CN112014478B - Defect echo blind extraction self-adaptive method submerged in ultrasonic grass-shaped signal - Google Patents

Defect echo blind extraction self-adaptive method submerged in ultrasonic grass-shaped signal Download PDF

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CN112014478B
CN112014478B CN202010885182.0A CN202010885182A CN112014478B CN 112014478 B CN112014478 B CN 112014478B CN 202010885182 A CN202010885182 A CN 202010885182A CN 112014478 B CN112014478 B CN 112014478B
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李晓红
徐万里
张俊
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Wuhan University WHU
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Abstract

In order to solve the problem that the existing defect echo extraction algorithm cannot suppress actual noise so as not to obtain a defect signal, the invention provides a defect echo blind extraction self-adaptive method submerged in an ultrasonic grass-shaped signal. The method comprises the following specific steps: firstly, carrying out similarity analysis on an acquired original signal sample by using an unsupervised machine learning algorithm; then, inputting the similar signal samples into a designed noise reduction self-encoder to train the noise reduction self-encoder, and enabling the noise reduction self-encoder to learn corresponding noise reduction rules; and finally, automatically reducing noise of the signal by using the trained self-encoder, and realizing intelligent extraction of the defect signal. Compared with the existing defect signal extraction technology, the method has stronger adaptability to the inhibition of actual noise, and the strong adaptability is derived from the capability of learning the characteristics of the defect signal and the noise signal respectively by analyzing the rich information provided by the original signal sample.

Description

Defect echo blind extraction self-adaptive method submerged in ultrasonic grass-shaped signal
Technical Field
The invention relates to the technical field of ultrasonic nondestructive testing, in particular to a defect echo blind extraction self-adaptive method submerged in an ultrasonic grass-shaped signal.
Background
Blind extraction of target signals from raw data is a research hotspot in the field of modern signal processing. The blind extraction is to extract the target signal accurately only by using the data collected by the sensor as an analysis basis without any reference data or any prior information about the characteristics, the frequency spectrum distribution and the like of the target signal. Because of this, blind extraction of signals has become an important technique in many high-tech fields such as speech enhancement, image processing, medical diagnosis, military reconnaissance, and the like.
In the field of ultrasonic nondestructive detection, with the requirement of automatic/intelligent detection development, the defect echo blind extraction submerged in the ultrasonic grass-shaped signal is solved, and the method has very important application value. The defect echo is a target signal in ultrasonic nondestructive detection, is important information for analyzing the size, position, distribution and properties of the defect, and is also an important basis for judging the quality and safety of the workpiece. However, due to the coarse material quality of the detected material, the uneven distribution of the texture and the grains, the large difference of the roughness of the surface of the workpiece and the like, the ultrasonic wave is scattered in the transmission process, and grass-shaped noise with the amplitude which is much higher than the sensitivity (the minimum defect size is found) of the detected defect is generated; if the time domain amplitude is used to extract the defect signal, the signal is definitely a blind image, which causes erroneous judgment or missed detection. The more troublesome problem is that the grass-shaped echo has numerous shapes and is complicated and complicated; different grain sizes produce different amplitude levels of grass-like noise, and different grain types (equiaxed grains and columnar grains) and different grain distributions also produce different appearances of grass-like noise. The most typical example is the inspection of welds in coarse grain austenitic stainless steels, which combines all the above features, with the distribution, size and type of grains varying along the length of the weld, resulting in various forms of grass-like noise during the inspection (fig. 1).
Laser ultrasound is a non-contact high-sensitivity nondestructive testing method, becomes an important means for finding micron-sized defects (such as unfused powder, air holes and the like) on the near surface inside a workpiece, is expected to become the most environment-friendly and highest cost performance real-time monitoring nondestructive testing technology in the field of additive manufacturing. However, laser-generated ultrasonic surface waves are highly susceptible to interference from material surface roughness. Unfortunately, additive manufacturing inevitably produces random surface roughness due to the unique layered additive manufacturing approach, which roughness is usually comparable in size to micron-scale defects (unfused powder, voids, etc.) produced in manufacturing. Therefore, when laser ultrasonic inspection is used for real-time monitoring, the defect echo can be buried by various grass-shaped noises caused by roughness (fig. 2). In addition, it is not feasible to polish the surface based on the need for real-time monitoring. In view of the above, it is necessary to develop an effective extraction algorithm for defect echoes in ultrasonic grass-like signals.
