A fast-converging adaptive active control method

Abstract

This invention discloses a fast-converging adaptive active control method, which includes the following steps: 1) For the sub-band signal f(n) after wavelet packet decomposition, f(n) is used as the continuous input reference signal in the time domain of the adaptive active control system; 2) The reference signal f(n) is divided into blocks; 3) The two cascaded data blocks are subjected to a 2L-point FHT transform to convert them to the Hartley domain signal F. H (k), according to F H (k) Construct an even function F He (k) and odd function F Ho (k) is used as the input signal to the Hartley domain filter; the input signal and the frequency domain control weight vector are subjected to butterfly filtering to obtain the frequency domain control output signal y. H (k), the time-domain control output signal y(n); and the Hartley domain error signal e are obtained. H (k); Calculate the weight coefficient correction term in the time domain; After padding the correction term with zeros, perform a 2L-point FHT transform, which, together with the iteration step size, completes the update of the Hartley domain control weight coefficients. Continuously updating the control weight coefficients effectively controls the error signal. The method of this invention can improve the convergence speed.

Description

Technical Field

[0001] The invention belongs to the technical field of adaptive control, and in particular relates to a fast convergence adaptive active control method. Background Art

[0002] The most widely used adaptive control algorithm is the feedforward filtered reference signal least mean square (filtered-x least-mean-square, FxLMS) algorithm that takes the secondary channel into account. It is a combination of the finite impulse response (FIR) filter and the least mean square (LMS) algorithm. The algorithm has a simple structure, is easy to implement, and has strong stability. However, in the actual mechanical equipment rotating line spectrum adaptive control system, there are still the following technical problems: 1) The secondary channel has a strong nonlinearity and is difficult to accurately identify, or the identification model is too complex, which is not conducive to the implementation of the control algorithm; 2) There are multiple line spectra that need to be controlled in the 20-200Hz frequency band, and the eigenvalues ​​of the autocorrelation function matrix of the reference signal are relatively scattered. The ordinary FxLMS algorithm is only effective for the 1 to 2 line spectra with the strongest vibration; the vibration source frequency fluctuates violently in a small range, and the ordinary narrowband filter is difficult to meet the control needs. Once the vibration source frequency is inconsistent with the center frequency of the narrowband filter, the filtered line spectrum signal is distorted;

[0003] In view of the multi-line spectrum excitation with violent frequency fluctuations, a wavelet packet adaptive control algorithm is proposed to decompose the reference signal into different band frequency signals and adopt a parallel control strategy. The introduction of wavelet packets in the control system is equivalent to data preprocessing of the reference signal and the error signal, dividing the signal into sub-bands with different frequencies and retaining the time-frequency details of the signal, which has a good control effect on the frequency fluctuation line spectrum. However, when the control filter weight coefficient is updated, the data is still a single sample value, which involves a large number of convolution and multiplication operations, and the convergence rate needs to be further improved. Summary of the invention

[0004] The main purpose of the present invention is to provide a fast convergence adaptive active control method to address the deficiencies in the prior art.

[0005] The technical solution adopted by the present invention is:

[0006] A fast convergence adaptive active control method comprises the following steps:

[0007] 1) For the sub-band signal f(n) after wavelet packet decomposition, f(n) is used as the continuous input reference signal in the time domain of the adaptive active control system;

[0008] 2) The reference signal f(n) is processed in blocks, and the length of the data block is L, which is consistent with the filter length;

[0009] 3) Perform a 2L-point FHT transformation on the two concatenated data blocks and convert them into Hartley domain signals F H (k), according to F H (k) Construct an even function F He (k) and the odd function F Ho (k), as the input signal of the Hartley domain filter; where k is the sequence number of the data block;

[0010] 4) Convert the input signal to an even function F He (k) and the odd function F Ho (k) performs butterfly filtering operation with the frequency domain control weight vector to obtain the frequency domain control output signal y H (k), frequency domain control output signal y H (k) Perform IFHT transformation and take the last L points as the control output signal y(n) in the time domain;

