CN116933119A - Signal data trend removal method based on convolutional neural network - Google Patents
Signal data trend removal method based on convolutional neural network Download PDFInfo
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Abstract
The method for removing the trend of the signal data segment based on the convolutional neural network comprises the following steps: step one: defining signal trend item evaluation indexes; step two: constructing a neural network model signal dataset; step three: determining signal segmentation points based on a convolutional neural network segmentation network recognition model; step four: removing the trend of the segmented signal by adopting a least square trend term algorithm; step five: calculating the prediction accuracy and analyzing the performance of the model. The method can realize automatic prediction of the position of the segmentation point of the data by constructing the convolutional neural network model, and remove the segmentation trend item according to the position of the segmentation point, and has the following beneficial effects: better results than the traditional trending method; the processing efficiency of large data volume is high; the low-frequency information is not deleted, and the original frequency information of the signal is well reserved. The problems of low removal efficiency and poor removal effect of trend items in actual data processing are solved, and the method has extremely high application value.
Description
Technical Field
The application relates to the field of signal processing.
Background
At present, in the field of signal processing, the traditional signal trending term method mainly comprises a linear method based on a least square method, an Empirical Mode Decomposition (EMD) method and a wavelet transformation method. The linear method based on the least square method removes trend terms through polynomial fitting, but the removal effect for nonlinear trend terms is not ideal. Empirical Mode Decomposition (EMD) trending is performed by designing a filter to remove the trending term by treating the trending term signal as a low pass signal. However, in the filter design process, the collected signals are different, the filter design parameters are also different, the field of signal processing is limited, and meanwhile, the signals with unknown frequencies are difficult to process. The wavelet transformation method can decompose the signal into signals with different frequencies, and the high frequency and the low frequency of the signal can be separated through the decomposition and the reconstruction of wavelet transformation, so that the trend term is removed. The wavelet analysis detrending term is affected by the choice of the number of base wavelet and decomposition levels,
the selection of the basis wavelets still mainly depends on experience selection, so that the application field of wavelet analysis is narrow. At present, the deep learning field and the engineering field are developed in a crossing way more and more widely, a plurality of complex problems can be solved by adopting machine learning and deep learning technologies, and in the signal trend term removal field, the trend term removal method based on machine learning and a neural network is not mature at present.
When engineering actual measurement signals are processed, such as high-frequency long-term monitoring signals of some vibration, millions or even tens of millions of data can be achieved in only 1 day, the trend item of the least square method is directly carried out on the whole data or real-time data, the data operation cost is huge, and great calculation force is required to be consumed. The frequency of the signal is generally assumed to be known when using EMD or the like. In fact, in complex practical engineering problems, there are often cases where the frequency of the acquired signal is unknown, so removing low-pass signals is not an efficient method in many situations. If the wavelet method is adopted, the number of layers of wavelet decomposition and the selection of the base wavelet have empirical selection, and cannot be directly used on some problems. Therefore, the conventional method is difficult to be suitable for the trending treatment of the signal data with large data volume at present, and an artificial intelligence technology is urgently required to be cited, so that a novel automatic trending method which is suitable for most cases and is not influenced by signal conditions is created.
Disclosure of Invention
In order to overcome the problems of the traditional signal trending item method, the application provides a signal data segmentation trending method based on a convolutional neural network.
