CN115342900B - Random forest-based laser self-mixing interference micro-vibration measurement method and system - Google Patents
Random forest-based laser self-mixing interference micro-vibration measurement method and system Download PDFInfo
- Publication number
- CN115342900B CN115342900B CN202210977324.5A CN202210977324A CN115342900B CN 115342900 B CN115342900 B CN 115342900B CN 202210977324 A CN202210977324 A CN 202210977324A CN 115342900 B CN115342900 B CN 115342900B
- Authority
- CN
- China
- Prior art keywords
- random forest
- vibration
- laser self
- features
- micro
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000007637 random forest analysis Methods 0.000 title claims abstract description 56
- 238000000691 measurement method Methods 0.000 title claims abstract description 15
- 238000005259 measurement Methods 0.000 claims abstract description 25
- 238000003066 decision tree Methods 0.000 claims abstract description 22
- 230000009466 transformation Effects 0.000 claims abstract description 16
- 238000012549 training Methods 0.000 claims abstract description 15
- 238000000034 method Methods 0.000 claims description 35
- 238000004422 calculation algorithm Methods 0.000 claims description 20
- 239000013598 vector Substances 0.000 claims description 13
- 238000005305 interferometry Methods 0.000 claims description 11
- 238000000605 extraction Methods 0.000 claims description 10
- 238000010606 normalization Methods 0.000 claims description 10
- 239000011159 matrix material Substances 0.000 claims description 9
- 238000005070 sampling Methods 0.000 claims description 8
- 238000012545 processing Methods 0.000 claims description 4
- 238000004590 computer program Methods 0.000 claims description 2
- 230000003287 optical effect Effects 0.000 abstract description 13
- 230000000737 periodic effect Effects 0.000 abstract description 8
- 238000006073 displacement reaction Methods 0.000 description 26
- 238000004088 simulation Methods 0.000 description 18
- 238000004458 analytical method Methods 0.000 description 13
- 238000001228 spectrum Methods 0.000 description 12
- 230000003595 spectral effect Effects 0.000 description 8
- 238000012360 testing method Methods 0.000 description 8
- 238000010586 diagram Methods 0.000 description 6
- 230000000694 effects Effects 0.000 description 6
- 239000000284 extract Substances 0.000 description 5
- 238000010801 machine learning Methods 0.000 description 4
- 238000004364 calculation method Methods 0.000 description 3
- 238000013473 artificial intelligence Methods 0.000 description 2
- 230000009286 beneficial effect Effects 0.000 description 2
- 238000010276 construction Methods 0.000 description 2
- 238000013139 quantization Methods 0.000 description 2
- 238000011160 research Methods 0.000 description 2
- 238000012300 Sequence Analysis Methods 0.000 description 1
- 238000013459 approach Methods 0.000 description 1
- 230000036772 blood pressure Effects 0.000 description 1
- 238000010835 comparative analysis Methods 0.000 description 1
- 238000013527 convolutional neural network Methods 0.000 description 1
- 238000013461 design Methods 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 238000002474 experimental method Methods 0.000 description 1
- 230000006870 function Effects 0.000 description 1
- 230000010354 integration Effects 0.000 description 1
- 238000011084 recovery Methods 0.000 description 1
- 230000000717 retained effect Effects 0.000 description 1
- 239000004065 semiconductor Substances 0.000 description 1
- 238000010183 spectrum analysis Methods 0.000 description 1
- 230000002123 temporal effect Effects 0.000 description 1
- 238000000844 transformation Methods 0.000 description 1
- 238000012795 verification Methods 0.000 description 1
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01H—MEASUREMENT OF MECHANICAL VIBRATIONS OR ULTRASONIC, SONIC OR INFRASONIC WAVES
- G01H9/00—Measuring mechanical vibrations or ultrasonic, sonic or infrasonic waves by using radiation-sensitive means, e.g. optical means
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01H—MEASUREMENT OF MECHANICAL VIBRATIONS OR ULTRASONIC, SONIC OR INFRASONIC WAVES
- G01H1/00—Measuring characteristics of vibrations in solids by using direct conduction to the detector
- G01H1/12—Measuring characteristics of vibrations in solids by using direct conduction to the detector of longitudinal or not specified vibrations
- G01H1/14—Frequency
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01H—MEASUREMENT OF MECHANICAL VIBRATIONS OR ULTRASONIC, SONIC OR INFRASONIC WAVES
- G01H1/00—Measuring characteristics of vibrations in solids by using direct conduction to the detector
- G01H1/12—Measuring characteristics of vibrations in solids by using direct conduction to the detector of longitudinal or not specified vibrations
- G01H1/16—Amplitude
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- G06N20/00—Machine learning
- G06N20/20—Ensemble learning
Landscapes
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Engineering & Computer Science (AREA)
- Theoretical Computer Science (AREA)
- Software Systems (AREA)
- Evolutionary Computation (AREA)
- Data Mining & Analysis (AREA)
- Medical Informatics (AREA)
- Computer Vision & Pattern Recognition (AREA)
- Computing Systems (AREA)
- General Engineering & Computer Science (AREA)
- Mathematical Physics (AREA)
- Artificial Intelligence (AREA)
- Measurement Of Mechanical Vibrations Or Ultrasonic Waves (AREA)
Abstract
A random forest-based laser self-mixing interference micro-vibration measurement method and system relate to the field of micro-vibration signal measurement. The invention aims to predict the amplitude and the frequency of a vibration signal under the condition that the intensity of optical feedback and a line width enhancement factor do not need to be measured, thereby improving the vibration measurement efficiency. The technical key points are as follows: constructing a random forest model integrated with a plurality of decision trees, and continuously adjusting the depth of the decision trees and the number of the child nodes of the decision trees during training to obtain a trained random forest model; and obtaining a laser self-mixing interference signal generated by the micro-vibration signal to be detected, and then respectively carrying out Fourier transformation and statistical transformation. After the frequency domain features are extracted after Fourier transformation, the statistical features are extracted after statistical transformation, and the time domain features of the laser self-mixing interference signals are extracted, the features of the laser self-mixing interference signals are extracted in total to serve as the input of a trained random forest model, the amplitude and the frequency of the micro-vibration to be detected are predicted, the amplitude and the frequency of the original vibration can be predicted rapidly, and the original periodic vibration signals can be reconstructed.
