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

Abstract

The invention discloses a fault diagnosis method for stacked noise-reducing self-encoded motors based on vibration and current signals, which is divided into five steps: the first step is to obtain the time-domain signals of vibration and current of different faults of the motor, preprocess them, and use them as a network Input; the second step is to determine the network parameters; the third step is to train layer by layer, using the hidden layer of the previous level of autoencoder (Auto encoder, AE) as the input layer of the next level of AE, so as to obtain the final feature encoding, It is used to train the Softmax network; the fourth step is to fine-tune the entire network to determine whether the expected accuracy requirements are met. If the requirements are met, the network training ends. If not, adjust the network parameters and repeat the third step; the fifth step is to build the network Finish. This method constructs a multi-layer SDAE network, combines the vibration frequency domain signal and the current time domain signal as input, trains the SDAE network and classifier in sequence, and fine-tunes the entire network under supervision, so as to achieve accurate motor fault diagnosis.

Description

Fault diagnosis method for stacked noise reduction self-encoder motor based on vibration and current signals

technical field

The invention belongs to the technical field of fault diagnosis of motors in industrial production, and in particular relates to a fault diagnosis method for motor vibration signals of multi-source signals (vibration signals and current signals) and stacked noise-reduction self-encoding.

Background technique

Asynchronous motors are more and more widely used in the production system of contemporary society, and are the main driving equipment for industrial production activities. Once a failure occurs, it will bring huge economic losses. Asynchronous motor is a comprehensive electrical equipment composed of stator, rotor, bearing, frame and fan, etc. It contains multiple complex subsystems inside, which makes the motor faults appear diverse, and its characteristics are also very different; and the same symptom has It may be caused by different reasons, and the characteristics of the same fault are also different. There is no one-to-one correspondence between the fault characteristics and fault types of asynchronous motors, and there is a strong nonlinear relationship between them. Therefore, it is of great practical significance to effectively diagnose motor faults to avoid serious faults and ensure the normal operation of mechanical equipment.

The motor fault diagnosis method belongs to the category of pattern recognition. Usually, the characteristics of the motor vibration signal are extracted first, so as to classify. The methods used include BP neural network, support vector machine (Support Vector Machine, SVM), radial basis network and so on. In recent years, due to the development of deep learning, deep networks have been widely used in image recognition and speech recognition.

Stacked denoising autoencoder (Stacked Denoising Autoencoder, SDAE), as a deep network, consists of multiple autoencoders, which can adaptively and unsupervisedly extract the features of signals. And through the fine-tuning mechanism of the stacked network, the network can be trained under supervision and the accuracy rate can be improved.

Contents of the invention

As the scale of industrial production increases, each industrial equipment needs more monitoring points, the sampling frequency of each measuring point is getting higher and higher, and the data collection time is getting longer and longer, which makes the amount of data obtained by the monitoring system larger and larger. , the field of mechanical health monitoring has entered the era of big data. When the traditional method realizes the fault diagnosis of the motor, the sample size used for the test is very small, but in the context of mechanical "big data", these small samples lose their practical significance. Therefore, it is necessary to choose the appropriate fault diagnosis method and improve the accuracy of fault diagnosis degree becomes more important.

In order to solve the problems of asynchronous motor fault diagnosis difficulties caused by factors such as complex motor structure, non-stationary vibration signal, and large mechanical data, this invention introduces deep learning theory and proposes a motor fault diagnosis method based on stacked noise reduction autoencoder network. This method constructs a multi-layer SDAE network, combines the vibration frequency domain signal and the current time domain signal as input, trains the SDAE network and classifier in sequence, and fine-tunes the entire network under supervision, so as to achieve accurate motor fault diagnosis.

Technical scheme of the present invention is as follows:

The input samples of the SDAE network should contain all the features of the fault signal as much as possible, the vibration signal contains complex bearing information, and the current signal contains rich rotor features, so this patent combines the vibration frequency domain signal and the current time domain signal as the input of the network ,As shown in Figure 1.

