An endpoint extension method for suppressing endpoint effect

Abstract

The present invention belongs to the field of communication technology, and specifically relates to an endpoint extension method for suppressing endpoint effects. The present invention constructs two slopes based on adjacent local extreme points (maximum points or minimum points), and then uses the average value of the two slopes to measure the trend of the upper / lower envelope, thereby determining the ordinate of the extension point. For the setting of the horizontal coordinate of the extension point, the solution of the present invention fixes the horizontal coordinate of the extension point to the horizontal coordinate corresponding to the start and end positions of the endpoints on both sides of the signal. After applying this technical solution, when applying empirical mode decomposition to analyze and process damped oscillation signals, the endpoint effect of the damped oscillation signal can be effectively suppressed, providing support for subsequent further precise quantitative analysis.

Description

Technical Field

[0001] The present invention relates to an endpoint extension method, and in particular to an endpoint extension method for effectively suppressing the endpoint effect of a damped oscillation signal. Background Art

[0002] Endpoint extension is a key link in empirical mode decomposition (EMD). Different endpoint extension methods will lead to differences in the intrinsic mode functions (IMFs) extracted by EMD, especially large fluctuations at the signal endpoints. This phenomenon is called the endpoint effect. Suppressing the endpoint effect is an important goal of the endpoint extension algorithm design. Different endpoint extension algorithms have different design ideas, inconsistent algorithm time complexity, and different endpoint effect suppression effects. In addition, different endpoint extension methods have different endpoint effect suppression effects on different signals. Finding an endpoint extension algorithm with low time complexity and good endpoint effect suppression effect is an important research content in this field. The present invention discloses an endpoint extension method that uses the slope mean to measure the envelope trend to suppress the endpoint effect of the damped oscillation signal, which is particularly suitable for EMD analysis and processing of damped oscillation signals generated by mechanical vibration systems or circuit systems.

[0003] The slope-based method (SBM) was proposed by Marcus in 2004. et al. ( Figure 2 ). The design idea of ​​SBM is to use the relationship between the maximum and minimum points at both ends of the signal to construct different slopes, then construct straight lines based on the slopes, and then obtain the extension points through the intersections between the straight lines. In view of the defect that the position of the extension point may be within the definition domain of the signal, resulting in the extension envelope not covering the signal, in 2008 WU et al. proposed an improved slope endpoint extension method ( Figure 3 ). The slope-based continuation method has a clear design idea and a simple algorithm. It can achieve good results for most signals and is a recommended continuation method. However, this method will lead to poor performance for signals such as damped oscillation (XU et al., 2021).

[0004] Based on the slope (Marcus et al., 2004) and the extended method of improved slope (WU et al., 2008) are not ideal for suppressing the endpoint effect of damped oscillation signals (XU et al., 2021). The main reason is that the construction of the slope uses both the local maximum and local minimum of the signal. For damped oscillation signals with opposite upper and lower envelope trends, since the upper and lower envelopes tend to separate rapidly at one end of the signal, a more reasonable strategy is to only use the local maximum of the signal when measuring the upper envelope trend and constructing the upper envelope extended point; similarly, only use the local minimum of the signal when measuring the lower envelope trend and constructing the lower envelope extended point, rather than using both the local maximum and local minimum of the signal to measure the envelope trend and then construct the extended point. Summary of the invention

[0005] In view of the problems existing in the background technology, the present invention provides an endpoint extension method for suppressing the endpoint effect, which is intended to solve the technical problem mentioned in the background technology that the prior art has an unreasonable effect on suppressing the endpoint effect of the damped oscillation signal.

[0006] The present invention solves the above technical problems and provides the following technical solutions:

[0007] An endpoint extension method for suppressing endpoint effect comprises the following steps:

[0008] Step 1: Input the signal to be processed y(x) and find all local minima (x) of the signal y(x). low (i),y low (i)), (i=1,...,n) and mark them, where n is the number of local minima, x low (i) and y low (i) represents the abscissa and ordinate of the i-th local minimum of the signal to be processed, respectively; the subscript low is used to identify the local minimum of the signal to be processed; correspondingly, up is usually used to identify the local maximum;

[0009] Step 2: Set the horizontal coordinates of the left and right extension points to the horizontal coordinates of the signal endpoints, that is, and in represents the horizontal coordinate of the left extension point of the lower envelope, and x(1) is the horizontal coordinate of the starting point of the signal; correspondingly, is the horizontal coordinate of the extension point on the right side of the lower envelope, and x(end) is the horizontal coordinate of the end position of the signal; correspondingly, the horizontal coordinates of the extension points on the left and right sides of the upper envelope are and

