CN113362853B - EMD endpoint effect suppression method based on LSTM network - Google Patents

EMD endpoint effect suppression method based on LSTM network Download PDF

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CN113362853B
CN113362853B CN202010139218.0A CN202010139218A CN113362853B CN 113362853 B CN113362853 B CN 113362853B CN 202010139218 A CN202010139218 A CN 202010139218A CN 113362853 B CN113362853 B CN 113362853B
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刘福来
胡忠意
杜瑞燕
张艾怡
黄彩梅
徐嘉良
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Northeastern University Qinhuangdao Branch
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Abstract

The invention belongs to the technical field of signal processing, and particularly relates to an EMD endpoint effect suppression method based on an LSTM network. The method effectively combines the prediction of the LSTM network on the signal and the application of EMD decomposition in the single-channel blind source separation technology, and searches the time step length of the LSTM network according to the characteristics of the signal, thereby effectively improving the prediction precision, effectively solving the problem of end effect of the EMD method in the single-channel blind source separation, and obtaining better effect on solving the problem of sound separation in the complex factory environment. The method can effectively solve the problem of end effect in nonlinear non-stationary time sequence analysis, and can be applied to the separation of single-channel blind source mixed signals.

Description

EMD endpoint effect suppression method based on LSTM network
Technical Field
The invention belongs to the technical field of signal processing, and particularly relates to an EMD endpoint effect suppression method based on an LSTM network.
Background
The blind source separation technique refers to a process of separating each source signal only using an observation signal according to the statistical characteristics of the source signal under the condition that a transmission channel and the source signal are unknown. In fact, most of the acquired signals are single-channel signals, single-channel blind source separation is an extreme condition of underdetermined blind source separation, and multi-channel source signals are separated only by utilizing characteristic information of single-channel observation signals, so that the problem is very difficult to solve. The signal processing method for firstly performing empirical Mode decomposition on a list of time sequence data and then performing Hilbert transform on each component, which is firstly proposed by Norden E.Huang of the United states aerospace agency in 1998, decomposes signals of the time sequence into a group of Intrinsic Mode Functions (IMF) through EMD, can analyze linear steady-state signals and nonlinear and unsteady-state signals, and has a good effect on the single-channel blind source separation problem.
However, in the use of the EMD method, the end-point effect becomes a major factor affecting the accuracy of the method. There are two end effects, one is the end effect of spline interpolation in EMD decomposition; the other is the end-point effect of the eigenmode function when performing the hubert transform. The endpoint effect in cubic spline interpolation and Hilbert transform has a great influence on the EMD-based time-frequency analysis method, and the effect of the time-frequency analysis method is influenced or fails due to poor processing of the problem. Because the end effect has a great influence on the EMD, the research on the technology for weakening or eliminating the end effect in the EMD time-frequency analysis becomes a precondition and a key technology for using the method. Aiming at the problem of the empirical mode decomposition end effect, a plurality of suppression methods exist at present, and the commonly used main methods include a mirror image continuation method, a self-adaptive waveform matching method, an integral continuation method and the like. Although the methods can inhibit the end effect of empirical mode decomposition to a certain extent, the methods also have respective defects that extension prediction is not accurate enough, and the predicted extreme point has a large difference from the original extreme point. The long-short term memory network (LSTM) is a recurrent neural network which has outputs at each time step, has cyclic links between hidden units, and generates a single output after reading the whole sequence. Each unit of the LSTM has the same input and output, and there are more gating unit systems for parameter and control information flow, which have made great success in the fields of speech recognition, handwriting generation, etc., so that it has more accurate effect when applied to prediction of complex signal data. However, in the application, the LSTM network time step parameter selection has a large influence on the prediction result, so that determining the LSTM time step to improve the prediction performance of the data is a key problem for suppressing the EMD endpoint effect.
Disclosure of Invention
In order to solve the above problems in the prior art, the present invention provides an end effect suppression method for Empirical Mode Decomposition (EMD) based on long and short term memory network (LSTM), which calculates a signal period according to a frequency component of a signal, determines an LSTM time step, performs LSTM processing on the received signal according to the selected time step, extends both ends of data respectively, and obtains an optimal signal extension extreme point, so that EMD decomposition achieves a better effect, and a better effect is obtained on sound separation in a complex factory environment.
