US 2021/0197335 A1 · Data Augmentation Method Based On Generative Adversarial Networks In Tool Condition Monitoring

Abstract

The invention provides a data augmentation method based on generative adversarial networks in tool condition monitoring. Firstly, the sensor acquisition system is used to obtain the vibration signal and noise signal during the cutting process of the tool; second, the noise data subject to the prior distribution is input to the generator to generate data, and the generated data and the collected real sample data are input to the discriminator for identification, the confrontation training between the generator and the discriminator until the training is completed; then, use the trained generator to generate sample data, and determine whether the generated sample data and the actual tool state sample data are similar in distribution; finally, combined with the accuracy of the deep learning network model to predict the state of the tool to verify the availability of the generated data.

A data augmentation method based on generative adversarial networks in tool condition monitoring, firstly, sensor acquisition system is used to obtain vibration signal and noise signal during cutting process of the tool;

second, noise data subject to prior distribution is input to generator to generate data, and the generated data and collected real sample data are input to discriminator for identification, confrontation training between the generator and the discriminator until training is completed;
then, use the trained generator to generate sample data, and determine whether the generated sample data and actual tool state sample data are similar in distribution;
finally, combined with accuracy of deep learning network model to predict state of the tool to verify availability of the generated data;
wherein the steps are as follows:
first step, collect vibration and sound signals during tool cutting
two acceleration sensors are installed on nose of spindle and front bearing of the spindle respectively to collect the vibration signals during machining process, and acoustic sensor is installed on worktable to collect cutting noise signals during the machining process;
second step, build a generative adversarial network model and conduct adversarial training
the generative adversarial network framework adopted by the method is composed of a generator and a discriminator;
both the generator and the discriminator are multi-layer perceptron structures, where the generator is responsible for generating pseudo data with the same dimensions as real data, and the discriminator is responsible for distinguishing the real data from the generated data;
during the adversarial training process, the generator attempts to use generated pseudo data to fool the discriminator to make it discriminate true, and the discriminator distinguishes the generated data and the real data by improving its discriminating ability, and the two play the game, and eventually reach Nash equilibrium, that is, the sample data generated by the generator is no different from the real sample data, and the discriminator cannot distinguish the generated sample data from the real sample data;
the number of tool state samples collected by the method is 1, and dimension of the vibration signal is 6000, which is set to {v(i)}i=1l, where v(i)∈(m), m=6000, dimension of the noise data set is 1000, which is set to {n(i)}i=1l, where n(i)∈(k), k=1000, tool state data set {tool(i)}i=1l={v(i), n(i)}i=1l, where tool(i)∈(u), u=7000;
the tool state data set of input discriminator is normalized by the maximum-minimum method, so that the input data is converted into a number between [0,1], and after the sample data is generated, inverse normalization processing is carried out, form of normalization function is shown in formula (1), and form of inverse normalization function is shown in formula (2):
tool
(
i
)

′
=
tool
(
i
)
-
tool
min
(
i
)
tool
max
(
i
)
-
tool
min
(
i
)
(
1
)
tool
(
i
)
=
(
tool
max
(
i
)
-
tool
min
(
i
)
)
*
tool
(
i
)

′
+
tool
min
(
i
)
(
2
)
where, tool(i) is original data of the tool state, tool(i)′ is normalized data, toolmin(i) is minimum number in the data sequence, toolmax(i) is maximum number in the sequence;
both the generator and the discriminator use a three-layer fully connected neural network;
input data set is normalized data set;
mapping formula from input layer to hidden layer and the hidden layer to output layer is shown in equation (3):
hi=ƒθ(w*tool(i)′+b) (3)
where, ƒ is activation function and θ={w,b} is parameter matrix of the network, where w is connection weight between neurons in the input layer, hidden layer, and output layer, and b is threshold of neurons in the hidden layer and output layer;
the activation function of the hidden layer uses ReLU function, and the function form is as shown in formula (4):
ReLU

(
x
)
=
{
x
if


x
<
0
0
if


x
≥
0
(
4
)
the activation function of the output layer uses Sigmoid function, and the function form is as shown in formula (5):
f

