CN107957551A - Stacking noise reduction own coding Method of Motor Fault Diagnosis based on vibration and current signal - Google Patents

Stacking noise reduction own coding Method of Motor Fault Diagnosis based on vibration and current signal Download PDF

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CN107957551A
CN107957551A CN201711321716.1A CN201711321716A CN107957551A CN 107957551 A CN107957551 A CN 107957551A CN 201711321716 A CN201711321716 A CN 201711321716A CN 107957551 A CN107957551 A CN 107957551A
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赵晓平
吴家新
周子贤
杨家巍
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Nanjing University of Information Science and Technology
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Nanjing University of Information Science and Technology
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    • G01MEASURING; TESTING
    • G01RMEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
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Abstract

The invention discloses the stacking noise reduction own coding Method of Motor Fault Diagnosis based on vibration and current signal, it is divided into five steps:The first step, obtains the vibration of motor different faults and the time-domain signal of electric current, it is pre-processed, as network inputs;Second step, determines network parameter;3rd step, is successively trained, by input layer of the hidden layer of upper level self-encoding encoder (Auto encoder, AE) as next stage AE, so that final feature coding is obtained, for training Softmax networks;4th step, finely tunes whole network, judges whether to reach expected precise requirements, terminate if meeting the requirements network training, if not satisfied, adjusting network parameter, repeats the 3rd step;5th step, network struction are completed.This method builds multilayer SDAE networks, and vibration frequency-region signal and electric current time-domain signal are combined as input, train SDAE networks and grader successively, and has being finely adjusted to whole network for supervision, so as to fulfill accurate Diagnosing Faults of Electrical.

Description

Stacking noise reduction own coding Method of Motor Fault Diagnosis based on vibration and current signal
Technical field
The invention belongs to the fault diagnosis technology field of motor in industrial production, and in particular to source signal (vibration signal And current signal) and stack noise reduction own coding motor oscillating signal fault diagnosis method.
Background technology
Application of the asynchronous machine in contemporary society's production system is more and more extensive, is the main driving of industrial production activities Equipment, once breaking down, will bring huge economic loss.Asynchronous machine is by stator, rotor, bearing, engine base and fan Deng the Universal electric equipment of composition, it is internal comprising complicated multiple subsystems, electrical fault is showed diversity, it is showed The feature gone out is also multifarious;And caused by same symptom is likely to be different reasons, feature that same failure is shown Also it is not quite similar.Not corresponded between the fault signature and fault type of asynchronous machine, there are stronger non-linear therebetween Relation.Therefore, electrical fault is effectively diagnosed to be to avoiding the generation of catastrophe failure, and ensureing the normal operation of mechanical equipment has Major and immediate significance.
The method for diagnosing faults of motor belongs to the category of pattern-recognition, usually extracts the feature of motor oscillating signal first, So as to classify.The method used has BP neural network, support vector machines (Support Vector Machine, SVM), footpath To base net network etc..In recent years since the development of deep learning, profound network have obtained extensively in image recognition, speech recognition Application.
Noise reduction self-encoding encoder (Stacked Denoising Autoencoder, SDAE) is stacked as a kind of profound Network, is made of multiple self-encoding encoders, is capable of the feature of adaptive unsupervised extraction signal.And by stacking the micro- of network Tune mechanism, can there is the training network of supervision, improve accuracy rate.
The content of the invention
As commercial production scale becomes larger, the monitoring point that each industrial equipment needs is increased, the sample frequency of each measuring point Higher and higher, data collection time is increasingly longer, this make it that the data volume that monitoring system obtains is increasing, mechanical health monitoring Field enters the big data epoch.Conventional method is when realizing Diagnosing Faults of Electrical, sample size all very littles for experiment, and in machine Under tool " big data " background, these small samples just lose practical significance, therefore select suitable method for diagnosing faults and raising It is particularly important that fault diagnosis accuracy becomes.
In order to solve the asynchronous machine caused by the factors such as electric machine structure complexity, vibration signal non-stationary and mechanical big data The problems such as fault diagnosis is difficult, it is theoretical present invention introduces deep learning, it is proposed that based on the motor for stacking noise reduction autoencoder network Method for diagnosing faults.This method builds multilayer SDAE networks, and vibration frequency-region signal and electric current time-domain signal are combined as defeated Enter, train SDAE networks and grader successively, and have being finely adjusted to whole network for supervision, so as to fulfill the event of accurate motor Barrier diagnosis.
