A nonlinear signal prediction method and system based on a sparse gating kernel
By using a sparse gated kernel mechanism, the dictionary expansion and complexity problems of the traditional KLMS algorithm in nonlinear system signal prediction are solved, achieving efficient and stable nonlinear signal prediction, adapting to different signal characteristics and reducing computational load.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- QINGDAO UNIV OF SCI & TECH
- Filing Date
- 2026-04-15
- Publication Date
- 2026-07-14
AI Technical Summary
When dealing with nonlinear system signal prediction, the traditional KLMS algorithm suffers from dictionary expansion and computational complexity, making it difficult to achieve long-term stable operation with limited computing resources. In particular, when there is a lot of noise and redundant samples, the prediction accuracy and real-time performance are limited.
A sparse gated kernel mechanism is adopted, which controls the addition of samples to the dictionary set by adjusting the gating parameters and thresholds, and updates the weight coefficients only when necessary. The input vector is constructed by combining the Gaussian kernel function and time delay embedding, and the model is dynamically adjusted to adapt to the nonlinear signal characteristics.
It effectively reduces computational complexity and storage overhead, improves prediction accuracy and system stability, and maintains real-time performance and efficiency for long-term online operation.
Smart Images
Figure CN122386809A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of signal processing and predictive control technology, and in particular to a nonlinear signal prediction method and system based on sparse gate kernels. Background Technology
[0002] Nonlinear system signal prediction is widely used in industrial process control, equipment condition monitoring, fault early warning, and energy consumption optimization. In these scenarios, the measured signals typically exhibit significant nonlinearity, time-varying characteristics, and noise interference, and the systems often need to achieve online / real-time prediction with limited computing resources. Therefore, how to reduce model complexity while ensuring prediction accuracy and maintaining long-term online stable operation is one of the key technical challenges in this field.
[0003] In existing technologies, linear adaptive filtering algorithms such as Least Mean Square (LMS) are simple in structure and easy to implement. However, since they are essentially linear modeling methods, their prediction accuracy is limited when the system exhibits significant nonlinear characteristics. To improve the ability to represent nonlinear features, kernel-based adaptive filtering techniques have emerged, such as the Kernel Least Mean Square (KLMS) algorithm. This algorithm improves prediction performance by mapping the input to a high-dimensional feature space and using a kernel function for nonlinear modeling.
[0004] However, traditional KLMS typically requires constantly adding new samples to the dictionary set to update the model during online learning, causing the dictionary size to grow over time. This leads to the following problems: when facing long-term sequences or continuous running scenarios, the dictionary set may continuously expand, resulting in a decrease in the real-time performance of the algorithm or even difficulty in long-term stable operation; when there are many noisy or redundant samples, the addition of repeated or low-contribution samples to the dictionary will further increase the complexity, while contributing little to effective learning. Summary of the Invention
[0005] The purpose of this invention is to provide a nonlinear signal prediction method and system based on sparse gated kernels.
[0006] This invention is achieved through the following measures: In a first aspect, this application provides a nonlinear signal prediction method based on sparse gated kernels, characterized by comprising: S1. Acquire the nonlinear system signal to be predicted, discretize the continuous signal according to a preset sampling period to obtain a sampling point sequence, and combine the current sampling point signal value and its signal values at several past times into an input vector x based on the time delay; S2. Set the kernel width of the kernel function. Learning rate Gating adjustment parameters and gating threshold And initialize the dictionary set. With the set of weight coefficients; nuclear width ( The smoothness of the kernel function determines the sensitivity of similarity calculation.
[0007] Learning rate ( ): Adjust the step size of weight updates to ensure the convergence of the algorithm.
[0008] Gating adjustment parameters ( ): Used to adjust the activation sensitivity of the sparse gated weight function.
[0009] Gating threshold ( ): Used to determine whether to add the current sample to the dictionary set.
[0010] The dictionary set is used to store selected input vector samples, and the weight coefficient set is used to store the weight coefficients corresponding to the dictionary samples. S3: For each input vector sample, if the dictionary set is not empty, calculate the kernel function value between the input vector and each dictionary sample in the dictionary set; S4: Based on the kernel function value, the gating adjustment parameter, and the gating threshold, calculate the corresponding sparse gating weights; S5: Calculate the predicted output of the current input vector according to the kernel function value, the sparse gating weights, and the weight coefficient set; S6: Calculate the prediction error based on the target output value of the current sample and the predicted output, and update the weight coefficients.
[0011] Furthermore, the input vector is composed of the current sampled value and its previous sampled value. Composed of historical sample values, satisfying:
[0012] in, It is a sequence of sampling points. This represents the embedding length corresponding to the time delay.
[0013] The input vector can be dynamically adjusted according to the actual industrial process to ensure that it adapts to different signal characteristics.
