Meta-learning (MAML) for FxLMS Initialization

버전 1.0.1 (2.51 MB) 작성자: DONGYUAN SHI
It realizes the modified Model-Agnostic Meta-Learning to accelerate the convergence of the FxLMS algorithm in the adaptive ANC system.
다운로드 수: 16
업데이트 날짜: 2024/2/23

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The program implements a modified Model-Agnostic Meta-learning (MAML) algorithm in Matlab. This modified MAML algorithm takes the forgetting factor to alleviate the initial-zero-input issue of the adaptive filters. This work uses the proposed method to seek the best initial control filter for the adaptive active noise control system based on its noise dataset. With barely any additional computations, the modified MAML algorithm can assist the filtered reference square (FxLMS) algorithm in achieving fast convergence. The numerical simulation demonstrates that the FxLMS algorithm with the MAML initialization converges much faster than that with normal zero initialization when dealing with raw aircraft noise, as shown in Figure S3.
Figure S3: Aircraft noise reduction performance of the FxLMS algorithms with zero and MAML initializations.
The measured primary and secondary paths are available on GitHub. It also gives a detailed introduction to the code of the Meta-Learning algorithm. The reference paper is "Fast adaptive active noise control based on Modified model-agnostic meta-learning algorithm."
Code Explanation
  • Main_tst_function.m: the main function is utilized to test the proposed modified MAML algorithm.
  • MAML_Nstep_forget.m: the matlab code of the modified MAML algorithm.
  • FxLMS.m: the matlab code of the FxLMS algorithm.
  • 707_Sound_for_Simulation.mat: the raw data of an aircrat noise.
  • \path: the measured primary and secondary paths.
The explanation of Main_tst_function.m
The following code snippet offers a concise overview of Main_tst_function.m, which serves as the main function for evaluating the effectiveness of the proposed MAML method. For this numerical simulation, three distinct broadband sounds are utilized to train the MAML algorithm and obtain a single initial control filter. Subsequently, the aforementioned initial control is employed within an FxLMS algorithm to effectively eliminate actual aircraft noise. In comparison to zero initialization, the MAML technique can significantly enhance the convergence speed of the conventional FxLMS approach.
Contents:
Clean the memory and worksapace
Code snippet to clean workspace and set initial conditions.
%% Clean the memory and worksapace
close all ;
clear ;
clc ;
Configure the system simulation condition
This code snippet provides the system configuration for the numerical simulation. In this program, fs and T denote the system sampling rate and the simulation duration, respectively. LenN repesents the length of the control filter.
%% Configure the system simulation condition
fs = 16000 ; % The system sampling rate.
T = 3 ; % The duration of the simulation.
t = 0:1/fs:T ;
N = length(t); % The number of the data.
Len_N = 512 ; % Seting the length of the control filter.
%<<===Progress bar===>>
f = waitbar(0,'Please wait...');
pause(.5)
Build the broad band noise for training set
This section of the program produces filtered references, disturbances, and primary noises. These are then used in the modified MAML algorithm to obtain the initial control filter. The main sounds consist of three distinct broadband noises, as depicted in Figure S1.
%% Build the broad band noise for training set
%<<===Progress bar===>>
waitbar(0.25,f,'Build the broad band noise for training set');
pause(1)
%<<===Progress bar===>>
% Loading path
load('path\P1.mat') ;
load('path\S11.mat') ;
Pri_path = conv(P1,S11);