Description
Technical Field
The invention relates to the technical field of micro-vibration signal measurement, in particular to a random forest-based laser self-mixing interference micro-vibration measurement method and system.
Background
The laser SMI measuring technique [1,2] is an important and advanced ultra-precise measuring method. There are many interesting and important fields in which it is desirable, such as spectral measurement [3], phase, displacement and vibration measurements [1,4-6]. Since the SMI signal can reliably reflect the micro-vibration of the object, by analyzing the continuous SMI signal, the amplitude and frequency information in the micro-vibration of the object can be obtained.
In SMI vibration measurement, researchers often introduce a phase unwrapping method and a modulation method. Yufeng Tao, chunlei Jiang et al use a simplified phase modulation and demodulation scheme to convert the target change into phase information, which not only simplifies the experimental platform, but also improves the resolution of SMI non-contact measurements [7]. Saqib Amin et al propose a power spectrum analysis method for analyzing the SMI signal in case of optical feedback intensity (C) determination. It simplifies the optical element and effectively measures the original vibration [8]. However, these methods require that the real-time phase of the SMI be demodulated in advance, so as to obtain the real-time displacement of the SMI. Although the phase unwrapping method has high measurement accuracy, C and the line width enhancement factor (α) need to be calculated in advance. Wang Xiufang et al determined the V value using the phase unwrap concept [9] and reconstructed the amplitude of the target under secondary feedback [10]. In addition Zhang Zihua et al also employed a multiple feedback SMI technique to improve the resolution and accuracy of displacement reconstruction [11]. But these methods require more complex experimental equipment.
In recent years, artificial intelligence techniques have been used in the field of processing laser self-mixing signals [12]. IMRAN AHMED et al utilize generation of a countermeasure network (GAN) to enhance SMI signals corrupted by different noise types. The method performs noise removal and waveform enhancement on the SMI signal before displacement reconstruction under different noise conditions [13,14]. Ke Kou et al used ANN to determine the tilt direction of the stripes based on the number of stripes detected [15]. But this method can only identify a limited number of stripes.The et al construct an SMI displacement dataset using periodic vibration signals and reconstruct the displacement by means of a convolutional neural network [16]. However, this method requires not only a large number of samples, but also is not interpretable. These methods also require analysis where C and α are known. The research of characteristic engineering aiming at time sequence analysis [12] also brings convenience to the construction of regression models. For example, xiulin Wang et al extract the characteristic parameters of the pulse wave upon achieving pulse waveform reconstruction in combination with the inversion point of the SMI signal. They then construct a regression model using extreme learning techniques to predict the blood pressure value of the patient [17]. In contrast to the time consuming feature extraction methods described above, we refer to the feature extraction algorithm (TSFEL) developed by Barandas et al to achieve rapid extraction of features from the SMI signal [18].
The existing micro-vibration measuring method is characterized in that the optical feedback intensity (C) and the line width enhancement factor (alpha) are measured firstly, then the phase is calculated, then the original vibration signal is demodulated according to the phase, and the micro-vibration measurement is time-consuming and complex in calculation.
In the invention, a scheme for measuring SMI vibration of a random forest combined with characteristic engineering is provided. The original SMI signal will be used as input to a new time series algorithm. And extracting the characteristics of the SMI signal, and sending the characteristics into a pre-trained random forest model to predict the parameters of the vibration signal. The algorithm is separated from the traditional SMI vibration measurement idea, and the original vibration amplitude and frequency are directly recovered from the SMI signal, without the need of determining the values of C and alpha in advance and estimating other complex parameters.
Disclosure of Invention
The invention aims to solve the technical problems that:
The invention aims to provide a random forest-based laser self-mixing interference micro-vibration measurement method and system (a scheme for SMI vibration measurement of a random forest combined with characteristic engineering is provided), and the amplitude and frequency of a vibration signal are predicted under the condition that the optical feedback intensity (C) and the line width enhancement factor (alpha) do not need to be measured, so that the vibration measurement speed is improved.
The technical scheme adopted by the invention for solving the technical problems is as follows: the implementation process of the random forest-based laser self-mixing interference micro-vibration measurement method comprises the following steps:
Step one, extracting features of an SMI signal: selecting N laser self-mixing interference signals with the duration of 0.06 seconds, extracting features of each sample, extracting 52 features from a time domain, a frequency domain and a statistical domain to obtain 367 feature values, and obtaining N rows of 367-column training sample matrixes, wherein each row of feature vectors of the matrixes serve as input of a random forest model (RF), and the amplitude and the frequency of original micro-vibration are correspondingly output; n represents a plurality of N;
Normalizing each column of features of the training sample matrix, normalizing the value of each feature in a 0-1 interval, and improving the running efficiency and the prediction accuracy of the random forest model;
Step three, constructing a random forest model integrated with a plurality of decision trees, and randomly selecting partial features from SMI samples contained in any node of each decision tree to continuously divide sub-nodes; when training is carried out by utilizing the normalized training sample matrix, the depth of the decision tree and the number of child nodes of the decision tree are continuously adjusted to obtain the best random forest model, namely the trained random forest model is obtained, so that real-time measurement of vibration to be measured is carried out;
And step four, obtaining a laser self-mixing interference signal generated by the micro-vibration signal to be detected, and then respectively carrying out Fourier transformation and statistical transformation on the laser self-mixing interference signal. Extracting frequency domain features after Fourier transformation, extracting statistical features after statistical transformation, and extracting 367 feature values of 52 features of the laser self-mixing interference signal after extracting time domain features of the laser self-mixing interference signal; after the characteristics are subjected to normalization processing, the characteristics are used as input of a trained random forest model to predict the amplitude and frequency of the micro-vibration to be detected.
A random forest-based laser self-mixing interference micro-vibration measuring system is provided with a program module corresponding to the steps, and the steps in the random forest-based laser self-mixing interference micro-vibration measuring method are executed in running.
A computer readable storage medium storing a computer program configured to implement the steps of the random forest based laser self-mixing interferometry microvibration measurement method when invoked by a processor.
A microvibration measuring device comprising at least one processor and a memory communicatively coupled to the at least one processor, wherein the memory stores instructions executable by the at least one processor to enable the at least one processor to perform the random forest based laser self-mixing interferometry microvibration measuring method.