The technical scheme adopted by the application for achieving the purpose is as follows: a signal data removal trend method based on a convolutional neural network is characterized by comprising the following steps of: the method comprises the following steps:
step one: defining a signal trend term evaluation index, wherein the trend term offset ratio (DR) is defined as follows:
the Amplitude Ratio (AR) is defined as:
wherein ,xi (t) raw data obtained by experimental data measurement, N is the total amount of the number, x i-real (t) is a signal true value, mean represents an average value, rms represents a root mean square value, and the operation formulas are formula 1.3 and formula 1.4:
wherein t0 The mean is the initial time of the vibration signal and the final time of the signal; t is t i Is the i-th point in time in the signal; n is the total number of data points of the test signal;
step two: a neural network model signal dataset is constructed,
2.1 signal type establishment:
(1) indicating that the segment signal is of the full-plateau (steady) type, the data of the full-plateau has no segmentation points;
(2) the signal is represented as a type of stable before fluctuation, and a segmentation point is provided;
(3) the signal is expressed as fluctuation and then stable, and a segmentation point is arranged;
(4) representing the full wave (wave) type, without segmentation points;
2.2 selection method of signals:
firstly, two kinds of original data phi are selected from a signal data set, the length of the original data is far greater than the maximum signal length M, a data structure data set with the fixed length M is randomly selected from the phi by randomly taking segmentation points, the number of samples is 4L when the 4 kinds of data are respectively L groups, the label is 1X 2D, the first column indicates whether segmentation points exist, wherein 0 indicates that segmentation points exist, 1 indicates that segmentation points exist, the second column indicates the position N of the segmentation points, normalization processing is carried out on the data set, and maximum value and minimum value normalization processing is carried out on input, as shown in a formula 2.1:
the second column of labels is normalized as shown in equation 2.2:
after the position of the segmentation point is determined, performing inverse normalization to determine the specific position of the segmentation point in the signal;
step three: determining signal segment points based on the convolutional neural network segment network recognition model,
3.1 constructing a segment network identification model based on a convolutional neural network,
3.2 based on a convolutional neural network segment network recognition model:
importing the training set data into a network model, calculating the accuracy of the training set after iterative training is finished, obtaining a network model meeting the requirements when the training set meets the requirements, further carrying out segment point prediction on test data by adopting the network model, and outputting the segment point positions of the data by the network model;
step four: the segmented signal is trended by adopting a least squares trending term algorithm,
let the sampling data of the measured vibration test data be x k (k=1, 2,3, … n), since the sampled data is equally spaced, let the sampling interval Δt=1 for simplicity, a polynomial is set as shown in equation 2.5:
wherein isFitting data, a i Is a coefficient to be determined; m is the order;
all the sampling data can be calculated, and the method can be obtained:
wherein ,
solving for a functionIs a coefficient of uncertainty of a i (i=0, 1,2, … m) to let the function +.>And sample data x k The sum of squares of the errors between them is minimal, namely:
combining equation 2.6, find a for E pair i (i=0, 1,2, … m), there are:
let the partial derivative be zero, i.e. the minimum of the sum of squares of the errors, so there are:
A＝(K T K) -1 K T X (2.10)
m+1 undetermined coefficients can be obtained through the above formula, when m=0, the obtained trend term is the arithmetic mean of sampling data, when m=1, the obtained trend term is a linear trend term, when m is more than or equal to 2, the obtained trend term is a curve trend term, and the formula for eliminating the trend term is as follows:
performing trend term removal analysis on vibration sampling data by m=1-3;
step five: calculating the prediction accuracy and analyzing the performance of the model.
Defining an evaluation index according to the steps, wherein if DR is closer to 0, the signal removing effect on the overall trend item is better; the smaller the value of the |AR-1| is, the better the effect of removing the local trend term of the signal is, if the removal effect is found to not reach the expected effect through calculation, the second step is returned, more data sets are added to the model, further training is carried out, and the model with better processing effect can be obtained as long as the output result meets the requirement.
The step 3.1 is as follows: the convolution layer of the network model adopts a LeakyReLU activation function, the LeakyReLU activation function improves the negative interval of the ReLU to ensure that the ReLU has a small gradient in the negative interval, and the expression is expressed as formula 2.3:
wherein λ represents a super parameter;
the activation function used at the last layer of Branch1 is a Softmax function, defined as equation 2.4, by dividing the converted result by the sum of all converted results:
wherein ,zi For the output value of the ith node, c is the number of output nodes, namely the number of classified categories, the multi-classified output value is converted into the range of [0,1 ] by the Softmax function]And a probability distribution of 1.
In the fourth step, a linear regression model Linear Regression in sklearn. Linear is used, and Polynomial Features in sklearn. Preprocessing module is used to generate the polynomial.
The signal data removal trend method based on the convolutional neural network can realize automatic prediction of the segmentation point positions of the data by constructing the convolutional neural network model, and performs segmentation trend item removal according to the segmentation point positions, and has the following beneficial effects: better results than the traditional trending method; the processing efficiency of large data volume is high; the original frequency information of the signal is well reserved and no new noise is added. The problems of low removal efficiency and poor removal effect of trend items in actual data processing are solved, and the method has extremely high application value.
Drawings
FIG. 1 is a general flow chart of a method for removing trends in signal data segments based on convolutional neural network.
Fig. 2 is a schematic diagram of the signal segmentation process of the present application.