Therefore, the invention provides an EMD endpoint effect inhibition method based on an LSTM network, which comprises the following steps:
s1, estimating the signal period according to the frequency of the signal, and selecting the time step of the LSTM network;
s2, using the selected time step to process LSTM network to the received mixed signal data, extending the two ends of the data for half period, selecting extreme points in the extended data, and keeping the data between the two extreme points;
s3, performing EMD decomposition on data between the extreme points at the two ends to obtain an Intrinsic Mode Function (IMF);
s4, performing dimensionality reduction on the IMF through Principal Component Analysis (PCA) to obtain a proper IMF component, and performing Independent Component Analysis (ICA) on the IMF component to obtain a separated source signal;
and S5, separating the mixed sound in the environment of receiving the complex sound to obtain each separated sound signal so as to analyze the characteristics of the sound generated by the equipment.
Further, the step S1 calculates the signal period according to the frequency component of the signal, and selects the time step S of the LSTM network model according to the obtained period of the received mixed signal (that is, the LSTM considers that each input data is linked with how many previous successively input data), in the same model, the signal periodicity makes the data have a large influence on the prediction of the subsequent data within one period T, while the mixed sound signal is generally a periodic signal, so the time step S of the LSTM can be selected by estimating the number of sampling points of the signal period, thereby improving the prediction accuracy of the model;
further, the time step selected in step S2 is to perform LSTM processing on the discretization sequence x (N) of the received signal, first processing x (N) into an input sequence with a length S, and sequentially delaying the 1 st to nth data as a first input sequence:
(x1(n)＝[x(1),x(2),…,x(S+1)],x2(n)＝[x(2),x(3),…,(S+1)],…,xN-S(n)＝[x(N-S),x(N-S+1),…,x(N)]) Then, the sequence is used as the input of the LSTM network, the weight and the bias of the neural network are continuously updated according to the output of each time point and the difference value of x (n), and then the sequence x is usedN-S(n)＝[x(N-S),x(N-S+1),…,x(N)]Predicting the next data point to obtain x (N +1), and finally constructing a new input sequence x according to the predicted data point x (N +1)N-S+1(n)＝[x(N-S+1),x(N-S+2),…,x(N+1)]Continuously predicting data to extend to the right end for half period length to obtain x (N + S/2), obtaining the optimum signal extension extreme point from the x (N + S/2), because the LSTM network has output at each time step, the hidden units have cyclic links, but the cyclic neural network which generates single output after reading the whole sequence generates an output h at each time node in the process of reading in the x (t) data(t)The internal parameter matrix is then continuously updated by the difference with the input signal x (t), and the parameter update of LSTM cells is expressed as follows:
s2.1, internal State
Figure GDA0003646636220000031
The update can be expressed as:
Figure GDA0003646636220000032
wherein the content of the first and second substances,
Figure GDA0003646636220000033
represents a forgetting gate to control the weight of the self-loop, sigma represents that the sigmoid unit sets the weight to a value between 0 and 1,
Figure GDA0003646636220000034
denotes an external input gate, x(t)Represents the input discrete signal data, b represents the bias of LS TM cells, U represents the input weight in LSTM cells, W represents the circulating weight in LSTM cells, h(t)Represents the output of LSTM cells;
s2.2, the parameter update of the forgotten gate can be expressed as:
Figure GDA0003646636220000041
wherein h istRepresenting a forgetting gate hidden layer vector, which contains the output of the LSTM cell, bfIndicating a left behind door bias, UfInput weight, W, representing forgetting gatefA cyclic weight representing a forgetting gate, sigma representing a sigmoid cell;
s2.3, the parameter update of the input gate can be expressed as:
Figure GDA0003646636220000042
wherein, bgIndicating input gate offset, UgRepresents the input gate input weight, WgRepresenting input gate cycle weights;
s2.4, the parameter update of the output gate can be expressed as
Figure GDA0003646636220000043
Wherein, boIndicating output gate offset, WoIndicating the cyclic weight of the output gate, UoAn input weight representing an output gate;
s2.5, output h of LSTM cells(t)From the output gate
Figure GDA0003646636220000044
And cell status
Figure GDA0003646636220000045
Determine, i.e. that
Figure GDA0003646636220000046
The LSTM adopts a gating structure, so that the weight of self-circulation is determined according to the context, but is not fixed, the weight of gating self-circulation and the accumulated time scale can be dynamically changed, because the time constant is the output of the model, the mixed received signal is used for predicting the previous and subsequent data through the LSTM network, the previous and subsequent data are respectively widened to be half period, a good effect is obtained, and a proper extreme point is selected for interception for subsequent EMD decomposition.