The invention has the following beneficial technical effects:
The invention takes the original SMI signal as the input of a new time sequence algorithm, utilizes TSFEL to extract the characteristic with strong interpretation, predicts the amplitude and frequency of the vibration signal through a pre-trained random forest model, and directly recovers the amplitude and frequency of the original vibration from the SMI signal without determining the values of C and alpha in advance and estimating other complex parameters.
The invention provides a method for determining vibration by combining feature extraction and random forest aiming at laser self-mixing interferometry vibration. By utilizing the thought of feature engineering, a plurality of features are extracted from the time domain, the frequency spectrum and the statistical domain of the SMI signal, a one-dimensional feature vector is constructed and used as the interpretable input of the RF model, and then the parameters of the original vibration signal are predicted to recover the periodic vibration of the target. Experimental results have shown that the method combining the RF model and the feature extraction can simply and rapidly predict the amplitude and the frequency of the original vibration and successfully reconstruct the original periodic vibration signal without calculating the feedback intensity and the feedback factor.
Drawings
FIG. 1 shows the optical path process and schematic diagram (SMI system frame) of a laser self-mixing interference signal generated from a vibration signal;
FIG. 2 is a frame diagram of a random forest based laser self-mixing interferometry micro-vibration measurement (vibration measurement frame diagram of SMI system, A represents amplitude, f represents frequency) according to the present invention;
FIG. 3 is a diagram illustrating various angles of analysis of the SMI signal: (a) For a time domain signal, the sampling rate is 20khz, a=1.05 um, f=62.5 hz, c=0.1; (b) is a spectrogram of the SMI signal; (c) For SMI STFT analysis, hamming window length 256, overlap points 128;
Fig. 4 shows the feature parameters extracted from different angles after normalization: (a) 332 features in the frequency domain; (b) 17 features in the time domain; (c) 18 features on the statistical domain;
FIG. 5 is a graph of amplitude and frequency predictions in a simulation test;
the four figures in fig. 6 are each: (a) Representing the laser self-mixing signal corresponding to vibration at a=2.075um, f=25 Hz; (b) The laser self-mixing signal is subjected to wavelet denoising; (c) a frequency spectrum of the signal after fourier transform; (d) a time-frequency analysis plot of the signal; a hamming window; window sampling points: 256; window overlap points: 128.
FIG. 7 is a graph of feature importance analysis over two data sets;
FIG. 8 is a graph of model performance curves for various parameters: (a) Different maximum feature numbers and prediction precision curves of the same layer of nodes; (b) Maximum depth and prediction precision curves of the same decision tree;
Fig. 9 is a diagram showing vibration parameter prediction on SMI experimental data.
Description: english in the drawings of the specification is a well-known term in the art.
Detailed Description
The implementation process and related technical details of the random forest-based laser self-mixing interference micro-vibration measurement method are described as follows:
1. theory of laser self-mixing interferometry (SMI)
The light output by the laser is reflected when striking an external object. The feedback light carrying the external object information is returned to the resonant cavity of the laser and then interferes with the laser in the cavity, so that the output characteristic of the laser is modulated, and an SMI signal is generated. The circuit forming the SMI system is shown in fig. 1.
In combination with Lang-Kobayashi theory [19], the phase equation and output equation of SMI are expressed as:
φ0(t)＝φF(t)+C sin[φF(t)+tan-1α] (1)
PF(t)＝P0[1+m cos(φF(t))] (2)
It can be seen that the power of the SMI is related to the phase of the feedback light. In SMI, L (t) is the external cavity length, which varies with vibration target. Phi 0 (t) and phi F (t) represent the phases with and without optical feedback, respectively. With the periodic variation of L (t), phi 0 (t) and phi F (t) also vary linearly therewith.
In Eq. (1), when C is not less than 4.6, the feedback state is strong. When C is more than 1 and less than or equal to 4.6, the feedback state is medium. When 0 < C.ltoreq.1, a weak feedback state is assumed, and the signal is almost sinusoidal [20]. Without adding optical components, we only study the SMI signal in the weak feedback state.
In the weak feedback state, assuming that the amplitude of the periodic vibration signal is a 0, the frequency is f 0, and the distance between L (t) and the target is expressed as:
L(t)＝L0+A0 cos(2πf0t) (5)
where L 0 is the initial distance of the LD from the moving object. Once C and α are determined, the SMI phase equation is also determined. Thus, the real-time phases φ 0 (t) and φ F (t) of the SMI can be determined in combination with Eq. (2). And Eq. (3) shows that L (t) is determined based on φ 0 (t). However, the values of C and α in the actual optical path are constantly changing, and different feedback coefficients affect the real-time phase of the SMI. Furthermore, due to the continuity of amplitude and frequency, the number of fringes in one period in the SMI signal is not necessarily an integer multiple of half wavelength, resulting in instability of amplitude and frequency measurements. Therefore, we have attempted to quickly determine the amplitude and frequency of the target vibration in a weak feedback state using machine learning theory without adding an optical instrument, without considering the values of C and α.
2. The implementation process of the random forest-based laser self-mixing interference micro-vibration measurement method comprises the following steps:
step one, extracting features of an SMI signal: under the sampling rate of 20kHz, selecting 48000 laser self-mixing interference signals with the duration of 0.06 seconds, extracting characteristics of each sample, extracting 52 characteristics from a time domain, a frequency domain and a statistical domain to obtain 367 characteristic values, and obtaining a 48000 line 367 column training sample matrix, wherein each line characteristic vector of the matrix is used as input of a random forest model (RF), and the amplitude and the frequency of the original micro-vibration are correspondingly output; n represents a plurality of N;
Normalizing each column of features of the training sample matrix, normalizing the value of each feature in a 0-1 interval, and improving the running efficiency and the prediction accuracy of the random forest model;
The normalization algorithm is as follows:
Where x i is the value in attribute A, and Max A,minA is the maximum and minimum values of attribute A over N observations; x' i is the value falling within the [0,1] interval after normalization; these attributes, normalized, are converted to one-dimensional vectors, which become the inputs to the RF model.
Step three, constructing a random forest model integrated with a plurality of decision trees, and randomly selecting partial features from SMI samples contained in any node of each decision tree to continuously divide sub-nodes; when training is carried out by utilizing the normalized training sample matrix, the depth of the decision tree and the number of child nodes of the decision tree are continuously adjusted to obtain the best random forest model, namely the trained random forest model is obtained, so that real-time measurement of vibration to be measured is carried out;
And step four, obtaining a laser self-mixing interference signal generated by the micro-vibration signal to be detected, and then respectively carrying out Fourier transformation and statistical transformation on the laser self-mixing interference signal. Extracting frequency domain features after Fourier transformation, extracting statistical features after statistical transformation, and extracting 367 feature values of 52 features of the laser self-mixing interference signal after extracting time domain features of the laser self-mixing interference signal; after the characteristics are subjected to normalization processing, the characteristics are used as input of a trained random forest model to predict the amplitude and frequency of the micro-vibration to be detected.