Fig. 3 is a schematic diagram of the signal dataset classification of the present application.
Fig. 4 is a block diagram of a convolutional neural network of the present application.
Fig. 5 is a graph of raw data of a signal vibration test of the present application.
Fig. 6a is a schematic diagram of a training set of the full-stationary (step) type.
Fig. 6b is a schematic diagram of a smooth-before-wavy training set.
Fig. 6c is a schematic diagram of a wave-front-stationary type training set.
Fig. 6d is a schematic diagram of a full wave (wave) type training set.
Fig. 7 is a graph of accuracy of network training of the present application.
FIG. 8 is a graph of the segmentation results of experimental data of the present application.
FIG. 9 is a graph of simulation results of the present application based on segment trend term removal of convolutional neural networks.
FIG. 10 is a graph of the linear detrending term of the least squares method of the present application.
FIG. 11 is a graph of the wavelet analysis detrending term of the present application.
Detailed Description
The method for removing trend of signal data segments based on convolutional neural network provided by the application is shown in figure 1,
step one: defining signal trend item evaluation indexes;
step two: a neural network model signal dataset is constructed.
Step three: determining signal segmentation points based on a convolutional neural network segmentation network recognition model;
step four: removing the trend of the segmented signal by adopting a least square trend term algorithm;
step five: calculating prediction accuracy and analyzing model performance;
according to the method, the fact that the collected test signals are mixed with the nonlinear trend and the linear trend is considered, the data can be subjected to sectional processing, and then trend items are removed according to sectional results. The acquired vibration test signals are divided into data with different lengths according to time sequences, and the data are shown in fig. 2. The basis of segmentation is that the data are regularly changed in different time periods in time sequence, as shown in fig. 2 a, b, c, d, e and f, and the trend term removal after segmentation ensures the processing efficiency and the processing result, and meanwhile, high calculation cost is not required.
The method comprises the following steps:
step 1, defining signal trend item evaluation indexes:
the application defines two signal trend item evaluation indexes: trend term offset Ratio (DR) and Amplitude Ratio (AR). The trend term offset Ratio (DR) measures the degree to which a signal deviates from a baseline on an overall trend, and the Amplitude Ratio (AR) measures the degree of local deviation.
Wherein the trend term offset ratio (DR) is defined as:
the Amplitude Ratio (AR) is defined as:
wherein ,xi (t) raw data obtained by experimental data measurement, N is the total amount of the number, x i-real (t) is a signal true value, mean represents an average value; rms represents root mean square value. The operation formulas are formula 1.3 and formula 1.4:
wherein t0 The mean is the initial time of the vibration signal and the final time of the signal; t is t i Is the i-th point in time in the signal; n is the total number of data points of the test signal.
The trend term offset ratio (DR) is an indicator that measures the degree to which a signal deviates from a baseline over an overall trend, and the overall offset of the signal curve increases as the DR value increases. Dr=0 indicates that the signal does not have a trend term shift, and it should be noted that the baseline correction of the present application targets DR <0.01 due to the complex occurrence of the trend term. On the other hand, the Amplitude Ratio (AR) may be used to measure the degree of local deviation. The larger the value of AR, the more pronounced the local offset of the signal. The result of the suggested trend term correction satisfies |ar-1| <0.5.
1.2 step two: constructing a neural network model signal dataset:
1.2.1 signal type establishment:
for a neural network model, it is important to construct a data set, which is constructed from actual time domain signal data in order to ensure the authenticity and validity of the data. Considering the overall trend of time domain data, for a piece of signal data, it can be divided into 4 basic types: full steady, wave-first then steady, wave-first steady then wave-second full wave. As shown in fig. 3:
(1) indicating that the segment signal is of the full-plateau (steady) type, the data of the full-plateau has no segmentation points;
(2) the signal is represented as a type of stable before fluctuation, and a segmentation point is provided;
(3) the signal is expressed as fluctuation and then stable, and a segmentation point is arranged;
(4) indicating the full wave (wave) type, without segmentation points.
Assuming that the maximum signal length of a single segmentation point is M, namely that two or more segmentation points cannot occur in the length, if the maximum signal length is too small, the effective features are too small to be fully extracted, and when the original data length is too large, the signal is divided according to the M length, so that the problems of excessive segmentation number, excessive model complexity, higher redundancy and the like are caused, and the quality and accuracy of test data are affected.