Technical solution of the present invention is as follows:
The input sample of SDAE networks should include all features of fault-signal as far as possible, and vibration signal includes complicated axis Information is held, current signal includes abundant rotor characteristic, therefore this patent is mutually tied frequency-region signal is vibrated with electric current time-domain signal Cooperate the input for network, as shown in Figure 1.
SDAE electrical fault network training process is divided into 5 steps:
The first step:The vibration of motor different faults and the time-domain signal of electric current are obtained, it is pre-processed, it is defeated as network Enter;
Second step:Determine network parameter (the network number of plies, each node layer number, learning rate, iterations etc.);
3rd step:Successively train, by the hidden layer of upper level self-encoding encoder (Auto encoder, AE) as next stage AE Input layer, so that final feature coding is obtained, for training Softmax networks;
4th step:Whole network is finely tuned, judges whether to reach expected precise requirements, if meeting the requirements network training knot Beam, if not satisfied, then adjusting network parameter, repeats the 3rd step;
5th step:Network struction is completed.
Beneficial effect
Using SDAE respectively the vibration time-domain signal to motor, vibration frequency-region signal, vibration time-domain signal+frequency-region signal and Vibrate 4 class sample analysis of frequency-region signal+electric current time-domain signal diagnosis.Found by test of many times, as shown in figure 4, to vibrate frequency Domain+electric current time-domain signal is input sample, (the network structure in 4 layers of SDAE networks:2000-100-100-100-7), accuracy rate Apparently higher than other three kinds, reach highest 99.86%.
In order to which compared with traditional intelligence method, this experiment utilizes this 2 kinds of methods of EMD+SVM, diagnostic characteristic+SVM to motor Fault diagnosis is carried out, the 75% of all samples is equally chosen and is used to train, remaining 25% is used to test, its result such as institute of table 1 Show.
The diagnostic result of 1 distinct methods of table
Although two methods of EMD+SVM and diagnostic characteristic+SVM can preferably realize Diagnosing Faults of Electrical, and it is diagnosed Accuracy is higher (being respectively 90.15% and 93.65%).But SDAE is by the way that deep layer network can adaptively unsupervised extraction be more Accurate feature representation, and have the fine setting whole network of supervision, so as to fulfill the Diagnosing Faults of Electrical of intelligent and high-efficiency, it diagnoses essence Spend for 99.86%.
In order to compare the ability of DAE and SDAE networks extraction feature, to vibrate frequency-region signal+electric current time-domain signal in experiment DAE and SDAE (4 hidden layer) network is respectively trained for sample, utilizes principal component analysis (Principal Component Analysis, PCA) extraction the 4th layer of feature two important components (be respectively principal component component x and principal component component y) simultaneously can Depending on change, as shown in Figure 5.
Fig. 5 (a) is the scatter diagram that DAE network characterizations are drawn, and Fig. 5 (b) is the scatter diagram that SDAE network characterizations are drawn.From figure In it can be seen that SDAE network characterizations can be distinguished significantly, and DAE network characterizations overlap, can not obvious area Point.
Brief description of the drawings
Fig. 1 is the splicing of vibration frequency-region signal and electric current time-domain signal;
Fig. 2 is the flow chart of Diagnosing Faults of Electrical;
Fig. 3 is noise reduction self-encoding encoder schematic diagram;
Fig. 4 is the diagnostic result of different depth network under different samples;
Fig. 5 is the feature scatter diagram under two kinds of networks, and (a) is the feature scatter diagram of DAE, and (b) is the feature scatterplot of SDAE Figure;
Fig. 6 is to have supervision SDAE networks when network is finely tuned.
Embodiment
With reference to the attached drawing of the present invention, embodiment of the present invention is described in detail.
The first step:Gathered data.Using the asynchronous machine of power transmission fault diagnosis multi-function test stand as research object, experiment Platform is made of four parts such as asynchronous machine, two-stage planetary gear, fixed axis gear case and magnetic powder brake.By replacing motor 7 kinds of different malfunctions are simulated, list 7 kinds of different malfunctions as shown in table 2, in table.