[0010] Step 3: To measure or predict the changing trend of the upper and lower envelopes, the three adjacent extreme value points on the left and right sides of the signal are used to construct two straight lines for measuring the changing trend of the envelope based on their slopes. The two intersection points of these two straight lines and the boundary lines on the left and right ends of the signal, i.e., x=x(1) and x=x(end), are calculated, and then the average value of the ordinates of the two intersection points is calculated as the ordinate value of the extension point. For the ordinate of the left lower envelope extension point, the three adjacent minimum value points (x low (i),y low (i)), (i=1,2,3), construct two straight lines and Calculate the ordinates of the two intersection points of the two straight lines and the straight line x=x(1) corresponding to the left boundary of the signal, that is, and The average value of the ordinates of the two intersection points is used as the ordinate value of the extension point: Thus, the ordinate of the left lower envelope extension point is obtained; the ordinate of the left upper envelope extension point can be calculated by simply replacing the subscript low in step 3 with up;

[0011] Step 4: For the calculation of the ordinate of the right lower envelope extension point, use the three adjacent minimum points on the right side of the signal (x low (i),y low (i)), (i=n,n-1,n-2), construct two straight lines to measure the envelope change trend and Calculate the ordinate of the intersection of the two straight lines and the signal right boundary straight line x = x (end), that is, and The average value of the ordinates of the two intersection points is used as the ordinate value of the extension point: Thus, the ordinate of the right lower envelope extension point is obtained; accordingly, the ordinate of the right upper envelope extension point can be calculated by simply replacing the above subscript low with up;

[0012] Furthermore, the horizontal coordinates of the two end extension points in step 2 are set to the start and end horizontal coordinate values ​​of the signal, so that the upper and lower envelopes after extension can completely cover the signal.

[0013] Furthermore, the calculation formula of step three is as follows:

[0014] If n ≥ 3,

[0015] calculate and

[0016]

[0017] set up

[0018] If n=2,

[0019] Where n is the number of signal minimum points, (x low (i),y low (i)), (i=1,2,3) are the horizontal and vertical coordinates of the three adjacent minimum points on the left side of the signal, x(1) is the horizontal coordinate of the starting point of the signal, and The ordinates of the two intersection points of the two trend lines of the lower envelope of the signal on the left and the boundary line x=x(1) on the left side of the signal, It is the ordinate of the left lower envelope extension point.

[0020] Furthermore, the calculation formula of step 4 is as follows:

[0021] If n ≥ 3,

[0022] calculate and

[0023]

[0024] set up

[0025] If n=2,

[0026] Where n is the number of signal minimum points, (x low (i),y low (i)), (i=n,n-1,n-2) are the horizontal and vertical coordinates of the three adjacent minimum points on the right side of the signal, and x(end) is the horizontal coordinate of the signal end position. and It is the ordinate of the two intersection points of the two trend lines of the lower envelope on the right side of the signal and the boundary line on the right side of the signal x=x(end), It is the vertical coordinate of the lower envelope extension point on the right side.

[0027] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0028] 1. The present invention is mainly used to analyze and process damped oscillation signals generated by mechanical vibration systems or circuit systems. When applying empirical mode decomposition to analyze and process damped oscillation signals, the endpoint effect of damped oscillation signals can be effectively suppressed, providing support for subsequent further precise quantitative analysis.

[0029] 2. The construction of the slope of the present invention is based on local maximum points or local minimum points. Specifically, for the prediction of the upper envelope extension points, only the local maximum points are used to construct the slope, while for the prediction of the lower envelope extension points, only the local minimum points are used to construct the slope. This is essentially different from the slope-based and improved slope methods that use both local maximum points and local minimum points to construct the slope. This is also the key difference between the technical solution of the present invention and the slope-based and improved slope extension methods. It is this difference in design that leads to performance differences in suppressing the endpoint effect of damped oscillation signals.

[0030] 3. The solution of the present invention is to construct two slopes based on adjacent local extreme points (maximum points or minimum points), and then use the average of the two slopes to measure the trend of the upper / lower envelope, and then determine the ordinate of the extension point. From the perspective of prediction, the mathematical essence of this method is weighted average prediction; from the perspective of signal processing, it is finite impulse response (FIR) filtering.

[0031] 4. Regarding the setting of the horizontal coordinate of the extension point, the solution of the present invention fixes the horizontal coordinate of the extension point to the horizontal coordinate corresponding to the start and end positions of the endpoints on both sides of the signal, thereby achieving the purpose of covering the signal. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 It is a schematic diagram of the technical solution of the present invention (taking the local minimum extension point on the right side of the signal lower envelope as an example).

