CN111103111A - Feature extraction and noise reduction method for impact signal - Google Patents

Feature extraction and noise reduction method for impact signal Download PDF

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CN111103111A
CN111103111A CN201911347829.8A CN201911347829A CN111103111A CN 111103111 A CN111103111 A CN 111103111A CN 201911347829 A CN201911347829 A CN 201911347829A CN 111103111 A CN111103111 A CN 111103111A
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matrix
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formula
submatrix
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赵海峰
张亚
郭燕
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Nanjing College of Information Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M7/00—Vibration-testing of structures; Shock-testing of structures
    • G01M7/08—Shock-testing
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01H—MEASUREMENT OF MECHANICAL VIBRATIONS OR ULTRASONIC, SONIC OR INFRASONIC WAVES
    • G01H17/00—Measuring mechanical vibrations or ultrasonic, sonic or infrasonic waves, not provided for in the preceding groups
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M17/00—Testing of vehicles
    • G01M17/007—Wheeled or endless-tracked vehicles
    • G01M17/0078—Shock-testing of vehicles

Abstract

The invention discloses an impact signal characteristic extraction and noise reduction method, which comprises the steps of reconstructing an attractor track matrix by utilizing a phase space reconstruction theory, carrying out singular value decomposition on a submatrix B, determining the optimal row number of the reconstructed submatrix B, determining the effective order of the reconstructed submatrix B and reconstructing the submatrix B, and obtaining an impact signal subjected to noise reduction; aiming at the problems that the wavelet denoising method in the prior art is not ideal in denoising effect and the signal-to-noise ratio of denoised impulse signals is low, the impulse signal feature extraction and denoising method provided by the invention is ideal in denoising effect, and reconstructed signals after denoising have higher signal-to-noise ratio.

