;

[0051] 2. The distributed active vibration control method based on diffusion structure used in this invention can significantly reduce the amount of computation compared with centralized active vibration control technology and general diffusion-based active vibration control technology.

[0052] 3. Compared with the decentralized vibration active control algorithm, this invention considers the coupling relationship between nodes, performs unified control of all nodes, improves the stability of the system, and avoids the problem of convergence followed by divergence in practical applications of decentralized methods. Attached Figure Description

[0053] Figure 1 This is a schematic diagram of the design process of the diffusion multi-channel vibration active control method based on adaptive fusion matrix of the present invention;

[0054] Figure 2 Here is a simplified flowchart of the provided adaptive diffusion FXLMS algorithm;

[0055] Figure 3 A simplified flowchart illustrating the application of the adaptive diffusion FXLMS algorithm to reduce mechanical vibration in one embodiment of the present invention;

[0056] Figure 4 This is a simplified diagram of the information interaction principle of the control nodes in one embodiment of the present invention. The four nodes in the diagram exchange the intermediate weight vector ψ at a certain sampling time i based on the neighbor relationship and the fusion matrix coefficients.

[0057] Figure 5 This is a block diagram illustrating the principle of an active vibration control method based on the FXLMS algorithm.

[0058] Figure 6 This is a simulation diagram of one embodiment of the present invention;

[0059] Figure 7 This is a simulation diagram of an embodiment of the present invention. Detailed Implementation

[0060] To make the objectives, technical solutions, and advantages of the present invention clearer, the technical solutions of the present invention will be further described below.

[0061] In this embodiment, the design process of the provided diffusion multi-channel vibration active control method based on adaptive fusion matrix may include steps S101-S108:

[0062] Step S101: Obtain the secondary channel transfer function of the multi-channel mechanical vibration system.

[0063] The vibration transfer function described in this embodiment is used to characterize the vibration transfer relationship of each control node, and is denoted as the secondary channel transfer function.

[0064] The aforementioned transfer function includes both error channel information caused by components such as the D / A converter and power amplifier, and coupling channel information.

[0065] The method for obtaining the secondary channel transfer function may include: isolating the vibration source, performing open-loop excitation on the target control node, and then obtaining the vibration transfer function of the target control node to all control nodes through the LMS algorithm.

[0066] Step S102: Establish a model of a multi-channel distributed active vibration control system.

[0067] The error signal model considering crosstalk is established as follows:

[0068]

[0069] Where i represents the sampling time, and when i appears in subscript form, the corresponding term is a vector; otherwise, the corresponding term is a scalar. The subscript k refers to the term corresponding to control node k, e k (i) represents residual vibration, d k (i) is the vibration to be reduced caused by the vibration source. It is the filtered input signal, w l (i) is the neighbor node filter weight vector, and N is the total number of control nodes.

[0070] Step S103: Propose the global cost function and the local cost function.

[0071] The local cost function is:

[0072] J k =E{e k 2 (i)}

[0073] The global cost function is:

[0074]

[0075] Step S104: Modify the local cost function.

[0076] This invention, based on local cost functions and global cost functions, modifies the local cost function as follows:

[0077]

[0078] Where b lk These are weighting coefficients, and are subject to the following constraints:

[0079] b lk ≥0, And when time b lk =0

[0080] In the local cost function This represents the set of neighbors of the controlling node k, excluding the node itself.

[0081] Step S105: Design the filter update formula.

[0082] Based on the modified local cost function and using the gradient descent method, this invention obtains a filter update formula suitable for multi-channel strongly coupled active vibration control systems.

[0083] Step S106: Analyze steady-state second-order performance.

[0084] In one embodiment of the present invention, after applying the aforementioned active control method for diffused vibration to control a multi-channel strongly coupled system, the second-order global performance index at steady state is analyzed:

[0085]

[0086] Step S107: Design the fusion matrix coefficients.

[0087] In one embodiment of the present invention, the control filter update expression for each node is:

[0088]

[0089]

[0090] The second line of the above equation represents the fusion step, which uses the weight coefficients a of the fusion matrix. lk (i) Implement the intermediate weight vector ψ of each node k,i Information exchange. Based on the analyzed steady-state second-order global performance index MSE network Using the gradient descent method, a time-varying fusion matrix weight selection method is designed that can adaptively learn unknown parameters and adapt to non-stationary environments.

[0091] Step S108: Experimental verification.