[0033] Figure 2 Schematic diagram of the endpoint extension algorithm based on the slope method (front end / right side).

[0034] Figure 3 Schematic diagram of the improved slope continuation method.

[0035] Figure 4 It is a comparison diagram of the extension effect on the damping signal based on the present invention and the improved slope.

[0036] Figure 5 The present invention and the extended signal y1(t)=sin(πt)e based on the improved slope 0.1t Comparison chart of post-EMD decomposition results.

[0037] Figure 6 The present invention and the extended signal y2(t)=sin(πt)e based on the improved slope -0.1t Comparison chart of post-EMD decomposition results.

[0038] Figure 7This is a comparison chart of the EMD decomposition results of fNIRS signals acquired using functional near-infrared spectroscopy (fNIRS) detection using different continuation methods.

[0039] Figure 8 A comparison chart of EMD decomposition results of bearing signals using different extension methods. DETAILED DESCRIPTION

[0040] In order to make the technical means, features and effects achieved by the present invention easier to understand, the technical solutions in the embodiments of the present invention are clearly and completely described below in conjunction with specific embodiments and the drawings in the embodiments of the present invention.

[0041] like Figure 1-Figure 8 As shown, the present invention provides the following technical solutions:

[0042] The schematic diagram of the technical solution of the present invention is as follows Figure 1 As shown, the detailed steps are described in the algorithm in Table 1. It should be pointed out that Figure 3 Table 1 and Table 1 only illustrate the technical processing process of the present invention using the lower envelope minimum extension point of the signal. For the upper envelope extension point of the signal, the same idea is used for generalization processing: for example, for Table 1, it is only necessary to change low to up to obtain the calculation process of the upper envelope extension point.

[0043]

[0044]

[0045] In order to allow those skilled in the art to better understand the technical principles of the present invention, the following is explained in conjunction with the accompanying drawings:

[0046] From both qualitative and quantitative perspectives, the extension effects of the method of the present invention and the improved slope method on the same damped oscillation signal are analyzed. The results show that the method of the present invention has obvious advantages and significant effects in suppressing the endpoint effect of the damped oscillation signal.

[0047] 1. Intuitive qualitative comparison of different extension methods

[0048] Figure 4 Examples of two divergent and convergent damped oscillating signals y1(t)=sin(πt)e 0.1t and y2(t)=sin(πt)e -0.1t , and the comparison effect of the extension point is obtained by respectively extending the endpoint based on the improved slope and the method of the present invention. Figure 4 From a qualitative point of view, it is clearly shown that the extension points obtained by the method of the present invention are significantly better than the method based on improved slope in terms of overall effect: Figure 4The upper right and lower left extension points of (a) and Figure 4 Specifically, the extension points obtained by the method of the present invention are consistent with the trend of the upper and lower envelopes of the signal, while the method based on improved slope will cause some extension points to deviate from the trend of the upper and lower envelopes of the signal.

[0049] 2. Quantitative analysis results of different extension methods

[0050] From a quantitative perspective, Figure 4 The two damped signals are extended using the method of the present invention and the method based on the improved slope, and then EMD decomposition is performed. The decomposition results are as follows: Figure 5 and Figure 6 As shown in Table 2, two quantitative evaluation indicators, the mean square error (MSE) and the orthogonality index (IO), of the decomposition results are calculated, as shown in Table 2. The quantitative comparison results of the orthogonality index and the mean square error in Table 2 show that the method of the present invention is superior to the method based on the improved slope in suppressing the endpoint effect after performing the endpoint extension on the damped oscillation signal and then performing the EMD decomposition. This quantitative advantage is Figure 5 and Figure 6 The oscillation amplitude of each IMFs endpoint extracted is reflected, among which Figure 5 The results of EMD decomposition of the same divergent damped signal using the present invention and the improved slope method are shown. Figure 6 The results of EMD decomposition of the same convergent damped signal using the present invention and the improved slope method are compared. Specifically, the oscillation amplitude of each IMFs extracted by the present invention at the endpoint is significantly lower than that based on the improved slope method, that is, the endpoint effect is better suppressed.