In the prior art, some defect signal extraction algorithms, such as Fourier Transform (FT), Short Time Fourier Transform (STFT), wavelet transform, split spectrum analysis (SSP), sparse decomposition, Ensemble Empirical Mode Decomposition (EEMD), and variance mode decomposition, etc., exist, and the noise reduction process of these algorithms depends on the prior model (noise is a certain mathematical distribution or high frequency component). Therefore, they are widely used in suppressing grass-like noise at high frequencies or close to Gaussian distributions (e.g., Manjula K, Vijayarekha K, Venkatraman B. quality Enhancement of Ultrasonic TOFD Signals from Carbon Steel Weld Pad with notes [ J ]. Ultrasonics,2017,84:264- & 271.).
The inventor of the present application finds that the method of the prior art has at least the following technical problems in the process of implementing the present invention:
the algorithm partially solves some defect signal extraction under the background of specific distributed noise. However, these methods cannot adapt to various noise environments to acquire a defect signal.
Disclosure of Invention
The invention provides a defect echo blind extraction self-adaptive method submerged in an ultrasonic grass-shaped signal, which is used for solving or at least partially solving the technical problem of poor adaptability of the method in the prior art.
In order to solve the technical problem, the invention provides an adaptive method for blind extraction of a defect echo submerged in an ultrasonic grass-shaped signal, which comprises the following steps:
s1: carrying out similarity analysis on the collected original signal samples by using an unsupervised machine learning algorithm, and classifying the similar signals into one class, wherein the unsupervised machine learning algorithm is k-means or DBSCAN, and the original signal samples are ultrasonic A scanning signals, B scanning signals and C scanning signals which are collected aiming at the same test block under the same experimental condition;
s2: inputting the similar signals obtained in the step S1 into a pre-designed noise reduction self-encoder to train the same, so that the pre-designed noise reduction self-encoder learns corresponding noise reduction rules, wherein the pre-designed noise reduction self-encoder is a three-layer neural network with input equal to output, and the form is as follows: n-h-n, where n represents the number of neurons in input and output and h represents the number of neurons in the crypt layer;
s3: and denoising the signal to be processed by utilizing the trained denoising self-encoder.
In one embodiment, S1 specifically includes:
s1.1: determining the cluster number of signal clusters;
s1.2: selecting a signal similarity evaluation criterion;
s1.2: and performing similarity analysis on the acquired original signal samples according to the cluster number of the signal cluster and a signal similarity evaluation criterion.
In one embodiment, S1.1 specifically includes:
determining the number of clustering clusters according to the number of signals or the number of target micro-areas, wherein one tenth of the number of acquired signals is set as the number of clusters when the number of signals is taken as a basis; when the target micro-area is taken as the number, the number of the target micro-area is taken as the cluster number.
In one embodiment, S1.2 specifically includes:
the Euclidean distance is taken as a signal similarity evaluation criterion, and the expression is as follows:
Figure BDA0002655358310000031
wherein S is1,S2Respectively representing two different signals, s1i,s2iThe smaller the euclidean distance between the signals, the higher the similarity between them, respectively, at their corresponding sample points.
In one embodiment, S2 specifically includes:
s2.1: preprocessing raw data, wherein a standardized formula of preprocessing is as follows:
Figure BDA0002655358310000032
wherein X represents the original data, minX represents the minimum value of X, maxX represents the maximum value of X, X represents a data point in the original data set, and X' represents the normalized data point;
s2.2: the noise-reducing self-encoder is configured,
the network structure is a coding-decoding three-layer network structure n-h-n, the number n of neurons in an input layer and the number n of neurons in an output layer are determined according to the number of sampling points of signals, and the number h of neurons in an implicit layer is determined according to a final training result, wherein the activation function of an automatic coder is set as a modified linear unit with Relu (x) max (0, x), and all training variables in the neural network adopt a sliding average;
s2.3: training the noise reduction self-encoder, and adopting a regularization loss function which enables the network generalization capability to be stronger in the network training process, wherein MSEreg is defined as:
Figure BDA0002655358310000041
wherein, wjFor the weight, γ is a super-parameter set manually, n is the number of weights, MSE is the mean square error, defined as:
Figure BDA0002655358310000042
wherein N is the number of training samples,
Figure BDA0002655358310000043
for the target value, y is a prediction value of the noise reduction self-encoder based on the input training data, and an attenuation learning rate with an initial value of 0.01 is set.