Track_num = 3 ; % Seting the number of the track for the trainning noise.
if exist('Primary_noise.mat', 'file') == 2
disp('Primary_noise exists in the current path.\n');
% Loading the primary noise
load('Primary_noise.mat');
load('Disturbance.mat') ;
load('Reference.mat') ;
else
Noise = randn(N,1);
% filter
filter_1 = fir1(512,[0.05 0.25]);
filter_2 = fir1(512,[0.20 0.55]) ;
filter_3 = fir1(512,[0.5,0.75]) ;
% Primary noise
Pri_1 = filter(filter_1,1,Noise) ;
Pri_2 = filter(filter_2,1,Noise) ;
Pri_3 = filter(filter_3,1,Noise) ;
% Drawing fiture
data = [Pri_1,Pri_2,Pri_3];
figure ;
len_fft = length(Pri_1) ;
len_hal = round(len_fft/2);
title('Frequency spectrum of primary noises')
for ii = 1:3
freq = 20*log(abs(fft(data(:,ii))));
subplot(3,1,ii);
plot(0:(fs/len_fft):(len_hal-1)*(fs/len_fft), freq(1:len_hal));
grid on ;
title("The "+num2str(ii)+"th primary noise")
xlabel('Frequency (Hz)')
end
% Save primary noise into workspace
save('Primary_noise.mat','Pri_1','Pri_2','Pri_3');
% Generating Distrubance
Dis_1 = filter(Pri_path,1,Pri_1);
Dis_2 = filter(Pri_path,1,Pri_2);
Dis_3 = filter(Pri_path,1,Pri_3);
% Save distrubancec into workspace
save('Disturbance.mat','Dis_1','Dis_2','Dis_3');
% Genrating Filtered reference signal
Rf_1 = filter(S11,1,Pri_1);
Rf_2 = filter(S11,1,Pri_2);
Rf_3 = filter(S11,1,Pri_3);
% Save filter reference signal into workspace
save('Reference.mat','Rf_1','Rf_2','Rf_3');
end
Figure S1: The frequency spectrum of the primary noises for the MAML algorithm.
Randomly sampling the noise tracks to build dataset for the MAML algorithm
This part of the program randomly samples the previously generated three types of noise tracks and their corresponding reference signals and disturbances to form the dataset. The length of the sampled vector equals that of the control filter, and these samples will be used in the proposed MAML algorithm to get the best initial control filter.
%% Radomly sampling the noise tracks to build dataset for the MAML algorithm
%<<===Progress bar===>>
waitbar(0.5,f,'Radomly sampling the noise tracks to build dataset for the MAML algorithm');
pause(1)
%<<===Progress bar===>>
if exist('Sampe_data_N_set.mat', 'file') == 2
disp('Sampe_data_N_set in the current path.\n');
load('Sampe_data_N_set.mat');
else
N_epcho = 4096 * 80 ; % Setting the number of the epcho
Trac = randi(Track_num,[N_epcho,1]); % Randomly choosing the different tracks.
Len_data = length(Dis_1) ;
% Seting the N steps
len = 2*Len_N -1 ;
Fx_data = zeros(Len_N,N_epcho);
Di_data = zeros(Len_N,N_epcho);
Ref_data = [Rf_1,Rf_2,Rf_3] ;
Dis_data = [Dis_1,Dis_2,Dis_3];
for jj = 1:N_epcho
End = randi([len,Len_data]);
Di_data(:,jj) = Dis_data(End-511:End,Trac(jj));
Fx_data(:,jj) = Ref_data(End-511:End,Trac(jj));
end
save('Sampe_data_N_set.mat','Di_data','Fx_data');
end
Using Modified MAML algorithm to get the best initial control filter
This segment of the program applies the proposed modified MAML algorithm to compute the best initial control filter for the conventional FxLMS algorithm. The step size of the FxLMS algorithm, the learning rate of the MAML algorithm, and the forgetting factor are set to $0.003$, $0.5$, and $0.99$, respectively. Figure S2 illustrates the proposed MAML algorithm's learning curve and demonstrates the proposed algorithm's convergence.
%<<===Progress bar===>>
waitbar(0.75,f,'Using Modified MAML algorithm to get the best initial control filter');
pause(1)
%<<===Progress bar===>>
if exist('Weigth_initiate_Nstep_forget.mat', 'file') == 2
disp('Weigth_initiate_Nstep_forget in the current path.\n');
load('Weigth_initiate_Nstep_forget.mat');
else
% Create a MAML algorithm
a = MAML_Nstep_forget(Len_N);
N = size(Di_data,2) ; % The number of the sample in training set.