[0011] 5) After the control output y(n) in the time domain is offset by the desired signal d(n) through the physical secondary channel, the error signal e(n) is obtained. The leading zero is padded to make its length 2L, and the FHT transformation of 2L points is performed to obtain the Hartley domain error signal e H (k);

[0012] 6) Perform secondary channel filtering on the reference signal f(n) to obtain a time domain filtering reference signal Block processing, level ^^

[0013] After the connection, perform FHT transformation of 2L points to construct and With the error signal e H (k) and e H (2L-k) performs butterfly operation to obtain the frequency domain weight vector correction term, which is converted into the time domain through IFHT, and the first L points are taken as the weight coefficient correction term in the time domain;

[0014] 7) After filling the correction term with zero, perform FHT transformation of 2L points, and complete the update of Hartley domain control weight coefficient together with the iteration step size. The updated value is used as the next data block input during step 3), and the control weight coefficient is continuously updated to effectively control the error signal.

[0015] According to the above scheme, in step 3), the two cascaded data blocks are subjected to a 2L-point FHT transformation to convert them into a Hartley domain signal F H (k) as follows:

[0016]

[0017] According to the above scheme, in step 3), according to F H (k) Construct an even function F He (k) and the odd function F Ho (k) are as follows:

[0018] F He (k)=(F H (k)+F H (-k)) / 2;

[0019] F Ho (k)=(F H (k)-F H (-k)) / 2.

[0020] The beneficial effects produced by the present invention are:

[0021] The method of the present invention effectively solves the problem of complex and difficult data calculation when updating the weight coefficients of the control filter in the sub-band after multi-frequency line spectrum division, and can realize fast convolution and correlation operations in the frequency domain, thereby improving the convergence speed of the main control link, and providing technical support for the functional realization of the active vibration isolation system of ship equipment. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 is a flow chart of a control method according to an embodiment of the present invention;

[0023] Figure 2 A schematic diagram of a butterfly filter operation unit according to an embodiment of the present invention;

[0024] Figure 3 4 is a comparison chart of the number of multiplications of various algorithms in the embodiments of the present invention. DETAILED DESCRIPTION

[0025] The applicant will further explain the present invention in detail below in conjunction with specific embodiments so that those skilled in the art can more clearly understand the present invention. However, the following content should not be construed as limiting the scope of protection of the claims of the present invention.

[0026] The present invention adopts the block LMS algorithm so that the filter is self-adapted block by block. The filter output signal is the linear convolution of the reference signal and the weight coefficient, and the weight coefficient correction term is the linear correlation between the filter reference signal and the error signal. The key problem of the block LMS algorithm lies in the specific implementation of fast convolution and linear correlation operations. Hartley transform uses real numbers as the transformation kernel and is a unitary transform. Signal processing can be completed only in the real number domain. Fast operations such as convolution and correlation can be realized based on the fast Hartley transform (FHT), and the block LMS (HBFxLMS) filtering algorithm is completed in the transform domain.

[0027] like Figure 1 , a fast convergence adaptive active control method, comprising the following steps:

[0028] 1) For the sub-band signal f(n) after wavelet packet decomposition, f(n) is used as the continuous input reference signal in the time domain of the adaptive active control system;

[0029] For the sub-band signal f(n) after wavelet packet decomposition, the control weight coefficient does not change during the data block input period, and it is only iterated and updated when the data block input is completed, replacing the instantaneous estimate with the unbiased time average of the input data. The iteration step size can be set to

[0030]

[0031] 2) f(n) is processed in blocks, and the block data length is L, which is consistent with the filter length;

[0032] 3) Cascade two data blocks to perform 2L-point FHT transformation to convert the time domain data into Hartley domain signal F H (k), according to F H (k) Construct an even function F He (k) and the odd function F Ho (k), as the input signal of the Hartley domain filter;

[0033] Use FHT to implement fast convolution of real number sequences, which is specifically expressed as

[0034]

[0035] Among them, X 1H (k), X 2H (k) are the DHT transformations of the real number sequences x1(n) and x2(n), respectively, and

[0036]

[0037] Similarly, the cross-correlation operation implemented by FHT can be expressed as

[0038]

[0039] The input data is transformed into two consecutive sub-blocks, a diagonal matrix of type 2L×2L, and the FHT transformation is performed on it to obtain

[0040] F He (k), F Ho (k) are respectively H (k) The constructed even and odd functions can be specifically expressed as: F He(k)=(F H (k)+F H (-k)) / 2,F Ho (k)=(F H (k)-F H (-k)) / 2.