Further, in the implementation process of the LSTM method in step S2, a proper LSTM network parameter is determined according to the selected time step, the sampled sequence is read into the neural network, the weights and biases of the input gate, the output gate and the forgetting gate of the neural network are trained, the data is predicted, and the original sampling signal is extended for half a cycle.
Further, in step S3, performing EMD decomposition on the data between the extreme points at the two ends to obtain an eigenmode function component; the specific implementation method of EMD decomposition is that firstly all local extreme points of extended signals x' (t) are determined, and then all the local extreme points are connected by cubic spline interpolation to form an upper envelope line em(t) connecting the minimum points by cubic spline interpolation to form a lower envelope curve el(t), finally obtaining the IMF component according to the EMD decomposition step.
Further, in step S4, performing Principal Component Analysis (PCA) on the IMF components to perform dimensionality reduction, retaining a portion of the IMF components including the main information, and performing Independent Component Analysis (ICA) on the retained IMF components to obtain the separated source signals.
Further, the method is applied to the characteristic analysis of the mixed sound generated by the complex signal sources when the factory equipment is operated. Specifically, mixed sound in a complex sound receiving environment is separated to obtain separated sound signals, so that feature analysis is performed on sound generated by equipment.
The invention has the beneficial effects that: compared with the prior art, the invention effectively combines the prediction of the LSTM network on the signal and the application of EMD decomposition in the single-channel blind source separation technology, and searches the time step length of the LSTM network according to the characteristics of the signal, thereby effectively improving the prediction precision, effectively solving the problem of endpoint effect in the EMD method in the single-channel blind source separation, and obtaining better effect in solving the sound separation problem in the complex factory environment. The method can effectively solve the problem of end effect in nonlinear non-stationary time sequence analysis, and can be applied to the separation of single-channel blind source mixed signals.
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FIG. 1 is a flow chart of the algorithm of the present invention;
FIG. 2 is a graph showing the effect of source signals and synthesized signals used in additional experiments of the present invention;
FIG. 3 is a graph of the IMF components of the present invention obtained without applying the EMD method of the present invention;
FIG. 4 is a graph showing the addition of an ICA isolated signal to the present invention without the use of the patented method; (
FIG. 5 is a continuation of the modified LSTM method for the right end of the mixed signal according to the present invention;
FIG. 6 is a graph of IMF components obtained for a mixed signal EMD according to the method of the present invention;
FIG. 7 is a signal isolated by the ICA method of the present invention for selected IMF components;
FIG. 8 is a sample diagram of a complex sound environment received by the method of the present invention;
FIG. 9 is a graph of the separation of complex sound environments by the method of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention are clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present invention without making any creative effort, shall fall within the protection scope of the present invention.
The embodiment of the invention comprises the following steps:
an EMD endpoint effect suppression method based on LSTM network, as shown in fig. 1, includes the following steps:
s1.1, collecting mixed sound signals of a plurality of indoor mechanical devices by using wireless measurement equipment, wherein x (t) is not set as a mixed signal at a moment t, the sounds and noises of the plurality of devices are mixed in the mixed signal x (t), and the noise components in the mixed signal x (t) are reduced as much as possible by processing the mixed signal x (t) by using a wavelet noise reduction method;
s1.2, calculating a signal period, and selecting an LSTM time step. Calculating the period T of the signal period x (T) by using the frequency components of the mixed signal x (T), and determining the LSTM time step S as T;
s1.3, the mixed signal x (t) is sampled as x (n) ═ x (1), x (2) … x (n);
s2, carrying out LSTM processing on the sampled signal x (n) according to the selected sliding step S through the LSTM network extension data;
s2.1, processing x (N) into an input sequence with the length of S, taking the 1 st to Nth data as a first input sequence, and sequentially carrying out the following steps: (x)1(n)＝[x(1),x(2),…,x(S+1)],x2(n)＝[x(2),x(3),…,(S+1)],…,xN-S(n)＝[x(N-S),x(N-S+1),…,x(N)])；
S2.2, taking the sequence as the input of the LSTM network, continuously updating the weights and the offsets of the input gate, the output gate and the forgetting gate of the neural network according to the output of each time point and the difference value of x (n), and then according to xN-S(n)＝[x(N-S),x(N-S+1),…,x(N)]Predicting the next data point to obtain x (N + 1);