Er = zeros(N,1) ; % Residual error vector
% Seting the step size for the embeded FxLMS algorithm
mu = 0.0003 ;
% Seting the forget factor
lamda = 0.99 ;
% Seting the learning for MAML
epslon = 0.5 ;
% Runing the MAML algorithm
for jj = 1:N
[a, Er(jj)] = a.MAML_initial(Fx_data(:,jj),Di_data(:,jj),mu,lamda,epslon);
end
% Drawing the residual error of the Modified MAML algorihtm
figure ;
plot(Er) ;
grid on ;
title('Leanring curve of the modified MAML algorithm');
xlabel('Epoch');
ylabel('Residual error');
% Getting the optimal intial control filter
Wc = a.Phi ;
% Saving the best initial control filter into workspace
save('Weigth_initiate_Nstep_forget.mat','Wc');
end
Figure S2: The learning curve of the modified MAML algorithm.
Testing aircraft noise cancellation by using MAML initial control filter
The program employs the FxLMS algorithms, utilizing zero initialization and MAML initialization, to reduce the impact of aircraft noise. Figure S3 illustrates the error signal produced by the FxLMS algorithm during both the on and off states. It has been observed that the utilization of MAML initialization significantly enhances the convergence rate of the adaptive algorithm in comparison to the conventional zero initialization approach.
%% Testing aircraft noise cancellation by using MAML initial control filter
%<<===Progress bar===>>
waitbar(0.95,f,'Testing aircraft noise cancellation by using MAML initial control filter');
pause(1)
%<<===Progress bar===>>
% Loading aricrat noise data
aircrat = load('707_Sound_for_Simulation.mat');
% Building primary noise
Pri_1 = aircrat.PilingNoise(1:153945) ;
% Generating the disturbacne
Dis_1 = filter(Pri_path,1,Pri_1) ;
% Generating the filter reference
Rf_1 = filter(S11,1,Pri_1) ;
% Runging the FxLMS with the zero-initialization control filter
Wc_initial = zeros(Len_N,1);
muw = 0.00001 ; % Step size of All FxLMS algorithms.
Er = FxLMS(Len_N, Wc_initial, Dis_1, Rf_1, muw);
% Runging the FxLMS with the MAML-initialization control filter
Wc_initial = Wc;
Er1 = FxLMS(Len_N, Wc_initial, Dis_1, Rf_1, muw);
figure
% Drawing the figures of the MAML and FxLMS
plot((0:length(Dis_1)-1)*(1/fs),Dis_1,(0:length(Er)-1)*(1/fs),Er,(0:length(Er1)-1)*(1/fs),Er1);
title('Aircraft noise cancellation')
xlabel('Time (seconds)')
ylabel('Error signal')
legend({'ANC off','FxLMS with zero-initialization','FxLMS with MAML-initialization'})
grid on;
%<<===Progress bar===>>
waitbar(1,f,'Finishing');
pause(1)
%<<===Progress bar===>>
%-------------------------------end----------------------------------------
Figure S3: Aircraft noise reduction performance of the FxLMS algorithms with the zero and MAML initializations.
Summray
The document provides a detailed introduction to implementing a modified Model-Agnostic Meta-learning (MAML) algorithm in Matlab. This modified MAML algorithm takes the forgetting factor to alleviate the initial-zero-input issue of the adaptive filters. This work uses the proposed method to seek the best initial control filter for the adaptive active noise control system based on its noise dataset. With barely additional computations, the modified MAML algorithm can assist the filtered reference square (FxLMS) algorithm in achieving fast convergence. The numerical simulation demonstrates that the FxLMS algorithm with the MAML initialization converges much faster than that with normal zero initialization when dealing with raw aircraft noise.

인용 양식

DONGYUAN SHI (2024). Meta-learning (MAML) for FxLMS Initialization (https://www.mathworks.com/matlabcentral/fileexchange/160018-meta-learning-maml-for-fxlms-initialization), MATLAB Central File Exchange. 검색됨 .

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