[0014] Furthermore, the kernel function is a Gaussian kernel function:
[0015] In the formula For kernel width, This is a sample dictionary from the dictionary set.
[0016] Furthermore, the sparse gating weights are generated by a gating weight function, and the gating weight function is at least related to the kernel function value. The gate control adjustment parameters and the gate threshold Related, and satisfying: when the kernel function value is below the gate threshold When the kernel value is higher than the gate threshold, the corresponding sparse gating weights decrease or become zero; when the kernel value is higher than the gate threshold... When the value is zero, the corresponding sparse gating weight is non-zero.
[0017] Furthermore, the gating weight function is:
[0018] In the formula, For gating adjustment parameters, The threshold value is used for gate control. This is the kernel function value.
[0019] Furthermore, based on the kernel function value sparse gating weights The predicted output is calculated using the set of weighted coefficients.
[0020] In the formula, For dictionary samples The corresponding weighting coefficients.
[0021] Furthermore, based on the target output value of the current sample With predicted output Calculate prediction error When the prediction error Meets the preset error threshold When conditions are met, the current input vector will be used. Add to dictionary collection And based on the prediction error With learning rate Update the weighting coefficients; when the prediction error does not meet the preset error threshold. Under certain conditions, do not use the current input vector. Add to dictionary collection Based solely on prediction error With learning rate Update the weighting coefficients.
[0022] Furthermore, the updated weighting coefficients are:
[0023] Furthermore, it also includes a test evaluation step: for each test sample in a fixed dictionary set Calculating the predicted output with weighted coefficients And calculate the mean square error of the test. :
[0024] In the formula, The total number of test samples, For the first The target output value for each test sample This corresponds to the predicted output.
[0025] Secondly, this embodiment provides a nonlinear signal prediction system based on a sparse gated kernel, characterized in that it includes: The input vector construction module is used to acquire and discretize nonlinear system signals, and construct the input vector x based on time delay embedding; the parameter and dictionary management module is used to set the kernel width. Learning rate Gating adjustment parameters and threshold and initialize and maintain the dictionary set. And a set of weight coefficients; a kernel similarity calculation module, used to calculate the similarity in the dictionary set. The kernel function value is calculated in non-space time; the sparse gating weight calculation module is used to calculate the corresponding sparse gating weight based on the kernel function value, the gating adjustment parameter and the threshold; the error calculation module calculates the prediction error and updates the weight coefficients based on the target output value of the current sample and the prediction output.
[0026] The beneficial effects of the technical solution provided by the embodiments of the present invention are as follows: The sparse gating mechanism in the present invention solves the problems of dictionary expansion and computational complexity encountered by the traditional KLMS algorithm when dealing with complex nonlinear systems. By dynamically selecting samples through the gating mechanism and updating the dictionary and weight coefficients only when necessary, the computational load is significantly reduced while maintaining high-precision prediction performance, and the stability and real-time performance of the system are improved. Attached Figure Description
[0027] To more clearly illustrate the technical solution of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. Obviously, the drawings listed below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0028] Figure 1 This is a flowchart of a nonlinear signal prediction method based on sparse gated kernels in an embodiment of the present invention; Figure 2 This is a comparison chart of the running time of the method of this invention with that of traditional KLMS and LMS algorithms; Figure 3 This is a comparison chart of the prediction accuracy of the method of this invention with that of traditional KLMS and LMS algorithms; Figure 4These are curves showing the mean square error (MSE) of each algorithm over time during the simulation verification test phase with additive white Gaussian noise added. Figure 5 These are curves showing the mean square error (MSE) of each algorithm over time during the simulation verification test phase with added chaotic noise. Figure 6 The change in the size of the dictionary set over time during the operation of this invention. Detailed Implementation
[0029] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. Of course, the specific embodiments described herein are merely illustrative and not intended to limit the invention.
[0030] Example 1: See Figure 1 This application provides a nonlinear signal prediction method based on sparse gated kernels, characterized by comprising: S1. Acquire the nonlinear system signal to be predicted, and discretize the continuous signal according to a preset sampling period to obtain a sampling point sequence. To adapt to adaptive filtering, combine the current sampling point signal value and its signal values at several past times into an input vector based on the time delay. ; The input vector is composed of the current sample value and its previous values. It consists of historical sample values, satisfying:
[0031] in, It is a sequence of sampling points. This represents the embedding length corresponding to the time delay.
[0032] This input vector can be dynamically adjusted according to the actual industrial process to ensure adaptation to different signal characteristics. S2, Set the kernel width of the kernel function. Learning rate Gating adjustment parameters and gating threshold And initialize the dictionary set. With the set of weight coefficients; nuclear width ( The smoothness of the kernel function determines the sensitivity of similarity calculation.
[0033] Learning rate ( ): Adjust the step size of weight updates to ensure the convergence of the algorithm.