The names of the 52 features and the number of the defined corresponding feature values in the first step and the fourth step are as follows:
the references to the above table are:
1)Barandas Marília,Folgado Duarte,Fernandes Letícia,Santos Sara,Abreu Mariana,Bota Patrícia,Liu Hui,Schultz Tanja,and Gamboa Hugo,"TSFEL:Time Series Feature Extraction Library,"SoftwareX 11,100456(2020).https://doi.org/10.1016/j.softx.2020.100456
2)Peeters Geoffroy,Giordano Bruno L.,Susini Patrick,Misdariis Nicolas,and McAdams Stephen,"The Timbre Toolbox:Extracting audio descriptors from musical signals,"The Journal of the Acoustical Society of America 130,2902-2916(2011).https://doi.org/10.1121/1.3642604.
3. Description of the random forest algorithm underlying the present invention
3.1 Algorithm description
As shown in fig. 2, for the SMI signal, in the left half of fig. 2, we randomly select a frame of the SMI signal for feature extraction and then combine the three aspects to obtain the multi-component feature. First, the SMI waveform in the time domain changes in the direction of the stripe inclination due to the difference in the vibration direction. This variation is a time domain feature. In addition, the SMI waveform includes other rich time domain features and statistical features that can be fully extracted. Second, the spectrum of the SMI signal will also reflect some more details about the vibration waveform through FFT and STFT transforms. This spectrum contains not only the SMI phase change, but also many efficient and interesting features for analyzing SMI signals, such as power spectral energy distribution, spectral density, information entropy, etc.
Of course, it is inevitable that the feature values of different attributes are not at the same quantization level. The property with smaller quantization units increases the dependency of the model on the unit of measure. To avoid excessive reliance on units of measure, all features need to be standardized. The present invention processes the data using equation 6 and scales the attribute values for each feature to be within the interval 0, 1. Therefore, the convergence time of the algorithm is reduced, and the accuracy of SMI signal identification is improved. The normalization algorithm is as follows:
Where x i is the value in attribute A and Max A,minA is the maximum and minimum of attribute A over N observations. x' i is the value that falls within the [0,1] interval after normalization. These attributes, normalized, are converted to one-dimensional vectors, which become the inputs to the RF model.
To accurately measure micro-vibrations of objects in an SMI system, we use a nonlinear regression model based on random forest rules [21] to predict the required amplitude frequency information. Random forest regressors are a collection of various decision trees that are combined by integration and the predictions for each tree are averaged to find the best prediction. The algorithm for random forest regression is shown in the right half of fig. 2:
assuming that the original SMI dataset has N samples, each sample has M features
From a=1 to a=k, N SMI new sample sets are obtained on the basis of randomly sampling N times with a put back:
1. M 0 features are selected from the M features.
2. Repeating the following steps to create an a decision tree:
i. the M variables are randomly selected from the M variables.
Splitting the node into child nodes and selecting the node d using the best split point.
Thus, K decision tree sub-models were trained. When predicting our SMI parameters, one-dimensional feature vector with length M is input into each decision tree to predict. We take the mean of the predicted results as the final predicted value for the RF model as the amplitude and frequency information of the original periodic vibration recovered from the SMI signal.
3.2. Verification analysis based on simulation data set
Using the SMI system simulation codes summarized in formulas 1-4 and [1], we performed system simulations on Matlab and python3.6, with a simulated set light wavelength of 650nm. Under the condition of weak feedback, the characteristic parameters of the SMI signal are extracted from three angles of a time domain, a statistical domain and a frequency spectrum domain by combining a frequency spectrum and a time-frequency analysis chart, so that a large number of SMI analog data sets are formed. In fig. 3, in conjunction with FFT analysis, the spectrum of the SMI signal is concentrated in one interval, which can be extracted from TSFEL to rich feature parameters. In combination with time-frequency analysis, we also see the fluctuation of frequency in different fourier short time windows, and these features can also be extracted as RF model inputs.
Thus, we obtained a total of 700000 samples at a frequency of 0-100 Hz and an amplitude range of 0-7 um. Also, for each SMI signal, with 1200 sampling points as windows, flexible feature extraction is performed using TSFEL, and as shown in fig. 4, 367 feature parameters corresponding to the amplitude and frequency of the original vibration signal are obtained. Using feature engineering and RF models we have trained and tested the simulation dataset. Wherein 30% of the samples in the dataset are retained for testing.
In FIG. 5, we used Score R2 to observe the predictive effect of the model [22]. The calculation method of Score R2 is as follows:
wherein, in the prediction of N samples, the ith input sample The corresponding true value is y i, and the predicted value is/>The average value of the true tags of the N samples is/>We use the mean square error (RMSE) and variance (Var) to measure the degree of fit and the degree of mathematically expected deviation of our model.
In the figure, we give partial predictions of the simulated test data. As shown in FIG. 5, the performance score of the model in the simulation test set is 0.981, which indicates that the random forest model has a high predictive power for the SMI signal.
As we have obtained a lot of data from the experimental platform. In the next section, we will use this model to test and verify the actual data.
4. Analysis of experimental results
4.1 Laser SMI Experimental data set
To generate the SMI dataset, we set the output wavelength of the laser diode to 650nm and the sampling frequency of the acquisition card to 20KHz. We transmitted the acquired data to the PC using a USB4431 acquisition card. The experimental data set is continuously expanded, different vibration parameters of a vibration source are changed within the range of 1-7 um of amplitude and the range of 5-25 Hz of frequency, a large number of samples are established, and the SMI experimental data set is formed. We collected 60000 points for the signal under each pair of parameters, with 1200 sample points and corresponding amplitudes and frequencies as a set of samples. These data are exported as Excel-type data, facilitating the construction and training of subsequent models.