The SDAE motor fault network training process is divided into 5 steps:

Step 1: Obtain the time-domain signals of the vibration and current of different faults of the motor, preprocess them, and use them as network input;

The second step: determine the network parameters (number of network layers, number of nodes in each layer, learning rate, number of iterations, etc.);

The third step: training layer by layer, using the hidden layer of the upper-level autoencoder (Auto encoder, AE) as the input layer of the next-level AE, so as to obtain the final feature encoding, which is used to train the Softmax network;

Step 4: Fine-tune the entire network to determine whether the expected accuracy requirements are met. If the requirements are met, the network training ends. If not, adjust the network parameters and repeat the third step;

Step 5: The network construction is completed.

Beneficial effect

SDAE is used to analyze and diagnose the four types of samples of motor vibration time domain signal, vibration frequency domain signal, vibration time domain signal + frequency domain signal and vibration frequency domain signal + current time domain signal. After many experiments, it is found that, as shown in Figure 4, the accuracy rate is significantly higher when the vibration frequency domain + current time domain signal is used as the input sample in a 4-layer SDAE network (network structure: 2000-100-100-100-7). Compared with the other three, it reaches the highest 99.86%.

In order to compare with traditional intelligent methods, this experiment uses two methods of EMD+SVM and diagnostic features+SVM to diagnose motor faults, and also selects 75% of all samples for training, and the remaining 25% for testing. The results are as follows: Table 1 shows.

Table 1 Diagnosis results of different methods

Although the two methods of EMD+SVM and diagnostic features+SVM can better realize motor fault diagnosis, and their diagnostic accuracy is higher (90.15% and 93.65% respectively). However, SDAE can adaptively and unsupervisedly extract more accurate feature expressions through the deep network, and fine-tune the entire network with supervision, so as to realize intelligent and efficient motor fault diagnosis, and its diagnosis accuracy is 99.86%.

In order to compare the ability of DAE and SDAE networks to extract features, in the experiment, the vibration frequency domain signal + current time domain signal were used as samples to train the DAE and SDAE (4 hidden layer) networks respectively, and principal component analysis (Principal Component Analysis, PCA) was used to extract the fourth Two important components of layer features (principal component component x and principal component component y, respectively) are visualized, as shown in Figure 5.

Fig. 5(a) is a scatter diagram of DAE network characteristics, and Fig. 5(b) is a scatter diagram of SDAE network characteristics. It can be seen from the figure that the SDAE network features can be clearly distinguished, while the DAE network features overlap and cannot be clearly distinguished.

Description of drawings

Figure 1 is the splicing of vibration frequency domain signals and current time domain signals;

Figure 2 is a flow chart of motor fault diagnosis;

Fig. 3 is a schematic diagram of a noise reduction self-encoder;

Figure 4 shows the diagnostic results of different depth networks under different samples;

Figure 5 is the characteristic scatter diagram under two kinds of networks, (a) is the characteristic scatter diagram of DAE, (b) is the characteristic scatter diagram of SDAE;

Figure 6 shows the supervised SDAE network during network fine-tuning.

Detailed ways

Embodiments of the present invention are described in detail with reference to the accompanying drawings of the present invention.

Step 1: Collect data. Taking the asynchronous motor of the power transmission fault diagnosis comprehensive test bench as the research object, the test bench is composed of four parts: asynchronous motor, two-stage planetary gearbox, fixed shaft gearbox and magnetic powder brake. By replacing the motor to simulate 7 different fault states, as shown in Table 2, 7 different fault states are listed in the table.

Table 2 Seven states of the motor

In order to ensure the diversity of experimental data, 10 different working conditions were simulated when collecting data, corresponding to 5 speeds (speed up and down, 3560RPM, 3580RPM, 3560RPM, 3620RPM), and 2 states (loaded and unloaded). Considering the influence of the position of the sensor, two acceleration sensors are arranged at the front end of the motor at 12 o'clock and 9 o'clock, and the current signal of the motor is collected by using the clamp current sensor at the same time. The sampling frequency of the sensor is set to 5kHz. When selecting data, 200 samples are used for each working condition, including 100 acceleration sensor signals at the 12 o'clock and 9 o'clock positions. Therefore, the total number of samples for each type of fault is 2000, and each sample corresponds to the vibration signal of 2000 points. And select 2000 sets of current signals corresponding to the time. A total of 14,000 sets of vibration time-domain signals and 14,000 sets of current time-domain signals corresponding to time were obtained. 75% of each working condition of each fault is randomly selected as training samples, and the remaining 25% are used as test samples.