One or more technical solutions in the embodiments of the present application have at least one or more of the following technical effects:
the method does not use the traditional prior noise model, but uses the structural characteristics of the signal data to summarize the regular characteristics of the noise and the defect signal, and further learns the corresponding noise reduction rule. That is, for a set of signals containing unknown noise, the method of the present invention firstly analyzes and summarizes the data characteristics thereof, and then forms the corresponding noise reduction rule according to the analysis result. Therefore, the present invention is more adaptive to the suppression of actual unknown noise, which is derived from its ability to learn the characteristics of the defect signal and the noise signal separately by analyzing the rich information provided by the original signal samples. The method can be used for suppressing noise caused by coarse grains, rough surfaces and the like, such as detection of austenitic stainless steel welding seams, laser ultrasonic real-time monitoring of additive manufacturing parts and the like, and can realize intelligent extraction of defect signals submerged by the noise.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 illustrates the grass noise caused by different grain sizes in an embodiment.
FIG. 2 illustrates different grass-like noises caused by different roughnesses in an exemplary embodiment.
FIG. 3 is a weld of an austenitic stainless steel flat plate with embedded cross-hole defects according to an exemplary embodiment.
FIG. 4 shows the noise reduction of the signal at the cross-hole in the exemplary embodiment.
FIG. 5 shows a stainless steel sheet and its internal defect distribution produced by a selective laser melting process (SLM) in an embodiment.
Fig. 6 is a laser ultrasonic scanning pattern in an exemplary embodiment.
FIG. 7 is a diagram illustrating the noise reduction of the laser ultrasonic A-scan signal in an exemplary embodiment.
FIG. 8 is a diagram illustrating the B-scan noise reduction result of the laser ultrasound in the exemplary embodiment.
Fig. 9 is a flowchart of the blind extraction adaptive method provided in the present invention.
Detailed Description
The inventor of the application finds out through a great deal of research and practice that: the prior art methods partially solve some of the problem of extracting defective signals with a specific background of distributed noise. However, as described in the background art, the actual noise is complex and various, and the signal extraction algorithm that we need more is blind-extracted and adaptive, that is, without using any prior knowledge, the intelligent extraction of the defect signal can be realized only by analyzing the data rule or feature of the acquired ultrasonic signal and simultaneously adapting to the grass-like noise environment of any different type and intensity. Therefore, based on the requirement, the invention provides an adaptive method for blind extraction of defect echoes submerged in an ultrasonic grass-like signal. The algorithm can realize intelligent extraction of defect signals under grass-shaped noise backgrounds caused by different grain sizes, different grain types, different grain distributions and different roughness.
Specifically, in order to solve the problem that the existing extraction algorithm cannot adapt to various noise environments and cannot acquire defect signals in ultrasonic nondestructive testing, the invention provides a signal reconstruction method based on statistical reasoning and machine learning. The method can automatically learn the characteristics of the defect signal and the noise signal by analyzing the rich information provided by the collected original signal sample, thereby realizing the effective inhibition of the noise and the intelligent extraction of the defect signal
In order to achieve the technical effects, the main concept of the invention is as follows:
firstly, carrying out similarity analysis on an acquired original signal sample by using an unsupervised machine learning algorithm; then, inputting the similar signal samples into a designed noise reduction self-encoder to train the noise reduction self-encoder, and enabling the noise reduction self-encoder to learn corresponding noise reduction rules; and finally, automatically reducing noise of the signal by using the trained self-encoder, and realizing intelligent extraction of the defect signal. Compared with the existing defect signal extraction technology, the method has stronger adaptability to the inhibition of actual noise, and the strong adaptability is derived from the capability of learning the characteristics of the defect signal and the noise signal respectively by analyzing the rich information provided by the original signal sample.