[0051] Table 2 Performance comparison between the present invention and the improved slope method based on extending the damping signal and then performing EMD decomposition

[0052]

[0053] The technical solution of the present invention is not only applicable to the analysis and processing of damping signals generated by mechanical vibration systems and circuit systems, but can also be extended and generalized to the EMD analysis and processing of most nonlinear and non-stationary signals in engineering applications. Figure 7 and Figure 8 The EMD decomposition results of the accelerometer data signal and fNIRS signal at the driving end of the ball bearing are demonstrated using three different methods: this scheme, ISBM (WU et al., 2008) and CSBM (XU et al., 2021). Figure 7The results of using different extension methods to perform endpoint extension on fNIRS signals and then perform EMD decomposition are compared. Figure 8 The results of using different extension methods to implement endpoint extension on the measured signal of the mechanical transmission bearing and then perform EMD decomposition are compared, and the orthogonality index (index orthogonality, IO) numerical comparison results are shown in Table 3. The orthogonality index results show that the performance of the method of the present invention is better than the method based on the improved slope.

[0054] Table 3. Comparison of IO performance of the present invention and the improved slope method extended to fNIRS and bearing signals

[0055] |IO| Based on improved slope The present invention fNIRS 0.629265 0.612225 Bearing signal 0.016617 0.0052634

[0056] It will be apparent to those skilled in the art that the invention is not limited to the details of the exemplary embodiments described above and that the invention can be implemented in other specific forms without departing from the spirit or essential features of the invention. Therefore, the embodiments should be considered exemplary and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description, and it is intended that all variations falling within the meaning and scope of the equivalent elements of the claims be included in the invention. Any reference numeral in a claim should not be considered as limiting the claim to which it relates.

Claims

1. An endpoint extension method for suppressing endpoint effect, characterized in that: The following steps are involved: Step 1: Input damped oscillation signal y(x) , find the signal y(x) All local minima of And mark, where n is the number of local minima, and They represent the damped oscillation signal i The horizontal and vertical coordinates of the local minimum; Corner mark low Used to identify the local minimum of the damped oscillation signal; correspondingly, it is usually used up Identify local maxima; Step 2: Set the horizontal coordinates of the left and right extension points to the horizontal coordinates of the signal endpoints, that is, ;in Represents the horizontal coordinate of the left extension point of the lower envelope, is the abscissa of the starting point of the signal; accordingly, is the horizontal coordinate of the extension point on the right side of the lower envelope, is the horizontal coordinate of the signal end position; Correspondingly, the horizontal coordinates of the left and right extension points of the upper envelope are ; Step 3: Use the three adjacent extreme points on the left and right sides of the signal to construct two straight lines to measure the envelope change trend, and calculate the boundary lines between these two straight lines and the left and right ends of the signal, that is, and The two intersection points are calculated, and then the average value of the ordinates of the two intersection points is taken as the ordinate value of the extension point; The ordinate of the left lower envelope extension point: using the three adjacent minimum points on the left side of the signal Two adjacent minimum points in the middle construct two straight lines to measure the change trend on the left side of the lower envelope, and calculate the two straight lines and the corresponding straight line on the left boundary of the signal. The ordinates of the two intersection points are calculated, and the average of the ordinates of the two intersection points is used as the ordinate value of the extension point to obtain the ordinate of the left lower envelope extension point; The calculation formula is as follows: when , calculate ;and ;set up ; when , ; Where n is the number of signal minimum points, are the horizontal and vertical coordinates of the three adjacent minimum points on the left side of the signal, is the horizontal coordinate of the signal starting point, and The two trend lines of the lower left envelope of the signal and the left boundary line of the signal The ordinates of the two intersection points are is the ordinate of the left lower envelope extension point; The calculation method of the ordinate of the left upper envelope extension point is the same as that of the left lower envelope extension point. You only need to change the corner mark in step 3. low Replace up That's it; Step 4: Calculation of the ordinate of the right lower envelope extension point: Use the three adjacent minimum points on the right side of the signal Two adjacent minimum points in the middle construct two straight lines to measure the right side change trend of the lower envelope, and calculate the two straight lines and the right side boundary line of the signal. The ordinate of the intersection point, and the average of the ordinates of the two intersection points is used as the ordinate value of the extension point, to obtain the ordinate of the right lower envelope extension point; The calculation formula is as follows: when , calculate ; and ; set up ; when , ; Where n is the number of signal minimum points, The horizontal and vertical coordinates of the three adjacent minimum points on the right side of the signal, is the abscissa of the signal termination position, and The two trend lines of the lower envelope on the right side of the signal and the boundary line on the right side of the signal The ordinates of the two intersection points are is the ordinate of the right lower envelope extension point; The calculation method of the ordinate of the upper envelope extension point on the right is the same as that of the lower envelope extension point on the right. low Replace up That's it.

2. The endpoint extension method for suppressing the endpoint effect according to claim 1, characterized in that: In step 2, the horizontal coordinates of the two end extension points are set to the start and end horizontal coordinate values ​​of the signal, so that the upper and lower envelopes after extension can completely cover the signal.

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