Step 2: Perform frequency domain analysis on the collected vibration time domain signals of different faults with fast Fourier transform, extract frequency domain signals (length is 1000), and then combine them with current time domain signals (length is 1000) in the manner shown in Figure 1 1000) for splicing, as the sample x (length 2000) input by the network.

Step 3: Before network training, the samples need to be normalized, such as formula (1).

A denoising autoencoder is then constructed, and a single autoencoder is shown in Figure 3. Encoding is to propagate the sample x from the input layer to the hidden layer. In order to make the features learned by each hidden layer of the autoencoder (AE: Auto Encoder) more robust, noise is added to the training samples with a certain probability, that is, random The input data of each hidden layer is set to zero. Then the noise-added data is mapped into a k-dimensional vector h∈[] ^k×1 (such as formula (3)) through the sigmoid activation function (such as formula 2).

In the formula: x is the input sample; f(·) is the activation function; θ ₁ ={w ₁ ,b ₁ } is the network parameter; w ₁ is the weight, and b ₁ is the bias.

Decoding is to propagate the feature code from the hidden layer to the output layer, and map it into an m-dimensional vector through the activation function The process of reconstructing sample x, as in formula (4).

In the formula: is the reconstruction of the sample x; f(·) is the activation function, θ ₂ ={w ₂ ,b ₂ } is the network parameter; W ₂ is the weight, and b ₂ is the bias.

The training goal of the AE network is to find a set of optimal parameters The error between the output data and the input data is made as small as possible, that is, the loss function L(w ₁ , w ₂ , b ₁ , b ₂ ) is minimized, and the expression of the loss function is as follows.

In the formula: the first item on the right side of the equation represents the sum of the errors between the input data and the output data of the network; the second item is a regularization constraint item, which is used to prevent training from overfitting; x ⁽ⁱ⁾ and Represent the input vector and reconstruction vector of the i-th sample, respectively; Denotes x ⁽ⁱ⁾ with The mean square error between , its expression is as follows.

The AE network realizes the minimization of the error function L(w ₁ ,w ₂ ,b ₁ ,b ₂ ) through the error backpropagation and gradient descent method. It enables AE to adapt to the characteristics of unsupervised learning samples.

Step 4: Use the output of the hidden layer of the first AE encoder as an input sample to construct the second AE, repeat the third step, and so on to construct multiple AEs.

Step 5: Take out the hidden layers of each AE network encoder that has been unsupervisedly trained in the fourth step, stack them layer by layer as shown in Figure 6, and add a softmax classifier to the last layer for supervised fine-tuning. The Softmax classifier classifies and identifies the feature vectors. Assuming that the input sample in the training data is x, and the corresponding label is y, then the probability of judging the sample as a certain category J is p(y=j|x). Therefore, for a K-type classifier, the output will be a K-dimensional vector (the sum of the elements of the vector is 1), as shown in formula (7).

In the formula: θ ₁ ; θ ₂ ;  …; is the model parameter; is a normalization function that normalizes the probability distribution such that the sum of all probabilities is 1.

In the training, the gradient descent method is used to find the optimal parameters, so that the cost function J(θ) of Softmax reaches the minimum, thus completing the network training. The cost function J(θ) is shown in formula (8).

In the formula: 1{ } is an indicative function, that is, when the value inside the braces is true, the result of the function is 1, otherwise the result is 0.

Step 6: After multiple iterations, when the loss loss converges, the network training is completed. And use the verification set data to evaluate the network performance, if the accuracy rate meets the requirements, output the network, otherwise change the network parameters and continue training.

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.