[0092] This embodiment applies the above-mentioned diffusion multi-channel vibration active control method based on adaptive fusion matrix to a strongly coupled distributed vibration active control system with 6 nodes, and verifies its effectiveness through simulation.

[0093] like Figure 2 As shown, in one embodiment of the present invention, the provided adaptive diffusion FXLMS algorithm may include steps S201-S204:

[0094] Step S201: Initialize all parameters. The parameters include the filter weight vector w, composed of the tap coefficients of each node filter. k,-1 The intermediate weight vector ψ represents the local filter vector. k,-1 γ, the estimated value of the product of variance lk 2 (-1), Fusion Matrix A i-1 Fixed step size μ k and v k Where l is a neighbor of node k, denoted as k = 1, 2, ..., N, where N is the total number of control nodes;

[0095] Step S202: Based on the filter vector of each control node, fix the step size μ. k The accelerometer data is combined with the filtered input signals from neighboring nodes to update the intermediate weight vector;

[0096] Step S203: Update the fusion matrix based on the topology and variance product estimate;

[0097] Step S204: Update the filter weight vector based on the fusion matrix.

[0098] like Figure 3 As shown, in one embodiment of the present invention, the distributed active vibration control method for reducing mechanical vibration by applying the adaptive diffusion FXLMS algorithm may include steps S301-S303:

[0099] Step S301: Obtain the vibration transfer function of each control node actuator to all control node acceleration sensors, including the node itself.

[0100] Step S302: Based on the secondary channel transfer function, the actuation intensity of the control node is continuously updated using the provided adaptive diffusion FXLMS algorithm;

[0101] Step S303: If the mean square values ​​of the acceleration sensor data of the control nodes all converge to a fixed range, then stop updating the actuation intensity of all control nodes.

[0102] like Figure 4 As shown, nodes 1, 2, 3, and 4 form a topology graph that reflects the communication between the four nodes. If there is a line segment from node 1 to node 2, then node 2 can receive information from node 1, and node 1 is a neighbor of node 2. If there is no line segment from node 2 to node 3, then node 3 cannot receive information from node 2, and node 2 is not a neighbor of node 3. Communication between any two nodes can be either unidirectional or bidirectional.

[0103] like Figure 5 As shown, the vibration active control method based on the FXLMS algorithm of this invention can identify the secondary channel transfer function offline, filter the input signal through the secondary channel transfer function, and then input the filtered input signal into the controller, thereby initially reducing the influence of error channels and coupling channels in the system.

[0104] In this invention, considering crosstalk between nodes, the input vector from the LMS algorithm is no longer used when updating the filter weight vector. Instead, the sum of the filtered input signals of any node k's neighboring control nodes is used, denoted as X. k,i ,and in The filtered input vector at time i refers to the input signal after being filtered by the secondary channel transfer function from node l to node k.

[0105] To illustrate this solution more thoroughly and clearly, a complete implementation example is described below, but the scope of protection of this invention is not limited to the following implementation example.

[0106] A mechanical device generates periodic vibrations during operation, which are transmitted to a nearby small platform. To reduce the vibration of the entire platform, it is proposed to arrange six actuators and six acceleration sensors on the platform, with one actuator and one acceleration sensor corresponding to each other. Each actuator, one acceleration sensor, and one control filter constitute a control node, thus forming a multi-channel active vibration control system consisting of six control nodes. Figure 6 and Figure 7 As shown.

[0107] First, shut down the mechanical equipment and obtain a total of 30 secondary channel transfer functions through open-loop excitation based on the LMS algorithm.

[0108] Next, the adaptive diffusion FXLMS algorithm is iterated using the following formula to achieve vibration suppression:

[0109]

[0110]

[0111]

[0112] Where i represents the sampling time, and when i appears in subscript form, the corresponding term is a vector; otherwise, the corresponding term is a scalar. The subscript k refers to the term corresponding to control node k, e k (i) represents the sensor measurement value. This represents the filter input weight vector, with a step size of μ. k and v k It is a very small positive number, ψ k,i γ represents the intermediate weight vector. lk 2 (i) represents the estimated product of variances, w k,i This represents the filter weight vector.

[0113] The above are merely preferred embodiments of the present invention and do not constitute any limitation on the present invention. Any equivalent substitutions or modifications made by those skilled in the art to the technical solutions and content disclosed in the present invention without departing from the scope of the present invention shall be deemed to have remained within the protection scope of the present invention.