7 kinds of states of 2 motor of table
To ensure the diversity of experimental data, when gathered data, simulates 10 kinds of different operating modes, and corresponding 5 kinds of rotating speeds (rise Reduction of speed, 3560RPM, 3580RPM, 3560RPM, 3620RPM), 2 kinds of states (have load, non-loaded).In view of sensing station Influence, in two acceleration transducers of 12 o'clock of front end of motor and 9 o'clock location arrangements, while passed using pincerlike electric current Sensor acquires current signal during motor operation.The sample frequency of sensor is set to 5kHz.When choosing data, every kind of operating mode Using 200 samples, wherein each 100 of the acceleration transducer signals of 12 o'clock and 9 o'clock position.Therefore, each failure Total number of samples be 2000, each sample corresponds to the vibration signal of 2000 points.And choose 2000 groups of electricity of corresponding time Flow signal.14000 groups of vibration time-domain signals and 14000 groups of electric current time-domain signals of corresponding time are obtained altogether.Randomly select every kind of The 75% of each operating mode of failure is used as training sample, and residue 25% is used as test sample.
Second step:The vibration time-domain signal of different faults to collecting carries out frequency-domain analysis with Fast Fourier Transform (FFT), Frequency-region signal (length 1000) is extracted, is then spliced in a manner of Fig. 1 with electric current time-domain signal (length 1000), is made For the sample x (length 2000) of network inputs.
3rd step:, it is necessary to which sample is normalized before network training, such as formula (1).
Then noise reduction self-encoding encoder is built, single self-encoding encoder is as shown in Figure 3.Coding be by sample x from input Es-region propagations To hidden layer, to make self-encoding encoder (AE:Auto Encoder) feature that learns of each hidden layer has more robustness, with certain general Rate adds noise in training sample, i.e., at random by the input data zero setting of each hidden layer.Then plus the data made an uproar are passed through Sigmoid activation primitives (such as formula 2), are mapped to k dimensional vector h ∈ []k×1(such as formula (3)).
In formula:X is input sample;F () is activation primitive;θ1={ w1,b1It is network parameter;w1For weights, b1To be inclined Put.
Decoding is that feature coding is propagated to output layer from hidden layer, and m dimensional vectors are mapped to by activation primitiveThe process of reconstructed sample x, such as formula (4).
In formula:It is the reconstruct to sample x;F () is activation primitive, θ2={ w2,b2It is network parameter;W2For weights, b2For biasing.
The training objective of AE networks is by finding one group of optimal parameterSo that output data Error between input data reaches small as far as possible, that is, realizes loss function L (w1,w2,b1,b2) minimize, loss function table It is as follows up to formula.
In formula:Section 1 represents the sum of the deviations of network inputs data and output data on the right of equation;Section 2 is canonical Change bound term, for preventing from training over-fitting;x(i)WithThe input vector and reconstruct vector of i-th of sample are represented respectively;Represent x(i)WithBetween mean square deviation, its expression formula is as follows.
AE networks are by error Back-Propagation and gradient descent method, to realize error function L (w1,w2,b1,b2) minimize.Make AE is capable of the feature of adaptive unsupervised learning sample.
4th step:With the output of first AE encoder hidden layer, as input sample, second AE is built, repeats the Three steps, and so on the multiple AE of structure.
5th step:Unsupervised trained each AE network encoders hidden layer in 4th step is taken out, such as Fig. 6 successively heaps It is folded, and in last layer supervision fine setting has been carried out plus softmax graders.Softmax graders divide feature vector Class identifies.Assuming that input sample is x, corresponding label y in training data, then sample is determined as that the probability of some classification J is p (y=j | x).So for a K class grader, output will be a K dimensional vector (vectorial element and for 1), such as formula (7) shown in.
In formula:θ1;θ2;…;For model parameter;For normalized function, probability is divided Cloth is normalized so that the sum of all probability are 1.
In training, optimized parameter is found using gradient descent method so that the cost function J (θ) of Softmax reaches most It is small, so as to complete network training.Cost function J (θ) is as shown in formula (8).
In formula:1 { } is an indicative function, i.e., when value is true in braces, which is just 1, otherwise As a result it is just 0.
6th step:Successive ignition, when losing loss convergences, completes network training.And use verification collection data assessment net Network performance, if rate of accuracy reached to requiring, exports network, otherwise changes network parameter, continue to train.