s2.3, constructing a new input sequence x according to the predicted data points x (N +1)N-S+1(n)＝[x(N-S+1),x(N-S+2),…,x(N+1)]；
S2.4, repeating S2.3 and S2.3 to extend the length of a half period to the right end to obtain x (N + S/2);
s2.5, obtaining a sequence after continuation of the left end of the sequence by the same method;
s2.6, finding out a local maximum value (or minimum value) point of the extended signal, and taking the local maximum value (or minimum value) point as a new endpoint to intercept as a new extended signal x' (t);
s3.1, performing EMD decomposition on the extended signal, determining all local extreme points of the extended signal x' (t), and then connecting all the local extreme points by cubic spline interpolation to form an upper envelope line em(t) connecting the minimum points by cubic spline interpolation to form a lower envelope curve el(t), finally obtaining an IMF component according to the EMD decomposition step;
s3.2, removing extension data at two ends of the IMF component, and only keeping the IMF component of the original data length;
s4, selecting a proper IMF component, performing Principal Component Analysis (PCA) on the IMF component for dimensionality reduction, and reserving the proper IMF component;
s5, performing Independent Component Analysis (ICA) on the IMF component obtained after dimensionality reduction of PCA to obtain a separation result of the mixed signal and a separation result obtained by an EMD method based on the self-adaptive time step LSTM;
s6, receiving the single-channel signal of the mixed sound of each signal source in the complex sound environment of the factory, as shown in fig. 8, and performing the above steps to obtain the separated sound source signals, as shown in fig. 9.
The verification method comprises the following steps:
in order to illustrate that the EMD endpoint effect suppression method based on LSTM network of the present invention can effectively solve the endpoint effect problem, the present invention uses sinusoidal signals with frequencies of 10, 50 and 100 as source signals, and linearly superimposes them into a mixed signal x (t) as shown in fig. 2. The mixed signal x (t) is extended to the left and right ends respectively through the LSTM model, and the extension result of the right end is shown in FIG. 5. The IMF component obtained by subjecting it to the method of the present invention is shown in FIG. 6. The obtained separation results are shown in fig. 7. The IMF component and the separation result compared to the EMD decomposition result without the method of the present invention are shown in fig. 3 and 4. Therefore, the method has obvious effect on inhibiting the end effect, and has no obvious distortion deformation at the end; the separation result is more similar to the source signal, and the obtained separation result is better, so that the system performance is obviously improved.
Although the present invention has been described in detail with reference to the embodiments, it will be understood by those skilled in the art that the embodiments may be modified or changed without departing from the spirit of the present invention within the scope of the appended claims.

Claims (7)

1. An EMD end effect suppression method based on an LSTM network is characterized in that: the method comprises the following steps:
s1, estimating the signal period according to the frequency of the signal, and selecting the time step of the LSTM network;
s2, using the selected time step to process LSTM network to the received mixed signal data, extending the two ends of the data for half period, selecting extreme points in the extended data, and keeping the data between the two extreme points;
s3, performing EMD decomposition on data between the extreme points at the two ends to obtain an Intrinsic Mode Function (IMF);
s4, performing dimensionality reduction on the IMF through Principal Component Analysis (PCA) to obtain a proper IMF component, and performing Independent Component Analysis (ICA) on the IMF component to obtain a separated source signal;
s5, separating the mixed sound in the environment of receiving complex sound to obtain each separated sound signal, so as to analyze the characteristics of the sound generated by the equipment;
in step S2, the discretization sequence x (N) of the received signal is subjected to LSTM processing by using the selected time step, first processing x (N) into an input sequence with length S, and sequentially delaying the 1 st to nth data as a first input sequence: (x)1(n)＝]x(1),x(2),…,x(S+1)],x2(n)＝[x(2),x(3),…,(S+1)],…,xN-S(n)＝[x(N-S),x(N-S+1),…,x(N)]) Then, the sequence is used as the input of the LSTM network, the weight and the bias of the neural network are continuously updated according to the output of each time point and the difference value of x (n), and then the sequence x is usedN-S(n)＝[x(N-S),x(N-S+1),…,x(N)]Predicting the next data point to obtain x (N +1), and finally constructing a new input sequence x according to the predicted data point x (N +1)N-S+1(n)＝[x(N-S+1),x(N-S+2),…,x(N+1)]Continuously predicting data to extend to the right end for half cycle length to obtain x (N + S/2), and obtaining a sequence extended at the left end of the sequence by the same method; and finding a local maximum value (or minimum value) point of the extended signal, and taking the local maximum value (or minimum value) point as a new endpoint to be intercepted as a new extended signal.