Claims

1. A method for active control of diffusion-based multi-channel vibration based on an adaptive fusion matrix, characterized in that, Includes the following steps: Step 1: Establish a model for a multi-channel distributed active vibration control system. The error signal model considering crosstalk is established as follows: ， ； In the formula, Indicates the sampling time, and when When an item appears in subscript form, the corresponding item is a vector; otherwise, the corresponding item is a scalar. Control node The corresponding items, It is residual vibration. It is the vibration to be reduced caused by the vibration source. It is a filtered input signal. It is the neighbor node filter weight vector. To control the total number of nodes; Step 2: Derive the adaptive diffusion FXLMS algorithm and the adaptive fusion matrix iteration formula applicable to this scenario, and analyze its steady-state mean square performance. Based on this, derive the fusion matrix iteration update formula for adaptive learning of unknown parameters. Step 3: Initialize all parameters, including the filter weight vector composed of the filter tap coefficients at each node. The intermediate weight vector representing the local filter vector Variance product estimate Fusion Matrix Fixed step size and ;in, It is a node The neighbor, recorded as Step length It is a very small positive number; Step 4: Update the intermediate weight vector: ； Step 5: Update the fusion matrix based on the topology and variance product estimate: ； Step 6: Update the filter weight vector based on the fusion matrix: ； Step 7: Iterate and update the intermediate weight vector, the fusion matrix, and the filter weight vector until the residual vibration of each control node converges to a small range.

2. The active control method for diffusion multi-channel vibration based on adaptive fusion matrix according to claim 1, characterized in that, In step 2, based on the system model with crosstalk, and combining the idea of ​​using neighbor communication to control all nodes through a diffusion structure, the local cost function and global cost function of the node are written. Based on the global cost function and the cost function of the neighbor node, the cost function of each control node is modified so that it can approximate the global cost function.

3. The active control method for diffusion multi-channel vibration based on an adaptive fusion matrix according to claim 2, characterized in that, Specifically, the following steps are included: Step 2.1: Propose the global cost function and the local cost function; The local cost function is: ； The global cost function is: ； Step 2.2: Correct the local cost function; Based on the local cost function and the global cost function, the local cost function is modified as follows: ； in These are weighting coefficients, and are subject to the following constraints: , , and when hour 0; In the local cost function Indicates control node The set of neighbors, excluding the node itself; Step 2.3: Design the filter update formula; Based on the modified local cost function and using the gradient descent method, a filter update formula suitable for multi-channel strongly coupled active vibration control systems is obtained. Step 2.4: Analyze steady-state second-order performance; After controlling a multi-channel strongly coupled system using the active control method for diffused vibration, the second-order global performance index at steady state is analyzed: ； Step 2.5: Design the fusion matrix coefficients; The update expressions for the control filters at each node are as follows: ； 。 4. The active control method for diffusion multi-channel vibration based on adaptive fusion matrix according to claim 1, characterized in that, In step 1, before the system model is established, the secondary channel transfer function of the multi-channel mechanical vibration system is obtained to characterize the vibration transmission relationship of each control node. The transfer function includes both error channel information caused by the D / A converter and power amplifier stages, and coupling channel information.

5. The active control method for diffusion multi-channel vibration based on an adaptive fusion matrix according to claim 4, characterized in that, Methods for obtaining the secondary channel transfer function include: isolating the vibration source, performing open-loop excitation on the target control node, and then obtaining the vibration transfer function of the target control node to all control nodes through the LMS algorithm.

6. The active control method for diffusion multi-channel vibration based on adaptive fusion matrix according to claim 1, characterized in that, Step 7 includes the following steps: Step 7.1: Obtain the vibration transfer function of each control node actuator to all control node acceleration sensors, including the node itself; Step 7.2: Based on the secondary channel transfer function, the actuation intensity of the control node is continuously updated using the provided adaptive diffusion FXLMS algorithm. The actuation intensity of the control node includes the intermediate weight vector, the fusion matrix, and the filter weight vector. Step 7.3: Stop updating the actuation intensity of all control nodes when the mean square value of the acceleration sensor data of the control nodes converges to a fixed range.

7. The active control method for diffusion multi-channel vibration based on adaptive fusion matrix according to claim 1, characterized in that, In step 7, by continuously updating the intermediate weight vector, the fusion matrix, and the filter weight vector, the mean square values ​​of the acceleration sensor data of the control node are all converged to a fixed range, thereby applying the adaptive diffusion FXLMS algorithm to reduce mechanical vibration.

Images