[0034] Gating adjustment parameters ( ): Used to adjust the activation sensitivity of the sparse gated weight function.
[0035] Gating threshold ( ): Used to determine whether to add the current sample to the dictionary set.
[0036] The dictionary set is used to store the selected input vector samples, and the weight coefficient set is used to store the weight coefficients corresponding to the dictionary samples. S3. For each input vector sample, if the dictionary set is not empty, calculate the kernel function value between the input vector and each dictionary sample in the dictionary set; The kernel function is a Gaussian kernel function:
[0037] In the formula, For kernel width, S4. Based on the kernel function value, the gating adjustment parameter, and the gating threshold, calculate the corresponding sparse gating weights; The sparse gated weights are generated by a gated weight function, which is at least related to the kernel function value. The gate control adjustment parameters and the gate threshold Related, and satisfying: when the kernel function value is below the gate threshold When the kernel value is higher than the gate threshold, the corresponding sparse gating weights decrease or become zero; when the kernel value is higher than the gate threshold... When the value is zero, the corresponding sparse gating weight is non-zero.
[0038] The gating weight function is:
[0039] In the formula, For gating adjustment parameters, The threshold value is used for gate control. This is the kernel function value.
[0040] The contribution of dictionary samples with low kernel similarity is suppressed, so that the predicted output is dominated by dictionary samples that are highly relevant to the current input. This gating mechanism can reduce the interference of low-relevance samples on the output, improve the stability of the model output, and reduce the number of samples that effectively contribute in actual implementation, thereby further improving computational efficiency. S5. Calculate the predicted output of the current input vector based on the kernel function value, the sparse gating weights, and the set of weight coefficients; Based on the kernel function value sparse gating weights The predicted output is calculated using the set of weighted coefficients.
[0041] In the formula, For dictionary samples The corresponding weighting coefficients.
[0042] Based on the target output value of the current sample With predicted output Calculate prediction error When the prediction error Meets the preset error threshold Conditions ( ), the current input vector Add to dictionary collection And based on the prediction error With learning rate Update the weighting coefficients; when the prediction error does not meet the preset error threshold. Conditions ( ), do not use the current input vector Add to dictionary collection Based solely on prediction error With learning rate Update the weighting coefficients.
[0043] By setting an error threshold as the trigger condition for dictionary updates, the current sample is only added to the dictionary when the prediction error reaches a certain level. This mechanism reduces the probability of redundant samples entering the dictionary and avoids the dictionary size from growing unconstrainedly over time. As a result, the computational and storage overhead of long-term online operation is significantly reduced, and the real-time performance and sustainable operation capabilities are improved.
[0044] The updated weighting coefficients are:
[0045] S6. Calculate the prediction error and update the weight coefficients based on the target output value of the current sample and the predicted output.
[0046] It also includes a test evaluation step: for each test sample, in a fixed dictionary set Calculating the predicted output with weighted coefficients And calculate the mean square error of the test. :
[0047] In the formula, The total number of test samples, For the first The target output value for each test sample This corresponds to the predicted output.
[0048] Example 2: See Figures 2-5Based on Example 1, comparative data of the method of the present invention with traditional KLMS and LMS algorithms are provided.
[0049] Figure 2 The horizontal axis represents the algorithm name, and the vertical axis represents the algorithm running time (seconds). As can be seen from the figure, the computational complexity of the traditional KLMS algorithm increases significantly over time due to the continuous growth of the dictionary size. However, this invention effectively limits the number of dictionary samples participating in the calculation by introducing a sparse gating mechanism, thereby significantly slowing down the overall growth trend of running time.
[0050] Figure 3 The horizontal axis represents time, and the vertical axis represents signal amplitude. The graph typically includes the actual signal curve and the predicted output curves of each algorithm. As can be observed from the graph, the predicted output curve of the method of this invention achieves a similar degree of fit to KLMS while having a shorter running time and lower cost. This graph verifies the advantages of this invention in nonlinear modeling.
[0051] Figure 4 and Figure 5 The figure shows the mean squared error (MSE) of each algorithm over time during simulation verification tests under additive white Gaussian noise and chaotic noise environments. The horizontal axis represents the number of iterations, and the vertical axis represents the magnitude of the MSE. This figure is used to measure the convergence performance and stability of the algorithms. As can be seen from the figure, the MSE of the method of this invention decreases rapidly and converges to a low level in a short time, indicating its fast learning ability; at the same time, its steady-state error is low and has small fluctuations, indicating good stability. In contrast, traditional methods may suffer from slow convergence speed or high steady-state error.
[0052] Figure 6 The diagram illustrates how the dictionary size changes over time during algorithm execution. For traditional KLMS algorithms, the dictionary size typically grows linearly with increasing input samples, leading to a continuously increasing storage and computational burden. This invention, however, introduces a dual constraint mechanism based on gating thresholds and error criteria, adding new samples to the dictionary only when necessary, thus effectively suppressing dictionary size growth.