2. The method for suppressing EMD endpoint effect based on LSTM network according to claim 1, wherein: the step S1 determines the time step of the LSTM network model according to the period of the estimated received signal, calculates a period of the mixed signal through each frequency component of the signal according to the periodicity of the signal in the same model, and selects the LSTM network time step according to the number of sampling points of the period, thereby improving the prediction accuracy of the model.
3. The method for suppressing EMD endpoint effect based on LSTM network according to claim 1, wherein: in step S2, since the LSTM network has an output at each time step, and a cyclic link exists between hidden units, but a cyclic neural network that generates a single output after reading the entire sequence generates an output h at each time node during the process of reading in x (t) data(t)The internal parameter matrix is then continuously updated by the difference with the input signal x (t), and the parameter update of LSTM cells is expressed as follows:
s2.1, internal State
Figure FDA0003646636210000021
The update can be expressed as:
Figure FDA0003646636210000022
wherein f isi (t)Represents a forgetting gate to control the weight of the self-loop, sigma represents that the sigmoid unit sets the weight to a value between 0 and 1,
Figure FDA0003646636210000023
denotes an external input gate, x(t)Represents the input discrete signal data, b represents the bias of the LSTM cells, U represents the input weight in the LSTM cells, W represents the circulating weight in the LSTM cells, h(t)Represents the output of LSTM cells;
s2.2, the parameter update of the forgetting gate can be expressed as:
Figure FDA0003646636210000024
wherein h istRepresenting a forgetting gate hidden layer vector, which contains the output of the LSTM cell, bfIndicating the offset of the left behind door, UfInput weight, W, representing forgetting gatefA cyclic weight representing a forgetting gate, sigma representing a sigmoid cell;
s2.3, the parameter update of the input gate can be expressed as:
Figure FDA0003646636210000025
wherein, bgIndicating input gate offset, UgRepresents the input gate input weight, WgRepresenting input gate cycle weights;
s2.4, the parameter update of the output gate can be expressed as
Figure FDA0003646636210000026
Wherein, boIndicating output gate offset, WoIndicating the cyclic weight of the output gate, UoAn input weight representing an output gate;
s2.5, export of LSTM cells h(t)Output gate
Figure FDA0003646636210000027
And cell status
Figure FDA0003646636210000028
Determine, i.e. that
Figure FDA0003646636210000029
The LSTM adopts a gating structure, so that the weight of self-circulation is determined according to the context rather than fixed, the weight of gating self-circulation and the accumulated time scale can be dynamically changed, the mixed received signals pass through the LSTM network to predict previous and subsequent data, the previous and subsequent data are respectively widened to a half period, and a proper extreme point is selected from the previous and subsequent data to be intercepted for subsequent EMD decomposition.
4. The LSTM-based network EMD endpoint effect suppression method of claim 3, comprising: in the implementation process of the LSTM method in step S2, a proper LSTM network parameter is determined according to the selected time step, the sampled sequence is read into the neural network, the weights and biases of the input gate, the output gate and the forgetting gate of the neural network are trained, the data is predicted, and the original sampling signal is extended for half a cycle.
5. The method for suppressing EMD endpoint effect based on LSTM network according to claim 1, wherein: step S3, EMD decomposition is carried out on the data between the extreme points at the two ends to obtain an intrinsic mode function component; the specific implementation method of EMD decomposition is that firstly all local extreme points of extended signals x' (t) are determined, and then all the local extreme points are connected by cubic spline interpolation to form an upper envelope line em(t) connecting the minimum points by cubic spline interpolation to form a lower envelope curve elAnd (t) finally obtaining the IMF component according to the EMD decomposition step.
6. The LSTM network-based EMD endpoint effect suppression method of claim 1, wherein the step S4 performs Principal Component Analysis (PCA) on the IMF components to perform dimension reduction, retains a part of the IMF components including the principal information, and performs Independent Component Analysis (ICA) on the retained IMF components to obtain the separated source signals.
7. The EMD endpoint effect suppression method based on the LSTM network according to any of claims 1-6, wherein: the method is applied to the characteristic analysis of mixed sound generated by a complex signal source when the factory equipment is in production operation.
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