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The embodiment of the invention provides a defect echo blind extraction self-adaptive method submerged in an ultrasonic grass-shaped signal, which comprises the following steps:
s1: carrying out similarity analysis on the collected original signal samples by using an unsupervised machine learning algorithm, and classifying the similar signals into one class, wherein the unsupervised machine learning algorithm is k-means or DBSCAN, and the original signal samples are ultrasonic A scanning signals, B scanning signals and C scanning signals which are collected aiming at the same test block under the same experimental condition;
s2: inputting the similar signals obtained in the step S1 into a pre-designed noise reduction self-encoder to train the same, so that the pre-designed noise reduction self-encoder learns corresponding noise reduction rules, wherein the pre-designed noise reduction self-encoder is a three-layer neural network with input equal to output, and the form is as follows: n-h-n, where n represents the number of neurons in input and output and h represents the number of neurons in the crypt layer;
s3: and denoising the signal to be processed by utilizing the trained denoising self-encoder.
Specifically, similar signals may be classified as one by step S1 and may be used as training data. In step S2, the obtained similar signals are used to learn and learn the corresponding noise reduction rules. The trained noise reduction self-encoder can be obtained through training, and therefore noise reduction processing on signals can be achieved.
In one embodiment, S1 specifically includes:
s1.1: determining the cluster number of signal clusters;
s1.2: selecting a signal similarity evaluation criterion;
s1.2: and performing similarity analysis on the acquired original signal samples according to the cluster number of the signal cluster and a signal similarity evaluation criterion.
In one embodiment, S1.1 specifically includes:
determining the number of clustering clusters according to the number of signals or the number of target micro-areas, wherein one tenth of the number of acquired signals is set as the number of clusters when the number of signals is taken as a basis; when the target micro-area is taken as the number, the number of the target micro-area is taken as the cluster number.
In one embodiment, S1.2 specifically includes:
the Euclidean distance is taken as a signal similarity evaluation criterion, and the expression is as follows:
Figure BDA0002655358310000061
wherein S is1,S2Respectively representing two different signals, s1i,s2iRespectively, between their corresponding sampling pointsThe smaller the formula distance, the higher the similarity between them.
In one embodiment, S2 specifically includes:
s2.1: preprocessing raw data, wherein a standardized formula of preprocessing is as follows:
Figure BDA0002655358310000071
wherein X represents the original data, minX represents the minimum value of X, maxX represents the maximum value of X, X represents a data point in the original data set, and X' represents the normalized data point;
s2.2: the noise-reducing self-encoder is configured,
the network structure is a coding-decoding three-layer network structure n-h-n, the number n of neurons in an input layer and the number n of neurons in an output layer are determined according to the number of sampling points of signals, and the number h of neurons in an implicit layer is determined according to a final training result, wherein the activation function of an automatic coder is set as a modified linear unit with Relu (x) max (0, x), and all training variables in the neural network adopt a sliding average;
s2.3: training the noise reduction self-encoder, and adopting a regularization loss function which enables the network generalization capability to be stronger in the network training process, wherein MSEreg is defined as:
Figure BDA0002655358310000072
wherein, wjFor the weight, γ is a super-parameter set manually, n is the number of weights, MSE is the mean square error, defined as:
Figure BDA0002655358310000073
wherein N is the number of training samples,
Figure BDA0002655358310000074
is a target ofThe value y is a prediction value of the noise reduction self-encoder based on the input training data, and the attenuation learning rate with an initial value of 0.01 is set.
Specifically, through the standardization process, gradient explosion or gradient disappearance in the network training process can be prevented, and the moving average, that is, all values in the variable change process are averaged, so that the screenshot enables the encoder to have good robustness.
Referring to fig. 7 to 9, fig. 7 is a diagram illustrating a noise reduction result of a laser ultrasonic a-scan signal in an embodiment, where a larger fluctuation is an original signal and a smaller fluctuation is a noise reduced signal, fig. 8 is a diagram illustrating a noise reduction result of a laser ultrasonic B-scan in an embodiment, and fig. 9 is a flowchart illustrating a blind extraction adaptive method according to the present invention, where a signal database is established to construct an original signal to be acquired into a database.