[0053] Example 3: This embodiment provides a nonlinear signal prediction system based on sparse gated kernels, characterized in that it includes: The input vector construction module is used to acquire and discretize nonlinear system signals, and construct input vectors based on time delay embedding. The parameter and dictionary management module is used to set the kernel width. Learning rate Gating adjustment parameters and threshold and initialize and maintain the dictionary set. And a set of weight coefficients; a kernel similarity calculation module, used to calculate the similarity in the dictionary set. The kernel function value is calculated in non-space time; the sparse gating weight calculation module is used to calculate the corresponding sparse gating weight based on the kernel function value, the gating adjustment parameter and the threshold; the error calculation module calculates the prediction error and updates the weight coefficients based on the target output value of the current sample and the prediction output.
[0054] For the specific functions of each module, please refer to the relevant descriptions in the above method embodiments, which will not be repeated here.
[0055] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.
Claims
1. A nonlinear signal prediction method based on sparse gated kernels, characterized in that, include: S1. Acquire the nonlinear system signal to be predicted, discretize the continuous signal according to the preset sampling period to obtain the sampling point sequence, and combine the current sampling point signal value and the signal values of several past moments into an input vector based on the time delay; S2. Set the kernel width, learning rate, gating adjustment parameters and gating threshold of the kernel function and initialize the dictionary set and weight coefficient set; S3. For each input vector sample, if the dictionary set is not empty, calculate the kernel function value between the input vector and each dictionary sample in the dictionary set; S4. Based on the kernel function value, the gating adjustment parameter and the gating threshold, calculate the corresponding sparse gating weight; S5. Calculate the predicted output of the current input vector based on the kernel function value, the sparse gating weights, and the set of weight coefficients; S6. Calculate the prediction error and update the weight coefficients based on the target output value of the current sample and the predicted output.
2. The nonlinear signal prediction method according to claim 1, characterized in that, The input vector is composed of the current sample value and its previous values. Composed of historical sample values, satisfying: in, No. The input vector at time t, It is a sequence of sampling points. This represents the embedding length corresponding to the time delay.
3. The nonlinear signal prediction method according to claim 1, characterized in that, The kernel function is a Gaussian kernel function: In the formula, For kernel width, A dictionary sample from the dictionary set. This is the kernel function value.
4. The nonlinear signal prediction method according to claim 1, characterized in that, The sparse gating weights are generated by a gating weight function, which is related to at least the kernel function value, the gating adjustment parameter, and the gating threshold, and satisfies the following: when the kernel function value is lower than the gating threshold, the corresponding sparse gating weight is reduced or becomes zero; when the kernel function value is higher than the gating threshold, the corresponding sparse gating weight is a non-zero value.
5. The nonlinear signal prediction method according to claim 4, characterized in that, The gating weight function is: In the formula, For gating adjustment parameters, The threshold value is used for gate control. For kernel function values, For sparse gating weights.
6. The nonlinear signal prediction method according to claim 5, characterized in that, The predicted output is calculated based on the kernel function value, sparse gating weights, and the set of weight coefficients. In the formula, For dictionary samples The corresponding weighting coefficients.
7. The nonlinear signal prediction method according to claim 6, characterized in that, The prediction error is calculated based on the target output value and the predicted output of the current sample. When the prediction error meets the preset error threshold condition, the current input vector is added to the dictionary set, and the weight coefficients are updated based on the prediction error and the learning rate. When the prediction error does not meet the preset error threshold condition, the current input vector is not added to the dictionary set, and the weight coefficients are updated only based on the prediction error and the learning rate.
8. The nonlinear signal prediction method according to claim 7, characterized in that, The updated weighting coefficients are: In the formula, For the first The prediction error at any given time.
9. The nonlinear signal prediction method according to claim 8, characterized in that, It also includes a test evaluation step: calculating the predicted output for each test sample with a fixed dictionary set and weighting coefficients, and calculating the test mean squared error. : In the formula, The total number of test samples, For the first The target output value for each test sample This corresponds to the predicted output.
10. A nonlinear signal prediction system based on sparse gated kernels, characterized in that, include: The input vector construction module is used to acquire and discretize nonlinear system signals, and construct input vectors based on time delay embedding. The parameter and dictionary management module is used to set the kernel width, learning rate, gating adjustment parameters and gating threshold, and to initialize and maintain the dictionary set and weight coefficient set. The kernel similarity calculation module is used to calculate the kernel function value when the dictionary set is not empty; The sparse gating weight calculation module is used to calculate the corresponding sparse gating weight based on the kernel function value, the gating adjustment parameter, and the gating threshold. The error calculation module calculates the prediction error and updates the weight coefficients based on the target output value of the current sample and the predicted output.