(
x
)
=
1
1
+
e
-
x
(
5
)
the output of the discriminator is a binary classification, the last layer uses Sigmoid function, and the output probability value is shown in equation (6):
p

(
y
=
1
|
x
)
=
1
1
+
e
-
θ
T
x


p

(
y
=
0
|
x
)
=
1
-
p

(
y
=
1
|
x
)
=
e
-
θ
T
x
1
+
e
-
θ
T
x
(
6
)
objective function set by the method is shown in equation (7):
min
G


max
D

V

(
D
,
G
)
=
E
x
∼
P
data

(
x
)

[
log


D

(
x
)
]
+
E
z
∼
P
z

(
z
)

[
log

(
1
-
D

(
G

(
z
)
)
)
]
(
7
)
the objective function and optimal solution of the discriminator are shown in equations (8) and (9):
max
D

V

(
D
,
G
)
=
E
x
∼
P
data

(
x
)

[
log

D

(
x
)
]
+
E
z
∼
P
z

(
z
)

[
log

(
1
-
D

(
G

(
z
)
)
)
]
(
8
)

D
G
*

(
x
)
=
p
data

(
x
)
p
data

(
x
)
+
p
z

(
x
)
(
9
)
the objective function of the generator is shown in equation (10):
min
G


V

(
D
,
G
)
=
E
z
∼
P
z

(
z
)

[
log

(
1
-
D

(
G

(
z
)
)
)
]
(
10
)
where, Pdata(x) is data distribution of the tool state data set{tool(i)′}i=1l, and Pz(z) is a prior noise distribution;
D(x) represents probability that x comes from {tool(i)′}i=1l;
D(G(z)) represents probability that G(z) comes from generated data, where G(z) is sample data generated by the generator from the noise data that obey the prior distribution;
Ex˜Pdata(x) represents expectation of x from the data distribution of {tool(i)′}i=1l, Ez˜Pz(z) represents expectation of z from the noise distribution;
the goal of the discriminator is to maximize error function to distinguish between real data and generated data, and the generator is to minimize the error function and generate data samples that are closer to the real sample data distribution;
based on the objective function, Adam optimization algorithm is used to update the parameters;
the training steps of the generative adversarial network are as follows:
(1) the generator generates p false tool state data samples {toolF(i)′}i=1p from random noise;
(2) the generated sample data {toolF(i)′}i=1p and original sample data {tool(i)′}i=1l with label 1 are mixed and input into the discriminator;
based on loss function, parameters of the generator are fixed, only parameters of the discriminator are updated, and the discriminator is trained to improve the discriminator's ability to distinguish true and false samples;
(3) after the discriminator is trained, the label of the generated sample {toolF(i)′}i=1p is set to 1;
based on the loss function, the error is back-propagation;
in this stage, parameters of the discriminator are frozen and cannot be updated, only parameters in the generator can be updated, and the generator is trained to produce more real data samples;
(4) steps (1) to (3) are a training period;
after completing a period, training process starts again from (1);
after repeating multiple cycles of training the discriminator and generator, the generator's network parameters are saved;
third step, compare similarity between the generated data and the real data use the trained generator to generate sample data, compare and analyze time-frequency graph of generated tool state sample data {toolF(i)′}i=1p and real tool state sample data {tool(i)′}i=1l, and determine whether distribution of the generated sample data and the real sample data is the same;
if they are the same, the generated sample data is denormalized, {toolF(i)′}i=1p is generated tool state sample data after denormalization, and {toolF(i)′}i=1p will be added to the original unbalanced data set {toolF(i)′}i=1l;
enhanced data set is {toolmix(i)}i=1l+p={{toolF(i)}i=1p;
{tool(i)}i=1l};
if they are not the same, return to the generative adversarial network to continue adversarial training, until the distribution of the generated sample data and the real sample data is the same;
fourth step, verify the availability of the generated sample data
the original unbalanced data set and the enhanced data set are used to train the deep learning network model to test prediction accuracy of the two and verify the availability of the generated data;
training set and test set do not have any intersection, and the test set is composed of real data.

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Data Augmentation Method Based On Generative Adversarial Networks In Tool Condition Monitoring

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Data Augmentation Method Based On Generative Adversarial Networks In Tool Condition Monitoring

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Abstract

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