After the original signal samples are trained, the self-encoder learns the corresponding noise reduction rule, and the original signals can be automatically filtered after passing through the trained self-encoder. It is noted that the described noise reduction rules are obviously not determined a priori, but by the experimental data itself, the whole noise reduction process being driven entirely by the data. Therefore, compared with the existing noise reduction technology, the method has stronger adaptability to the suppression of the actual noise, and the strong adaptability is caused by the capability of learning the characteristics of the defect signal and the noise signal respectively by analyzing the abundant information provided by the original signal sample.
The method provided by the invention does not use the traditional prior noise model, but uses the structural characteristics of the signal data to summarize the regular characteristics of the noise and the defect signal, thereby obtaining the corresponding noise reduction rule. That is, for a set of signals containing unknown noise, the invention firstly analyzes and summarizes the data characteristics of the signals, and then forms a corresponding noise reduction rule according to the analysis result. Therefore, the present invention is more adaptive to the suppression of actual unknown noise, which is derived from its ability to learn the characteristics of the defect signal and the noise signal separately by analyzing the rich information provided by the original signal samples. The method can be used for suppressing noise caused by coarse grains, rough surfaces and the like, such as detection of austenitic stainless steel welding seams, laser ultrasonic real-time monitoring of additive manufacturing parts and the like, and can realize intelligent extraction of defect signals submerged by the noise.
Embodiments of the present invention are described in detail below by way of examples with reference to specific examples.
The first embodiment is as follows: in the present embodiment, an austenitic stainless steel weld is used as a detection target.
The method comprises the following steps: and establishing a signal database. The tested block is an austenitic stainless steel flat plate butt welding seam, the grain distribution is extremely uneven along the welding seam direction, and the grain size fluctuates within 60-300 mu m. Scanning is carried out right above a welding line along the length direction of the welding line by adopting a 5MHz straight probe (figure 1), the step length is 1mm, the scanning distance is 130mm, the system gain is set to be 60dB, the sampling frequency is 100MHz, and the sampling depth is 1000. Finally, a 130 × 1000 signal matrix is obtained.
Step two: and (5) analyzing the similarity of the signals. And (3) adopting a k-means clustering algorithm to carry out similarity analysis on 1-610 sampling points of the A-scan signal, setting the number of clustering clusters to be 13, and setting the similarity criterion to be Euclidean distance.
Step three: and (5) network training. The 13 clusters of signals are respectively input into a designed self-encoder for training.
Step four: and inputting the original signal into a trained self-encoder for automatic noise filtering. Fig. 2 shows the noise reduction signal at the cross-hole. From the original signal it can be seen that the hole signal has been completely drowned by the noise, and after the noise reduction, the hole signal is well revealed.
The second embodiment is as follows: in the present embodiment, a stainless steel additive manufacturing test block is used as a detection target.
The method comprises the following steps: and establishing a signal database. The test piece was a rectangular stainless steel thin plate made by a selective laser melting process (SLM), 5mm thick, and 75 μm surface average roughness. The inside of the test block is processed with 6 groove defects with different buried depths, and the specific layout and related parameters are shown in fig. 3. Grid scanning is carried out on the three-dimensional signal matrix by adopting 2MHz laser ultrasound (figure 4), the scanning range is 20mm multiplied by 25mm, 6 defects are covered, the step length is 0.1mm, an A scanning signal is recorded on each grid point, the sampling depth is 2000, and finally, a 200 multiplied by 250 multiplied by 2000 three-dimensional signal matrix is obtained.
Step two: and (5) analyzing the similarity of the signals. And (3) adopting a k-means clustering algorithm to carry out similarity analysis on 1-500 sampling points of the A-scan signal, setting the number of clustering clusters to be 3000, and setting the similarity criterion to be Euclidean distance.
Step three: and (5) network training. 3000 clusters of signals are respectively input into a designed self-encoder for training.
Step four: and inputting the original signal into a trained self-encoder for automatic noise filtering. Fig. 5 shows the a-scan noise reduction result, and it can be seen that the surface waves after noise reduction are well shown. Fig. 6 shows the noise reduction result of B-scan formed by a sequence of a-scan combinations, and it can be seen that the image definition is greatly improved.