4.2 Analysis of results
First, we still extract features from experimental data and analyze them. As shown in fig. 6, the actual SMI signal is contaminated with a lot of noise and has a lot of burrs. We use wavelet transform to filter the SMI signal and smooth the curve. Then, the frequency spectrum and the time-frequency diagram are obtained by using FFT, STFT and other transformations. From the FFT analysis, the spectrum of the signal is interspersed with noise and cannot be completely eliminated. However, compared with the frequency spectrum of the simulation signal, the frequency spectrum is concentrated in one interval, and extraction of basic characteristic parameters is not affected. In analyzing STFT, short-term spectra within each window function can also extract many features.
Thus, we extract 367 features from the time domain, statistical domain, and spectral domain as input vectors for the RF model. As shown in fig. 7, in the simulation data, the spectral features are denser than other features, and these feature values are distributed stepwise, which is indispensable. The contribution degree distribution of different characteristics on experimental data to the prediction performance also supports the above-mentioned view.
As can be seen from fig. 7, the spectral features contribute most to the waveform of the signal. The attributes are also very dense. Although time domain features score higher on some attributes, these high-score attributes are less distributed and less widely distributed than spectral attributes. Furthermore, the degree of contribution of the spectral features to the original signal recovery is within a stable range, which helps to preserve the predictive effect of the model. Feature scores in the statistical field are low, but there are also some high-scoring features. Of course, the characteristic contribution of the actual SMI signal obtained from the optical platform is slightly lower than the simulation data. But these properties are all necessary.
Next, we also performed comparative analysis of the actual performance scores of the experimental dataset and the simulated dataset at different decision tree depths.
In fig. 8, the model is in the over-fit phase when max_depth < 10. In addition, as the depth of the RF decision tree increases, the predictive performance also steadily increases. When Max_depth is more than or equal to 10, the precision of the model on simulation and experimental data is more than 90%. Compared with the simulation data set, the experimental data is affected by the physical environment and has larger noise. Within the allowable range of the actual noise, the prediction score is not as high as the simulation data after the signal denoising is performed by wavelet transformation [23 ]. This has some effect on the performance of the model, but it is understood. Meanwhile, in order to better understand the influence of model parameters on actual prediction performance, different Max_features are analyzed on performance influence.
In the figure, as the selected feature subset continues to increase, the likelihood of finding the best feature increases at the nodes of each tree in the forest. We find that in the test set of simulations and experiments, around max_feature=50, r2_score starts the incoming flat phase. This means that the minimum vector length of the feature subset is around 50 when the model reaches the best performance. After removing the noise, the decision making ability of the model is still unaffected.
Using the final model trained with the above-described optimal parameters, we retrieve some of the SMI signal from the optical platform for testing and prediction. In fig. 9, we have adjusted different parameters of the original vibration source to obtain different SMI signals. With the RF model, the amplitude and frequency of the original signal are smoothly predicted.
It can be seen that although the actual signal fringes are less perfect than the simulation, the waveform instability is evident, but the original periodic vibration displacement can still be predicted.
The invention aims to utilize a random forest machine learning algorithm to reconstruct the displacement of the laser self-mixing interference system, and the method does not need to determine a feedback factor and feedback intensity, so that the method has enhanced interpretation and practicability in terms of the algorithm.
It should be noted that, the simulation and experimental SMI data required by the method are feature extraction by taking 1200 sampling points as a frame, and 367 valid features are extracted as RF input. We also try to change the data frame length and on this basis continuously improve the RF model to improve our model. In addition to RF, lasso and Ridge models have also been studied in various fields [24]. For SMI vibration measurements we compared one by one with the AI models using modified models. In table one, the accuracy of the RF model is substantially over 92% as each frame length increases. Although the test accuracy at 600 and 900 is slightly degraded, it can be improved by increasing the data amount of the SMI signal. Compared with the original prediction result, the modified RF method has shown that the algorithm model proposed by the user has no fixed limit on the size of the data frame, and is suitable for predicting the displacement of the SMI signal in real time. In contrast, the prediction performance of the Lasso model is relatively stable, but the accuracy is lower than that of the RF model, and the prediction model has no practicability on the SMI displacement reconstruction target and is limited by the size of an SMI signal data frame.
The effect influence of different SMI frame lengths on the model is shown
For the SMI signal displacement reconstruction target, we continue to discuss the predictive effects on two different data sets using different machine learning algorithms.
Performance comparison of Table two different algorithms
As shown in the table II, the RF model selected by the user keeps high precision in both simulation and experimental data, has the lowest error and is more practical. In fact, since our simulated data set is very perfect and noise free, models chosen with such noise free data are also best. The Lasso model is worst on simulation data, and its r2_score is lowest when predicting the actual SMI displacement. Whereas the actual SMI signal may be interspersed with various noise compared to the simulation data. From the model stability measurement, whether the Ridge model predicts the simulated displacement or the actual displacement, the MSE value is lower, and the capacity of fitting the SMI displacement is stronger than that of the Lasso model, so that the Ridge model is a better algorithm. When considering creating an integrated model, it may be beneficial to combine Ridge with RF so that the final model is not only more robust, but can reconstruct more accurate displacements.
5. Conclusion(s)
Aiming at restoring original vibration displacement by utilizing an SMI signal, the invention provides a displacement reconstruction algorithm based on characteristic engineering and random forests, which directly extracts the characteristic vector of the SMI signal on the premise of not determining various feedback coefficients and combines an RF model to restore the displacement of the original vibration signal. Experimental results based on a large amount of data show that the method is simple to operate, does not involve a complex optical platform and a complex calculation formula, and does not need to determine any feedback parameters. Therefore, the method can be applied to semiconductor laser self-mixing displacement measurement and has higher universality.
In extracting feature vectors, we combine TSFEL techniques to extract rich feature parameters from the frequency domain and the statistical and temporal domains as inputs to the RF. Such feature vectors provide a powerful interpretability for the displacement reconstruction model. In evaluating the feature importance of the RF model, each feature provides a stable contribution to the predicted performance, which also verifies that each feature extracted is essential. In addition, in the comparison analysis by using different algorithms, the RF model proposed by us is also verified to be the best and is most suitable for performing SMI displacement reconstruction.
In summary, in the SMI system, the machine learning technology is significant for rapidly implementing vibration measurement. It is believed that this approach can be a fast and convenient displacement sensing device without the need for complex hardware circuitry. It is believed that the displacement reconstruction model relying on massive SMI signals is not limited to displacement measurement and single mode setup, but can also be a very useful element of different types of laser sensing devices. Finally, we emphasize that artificial intelligence algorithms for displacement reconstruction in combination with SMI have few hard rules, and that such designs are often a field of research itself.