[0041] 4) Even function F He (k) and the odd function F Ho (k) Through butterfly filtering operation, the control output signal y is obtained H (k), perform IFHT transformation on it, and take the last L points as the control output signal y(n) in the time domain;

[0042] Butterfly filter operation unit such as Figure 2 ;

[0043] y H (k)=FHT[y(kL-L),y(kL-L+1),...y(kL+L-1)] T

[0044] =F He (k)W H (k)+F Ho (k)W H (2L-k)

[0045] In the formula, F He (k)=(F H (k)+F H (2L-k)) / 2,F Ho (k)=(F H (k)-F H (2L-k)) / 2.

[0046] Perform an inverse transform and take the values ​​of the last L points as the output vector of the Kth block of input data, that is,

[0047] y(n)=[y(kL),y(kL+1),...y(kL+L-1)] T =IFHT[y H (k)]

[0048] The last L elements of .

[0049] 5) After the time domain control signal y(n) passes through the physical secondary channel and cancels out the desired signal d(n), an error signal e(n) is generated. The leading zero is padded to make its length 2L, and a 2L-point FHT transformation is performed to obtain the Hartley domain error signal e H (k);

[0050]

[0051] 6) Perform secondary channel filtering on the reference signal f(n) to obtain a time domain filtering reference signal Block processing is performed on it, and after cascading, the FHT transformation of 2L points is performed to construct and With the error signal e H (k) and e H (2L-k) performs butterfly operation to obtain the frequency domain weight vector correction term, which is converted into a time domain signal through IFHT, and the first L points are taken as the weight coefficient correction term in the time domain;

[0052]

[0053] The first L elements of are used as the time domain correction terms of the control weight coefficient, with a length of L.

[0054] 7) After filling the correction term with zero, perform FHT transformation of 2L points, and complete the update of Hartley domain control weight coefficient together with the iteration step. The updated value is used as the input of the next data block in step (3), and the control weight coefficient is continuously updated to effectively control the error signal.

[0055] The time domain correction term ΔW(k) is padded with zeros to make its total length 2L, and the FHT transformation of 2L points is performed. At this time, the Hartley domain expression of the weight vector update is:

[0056]

[0057] Convergence characteristics analysis:

[0058] The fundamental difference between the block LMS algorithm and the traditional LMS algorithm lies in the different estimation methods of the gradient vector during the iteration process. The block algorithm uses the unbiased time-averaged gradient vector, and the estimation accuracy increases with the increase of the data block length. Assume that the convergence step size of the block algorithm is u B , the step length of the traditional algorithm is u, and the convergence condition of the block algorithm is obtained by convergence analysis:

[0059]

[0060] λ max is the maximum eigenvalue of the autocorrelation matrix R. The number of iterations required to reach convergence is

[0061]

[0062] The step size parameter u of the block algorithm B =Lu Substituting into the above formula, we can get

[0063]

[0064] It can be seen that the convergence rate of the block algorithm is basically the same as that of the basic LMS algorithm, except that the effective step size is increased by L times.

[0065] Computational complexity:

[0066] The computational complexity of the Hartley domain FHT block LMS algorithm (HBFxLMS), the frequency domain FFT block LMS algorithm (FBFxLMS) and the traditional algorithm in the time domain (FxLMS) are compared. The analysis is based on the multiplication operations involved in the algorithm.