The specific embodiments described herein are merely illustrative of the methods and steps of the present invention. Those skilled in the art to which the invention relates may make various changes, additions or modifications to the described embodiments (i.e., using similar alternatives), without departing from the principles and spirit of the invention or exceeding the scope thereof as defined in the appended claims. The scope of the invention is only limited by the appended claims.

Claims (4)

1. An adaptive method for blind extraction of defect echoes submerged in an ultrasonic grass-like signal, comprising:
s1: carrying out similarity analysis on the collected original signal samples by using an unsupervised machine learning algorithm, and classifying the similar signals into one class, wherein the unsupervised machine learning algorithm is k-means or DBSCAN, and the original signal samples are ultrasonic A scanning signals, B scanning signals and C scanning signals which are collected aiming at the same test block under the same experimental condition;
s2: inputting the similar signals obtained in the step S1 into a pre-designed noise reduction self-encoder to train the same, so that the pre-designed noise reduction self-encoder learns corresponding noise reduction rules, wherein the pre-designed noise reduction self-encoder is a three-layer neural network with input equal to output, and the form is as follows: n-h-n, where n represents the number of neurons in input and output and h represents the number of neurons in the crypt layer;
s3: carrying out noise reduction on a signal to be processed by utilizing a trained noise reduction self-encoder;
wherein, S2 specifically includes:
s2.1: preprocessing raw data, wherein a standardized formula of preprocessing is as follows:
Figure 64919DEST_PATH_IMAGE001
(2)
wherein, X represents the original data,
Figure 869540DEST_PATH_IMAGE002
it is indicated that the minimum value is taken for X,
Figure 10671DEST_PATH_IMAGE003
means to take the maximum value for X, X represents a data point in the original data set, and X' represents a normalized data point;
s2.2: the noise-reducing self-encoder is configured,
the network structure is a coding-decoding three-layer network structure n-h-n, the number n of neurons in an input layer and the number n of neurons in an output layer are determined according to the number of sampling points of signals, and the number h of neurons in an implicit layer is determined according to a final training result, wherein the activation function of the noise reduction self-encoder is set as a modified linear unit of Relu (x) = max (0, x), and all training variables in the neural network adopt a sliding average;
s2.3: training the noise reduction self-encoder, and adopting a regularization loss function which enables the network generalization capability to be stronger in the network training process, wherein MSEreg is defined as:
Figure 321698DEST_PATH_IMAGE004
(3)
wherein the content of the first and second substances,
Figure 890082DEST_PATH_IMAGE005
for the weight, γ is a super-parameter set manually, n is the number of weights, MSE is the mean square error, defined as:
Figure 653770DEST_PATH_IMAGE006
(4)
wherein N is the number of training samples,
Figure 395330DEST_PATH_IMAGE007
in order to achieve the target value,
Figure 560863DEST_PATH_IMAGE008
an attenuation learning rate with an initial value of 0.01 is set for the noise reduction self-encoder based on a predicted value of input training data.
2. The adaptive method for defect-echo blind extraction according to claim 1, wherein S1 specifically includes:
s1.1: determining the cluster number of signal clusters;
s1.2: selecting a signal similarity evaluation criterion;
s1.3: and performing similarity analysis on the acquired original signal samples according to the cluster number of the signal cluster and a signal similarity evaluation criterion.
3. The adaptive method for defect-echo blind extraction according to claim 2, wherein S1.1 specifically comprises:
determining the number of clustering clusters according to the number of signals or the number of target micro-areas, wherein one tenth of the number of acquired signals is set as the number of clusters when the number of signals is taken as a basis; and when the number of the target micro-areas is taken as the basis, taking the number of the target micro-areas as the cluster number.
4. The adaptive method for defect-echo blind extraction according to claim 2, wherein S1.2 specifically comprises:
the Euclidean distance is taken as a signal similarity evaluation criterion, and the expression is as follows:
Figure DEST_PATH_IMAGE009
(1)
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE011
Figure 172586DEST_PATH_IMAGE012
respectively, represent two different signals that are each,
Figure DEST_PATH_IMAGE013
Figure 485886DEST_PATH_IMAGE014
the smaller the euclidean distance between the signals, the higher the similarity between them, respectively, at their corresponding sample points.
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