The details of the references cited in the present invention are as follows:
[1]Kliese Russell,Taimre Thomas,Bakar A.Ashrif A.,Lim Yah Leng,Bertling Karl,Milan,Perchoux Julien,Bosch Thierry,and />Aleksandar D.,"Solving self-mixing equations for arbitrary feedback levels:a concise algorithm,"Appl.Opt.53,3723-3736(2014).https://doi.org/10.1364/AO.53.003723
[2]Fei Ligang and Zhang Shulian,"The discovery of nanometer fringes in laser self-mixing interference,"Optics Communications 273,226-230(2007).https://doi.org/10.1016/j.optcom.2006.12.022
[3]Zhang S.,Zhang S.,Sun L.,and Tan Y.,"Spectrum Broadening in Optical Frequency-Shifted Feedback of Microchip Laser,"IEEE Photonics Technology Letters 28,1593-1596(2016).https://doi.org/10.1109/LPT.2016.2556708
[4]Zhao Yunkun,Xiang Rong,Chen Jisun,Huang Zuotang,Wang Xiang,Ma Yangcheng,Yu Benli,and Lu Liang,"Absolute angle-measurement with a dihedral mirror of the multi-longitudinalmode laser self-mixing sensor,"Precision Engineering 68,256-261(2021).https://doi.org/10.1016/j.precisioneng.2020.12.005
[5]Zhao Yunkun,Fan Xuewei,Wang Chenchen,and Lu Liang,"An improved intersection feedback micro-radian angle-measurement system based on the Laser self-mixing interferometry,"Optics and Lasers in Engineering 126,105866(2020).https://doi.org/10.1016/j.optlaseng.2019.105866
[6]Wang Chenchen,Fan Xuewei,Guo You,Gui Huaqiao,Wang Huanqing,Liu Jianguo,Yu Benli,and Lu Liang,"Full-circle range and microradian resolution angle measurement using the orthogonal mirror self-mixing interferometry,"Opt.Express 26,10371-10381(2018).https://doi.org/10.1364/OE.26.010371
[7]Tao Yufeng,Wang Ming,Guo Dongmei,Hao Hui,and Liu Qiang,"Self-mixing vibration measurement using emission frequency sinusoidal modulation,"Optics Communications 340,141-150(2015).https://doi.org/10.1016/j.optcom.2014.10.071
[8]Amin S.,Zabit U.,Bernal O.D.,and Hussain T.,"High Resolution Laser Self-Mixing Displacement Sensor Under Large Variation in Optical Feedback and Speckle,"IEEE Sensors Journal 20,9140-9147(2020).https://doi.org/10.1109/JSEN.2020.2988851
[9]Wei L.,Xi J.,Yu Y.,and Chicharo J.,"Phase Unwrapping of Self-mixing Signals Observed in Optical Feedback Interferometry for Displacement Measurement,"in 2006 International Symposium on Intelligent Signal Processing and Communications,2006),780-783.https://doi.org/10.1109/ISPACS.2006.364765
[10]Wang Xiufang,Song Xinmin,Tan Renxue,Chen Peng,and Gao Bingkun,"Micro-vibration measurement based on current modulation and secondary feedback self-mixing interference technology,"Optical Review 26,241-246(2019).https://doi.org/10.1007/s10043-018-00489-w
[11]Zhang Zihua,Wang Fuli,Yuan Tao,and Li Chengwei,"Multiple self-mixing interferometry based on lock-in amplifier analysis for vibration measurement,"Optical Review 27,313-320(2020).https://doi.org/10.1007/s10043-020-00600-0
[12]Masini Ricardo P.,Medeiros Marcelo C.,and Mendes Eduardo F.,"Machine learning advances for time series forecasting,"Journal of Economic Surveys n/a(2021).https://doi.org/10.1111/joes.12429
[13]Ahmed I.,Zabit U.,and Salman A.,"Self-Mixing Interferometric Signal Enhancement Using Generative Adversarial Network for Laser Metric Sensing Applications,"IEEE Access 7,174641-174650(2019).https://doi.org/10.1109/ACCESS.2019.2957272
[14]Song M.,Zhang J.,Chen H.,and Li T.,"Towards Efficient Microarchitectural Design for Accelerating Unsupervised GAN-Based Deep Learning,"in 2018 IEEE International Symposium on High Performance Computer Architecture(HPCA),2018),66-77.https://doi.org/10.1109/HPCA.2018.00016
[15]Kou Ke,Wang Cuo,Lian Tianhong,and Weng Jun,"Fringe slope discrimination in laser self-mixing interferometry using artificial neural network,"Optics&Laser Technology 132,106499(2020).https://doi.org/10.1016/j.optlastec.2020.106499
[16]Barland Stéphane and Gustave Francois,"Convolutional neural network for self-mixing interferometric displacement sensing,"Opt.Express 29,11433-11444(2021).https://doi.org/10.1364/OE.419844
[17]Wang Xiu-lin,LüLi-ping,Hu Lu,and Huang Wen-cai,"Real-time human blood pressure measurement based on laser self-mixing interferometry with extreme learning machine,"Optoelectronics Letters 16,467-470(2020).https://doi.org/10.1007/s11801-020-0050-x
[18]Barandas Marília,Folgado Duarte,Fernandes Letícia,Santos Sara,Abreu Mariana,Bota Patrícia,Liu Hui,Schultz Tanja,and Gamboa Hugo,"TSFEL:Time Series Feature Extraction Library,"SoftwareX 11,100456(2020).https://doi.org/10.1016/j.softx.2020.100456
[19]Gao Yan,Yu Yanguang,Xi Jiangtao,and Guo Qinghua,"Simultaneous measurement of vibration and parameters of a semiconductor laser using self-mixing interferometry,"Appl.Opt.53,4256-4263(2014).https://doi.org/10.1364/AO.53.004256
[20]Donati S.,Giuliani G.,and Merlo S.,"Laser diode feedback interferometer for measurement of displacements without ambiguity,"IEEE Journal of Quantum Electronics 31,113-119(1995).https://doi.org/10.1109/3.341714
[21]Desai Shitanshu and Ouarda Taha B.M.J.,"Regional hydrological frequency analysis at ungauged sites with random forest regression,"Journal of Hydrology 594,125861(2021).https://doi.org/10.1016/j.jhydrol.2020.125861
[22]Hulot Pierre,Aloise Daniel,and Jena Sanjay Dominik,"Towards Station-Level Demand Prediction for Effective Rebalancing in Bike-Sharing Systems,"in Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery&Data Mining,(Association for Computing Machinery,London,United Kingdom,2018),pp.378–386.https://doi.org/10.1145/3219819.3219873
[23]Arneodo A.,Grasseau G.,and Holschneider M.,"Wavelet Transform of Multifractals,"Physical Review Letters 61,2281-2284(1988).https://doi.org/10.1103/PhysRevLett.61.2281
[24]Gana Rajaram,"Ridge regression and the Lasso:how do they do as finders of significant regressors and their multipliers?,"Communications in Statistics-Simulation and Computation,1-35(2020).https://doi.org/10.1080/03610918.2020.1779295
Claims (7)
1. The laser self-mixing interference micro-vibration measurement method based on the random forest is characterized by comprising the following implementation processes of:
step one, extracting features of an SMI signal: selecting N laser self-mixing interference signals with the duration of 0.06 seconds, extracting features of each sample, extracting 52 features from a time domain, a frequency domain and a statistical domain to obtain 367 feature values, and obtaining N rows of 367-column training sample matrixes, wherein each row of feature vectors of the matrixes serve as input of a random forest model, and the corresponding output is the amplitude and the frequency of original micro-vibration; n represents a plurality of N;
Normalizing each column of features of the training sample matrix, normalizing the value of each feature in a 0-1 interval, and improving the running efficiency and the prediction accuracy of the random forest model;
Step three, constructing a random forest model integrated with a plurality of decision trees, and randomly selecting partial features from SMI samples contained in any node of each decision tree to continuously divide sub-nodes; when training is carried out by utilizing the normalized training sample matrix, the depth of the decision tree and the number of child nodes of the decision tree are continuously adjusted to obtain the best random forest model, namely the trained random forest model is obtained, so that real-time measurement of vibration to be measured is carried out;
Step four, obtaining a laser self-mixing interference signal generated by the micro-vibration signal to be detected, and then respectively carrying out Fourier transform and statistical transform on the laser self-mixing interference signal; extracting frequency domain features after Fourier transformation, extracting statistical features after statistical transformation, and extracting 367 feature values of 52 features of the laser self-mixing interference signal after extracting time domain features of the laser self-mixing interference signal; after the characteristics are subjected to normalization processing, the characteristics are used as the input of a trained random forest model to predict the amplitude and the frequency of the micro-vibration to be detected;
the names of the 52 features and the number of the defined corresponding feature values in the first step and the fourth step are as follows:
2. The method for measuring the laser self-mixing interference micro-vibration based on the random forest according to claim 1, wherein in the first step, 48000 laser self-mixing interference signals with the duration of 0.06 seconds are selected, feature extraction is performed on each sample, 52 features are extracted from a time domain, a frequency domain and a statistical domain, 367 feature values are obtained, and a training sample matrix of 48000 rows and 367 columns is obtained.
3. A random forest based laser self-mixing interferometry microvibration measurement method according to claim 1 or 2, wherein in step one the selected laser self-mixing interferometry signal is obtained at a sampling rate of 20 kHz.
4. The method for measuring the self-mixing interference micro-vibration of the laser based on the random forest according to claim 1, wherein in the second step, the normalization algorithm is as follows:
Where x i is the value in attribute A, and max A,minA is the maximum and minimum values of attribute A over N observations; x i' is the value falling within the [0,1] interval after normalization; after the attributes are normalized, the attributes are converted into one-dimensional vectors and become the input of a random forest model.
5. A random forest-based laser self-mixing interference micro-vibration measurement system is characterized in that: the system having program modules corresponding to the steps of the random forest based laser self-mixing interferometry microvibration measurement method of any of claims 1-4, the steps of the random forest based laser self-mixing interferometry microvibration measurement method being performed at run-time.
6. A computer-readable storage medium, characterized by: the computer readable storage medium stores a computer program configured to implement the steps of the random forest based laser self-mixing interferometry microvibration measurement method of any of claims 1-4 when invoked by a processor.
7. A microvibration measuring device, characterized by: the microvibration measurement comprises at least one processor and a memory communicatively coupled to the at least one processor, wherein the memory stores instructions executable by the at least one processor to enable the at least one processor to perform the random forest based laser self-mixing interferometry microvibration measurement method of any of claims 1-4.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202210977324.5A CN115342900B (en) | 2022-08-15 | 2022-08-15 | Random forest-based laser self-mixing interference micro-vibration measurement method and system |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202210977324.5A CN115342900B (en) | 2022-08-15 | 2022-08-15 | Random forest-based laser self-mixing interference micro-vibration measurement method and system |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN115342900A CN115342900A (en) | 2022-11-15 |
| CN115342900B true CN115342900B (en) | 2024-04-30 |
Family
ID=83951314
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202210977324.5A Active CN115342900B (en) | 2022-08-15 | 2022-08-15 | Random forest-based laser self-mixing interference micro-vibration measurement method and system |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN115342900B (en) |
Citations (11)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104101420A (en) * | 2013-04-01 | 2014-10-15 | 北京师范大学 | Vibration sample internal reflection point small amplitude measurement method |
| CN104483009A (en) * | 2014-12-18 | 2015-04-01 | 哈尔滨工业大学 | Nanoscale amplitude measuring method of medium-high frequency vibration under low-frequency random disturbance |
| CN107992800A (en) * | 2017-11-10 | 2018-05-04 | 杭州晟元数据安全技术股份有限公司 | A kind of fingerprint image quality determination methods based on SVM and random forest |
| CN108760024A (en) * | 2018-07-02 | 2018-11-06 | 东北石油大学 | A kind of two vibration parameters detection methods and device based on oneself mixing of laser |
| CN108931291A (en) * | 2018-06-30 | 2018-12-04 | 东北石油大学 | A kind of contactless microvibration measuring system and method |