Description

Feature extraction and noise reduction method for impact signal
Technical Field
The invention relates to a method for extracting characteristics and reducing noise of an impact signal.
Background
Impact collisions are a phenomenon that often occurs in everyday life, such as automotive crash testing. In the researches, important parameters (impact time, maximum acceleration, maximum stress and the like) of an impact carrier in the impact collision process can be obtained through analyzing and processing the impact signals, and further important references are provided for parameters such as the structure and the strength of a vehicle body. However, during the impact process, the overload acceleration signal measured by the test system generally includes, in addition to the acceleration signal borne by the vehicle body during the impact process, vibration signals and external noise generated by the test device during the impact machine process, and these signals are inevitable during the test process and are components to be filtered when extracting the impact characteristics. The key point of the processing of the impact signal lies in finding a proper filtering method, eliminating the vibration signal of the testing device and the external noise generated in the impact process, and only keeping the acceleration signal formed by reflecting the impact resistance. In the prior art, a wavelet denoising method is generally used for denoising, noise is eliminated through short waves, and the problems of unsatisfactory denoising effect and low signal-to-noise ratio of denoised impact signals exist in the wavelet denoising method.
Disclosure of Invention
Aiming at the problems of unsatisfactory noise reduction processing effect and low signal-to-noise ratio of the denoised impact signal in the wavelet denoising method in the prior art, the invention aims to provide a method for extracting the characteristics of the impact signal and denoising, which has ideal noise reduction processing effect and higher signal-to-noise ratio of the denoised impact signal.
In order to solve the technical problems, the invention adopts the following technical scheme:
a method for extracting characteristics and reducing noise of an impact signal comprises the following steps:
the method comprises the following steps: reconstructing an attractor trajectory matrix by using a phase space reconstruction theory;
assuming that the impact signal s (t) is a one-dimensional time signal sequence with the length of N, and t is 1,2, …, N, reconstructing an attractor trajectory matrix by using a phase space reconstruction theory to obtain a submatrix B, as shown in formula (1):
Figure RE-GDA0002426563500000011
in the formula: n ═ L + (M-1) τ, τ ═ 1, and submatrix B is an L × M dimensional matrix;
step two: performing singular value decomposition on the sub-matrix B;
performing singular value decomposition on the sub-matrix B, as shown in formula (2):
BL×M＝UL×L∑L×MVT M×M(2)
in the formula: u is an L-order orthogonal matrix, and V is an M-order orthogonal matrix; Σ is a diagonal matrix: sigma is dig (delta)1，δ2，…，δL) Wherein δ1、δ2、…、δLIs the singular value of the submatrix B;
step three: determining the optimal row number of the reconstructed sub-matrix B;
let deltaiIs the i-th singular value, λ, of the submatrix BiThe ratio of the first i singular values to the sum of all singular values is shown in formula (3):
λi＝(δ1+δ2+...δi)/(δ1+δ2+...+δL) (3)
when the value of i is n, the condition that lambda is more than or equal to 0.95 is satisfiednN +1 is less than 1, and is the optimal row number of the reconstructed sub-matrix B;
wherein i is more than or equal to 1 and less than or equal to L-1;
step four: determining the effective order of the reconstructed sub-matrix B;
firstly, substituting L-n +1 into the formula (1) to obtain a sub-matrix B1, and performing singular value decomposition on the sub-matrix B1 according to the formula (2) to obtain singular values of the sub-matrix B1 which are delta respectively1、δ2、…、δn+1；
Let deltajFor the j-th singular value, singular value delta, of the submatrix B1jThe energy of the corresponding signal component is E, as shown in equation (4):
E＝δj 2(4)
let P be the proportion of the energy of the first j singular values in the sum of the energy of all singular values, as shown in formula (5):
Figure RE-GDA0002426563500000021
when the value k of j is set, P is more than or equal to 0.98 and less than 1, and k is the effective order of the reconstructed submatrix B;
wherein j is more than or equal to 1 and less than or equal to n;
step five: reconstructing the sub-matrix B to obtain an impact signal after noise reduction;
1) will be delta in the submatrix B1kThe subsequent singular value deltak+1、δk+2，…δn+1Zero setting is carried out, a sub-matrix B2 is obtained by substituting the formula (2), and the sub-matrix B2 is a matrix obtained by reconstructing the sub-matrix B;
2) and (3) inverting the sub-matrix B2 by using the formula (1) to obtain a signal sequence after the impact signal is subjected to noise reduction.
Compared with the prior art, the invention has the beneficial effects that:
the invention utilizes the optimal row number and the effective order to reconstruct the sub-matrix, thereby eliminating the vibration and noise signals mixed in the impact signal, extracting the main body signal formed by impact resistance, and then utilizing the reconstructed sub-matrix to carry out inversion by a delay method to obtain the signal sequence after the noise of the impact signal is reduced, the characteristics of the impact signal can be better reflected, the noise reduction processing effect is ideal, and the reconstructed signal after the noise reduction processing has higher signal to noise ratio.
Drawings
FIG. 1 is a flow chart of the steps in example 1.
FIG. 2 is a graph of the impact signal X (t) in example 1.
Fig. 3 is a graph showing singular values of the impact signal when L takes values of 2,3,4,5,8, and 20 in example 1.