1.2.2 selection method of signals:
to ensure randomness of the data set, two main classes of raw data Φ (full stationary and full wave) are first selected from the signal data set, which raw data length is much larger than the maximum signal length M. And randomly selecting data with fixed length M from phi by randomly taking segmentation points to construct a data set, wherein the number of samples is 4L when the data of the 4 types are respectively L groups. The label is 1 x 2 dimension, the first column indicates the presence or absence of a segmentation point, where 0 indicates no segmentation point, 1 indicates the presence of a segmentation point, and the second column indicates the segmentation point position N. Normalizing the data set, and normalizing the maximum value and the minimum value of the input: as shown in equation 2.1:
the second column of labels is normalized as shown in equation 2.2:
after the segmentation point position is determined, inverse normalization is performed to determine the specific position of the segmentation point in the signal.
1.3 step three: segmenting the signal based on a convolutional neural network segment network recognition model:
1.3.1 construction of a convolutional neural network-based segment network recognition model
The neural network structure used in the present application is shown in fig. 4.
According to the 2.1, the input feature dimension of the neural network is 1×m, in the convolution part, the convolution is divided into two layers, the convolution kernel of the first layer is 1×p, the step length is P, the effective feature of each second of sampled data is extracted, the convolution kernel of the second layer is 1×q, the step length is Q, the relation feature of each second of data is extracted, the third layer of full-connection layer comprises two branches of Branch1 and Branch2, wherein Branch1 is regarded as a two-class problem, whether a segmentation point exists in the data of the section is judged, 10 represents an uninterrupted point, 01 represents a discontinuous point, and finally the Output layer Output1 outputs a result; and regarding Branch2 as a regression problem, and predicting the point positions of the segments.
Unlike conventional convolutional neural networks, the network structure of the present application eliminates the pooling layer. The pooling layer is mainly used for feature dimension reduction and compression parameter quantity. The selected input feature dimension is different from the large-scale data processed by the common convolutional neural network, the input feature dimension is smaller, and if the pooling operation is carried out, effective features in the data are easily lost, so that the model prediction accuracy is reduced.
The convolution layer of the network model adopts a LeakyReLU activation function, and the LeakyReLU activation function improves the negative interval of the ReLU, so that the ReLU has a small gradient in the negative interval. The expression is shown in formula 2.3:
where lambda represents the hyper-parameter.
The activation function used in the last layer of Branch1 is the Softmax function, also known as the normalized exponential function. The method is a popularization of a classification function Sigmoid on multiple classifications, and aims to display the multi-classification result in a probability mode. To ensure that the sum of the probabilities of the individual predictors is equal to 1. Normalization processing is required for the converted result. The method is to divide the converted result by the sum of all converted results, and the Softmax function is defined as formula 2.4:
wherein ,zi And c is the number of output nodes, namely the number of classified categories, for the output value of the ith node. The multi-class output values can be converted to the range of [0,1 ] by the Softmax function]And a probability distribution of 1.
1.3.2 convolutional neural network based segment network identification model
And importing the training set data into a network model, calculating the accuracy of the training set after the iterative training is finished, and obtaining the network model meeting the requirements when the training set meets the requirements. And then the test data is subjected to segmentation point prediction by adopting the network model, and the network model outputs the segmentation point positions of the data.
1.4 step four: removing the trend of the segmented signal by adopting a least square method trend term removal algorithm for the signal
In the application, in order to simplify the operation time, the signals are segmented to remove trend terms according to the segmentation point prediction positions under the condition of not losing data precision.
Let the sampling data of the measured vibration test data be x k (k=1, 2,3, … n), since the sampled data is equally spaced, let the sampling interval Δt=1 for simplicity, a polynomial is set as shown in equation 2.5:
wherein isFitting data, a i Is a coefficient to be determined; m is the order.
All the sampling data can be calculated, and the method can be obtained:
wherein ,
solving for a functionIs a coefficient of uncertainty of a i (i=0, 1,2, … m) to let the function +.>And sample data x k The sum of squares of the errors between them is minimal, namely:
combining equation 2.6, find a for E pair i (i=0, 1,2, … m), there are:
let the partial derivative be zero, i.e. the minimum of the sum of squares of the errors, so there are:
A＝(K T K) -1 K T X (2.10)
m+1 undetermined coefficients can be obtained through the above formula. When m=0, the trend term is calculated as an arithmetic mean of the sampled data, when m=1, the trend term is calculated as a linear trend term, and when m is equal to or greater than 2, the trend term is calculated as a curve trend term. The formula for eliminating the trend term is as follows:
the vibration sample data is typically detritus analyzed by taking m=1 to 3.