| CN110188876A (en) * | 2019-04-22 | 2019-08-30 | 杭州电子科技大学 | Ultrasonic vibration device amplitude hard measurement prediction technique based on BP neural network |
| CN110796121A (en) * | 2019-11-21 | 2020-02-14 | 杭州电力设备制造有限公司 | Method for diagnosing mechanical fault of high-voltage circuit breaker by S transformation and optimized random forest |
| CN111160106A (en) * | 2019-12-03 | 2020-05-15 | 上海微波技术研究所（中国电子科技集团公司第五十研究所） | Method and system for extracting and classifying optical fiber vibration signal features based on GPU |
| CN112163472A (en) * | 2020-09-15 | 2021-01-01 | 东南大学 | Rolling bearing diagnosis method based on multi-view feature fusion |
| CN114386191A (en) * | 2022-01-11 | 2022-04-22 | 北京理工大学 | Method for detecting gear engagement, random forest model, training method and system |
| CN114626420A (en) * | 2022-03-25 | 2022-06-14 | 合肥工业大学 | phi-OTDR vibration event classification method based on CWT-Xceptance-RF |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108388860B (en) * | 2018-02-12 | 2020-04-28 | 大连理工大学 | Aero-engine rolling bearing fault diagnosis method based on power entropy spectrum-random forest |
-
2022
- 2022-08-15 CN CN202210977324.5A patent/CN115342900B/en active Active
Patent Citations (11)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104101420A (en) * | 2013-04-01 | 2014-10-15 | 北京师范大学 | Vibration sample internal reflection point small amplitude measurement method |
| CN104483009A (en) * | 2014-12-18 | 2015-04-01 | 哈尔滨工业大学 | Nanoscale amplitude measuring method of medium-high frequency vibration under low-frequency random disturbance |
| CN107992800A (en) * | 2017-11-10 | 2018-05-04 | 杭州晟元数据安全技术股份有限公司 | A kind of fingerprint image quality determination methods based on SVM and random forest |
| CN108931291A (en) * | 2018-06-30 | 2018-12-04 | 东北石油大学 | A kind of contactless microvibration measuring system and method |
| CN108760024A (en) * | 2018-07-02 | 2018-11-06 | 东北石油大学 | A kind of two vibration parameters detection methods and device based on oneself mixing of laser |
| CN110188876A (en) * | 2019-04-22 | 2019-08-30 | 杭州电子科技大学 | Ultrasonic vibration device amplitude hard measurement prediction technique based on BP neural network |
| CN110796121A (en) * | 2019-11-21 | 2020-02-14 | 杭州电力设备制造有限公司 | Method for diagnosing mechanical fault of high-voltage circuit breaker by S transformation and optimized random forest |
| CN111160106A (en) * | 2019-12-03 | 2020-05-15 | 上海微波技术研究所（中国电子科技集团公司第五十研究所） | Method and system for extracting and classifying optical fiber vibration signal features based on GPU |
| CN112163472A (en) * | 2020-09-15 | 2021-01-01 | 东南大学 | Rolling bearing diagnosis method based on multi-view feature fusion |
| CN114386191A (en) * | 2022-01-11 | 2022-04-22 | 北京理工大学 | Method for detecting gear engagement, random forest model, training method and system |
| CN114626420A (en) * | 2022-03-25 | 2022-06-14 | 合肥工业大学 | phi-OTDR vibration event classification method based on CWT-Xceptance-RF |
Non-Patent Citations (4)
| Title |
|---|
| Laser self-mixing interference displacement measurement based on VMD and phase unwrapping;Yan Zhao;Baofeng Zhang;Lianfu Han;Optics Communications;20201231;第456卷(第C期);第1-6页 * |
| 基于EMD算法的双外腔激光自混合微振动测量;高丙坤;刘径舟;张子超;;激光与红外;20200620(第06期);第37-43页 * |
| 基于特征选择和随机森林的电力系统受扰后动态频率预测;李冠争;李斌;王帅;李超;刘昊;田杨阳;电网技术;20211231(第007期);第2492-2502页 * |
| 随机森林集成学习模型在高压真空断路器振动信号分析中的应用;樊浩;苏海博;陈立;史宗谦;李兴文;;电器与能效管理技术;20191215(第23期);第9-13、58页 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN115342900A (en) | 2022-11-15 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Dhanya et al. | Nonlinear ensemble prediction of chaotic daily rainfall | |
| Samantaray | Decision tree-initialised fuzzy rule-based approach for power quality events classification | |
| CN113049084B (en) | Attention mechanism-based Resnet distributed optical fiber sensing signal identification method | |
| Abarbanel et al. | Obtaining order in a world of chaos [signal processing] | |
| CN110647788B (en) | Human daily behavior classification method based on micro-Doppler characteristics | |
| Cornish | Rapid and robust parameter inference for binary mergers | |
| CN112861066B (en) | Machine learning and FFT (fast Fourier transform) -based blind source separation information source number parallel estimation method | |
| CN116401532B (en) | Method and system for recognizing frequency instability of power system after disturbance | |
| Yang et al. | A training algorithm for sparse LS-SVM using compressive sampling | |
| Ma et al. | Underdetermined blind source separation based on source number estimation and improved sparse component analysis | |
| CN115342900B (en) | Random forest-based laser self-mixing interference micro-vibration measurement method and system | |
| CN107590604A (en) | The people having the same aspiration and interest unit grouping method and system of a kind of combination S-transformation and 2DPCA | |
| Jin | Theory on structure and coloring of maximal planar graphs (4)-operations and Kempe equivalent classes | |
| Marzocchi et al. | Detecting low‐dimensional chaos in geophysical time series | |
| Zhou et al. | Bearing fault diagnosis based on RF-PCA-LSTM model | |
| CN114978586B (en) | Power grid attack detection method and system based on attack genes and electronic equipment | |
| Ghaderi et al. | Automobile engine condition monitoring using sound emission | |
| Shu-Qing et al. | Research on the chaos recognition method based on differential entropy | |
| Gao et al. | Regularized state estimation and parameter learning via augmented Lagrangian Kalman smoother method | |
| Prepelitsa et al. | New nonlinear analysis, chaos theory and information technology approach to studying dynamics of chain of quantum autogenerators | |
| Ortega | Invariant measures as lagrangian variables: Their application to time series analysis | |
| Kadakia | Hybrid Monte Carlo with chaotic mixing | |
| Zhu et al. | Research on Vibration Event's Feature Extraction Method of Φ-OTDR System | |
| Tempelman et al. | Effects of correlated noise on the performance of persistence based dynamic state detection methods | |
| CN113608021B (en) | Chaotic oscillator circuit and weak signal detection system based on chaos theory |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |