CN113514547A - High-speed rail brake pad nondestructive testing method based on sound vibration method - Google Patents
High-speed rail brake pad nondestructive testing method based on sound vibration method Download PDFInfo
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Abstract
A high-speed rail brake pad nondestructive testing method based on a sound vibration method belongs to the field of deep learning. In order to solve various defects of the brake pad of the high-speed rail, a nondestructive testing method of the brake pad of the high-speed rail based on a sound vibration method is provided, excitation is applied to the brake pad of the high-speed rail, a vibration signal of the brake pad of the high-speed rail is obtained through a sensor, and time domain and frequency domain image data of the vibration signal are obtained; calculating each statistical parameter of the time domain signal and the frequency domain signal; performing data dimension reduction and feature extraction on the calculated statistical parameters, and selecting feature parameters related to the defect signals for statistics; analyzing and training the brake pad vibration characteristic parameters by using a deep learning method and an SVM method to obtain a brake pad analysis result; and carrying out nondestructive testing on the high-speed rail brake pad according to the obtained training result, and if the testing result does not relate to the relevant characteristic parameters of the defect signal, determining that the high-speed rail brake pad is nondestructive. The invention can quickly and accurately detect the service life of the brake pad.
Description
Technical Field
The invention relates to a nondestructive testing method for a high-speed rail brake pad based on a sound vibration method.
Background
When the high-speed running of the train is realized, how to ensure the safe stop of the train is also a problem to be considered. The train is stopped as well as running, so that the train can not be left off at high speed. According to the generation mode of the braking force, the braking modes adopted by the high-speed train can be divided into two categories of electric braking and air braking. The electric brake is that when the train brakes, the working condition of the motor of all traction motors is converted into the working condition of the generator, so as to generate brake torque and convert the mechanical energy of the train into electric energy, the brake force obtained by adopting the method is generated by a power transmission system, and the electric brake is also called as dynamic brake. In electric braking, if the electrical energy generated by the traction motors is fed back to the supply grid, it is called regenerative braking. If the generated electric energy can only be consumed by heating through a resistor on the train, the mode is resistance braking, which is also called dynamic braking. However, the rotation speed of the traction motor is reduced along with the reduction of the train speed during the braking process, and the electric braking power is reduced along with the reduction of the rotation speed, so the braking force generated by the electric braking is only suitable for the case that the train speed is more than 50 km/h. It is seen that it is difficult to achieve rapid stopping of the train using only electric braking.
The air brake is a friction resistance generated when two surfaces moving relatively contact each other by driving a brake pad through expansion of compressed gas, so that the aim of decelerating or stopping a train is fulfilled. The braking action of the friction pair is driven by the air compression cylinder, and is independent of the speed of the train, and the braking resistance generated by air braking is not reduced along with the reduction of the speed of the train. Therefore, air braking is essential to achieve safe and accurate stopping of the train.
Air braking is an energy conversion process, in which the kinetic energy of a moving machine or mechanism is converted into heat energy completely or partially by friction, and the heat is dissipated by the heat exchange between a brake and the outside, so that the air braking device of a train is essentially an energy converter. The braking power of the train and the speed of the train are in a 3-power relation, namely the speed of the train is doubled, and the braking power needs to be increased by 8 times. Thus, as the speed increases, the greater the load the train braking system is subjected to. Particularly, in the case of failure of electric braking of a train, all kinetic energy of the train is consumed by air braking, and the friction pair is inevitably subjected to strong impact, if the mechanical performance of the friction pair is reduced, sufficient braking force cannot be formed to prolong the braking distance, and more seriously, the friction pair fails due to the heavy load effect of hard bearing high temperature and high pressure, so that disastrous results are caused. International railroad consortium UIC provisions: in the event of a dynamic brake failure, air braking must ensure that the high speed train can stop within a prescribed braking distance to ensure safe operation of the train. Therefore, the braking technology is an important factor influencing the acceleration of the train, and the effectiveness of air braking is one of the key problems for ensuring the safe operation of the train.
The current research situation at home and abroad is that the high-speed rail brake pad belongs to a large market of consumables. The service life of the high-speed rail brake pad is generally 30 kilometres, the high-speed rail brake pad needs to be replaced for 3 times per year according to the average mileage of 90-100 kilometres per year of motor train units, 160 motor train units with the length of more than 300 kilometres are needed in each group, and the import price of each motor train unit is 13000-15000 yuan.
The current mechanical part detection method comprises mechanical part detection based on a sound vibration method, deep learning and application and research status of a support vector machine.
Deep learning is a general term of a type of pattern analysis method, and mainly relates to three types of methods in terms of specific research contents:
1. a neural network system based on convolution operations, i.e. a Convolutional Neural Network (CNN).
2. self-Coding neural networks based on multi-layer neurons include both self-Coding (Auto encoder) and Sparse Coding (Sparse Coding) which has received much attention in recent years.
3. And pre-training in a multilayer self-coding neural network mode, and further optimizing a Deep Belief Network (DBN) of the neural network weight by combining the identification information.
In recent years, several methods have been combined, such as unsupervised pre-training of a convolutional neural network originally based on supervised learning in combination with a self-coding neural network, and further using identification information to fine-tune a convolutional deep belief network formed by network parameters. Compared with the traditional learning method, the deep learning method presets more model parameters, so that the model training difficulty is higher, and the more the model parameters are, the larger the data volume needing to participate in training is.
In the eighties and ninety years of the 20 th century, the amount of data available for analysis was too small due to limited computer computing power and limitations of related technologies, and deep learning did not exhibit excellent recognition performance in pattern analysis. Since the CD-K algorithm proposed by Hinton et al to quickly calculate the weights and deviations of the Restricted Boltzmann Machine (RBM) network in 2006, RBM became a powerful tool to increase the depth of neural networks, resulting in the emergence of deep networks such as the later use of the extensive DBN (developed by Hinton et al and used in speech recognition by microsoft et al). Meanwhile, sparse coding and the like are also applied to deep learning because features can be automatically extracted from data. Convolutional neural network methods based on local data regions have also been studied in large quantities in the recent years.
Different from the traditional shallow learning, the deep learning is different in that:
(1) emphasizes the depth of the model structure, and usually has hidden layer nodes of 5 layers, 6 layers and even 10 layers;
(2) the importance of feature learning is clarified. That is, the feature representation of the sample in the original space is transformed to a new feature space by layer-by-layer feature transformation, thereby making classification or prediction easier. Compared with a method for constructing the features by artificial rules, the method for constructing the features by utilizing the big data to learn the features can depict the internal information rich in data.
A proper amount of neuron calculation nodes and a multilayer operation hierarchical structure are established through design, a proper person input layer and a proper output layer are selected, a functional relation from input to output is established through network learning and tuning, and although the functional relation between the input and the output cannot be found 100%, the functional relation can be as close to a real association relation as possible. The network model which is successfully trained is used, so that the automation requirement of the complex transaction processing can be met.
SVMs are classifiers developed by the generalized portrait algorithm (generalized portrait algorithm) in pattern recognition, and early work came from studies published in 1963 by the soviet union, Vladimir n.vapnik, and Alexander y.lerner. In 1964, the generalized portrait algorithm was further discussed by Vapnik and Alexey y. chervonenkis and a hard-edged linear SVM was established. In the 70-80 s of the twentieth century thereafter, SVMs were progressively theorized and become part of statistical learning theory with theoretical studies of maximum margin decision boundaries in pattern recognition, emergence of relaxation variable (slack variable) -based planning problem solving techniques, and the proposal of VC dimension (VC dimension). In 1992, Bernhard E.Boser, Isabelle M.Guyon and Vapnik have produced nonlinear SVM's by the kernel method. In 1995, Corinna cortex and Vapnik proposed a soft-edge-distance nonlinear SVM and applied it to the handwritten character recognition problem, and this research was noted and cited after publication, and provides references for the application of SVM in various fields.
The invention is based on the prior art, and aims at the design of a detection method for various defects of a brake pad of a high-speed rail so as to ensure that the defects of the brake pad can be detected in time.
Disclosure of Invention
The invention aims to provide a nondestructive testing method for a high-speed rail brake pad based on a sound vibration method, aiming at various defects of the high-speed rail brake pad.
The invention comprises the following contents:
a high-speed rail brake pad nondestructive testing method based on a sound vibration method is realized by the following steps:
step one, applying excitation to a high-speed rail brake pad, obtaining a vibration signal of the high-speed rail brake pad through a sensor, and obtaining time domain and frequency domain image data of the vibration signal;
secondly, calculating each statistical parameter of the time domain signal and the frequency domain signal by using the acquired time domain and frequency domain image data of the vibration signal;
step three, performing data dimension reduction and feature extraction on the calculated statistical parameters, and selecting feature parameters related to the defect signals for statistics;
analyzing and training the vibration characteristic parameters of the brake pad by using a deep learning method and an SVM method to obtain the analysis result of the brake pad;
and fifthly, carrying out nondestructive testing on the high-speed rail brake pad according to the obtained training result, and if the testing result does not relate to the relevant characteristic parameters of the defect signal, determining that the high-speed rail brake pad is nondestructive.
According to a preferred embodiment of the present invention, in the first step, the time domain signal in the obtained vibration signal is transmitted to the computer through the acceleration sensor, the processing circuit and the data acquisition card.
According to a preferred embodiment of the present invention, in the first step, the time domain signal is changed into the frequency domain signal by using fourier transform.
According to a preferred embodiment of the present invention, in the second step, the process of calculating each statistical parameter of the time domain signal and the frequency domain signal includes intercepting an effective characteristic interval, calculating a peak value, a mean square deviation, an effective value, a variance, a standard deviation, a skewness index, a kurtosis index, values of other dimensionless indexes, and a characteristic value of the frequency domain signal, and calculating an average value of the values as a final characteristic value by using a plurality of experimental data obtained from the same group;
wherein the content of the first and second substances,
1) the peak value is calculated or determined by:
the peak value is reflected by the maximum value of the amplitude value in a certain time period in the time domain signal, namely the peak value is generated at the moment when the brake pad is knocked in the knocking experiment;
2) the method for calculating or determining the mean value is:
the mean value of the tapping vibration signal is the integral average of the sample function x (k) ( k 1,2,3 …, N) on the time axis; the signal mean value estimation formula is as follows:
3) the mean square error calculation or determination method is:
the mean square error can reflect the fluctuation of the signal relative to the zero point, and the average energy of the signal can be identified, and the corresponding mathematical expression is as follows:
4) the method of calculating or determining a valid value is:
the effective value is also called root mean square value, and for the knocking vibration signal, the effective value and the vibration energy are corresponding, and the mathematical expression is as follows:
5) the variance calculation or determination method is:
the variance is used for describing the fluctuation condition of the knocking signal relative to the mean value, the variance reflects the dynamic component of the knocking signal, and the corresponding mathematical expression is as follows:
6) the method of calculating or determining the standard deviation is:
the standard deviation is the square of the variance and is expressed as:
7) the method for calculating or determining the skewness index and the kurtosis index comprises the following steps:
the skewness index is also called skewness, and it and kurtosis index are used to describe the normal distribution degree of the beat signal deviation, respectively using K3,K4Represents:
where p (x) is a probability distribution function expressed as:
8) the other dimensionless index calculation or determination method is:
theoretically, when parameters caused by the change of the knocking state change, dimensionless indexes change more obviously; the volatility index K, the peak index C, the pulse index I and the margin index L are dimensionless main indexes which are respectively expressed as follows:
fourier transform formula:
according to a preferred embodiment of the present invention, in the third step, the defect signal refers to characteristic information indicating damage or abnormality of the high-speed rail brake pair.
According to a preferred embodiment of the invention, in the fourth step, in the process of analyzing and training the vibration characteristic parameters of the brake pad by using a deep learning method and an SVM method,
the deep learning method comprises the following steps of,
defining a concept of a layer from the process of input to output, wherein when the process of solving the problem is more complex when the process comprises a leftmost input layer and a rightmost output layer, more hidden layers are possibly needed to calculate the final result;
the SVM method is carried out by the following steps,
the input is set as: data set (x)1,y1)(x2,y2)(x3,y3)(x4,y4)···(xn,yn)
xi∈χ=Rn,yi∈Y={-1,+1},i=1,2,…,N
The output is set as: separating the hyperplane and the classification decision function at maximum intervals;
1) constructing and solving an optimization problem with constraints:
αi≥0
obtaining the optimal solution alpha ═ (alpha)1,α2,…,αN)T
2) Calculating:
selecting a positive component alpha of alphaj>0, calculating:
this gives a separation hyperplane:
ω·Φ(x)+b=0
and a classification decision function:
y(x)=sign(ω·Φ(x)+b)
wherein phi (x) is a kernel function of x, which is equivalent to that x is subjected to one-dimensional transformation;
the value of ω, b depends only on the corresponding α in the training quantityiSample points ≧ 0, others had no effect on ω, b, and we corresponded the training data to αiPoints more than or equal to 0 become support vectors;
the support vectors take into account the original optimization:
1-yi(wT·Φ(xi)+b)≤0
points located on the boundary are called support vectors, i.e. points satisfying the following conditions:
1-yi(wT·Φ(xi)+b)=0
that is to say
ω·Φ(x)+b=±1。
The invention has the beneficial effects that:
according to the method, abnormal vibration signals generated in the abrasion process of the brake pad are input into a computer through a receiving device for drawing, image and data information are used for feature screening, and finally, the state of the high-speed rail brake pad is predicted by using a deep learning and support vector machine model, so that the purpose of predicting the service life of the brake pad is achieved.
The invention can realize on-site detection by collecting the vibration analysis defects of the friction plate by using a simple and easy-to-operate sound vibration method, avoids the complex process of analysis in a laboratory, greatly increases the efficiency, thereby prolonging the service cycle of the friction plate and saving the replacement cost of billions.
Specifically, a neural network and a support vector machine are used for training data, and accurate identification of the tiny defects is achieved. The sound vibration method is utilized to realize rapid detection, the expected target is achieved, and the field detection can be realized. The process of applying excitation to the high-speed rail brake pad utilizes the falling of the small balls to realize the accurate control of the excitation magnitude, and is convenient for experiments to obtain accurate and easily analyzed vibration signals.
Drawings
FIG. 1 is a flow chart of the present invention;
fig. 2 is a network diagram of deep learning to which the present invention relates.
Detailed Description
The first embodiment is as follows:
in the present embodiment, as shown in fig. 1, a nondestructive testing method for a brake pad of a high-speed rail based on a sound vibration method is implemented by the following steps:
step one, applying excitation to a high-speed rail brake pad, obtaining a vibration signal of the high-speed rail brake pad through a sensor, and obtaining time domain and frequency domain image data of the vibration signal;
secondly, calculating each statistical parameter of the time domain signal and the frequency domain signal by using the acquired time domain and frequency domain image data of the vibration signal;
step three, performing data dimension reduction and feature extraction on the calculated statistical parameters, and selecting feature parameters related to the defect signals for statistics;
analyzing and training the vibration characteristic parameters of the brake pad by using a deep learning method and an SVM method to obtain the analysis result of the brake pad;
and fifthly, carrying out nondestructive testing on the high-speed rail brake pad according to the obtained training result, and if the testing result does not relate to the relevant characteristic parameters of the defect signal, determining that the high-speed rail brake pad is nondestructive.
Wherein the content of the first and second substances,
(1) in the process of exciting the high-speed rail brake pad, in the process of designing hardware, the selection of the small ball for exciting and the selection of the falling height of the small ball need to find an excitation which can obtain a good vibration signal without damaging the joint point of the brake pad, and the selection of the experimental parameters needs to be tested for many times to achieve a good effect, so that high-quality signals can be obtained, and nondestructive detection can be realized.
(2) When signal acquisition is performed, signals transmitted by the sensor are amplified and filtered, other interferences under complex conditions need to be eliminated, noise from the inside of the sensor and interferences brought by the external environment possibly need to be eliminated when a circuit is designed.
(3) When data calculation is carried out, an effective characteristic interval needs to be intercepted, the intercepted size of the characteristic interval can influence the calculation result of statistical parameters and the effect of a training model for subsequent machine learning, so that signals of the effective vibration interval after excitation is generated can be found as far as possible when the characteristic interval is selected, and subsequent calculation is facilitated.
(4) The overfitting phenomenon may occur in the training result, after the training is finished, the resolution degree of the training sample is high, but the test result of the test sample is not ideal, the algorithm needs to be improved, and the statistical parameter features need to be reselected.
(5) The method is characterized in that different signals can be acquired for training machine learning only by distinguishing good brake pads and bad brake pads in advance, the distinguishing of fine defects is a difficult point, and how to distinguish the brake pads before the distinguishing of a device is not provided.
(6) The brake pad may have different defect types at the same time, if the defect types are overlapped, the brake pad is classified by finding a certain defect which is more obvious, the defect priority is set, and the brake pad is eliminated as long as the defect occurs, so that the defect type which is less obvious does not need to be distinguished.
The second embodiment is as follows:
different from the first specific embodiment, in the first step of the nondestructive testing method for the brake pad of the high-speed rail based on the acoustic vibration method, the time-domain signal in the obtained vibration signal is transmitted to the computer through the acceleration sensor, the processing circuit and the data acquisition card.
The third concrete implementation mode:
different from the first or second embodiment, in the first step of the nondestructive testing method for the brake pad of the high-speed rail based on the acoustic vibration method, the time domain signal is changed into the frequency domain signal by using fourier transform.
The fourth concrete implementation mode:
different from the third specific embodiment, in the second step, in the process of calculating each statistical parameter of the time-domain signal and the frequency-domain signal, intercepting an effective characteristic interval, calculating a peak value, a mean square deviation, an effective value, a variance, a standard deviation, a skewness index and a kurtosis index of the time-domain signal, values of other dimensionless indexes, and characteristic values of the frequency-domain signal, and calculating an average value of the values as a final characteristic value by using a plurality of experimental data obtained from the same group;
wherein the content of the first and second substances,
1) the peak value is calculated or determined by:
the peak value is reflected by the maximum value of the amplitude value in a certain time period in the time domain signal, namely the peak value is generated at the moment when the brake pad is knocked in the knocking experiment;
2) the method for calculating or determining the mean value is:
the mean value of the tapping vibration signal is the integral average of the sample function x (k) ( k 1,2,3 …, N) over the time axis. The signal mean value estimation formula is as follows:
3) the mean square error calculation or determination method is:
the mean square error can reflect the fluctuation of the signal relative to the zero point, and the average energy of the signal can be identified, and the corresponding mathematical expression is as follows:
4) the method of calculating or determining a valid value is:
the effective value is also called root mean square value, and for the knocking vibration signal, the effective value and the vibration energy are corresponding, and the mathematical expression is as follows:
5) the variance calculation or determination method is:
the variance is used for describing the fluctuation condition of the knocking signal relative to the mean value, the variance reflects the dynamic component of the knocking signal, and the corresponding mathematical expression is as follows:
6) the method of calculating or determining the standard deviation is:
the standard deviation, i.e. the square of the variance, is expressed as:
7) the method for calculating or determining the skewness index and the kurtosis index comprises the following steps:
the skewness index is also called skewness, and it and kurtosis index are used to describe the normal distribution degree of the beat signal deviation, respectively using K3,K4Represents:
wherein p (x) is a probability distribution function expressed as
8) The other dimensionless index calculation or determination method is:
the statistics are characteristic parameters, and other dimensionless indexes are also adopted. Theoretically, when parameters caused by the change of the knocking state change, the dimensionless indexes change more obviously. The volatility index K, the peak index C, the pulse index I and the margin index L are dimensionless main indexes which are respectively expressed as follows:
fourier transform formula:
the fifth concrete implementation mode:
different from the first, second or fourth specific embodiments, in the nondestructive testing method for a brake pad of a high-speed rail based on a sound vibration method according to the third embodiment, the defect signal refers to characteristic information representing damage or abnormality of a brake pair of the high-speed rail.
The sixth specific implementation mode:
different from the fifth embodiment, in the fourth step of the nondestructive testing method for the brake pad of the high-speed rail based on the sound vibration method, the process of analyzing and training the vibration characteristic parameters of the brake pad by using the deep learning method and the SVM method is that,
the deep learning method comprises the following steps of,
defining a concept of a layer from the process of input to output, wherein when the process of solving the problem is more complex when the process comprises a leftmost input layer and a rightmost output layer, more hidden layers are possibly needed to calculate the final result;
setting: the process of input to output from x1, x2, x3 defines a hierarchical concept, such as that of fig. 2, which includes four layers, including a leftmost input layer and a rightmost output layer, if this is a choice question, then the question is the input layer, and the ABCD choice result is the output layer, e.g., L1 and L2 of fig. 2 are the input layer and the output layer, respectively. The process of selecting the problem solving is not written, and we call the hidden layer, where L2 and L3 are hidden layers, the more difficult the problem is, the more information can be given, and the more complicated the process is, the more "hidden layers" can be needed to calculate the final result.
The SVM method is carried out by the following steps of,
the input is set as: data set (x)1,y1)(x2,y2)(x3,y3)(x4,y4)···(xn,yn)
xi∈χ=Rn,yi∈Y={-1,+1},i=1,2,…,N
The output is set as: separating the hyperplane and the classification decision function at maximum intervals;
1) constructing and solving an optimization problem with constraints:
αi≥0
obtaining the optimal solution alpha ═ (alpha)1,α2,…,αN)T
2) Calculating:
selecting a positive component alpha of alphaj>0, calculating:
this gives a separation hyperplane:
ω·Φ(x)+b=0
and a classification decision function:
y(x)=sign(ω·Φ(x)+b)
wherein Φ (x) is a kernel function of x, which is equivalent to performing a dimensional transformation on x.
The value of ω, b depends only on the corresponding α in the training quantityiSample points ≧ 0, others had no effect on ω, b, and we corresponded the training data to αiPoints > 0 become support vectors.
Support vector
Considering raw optimization
1-yi(wT·Φ(xi)+b)≤0
Points located on the boundary are called support vectors, i.e. points satisfying the following conditions:
1-yi(wT·Φ(xi)+b)=0
that is to say
ω·Φ(x)+b=±1。
The above is only a preferred embodiment of the present invention, and is not intended to limit the present invention, and various modifications and changes may be made to the present invention by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (6)
1. A high-speed rail brake pad nondestructive testing method based on a sound vibration method is characterized in that: the method is realized by the following steps:
step one, applying excitation to a high-speed rail brake pad, obtaining a vibration signal of the high-speed rail brake pad through a sensor, and obtaining time domain and frequency domain image data of the vibration signal;
secondly, calculating each statistical parameter of the time domain signal and the frequency domain signal by using the acquired time domain and frequency domain image data of the vibration signal;
step three, performing data dimension reduction and feature extraction on the calculated statistical parameters, and selecting feature parameters related to the defect signals for statistics;
analyzing and training the vibration characteristic parameters of the brake pad by using a deep learning method and an SVM method to obtain the analysis result of the brake pad;
and fifthly, carrying out nondestructive testing on the high-speed rail brake pad according to the obtained training result, and if the testing result does not relate to the relevant characteristic parameters of the defect signal, determining that the high-speed rail brake pad is nondestructive.
2. The nondestructive testing method for the brake pad of the high-speed rail based on the sound vibration method is characterized in that: in the first step, a time domain signal in the obtained vibration signal is transmitted into a computer through an acceleration sensor, a processing circuit and a data acquisition card.
3. The nondestructive testing method for the brake pad of the high-speed rail based on the sound vibration method is characterized in that: in the first step, the time domain signal is changed into the frequency domain signal by using Fourier transform.
4. The nondestructive testing method for the brake pad of the high-speed rail based on the sound vibration method is characterized in that: in the second step, the process of calculating each statistical parameter of the time domain signal and the frequency domain signal is to intercept an effective characteristic interval, calculate the peak value, the mean square error, the effective value, the variance, the standard deviation, the skewness index and the kurtosis index of the time domain signal, the numerical values of other dimensionless indexes and the characteristic numerical value of the frequency domain signal, and use a plurality of experimental data obtained from the same group to calculate the average value of the numerical values as the final characteristic numerical value;
wherein the content of the first and second substances,
1) the peak value is calculated or determined by:
the peak value is reflected by the maximum value of the amplitude value in a certain time period in the time domain signal, namely the peak value is generated at the moment when the brake pad is knocked in the knocking experiment;
2) the method for calculating or determining the mean value is:
the mean value of the tapping vibration signal is the integral average of the sample function x (k) (k 1,2,3 …, N) on the time axis; the signal mean value estimation formula is as follows:
3) the mean square error calculation or determination method is:
the mean square error can reflect the fluctuation of the signal relative to the zero point, and the average energy of the signal can be identified, and the corresponding mathematical expression is as follows:
4) the method of calculating or determining a valid value is:
the effective value is also called root mean square value, and for the knocking vibration signal, the effective value and the vibration energy are corresponding, and the mathematical expression is as follows:
5) the variance calculation or determination method is:
the variance is used for describing the fluctuation condition of the knocking signal relative to the mean value, the variance reflects the dynamic component of the knocking signal, and the corresponding mathematical expression is as follows:
6) the method of calculating or determining the standard deviation is:
the standard deviation is the square of the variance and is expressed as:
7) the method for calculating or determining the skewness index and the kurtosis index comprises the following steps:
the skewness index is also called skewness, and it and kurtosis index are used to describe the normal distribution degree of the beat signal deviation, respectively using K3,K4Represents:
where p (x) is a probability distribution function expressed as:
8) the other dimensionless index calculation or determination method is:
theoretically, when parameters caused by the change of the knocking state change, dimensionless indexes change more obviously; the volatility index K, the peak index C, the pulse index I and the margin index L are dimensionless main indexes which are respectively expressed as follows:
fourier transform formula:
5. the nondestructive testing method for the brake pad of the high-speed rail based on the sound vibration method is characterized in that the method comprises the following steps: in the third step, the defect signal refers to characteristic information representing damage or abnormality of the high-speed rail brake pair.
6. The nondestructive testing method for the brake pad of the high-speed rail based on the sound vibration method is characterized in that: in the fourth step, in the process of analyzing and training the vibration characteristic parameters of the brake pad by utilizing a deep learning method and an SVM method,
the deep learning method comprises the following steps of,
defining a concept of a layer from the process of input to output, wherein when the process of solving the problem is more complex when the process comprises a leftmost input layer and a rightmost output layer, more hidden layers are possibly needed to calculate the final result;
the SVM method is carried out by the following steps,
the input is set as: data set (x)1,y1)(x2,y2)(x3,y3)(x4,y4)···(xn,yn);
xi∈X=Rn,yi∈Y={-1,+1},i=1,2,…,N;
The output is set as: separating the hyperplane and the classification decision function at maximum intervals;
1) constructing and solving an optimization problem with constraints:
obtaining the optimal solution alpha ═ (alpha)1,α2,…,αN)T;
2) Calculating:
selecting a positive component alpha of alphaj>0, calculating:
this gives a separation hyperplane:
ω·Φ(x)+b=0
and a classification decision function:
y(x)=sign(ω·Φ(x)+b)
wherein phi (x) is a kernel function of x, which is equivalent to that x is subjected to one-dimensional transformation;
the value of ω, b depends only on the corresponding α in the training quantityiSample points ≧ 0, others had no effect on ω, b, and we corresponded the training data to αiPoints more than or equal to 0 become support vectors;
the support vectors take into account the original optimization:
1-yi(wT·Φ(xi)+b)≤0
points located on the boundary are called support vectors, i.e. points satisfying the following conditions:
1-yi(wT·Φ(xi)+b)=0
that is: ω · Φ (x) + b ═ 1.
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