[0067] The filter length is set to L. For FxLMS, ​​the number of multiplications required to update the weight vector and output the control signal is 2L. 2 ; For the FBFxLMS algorithm, the number of multiplications required for the N-point FFT (IFFT) is approximately Nlog2N, N = 2L, and 6 frequency transformations are required. The formula for FFT to achieve fast convolution and linear correlation is

[0068]

[0069]

[0070] X1(k) and X2(k) are both complex numbers. Convolution and correlation operations require 4N multiplications. The total number of multiplications for the frequency domain FFT block algorithm is

[0071] M FFT =6*N log2 N+8N

[0072] =12L log2 L+28L

[0073] For the HBFxLMS algorithm, the number of multiplications required for N-point FHT (IFHT) is approximately 6 frequency transformations. The FHT transformation is performed in the real number domain. Only 2N multiplications are required to implement convolution and correlation operations. The total number of multiplications is

[0074]

[0075] The filter lengths are set to 64, 128, 200, 256, and 512 orders respectively. The complexity trends of the three algorithms are as follows: Figure 3 The specific values ​​are shown in Table 1.

[0076] Table 1. Operation amount under different points

[0077]

[0078] The transform domain block algorithm can greatly reduce the complexity of the algorithm, and its advantages become more obvious as the number of points increases. The HBFxLMS algorithm does not involve complex operations, and the amount of calculation in each adaptive cycle is less than that of the FBFxLMS algorithm. When L = 256, the amount of calculation of the FBFxLMS algorithm is 31744, and the amount of calculation of the HBFxLMS algorithm is 11276, which is about 1 / 3 of that of the FBFxLMS algorithm. It can be seen that the performance of the HBFxLMS algorithm is better than that of the FBFxLMS algorithm, and it can be better applied in engineering practice.

[0079] The above embodiments are only for illustrating the technical concept and features of the present invention, and their purpose is to enable people familiar with the technology to understand the content of the present invention and implement it accordingly, and they cannot be used to limit the protection scope of the present invention. Any equivalent changes or modifications made according to the spirit of the present invention should be included in the protection scope of the present invention.

Claims

1. A fast convergence adaptive active control method, characterized in that: The steps include: 1) For the sub-band signal f(n) after wavelet packet decomposition, f(n) is used as the continuous input reference signal in the time domain of the adaptive active control system; 2) The reference signal f(n) is processed in blocks, and the length of the data block is L, which is consistent with the filter length; 3) Perform a 2L-point FHT transformation on the two concatenated data blocks and convert them into Hartley domain signals F H (k), according to F H (k) Construct an even function F He (k) and the odd function F Ho (k), as the input signal of the Hartley domain filter; 4) Convert the input signal to an even function F He (k) and the odd function F Ho (k) performs butterfly filtering operation with the frequency domain control weight vector to obtain the frequency domain control output signal y H (k), frequency domain control output signal y H (k) Perform IFHT transformation and take the last L points as the control output signal y(n) in the time domain; 5) After the control output y(n) in the time domain is offset by the desired signal d(n) through the physical secondary channel, the error signal e(n) is obtained. The leading zero is padded to make its length 2L, and the FHT transformation of 2L points is performed to obtain the Hartley domain error signal e H (k); 6) Perform secondary channel filtering on the reference signal f(n) to obtain a time domain filtering reference signal Block processing is performed on it, and after cascading, the FHT transformation of 2L points is performed to construct and With the error signal e H (k) and e H (2L-k) performs butterfly operation to obtain the frequency domain weight vector correction term, which is converted into the time domain through IFHT, and the first L points are taken as the weight coefficient correction term in the time domain; 7) After filling the correction term with zero, a 2L-point FHT transformation is performed, which together with the iterative step size completes the update of the Hartley domain control weight coefficient. The updated value is used as the Hartley domain control weight coefficient during the next data block input period. The control weight coefficient is continuously updated to effectively control the error signal.

2. The fast convergence adaptive active control method according to claim 1, characterized in that: In step 3), the two concatenated data blocks are transformed into a Hartley domain signal F by performing a 2L-point FHT transformation. H (k) as follows:

3. The fast convergence adaptive active control method according to claim 1, characterized in that: In step 3), according to F H (k) Construct an even function F He (k) and the odd function F Ho (k) are as follows: F He (k)=(F H (k)+F H (-k)) / 2; F Ho (k)=(F H (k)-F H (-k)) / 2。

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