Fig. 4 is a graph showing the proportion of the sum of the first i singular values of the impulse signal to the total singular value when L takes values 2,3,4,5,8, and 20 in example 1.
Fig. 5 is a graph of the impulse signal and error after noise reduction obtained by the singular value decomposition method when L takes a value of 5 and k takes a value of 2 in example 1.
Fig. 6 is a graph of a denoised impact signal obtained using a wavelet denoising method.
Detailed Description
The invention will be described in further detail with reference to the following figures and specific embodiments.
Example 1
As shown in fig. 1, a method for extracting features and reducing noise of an impulse signal includes the following steps:
the method comprises the following steps: reconstructing an attractor trajectory matrix by using a phase space reconstruction theory;
assuming that the impact signal s (t) is a one-dimensional time signal sequence with the length of N, and t is 1,2, …, N, reconstructing an attractor trajectory matrix by using a phase space reconstruction theory to obtain a submatrix B, as shown in formula (1):
Figure RE-GDA0002426563500000031
in the formula: n ═ L + (M-1) τ, τ ═ 1, and submatrix B is an L × M dimensional matrix;
step two: performing singular value decomposition on the sub-matrix B;
performing singular value decomposition on the sub-matrix B, as shown in formula (2):
BL×M＝UL×L∑L×MVT M×M(2)
in the formula: u is an L-order orthogonal matrix, and V is an M-order orthogonal matrix; Σ is a diagonal matrix: sigma is dig (delta)1，δ2，…，δL) Wherein δ1、δ2、…、δLIs the singular value of the submatrix B;
step three: determining the optimal row number of the reconstructed sub-matrix B;
let deltaiIs the i-th singular value, λ, of the submatrix BiThe ratio of the first i singular values to the sum of all singular values is shown in formula (3):
λi＝(δ1+δ2+...δi)/(δ1+δ2+...+δL) (3)
when the value of i is n, the condition that lambda is more than or equal to 0.95 is satisfiednN +1 is less than 1, and is the optimal row number of the reconstructed sub-matrix B;
wherein i is more than or equal to 1 and less than or equal to L-1;
step four: determining the effective order of the reconstructed sub-matrix B;
firstly, substituting L-n +1 into the formula (1) to obtain a sub-matrix B1, and performing singular value decomposition on the sub-matrix B1 according to the formula (2) to obtain singular values of the sub-matrix B1 which are delta respectively1、δ2、…、δn+1；
Let deltajFor the j-th singular value, singular value delta, of the submatrix B1jThe energy of the corresponding signal component is E, as shown in equation (4):
E＝δj 2(4)
let P be the proportion of the energy of the first j singular values in the sum of the energy of all singular values, as shown in formula (5):
Figure RE-GDA0002426563500000041
when the value k of j is set, P is more than or equal to 0.98 and less than 1, and k is the effective order of the reconstructed submatrix B;
wherein j is more than or equal to 1 and less than or equal to n;
step five: reconstructing the sub-matrix B to obtain an impact signal after noise reduction;
1) will be delta in the submatrix B1kThe subsequent singular value deltak+1、δk+2，…δn+1Zero setting is carried out, a sub-matrix B2 is obtained by substituting the formula (2), and the sub-matrix B2 is a matrix obtained by reconstructing the sub-matrix B;
2) and (3) inverting the sub-matrix B2 by using the formula (1) to obtain a signal sequence after the impact signal is subjected to noise reduction.
Fig. 2 is a graph of the impact signal x (t) in the present embodiment.
Fig. 3 is a graph showing singular values of the impulse signal when L takes values of 2,3,4,5,8, and 20 in this embodiment. It can be seen from the figure that when L is greater than or equal to 5, the first 5 singular value components are in a descending trend, and then the value of L is continuously increased, the singular value is relatively changed very little, and is in a stable change situation basically.
As shown in fig. 4, it is a graph of the proportion of the sum of the previous i singular values to the total singular value when L takes values 2,3,4,5,8, and 20 in this embodiment. It can be seen from the figure thatλiThe change is slower and slower with the increase of singular value, and when L takes 5, the sum of the first 4 singular value components already occupies more than 95% of the total component. Therefore, the value L of 5 in this embodiment is the optimal row number of the reconstructed sub-matrix B.
As shown in table 1 below, when L takes values of 2,3,4,5, and 8, the singular values of the impulse signal are respectively 0.716 and 0.112 for the first two singular values, and both values are lower than 0.1 for the last two singular values, as can be seen from table 1, the total energy ratio p occupied by the singular value energy of the first 2 times is 98%, which occupies most of the total energy, which indicates that the energy of the first 2 times carries the main body of the signal, so that k is 2 in this embodiment as the effective order of the reconstruction sub-matrix B.
TABLE 1
Figure RE-GDA0002426563500000051
As shown in fig. 5, it is a graph of the denoised impulse signal and error obtained by the singular value decomposition method when L takes a value of 5 and k takes a value of 2 in this embodiment. It can be seen from the figure that the impulse signal obtains a better noise reduction effect after singular value decomposition and reconstruction.
As shown in fig. 6, a graph of a denoised impulse signal obtained using a wavelet denoising method. In comparison with FIG. 4, it can be seen that the signal-to-noise ratio (SNR) of the de-noised impulse signal obtained by singular value decomposition method in this embodiment is better than that of the wavelet decomposition reconstructed signal (as shown in Table 2 below)
TABLE 2
Figure RE-GDA0002426563500000052

Claims (1)

1. A method for extracting characteristics of an impact signal and reducing noise is characterized by comprising the following steps: the method comprises the following steps:
the method comprises the following steps: reconstructing an attractor trajectory matrix by using a phase space reconstruction theory;
assuming that the impact signal s (t) is a one-dimensional time signal sequence with the length of N, and t is 1,2, …, N, reconstructing an attractor trajectory matrix by using a phase space reconstruction theory to obtain a submatrix B, as shown in formula (1):
Figure FDA0002333876690000011
in the formula: n ═ L + (M-1) τ, τ ═ 1, and submatrix B is an L × M dimensional matrix;
step two: performing singular value decomposition on the sub-matrix B;
performing singular value decomposition on the sub-matrix B, as shown in formula (2):
BL×M＝UL×L∑L×MVT M×M(2)
in the formula: u is an L-order orthogonal matrix, and V is an M-order orthogonal matrix; Σ is a diagonal matrix: sigma is dig (delta)1，δ2，...，δL) Wherein δ1、δ2、…、δLIs the singular value of the submatrix B;
step three: determining the optimal row number of the reconstructed sub-matrix B;
let deltaiIs the i-th singular value, λ, of the submatrix BiThe ratio of the first i singular values to the sum of all singular values is shown in formula (3):
λi＝(δ1+δ2+…δi)/(δ1+δ2+...+δL) (3)
when the value of i is n, the condition that lambda is more than or equal to 0.95 is satisfiednN +1 is less than 1, and is the optimal row number of the reconstructed sub-matrix B;
wherein i is more than or equal to 1 and less than or equal to L-1;
step four: determining the effective order of the reconstructed sub-matrix B;
firstly, substituting L-n +1 into the formula (1) to obtain a sub-matrix B1, and performing singular value decomposition on the sub-matrix B1 according to the formula (2) to obtain singular values of the sub-matrix B1 which are delta respectively1、δ2、…、δn+1；
Let deltajFor the j-th singular value, singular value delta, of the submatrix B1jThe energy of the corresponding signal component is E, as shown in equation (4):
E＝δj 2(4)
let P be the proportion of the energy of the first j singular values in the sum of the energy of all singular values, as shown in formula (5):
Figure FDA0002333876690000012
when the value k of j is set, P is more than or equal to 0.98 and less than 1, and k is the effective order of the reconstructed submatrix B;
wherein j is more than or equal to 1 and less than or equal to n;
step five: reconstructing the sub-matrix B to obtain an impact signal after noise reduction;
1) will be delta in the submatrix B1kThe subsequent singular value deltak+1、δk+2，…δn+1Zero setting is carried out, a sub-matrix B2 is obtained by substituting the formula (2), and the sub-matrix B2 is a matrix obtained by reconstructing the sub-matrix B;
2) and (3) inverting the sub-matrix B2 by using the formula (1) to obtain a signal sequence after the impact signal is subjected to noise reduction.
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EP0022671A1 (en) * 1979-07-13 1981-01-21 Westinghouse Electric Corporation Method and apparatus for determining the mass of an impacting object
CN2567674Y (en) * 2002-12-12 2003-08-20 谌德荣 Impact signal processing chip
CN102998118A (en) * 2012-11-29 2013-03-27 西安交通大学 Bearing quantitative diagnosis method based on morphological filtering and complexity measure
CN106845010A (en) * 2017-02-16 2017-06-13 西南交通大学 Based on the low-frequency oscillation dominant pattern discrimination method for improving SVD noise reductions and Prony
CN108387887A (en) * 2018-05-22 2018-08-10 西安邮电大学 A kind of mixing noise-reduction method of underwater sound signal

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Publication number Priority date Publication date Assignee Title
CN114506471A (en) * 2022-03-17 2022-05-17 北京机电工程研究所 Method for determining first-order bending frequency of airplane suspension

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