Linear regression (Linear Regression) is a statistical analysis method that uses regression analysis in mathematical statistics to determine the quantitative relationship of interdependence between two or more variables. Linear regression models the relationship between one or more independent and dependent variables using the error least squares method of the linear regression equation. The present application uses a linear regression model Linear Regression in sklearn. Polynomial Features in the sklearn.preprocessing module is employed for generating the polynomial.
Step five: calculating prediction accuracy and analyzing model performance:
evaluation index was defined according to section 1.1. DR, if closer to 0, indicates better signal removal on the overall trend term; the smaller the value of the |AR-1| is, the better the effect of removing the local trend term of the signal is, if the removal effect is found to not reach the expected effect through calculation, the second step is returned, more data sets are added to the model, further training is carried out, and the model with better processing effect can be obtained as long as the output result meets the requirement.
The application will now be further described with reference to examples, figures. Taking the trend removal of vibration signal test data measured by a strain gauge of a certain railway wagon as an example, the method is verified. The signal has a plurality of parking time periods, the acceleration of the parking time periods is close to zero, the sampling frequency is 500Hz, the time length of the signal is two hours, 360 ten thousand data points are taken in total, and the original data image is shown in figure 5.
The operation environment of the application is as follows: software is python3.8.6, pycharm2021.3, and hardware is processor Intel Core i5-8250u,12g memory, GPU model Radeon 520.
2.1 trending by the method of the application:
the trend removing operation for the signal data by adopting the method provided by the application is as follows:
(1) A data set is constructed and a data set is constructed,
the data set assumes that the maximum signal length M at which a single segment point occurs is 150000, i.e., two or more segment points do not occur within that length, and under this condition, the length of the data source Φ is much greater than the maximum signal length, meeting the random sampling requirement. If the maximum signal length is too small, the extraction of effective features will be affected, resulting in too low accuracy of the network model.
Based on the 1.2 method, four kinds of data are constructed, each kind of data randomly takes 200 groups of data, the length of each group of data is 150000, and the total number of samples is 800 groups. A schematic diagram thereof is shown in fig. 6.
In the data set, the ratio of the training set to the test set is 6:2. In the convolution layers, a convolution kernel of a first convolution layer 1 is set to be 1×500, the step length is set to be 500, then a second convolution layer 2 operation is carried out, the convolution kernel size is set to be 1×2, and the step length is set to be 1. And finally, integrating all the features by adopting a full-connection layer to finally obtain the segmented point network model. The parameters of the convolutional neural network used in the application are shown in table 1, the number of the first layer of convolutional kernels is 64, and the number of the second layer of convolutional kernels is 32. The number of neurons of the full connection layer is 32, 64 and 32 respectively. Lambda of the LeakyReLU activation function is 0.01. The maximum iteration number is 200, the learning rate is set to be 0.0001, and the Adam algorithm is selected as an optimization algorithm.
Table 1 convolutional neural network model parameter settings
(2) Training data
Based on the 1.3.1 model method, a constructed test set simulation experiment is imported, as shown in fig. 6, which is a simulation experiment result, and a curve is the accuracy of network training. From this, the network training accuracy graph of fig. 7 can be obtained, and it can be seen from the graph that the test sample estimation result is good, and the test accuracy reaches 0.99.
All the existing vibration test data are used for constructing a data set as a test sample according to the method mentioned in the 1.3 of the application, and the data set is used as a sample for testing the accuracy of the network model. As shown in fig. 7.
(3) The sample signal data is segmented into segments,
sample data was segmented using the 1.3 method. As can be seen from fig. 8, the simulation experiment result of the segmentation algorithm based on the convolutional neural network meets the expected value, and all the segmentation point estimation results are good.
(4) Trending the data according to signal segmentation points:
the signal is detrended by the segmentation points obtained by the method 1.4 of the original data, as shown in fig. 9.
(5) And (3) returning to the step (1) to increase the data set and train if the evaluation index does not meet the accuracy requirement.
2.2 comparing with the results of the conventional detrending method:
the application uses the segmentation trend term removal algorithm based on the convolutional neural network to remove the trend term, the sample data is 360 ten thousand pieces of data, the whole trend removal process is about 25 seconds according to the common computer software and hardware configuration in the section 2.1, the result is shown in fig. 9, the trend term in the original signal can be completely removed, and the purpose of the algorithm design is realized. Meanwhile, the signal is not added with new noise when the trend is in the trend item, and a good trend removing effect can be achieved.
Table 2 sample signal results vs. graph
Table 2 shows a comparison of the results of the process of the present application and the conventional process. It can be seen from Table 2 that the DR mentioned in this application is closest to 0, indicating that the trending term is best, while AR is closest to 1, far better than the conventional method. Therefore, compared with the method provided by the application, the method provided by the application has the highest precision after removing the trend item, and has better application value.
The following is a specific discussion in comparison to the conventional signal detrending method:
(1) Least square method linear declivity
The offset ratio (DR) and the Amplitude Ratio (AR) are respectively: dr=0.063, ar=1.20. It can be seen that the least squares method has poor effect of linearly removing the trend term, and does not completely remove the trend term. For the complex data mentioned in fig. 10, the linear detrending term alone cannot meet the data analysis requirement, and there may be a large error in the problem of impairing the data quality after the data processing, so that the removal of the trending term of the test data using the linear detrending term is limited.
(2) Wavelet analysis detrending term
The offset ratio (DR) and the Amplitude Ratio (AR) are respectively: dr=0.0445, ar=0.096. The wavelet transformation trend term is removed and selected as db5 wavelet. The number of decomposition layers was 8. As can be seen from fig. 11, when the trend term component of the vibration test signal is removed by wavelet analysis, different levels of decomposition are required for the base wavelet, however, the parameter selection and the number of decomposition layers of the base wavelet are difficult to accurately determine, but the parameter selection greatly affects the result of signal processing. Typically, the number of layers of the decomposition and the parameter selection of the base wavelet are empirically chosen. In addition, in the wavelet deconstructing and reconstructing process, the calculated amount is large, and the method is not suitable for processing massive data. Wavelet analysis is therefore limited to eliminating trend terms.
According to the segmentation trend term removal algorithm based on the convolutional neural network, the segmentation point positions can be automatically predicted by constructing a convolutional neural network model, and segmentation trend term removal is performed according to the segmentation point positions. The method has the beneficial effects that:
(1) Better results than the traditional trending method. As shown by the comparison result, the DR mentioned in the application is closest to 0, which shows that the trending term effect is best, and the AR is closest to 1, which is far better than the traditional method, and has better application value.
(2) The processing efficiency of large data volume is high. The trend item is removed after the data are segmented according to the segmentation points, so that the processing efficiency is guaranteed, the processing result is guaranteed, and meanwhile, high calculation cost is not required. The sample data is 360 ten thousand pieces of data, and the whole trend removal process is about 25 seconds according to the software and hardware configuration of a common computer.
(3) The original frequency information of the signal is well reserved and no new noise is added. The method avoids the limitation of a certain low-frequency signal by eliminating the limitation of the traditional method, ensures the frequency composition and the trend item of the signal, well reserves the original frequency information of the signal, does not add new noise, and can achieve good trend removal effect.
The method can solve the problems of low removal efficiency and poor removal effect of trend items in actual data processing, and has extremely high application value.
The present application has been described in terms of embodiments, and it will be appreciated by those of skill in the art that various changes can be made to the features and embodiments, or equivalents can be substituted, without departing from the spirit and scope of the application. In addition, many modifications may be made to adapt a particular situation or material to the teachings of the application without departing from the essential scope thereof. Therefore, it is intended that the application not be limited to the particular embodiment disclosed, but that the application will include all embodiments falling within the scope of the appended claims.
Claims (3)
1. A signal data removal trend method based on a convolutional neural network is characterized by comprising the following steps of: the method comprises the following steps:
step one: defining a signal trend term evaluation index, wherein the trend term offset ratio (DR) is defined as follows:
the Amplitude Ratio (AR) is defined as:
wherein ,xi (t) raw data obtained by experimental data measurement, N is the total amount of the number, x i-real (t) is a signal true value, mean represents an average value, rms represents a root mean square value, and the operation formulas are formula 1.3 and formula 1.4:
wherein t0 The mean is the initial time of the vibration signal and the final time of the signal; t is t i Is the i-th point in time in the signal; n is the total number of data points of the test signal;
step two: a neural network model signal dataset is constructed,
2.1 signal type establishment:
(1) indicating that the segment signal is of the full-plateau (steady) type, the data of the full-plateau has no segmentation points;
(2) the signal is represented as a type of stable before fluctuation, and a segmentation point is provided;
(3) the signal is expressed as fluctuation and then stable, and a segmentation point is arranged;
(4) representing the full wave (wave) type, without segmentation points;
2.2 selection method of signals:
firstly, two kinds of original data phi are selected from a signal data set, the length of the original data is far greater than the maximum signal length M, a data structure data set with the fixed length M is randomly selected from the phi by randomly taking segmentation points, the number of samples is 4L when the 4 kinds of data are respectively L groups, the label is 1X 2D, the first column indicates whether segmentation points exist, wherein 0 indicates that segmentation points exist, 1 indicates that segmentation points exist, the second column indicates the position N of the segmentation points, normalization processing is carried out on the data set, and maximum value and minimum value normalization processing is carried out on input, as shown in a formula 2.1:
the second column of labels is normalized as shown in equation 2.2:
after the position of the segmentation point is determined, performing inverse normalization to determine the specific position of the segmentation point in the signal;
step three: determining signal segment points based on the convolutional neural network segment network recognition model,
and 3.1, constructing a convolutional neural network-based segment network identification model.
3.2 based on a convolutional neural network segment network recognition model:
importing the training set data into a network model, calculating the accuracy of the training set after iterative training is finished, obtaining a network model meeting the requirements when the training set meets the requirements, further carrying out segment point prediction on test data by adopting the network model, and outputting the segment point positions of the data by the network model;
step four: the segmented signal is trended by adopting a least squares trending term algorithm,
let the sampling data of the measured vibration test data be x k (k=1, 2,3, … n), since the sampled data is equally spaced, let the sampling interval Δt=1 for simplicity, a polynomial is set as shown in equation 2.5:
wherein isFitting data, a i Is a coefficient to be determined; m is the order;
all the sampling data can be calculated, and the method can be obtained:
wherein ,
solving for a functionIs a coefficient of uncertainty of a i (i=0, 1,2, … m) to let the function +.>And sample data x k The sum of squares of the errors between them is minimal, namely:
combining equation 2.6, find a for E pair i (i=0, 1,2, … m), there are:
let the partial derivative be zero, i.e. the minimum of the sum of squares of the errors, so there are:
A＝(K T K) -1 K T X (2.10)
m+1 undetermined coefficients can be obtained through the above formula, when m=0, the obtained trend term is the arithmetic mean of sampling data, when m=1, the obtained trend term is a linear trend term, when m is more than or equal to 2, the obtained trend term is a curve trend term, and the formula for eliminating the trend term is as follows:
performing trend term removal analysis on vibration sampling data by m=1-3;
step five: calculating the prediction accuracy and analyzing the performance of the model.
Defining an evaluation index according to the steps, wherein if DR is closer to 0, the signal removing effect on the overall trend item is better; the smaller the AR is, the better the effect of removing the local trend term of the signal is, if the removal effect is found to not reach the expected effect through calculation, the second step is returned, more data sets are added to the model, further training is carried out, and the model with better processing effect can be obtained as long as the output result meets the requirement.
2. The method for removing trend from signal data based on convolutional neural network according to claim 1, wherein: the step 3.1 is as follows: the convolution layer of the network model adopts a LeakyReLU activation function, the LeakyReLU activation function improves the negative interval of the ReLU to ensure that the ReLU has a small gradient in the negative interval, and the expression is expressed as formula 2.3:
wherein λ represents a super parameter;
the activation function used at the last layer of Branch1 is a Softmax function, defined as equation 2.4, by dividing the converted result by the sum of all converted results:
wherein ,zi For the output value of the ith node, c is the number of output nodes, namely the number of classified categories, the multi-classified output value is converted into the range of [0,1 ] by the Softmax function]And a probability distribution of 1.
3. The method for removing trend from signal data based on convolutional neural network according to claim 1, wherein: in the fourth step, a linear regression model Linear Regression in sklearn. Linear is used, and Polynomial Features in sklearn. Preprocessing module is used to generate the polynomial.
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