Claims (2)

1. the stacking noise reduction own coding Method of Motor Fault Diagnosis based on vibration and current signal, it is characterised in that be divided into five Step:
The first step, gathered data;Using the asynchronous machine of power transmission fault diagnosis multi-function test stand as object, experimental bench is by asynchronous Motor, two-stage planetary gear, fixed axis gear case and magnetic powder brake, the malfunction different by replacing motor simulation, is Ensure the diversity of experimental data;Randomly select the 75% of each operating mode of every kind of failure and be used as training sample, residue 25% is as survey Sample sheet;
Second step, the vibration time-domain signal of the different faults to collecting carry out frequency-domain analysis with Fast Fourier Transform (FFT), extraction Frequency-region signal;
3rd step, it is necessary to which sample is normalized before network training, such as formula (1):
<mrow> <msup> <mi>X</mi> <mo>*</mo> </msup> <mo>=</mo> <mfrac> <mrow> <mi>x</mi> <mo>-</mo> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> <mo>-</mo> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>
Then noise reduction self-encoding encoder is built;Coding is that sample x is propagated to hidden layer from input layer, to make self-encoding encoder AE: The feature that each hidden layers of Auto Encoder learn has more robustness, noise is added in training sample with certain probability, i.e., At random by the input data zero setting of each hidden layer;Then plus the data made an uproar pass through sigmoid activation primitives, see formula (2), are mapped to K dimensional vector h ∈ []k×1, see formula (3)):
<mrow> <mi>f</mi> <mrow> <mo>(</mo> <mo>&amp;CenterDot;</mo> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mn>1</mn> <mo>+</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mi>t</mi> </mrow> </msup> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <mi>h</mi> <mo>=</mo> <msub> <mi>f</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;theta;</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>f</mi> <mrow> <mo>(</mo> <msub> <mi>w</mi> <mn>1</mn> </msub> <mo>&amp;CenterDot;</mo> <mi>x</mi> <mo>+</mo> <msub> <mi>b</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
In formula:X is input sample;F () is activation primitive;θ1={ w1,b1It is network parameter;w1For weights, b1For biasing;
Decoding is that feature coding is propagated to output layer from hidden layer, and m dimensional vectors are mapped to by activation primitive The process of reconstructed sample x, such as formula (4):
<mrow> <mover> <mi>x</mi> <mo>^</mo> </mover> <mo>=</mo> <msub> <mi>f</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;theta;</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> </msub> <mrow> <mo>(</mo> <mi>h</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>f</mi> <mrow> <mo>(</mo> <msub> <mi>w</mi> <mn>2</mn> </msub> <mo>&amp;CenterDot;</mo> <mi>h</mi> <mo>+</mo> <msub> <mi>b</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
In formula:It is the reconstruct to sample x;F () is activation primitive, θ2={ w2,b2It is network parameter;W2For weights, b2To be inclined Put;
The training objective of AE networks is by finding one group of optimal parameter θ*={ w1 *,w2 *,b1 *,b2 *So that output data with Error between input data reaches small as far as possible, that is, realizes loss function L (w1,w2,b1,b2) minimize, loss function expression Formula is as follows;
<mrow> <mtable> <mtr> <mtd> <mrow> <mi>L</mi> <mrow> <mo>(</mo> <msub> <mi>w</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>w</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>b</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>b</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mo>&amp;lsqb;</mo> <mfrac> <mn>1</mn> <mi>n</mi> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mi>J</mi> <mrow> <mo>(</mo> <msup> <mi>x</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msup> <mo>,</mo> <msup> <mover> <mi>x</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msup> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <mfrac> <mi>&amp;lambda;</mi> <mn>2</mn> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>l</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <msub> <mi>n</mi> <mi>l</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>s</mi> <mi>l</mi> </msub> </munderover> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>+</mo> <mn>1</mn> </mrow> <msub> <mi>s</mi> <mrow> <mi>l</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </munderover> <msup> <mrow> <mo>(</mo> <msup> <msub> <mi>W</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>l</mi> <mo>)</mo> </mrow> </msup> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
In formula:Section 1 represents the sum of the deviations of network inputs data and output data on the right of equation;Section 2 for regularization about Shu Xiang, for preventing from training over-fitting;x(i)WithThe input vector and reconstruct vector of i-th of sample are represented respectively;Represent x(i)WithBetween mean square deviation, its expression formula is as follows:
<mrow> <mtable> <mtr> <mtd> <mrow> <mi>J</mi> <mrow> <mo>(</mo> <msup> <mi>x</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msup> <mo>,</mo> <msup> <mover> <mi>x</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msup> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo>|</mo> <mo>|</mo> <msup> <mi>x</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msup> <mo>-</mo> <msup> <mover> <mi>x</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msup> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo>|</mo> <mo>|</mo> <msup> <mi>x</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msup> <mo>-</mo> <mi>f</mi> <mrow> <mo>(</mo> <msub> <mi>w</mi> <mn>2</mn> </msub> <mo>&amp;CenterDot;</mo> <mi>f</mi> <mo>(</mo> <mrow> <msub> <mi>w</mi> <mn>1</mn> </msub> <mo>&amp;CenterDot;</mo> <mi>x</mi> <mo>+</mo> <msub> <mi>b</mi> <mn>1</mn> </msub> </mrow> <mo>)</mo> <mo>+</mo> <msub> <mi>b</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>
AE networks are by error Back-Propagation and gradient descent method, to realize error function L (w1,w2,b1,b2) minimize;So that AE It is capable of the feature of adaptive unsupervised learning sample;
4th step, with the output of first AE encoder hidden layer, as input sample, builds second AE, repeats the 3rd step, And so on the multiple AE of structure;
5th step, unsupervised trained each AE network encoders hidden layer in the 4th step is taken out, and is added in last layer Softmax graders have carried out supervision fine setting;Softmax graders carry out Classification and Identification to feature vector;Assuming that training data Middle input sample is x, corresponding label y, then is determined as sample the probability of some classification J for p (y=j | x);So for One K class grader, output will be a K dimensional vector (vectorial element and for 1), as shown in formula (7);
<mrow> <msub> <mi>h</mi> <mi>&amp;theta;</mi> </msub> <mrow> <mo>(</mo> <msup> <mi>x</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msup> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mi>p</mi> <mrow> <mo>(</mo> <msup> <mi>y</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msup> <mo>=</mo> <mn>1</mn> <mo>|</mo> <msup> <mi>x</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msup> <mo>;</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>p</mi> <mrow> <mo>(</mo> <msup> <mi>y</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msup> <mo>=</mo> <mn>2</mn> <mo>|</mo> <msup> <mi>x</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msup> <mo>;</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>p</mi> <mrow> <mo>(</mo> <msup> <mi>y</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msup> <mo>=</mo> <mi>k</mi> <mo>|</mo> <msup> <mi>x</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msup> <mo>;</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <msubsup> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>k</mi> </msubsup> <mi>exp</mi> <mrow> <mo>(</mo> <msubsup> <mi>&amp;theta;</mi> <mi>j</mi> <mi>T</mi> </msubsup> <msup> <mi>x</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msup> <mo>)</mo> </mrow> </mrow> </mfrac> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mi>exp</mi> <mrow> <mo>(</mo> <msubsup> <mi>&amp;theta;</mi> <mn>1</mn> <mi>T</mi> </msubsup> <msup> <mi>x</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msup> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>exp</mi> <mrow> <mo>(</mo> <msubsup> <mi>&amp;theta;</mi> <mn>2</mn> <mi>T</mi> </msubsup> <msup> <mi>x</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msup> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>exp</mi> <mrow> <mo>(</mo> <msubsup> <mi>&amp;theta;</mi> <mi>k</mi> <mi>T</mi> </msubsup> <msup> <mi>x</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msup> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>
In formula:For model parameter;For normalized function, to probability distribution It is normalized so that the sum of all probability are 1;
In training, optimized parameter is found using gradient descent method so that the cost function J (θ) of Softmax reaches minimum, from And complete network training;Cost function J (θ) is as shown in formula (8):
<mrow> <mi>J</mi> <mrow> <mo>(</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>-</mo> <mfrac> <mn>1</mn> <mi>m</mi> </mfrac> <mo>&amp;lsqb;</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>m</mi> </munderover> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>k</mi> </munderover> <mn>1</mn> <mo>{</mo> <msup> <mi>y</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msup> <mo>=</mo> <mi>j</mi> <mo>}</mo> <mi>log</mi> <mfrac> <mrow> <mi>exp</mi> <mrow> <mo>(</mo> <msubsup> <mi>&amp;theta;</mi> <mi>j</mi> <mi>T</mi> </msubsup> <msup> <mi>x</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msup> <mo>)</mo> </mrow> </mrow> <mrow> <msubsup> <mo>&amp;Sigma;</mo> <mrow> <mi>l</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>k</mi> </msubsup> <mi>exp</mi> <mrow> <mo>(</mo> <msubsup> <mi>&amp;theta;</mi> <mi>l</mi> <mi>T</mi> </msubsup> <msup> <mi>x</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msup> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>&amp;rsqb;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>
In formula:1 { } is an indicative function, i.e., when value is true in braces, which is just 1, otherwise result It is just 0;
6th step, successive ignition, when losing loss convergences, completes network training;And use verification collection data assessment internetworking Can, if rate of accuracy reached to requiring, exports network, otherwise changes network parameter, continue to train.
2. the method as described in claim 1, it is characterised in that electric current time-domain signal length is 1000 in the second step, electricity It is 1000 to flow time-domain signal length, and the sample x length as network inputs is 2000.
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