Fault diagnosis of needle selector drive parts based on adaptive stochastic resonance with improved generative adversarial networks

Abstract

Piezoelectric needle selectors, as key weaving components in the jacquard knitting process of knitting machinery, are widely used in textile equipment. Accurate diagnostic procedures for needle selector drive faults are crucial to ensure the normal operation of the equipment. However, traditional vibration diagnosis methods cannot detect weak periodic signals, resulting in low accuracy of monitoring results. To address this issue, this paper proposes an adaptive stochastic resonance (SR) method based on an improved generative adversarial network (IGAN). Firstly, in order to solve the problem of difficulty in obtaining stochastic resonance parameters, SR is combined with IGAN, and IGAN provides the optimal SR parameters. Secondly, a soft threshold residual attention mechanism and residual network were introduced in the GAN network, and multiple generators were utilized to alleviate the problem of model collapse, in order to adapt to the actual working environment. In addition, due to the large amount of data, it is recommended to use feature parameters for training to improve the efficiency of model training. Finally, through a typical vibration data, the influence of different parameter quantities on the training accuracy of the model was studied, and the superiority of the proposed model compared to other models and the stability of the model under different environmental influences were explored. The results show that this method can effectively detect weak periodic signals of the needle selection driver, effectively alleviate the problem of model collapse in different environments, and is superior to existing methods in terms of accuracy and stability.

Keywords

Piezoelectric needle picker weak periodic signal signal detection stochastic resonance improved generative adversarial network fault diagnosis

Introduction

Electronic needle selectors play a key driver role in the jacquard work of knitting machines. There are two main types of needle selectors: electromagnetic needle selectors and piezoelectric needle selectors. In the textile industry, the piezoelectric needle selector is a key device that is used to control the selection and movement of needles during the weaving process. This device utilizes the properties of piezoelectric materials to move the needles by applying a voltage to achieve high precision and efficiency in weaving. Piezoelectric needle selector has the characteristics of rapid response, low heat generation, small volume, suitable for multi-way needle selection and fast response requirements, so most high-end textile equipment more than the use of piezoelectric needle selector, as a jacquard needle driver, in the selection of the needle hook into the loop process, its performance is related to the quality of jacquard knitting production. Nowadays, piezoelectric needle selectors are widely used in all kinds of looms, including spinning and weaving machines, for the production of various textile materials. As a result, the problem of malfunctioning piezoelectric needle selectors is becoming more common and is being paid more attention to. The working mechanism of the needle selector is generally a one-way controller to send jacquard knitting instructions to the needle selector, the needle selector drives the cutter head to act on the jacquard needles, to control the jacquard needles whether to participate in the loop, so as to realize the jacquard knitting control. In the process of knitting, once the needle selector action is abnormal, it will lead to wrong flowers, fabric holes and other defects, and even machine failures such as needle collision, needle breakage and so on. The abnormal operation of the needle selector is generally due to the gradual failure of the piezoelectric chip and transient failure, transient failure refers to the drop of the drive parts leading to abnormal needle selection, often easy to find, but the gradual failure of the needle selector, such as the piezoelectric chip crystal aging, breakage of the weak cyclic signal is difficult to be found. Troubleshooting of piezo needle selectors is crucial in the textile industry. Companies need to conduct regular equipment inspection and fault analysis to ensure production continuity and high product quality. At the same time, as technology continues to advance, the need for fault detection of piezoelectric needle selectors will become more significant in the future.

For the mechanical fault diagnosis of weak periodic signals, there are some detection methods, which are usually categorized into two major types: cycle detection based on signal decomposition techniques and cycle detection based on resonance techniques. Signal decomposition techniques are usually applied when the target signal is non-stationary and strongly disturbed.¹ Traditional fault diagnosis methods are difficult to overcome the strong noise background interference, resulting in low diagnostic accuracy. Moreover, it is difficult to ensure high accuracy when detecting weak periodic signals,² and it is difficult to effectively extract the periodic components.³ The stochastic resonance (SR) technique is widely used in signal processing, and its core concept is to enhance the target weak signal by random noise, thus strengthening the potential weak fault characteristics. Achieving an optimal stochastic resonance response depends on the best choice of nonlinear system parameters and noise intensity. In the current development of stochastic resonance, a number of different parameter selection methods have been proposed by researchers. Mi et al.⁴ developed a gene transcription regulation model driven by a combination of multiplicative Gaussian noise and additive Lévy noise, which helps to obtain optimal stochastic resonance by tuning the noise parameters to obtain genetic information. Zhang et al.⁵ presented two single-parameter-tuned SR models to optimize the output of SR by numerical simulations with different potential well parameters, noise intensity, signal frequency and damping ratio, which were fully investigated. Previous studies are usually based on experience and understanding by providing a set of system parameters and adjusting them appropriately when needed. However, this approach makes it difficult to obtain the optimal system parameters to achieve the desired SR response.

In order to obtain the optimal system parameters, there have also been several studies devoted to combining SR and machine learning. Chen et al.⁶ proposed a hybrid training algorithm for threshold neural networks using adaptive stochastic resonance to provide the algorithm with suitable generalization capabilities. Shao et al.⁷ trained a robust neural network that can recognize the raw data converted by the SR system into a special SR characteristic of the nonlinear waveforms. Yu et al. used⁸ stochastic resonance with tracking the rhythms of subthreshold pacemakers to significantly improve signal detection by broadening the optimal noise intensity range for subthreshold signals. Although these studies have combined machine learning techniques with classical SR theory, they are limited to integration at the mechanism level and have not yet been practically applied in the field of fault diagnosis.

Considering the capability of machine learning techniques in data mining and nonlinear fitting, this paper proposes to uncover the correlation features between vibration signals and SR parameters through neural networks.⁹ Thereby, an adaptive SR method is constructed so that the system will automatically generate the optimal SR parameters given the vibration time series.¹⁰ For the fault diagnosis of needle selector tip based on neural network method, there are two urgent problems to be solved. On the one hand, labeling a large amount of data is an extremely difficult task; on the other hand, it is difficult to collect data of the cutterhead in all operating states for training due to the excessive amount of data. To address these problems, Generative Adversarial Network (GAN) is proposed as an adaptive tool to obtain the optimal SR parameters, and this network model provides a new training mode which is able to expand the training samples under small sample conditions, and generates close to the real value by utilizing unlabeled samples for network training. Prediction results. In the current research, GAN has been applied in some fields. Guo et al.¹¹ proposed a graphical generative adversarial network model, which maps the real data to the potential space by adding an encoder to improve the training efficiency and stability for anomaly detection in dynamic networks; in the field of fault diagnosis, Zhang et al.¹² pre-processed the data through the feature pre-extraction mechanism based on the wavelet transform, and combined the limited number of labeled samples and the large number of unlabeled samples with a large number of labeled samples. In the field of fault diagnosis, Wang et al.¹³ preprocessed the data through a feature pre-extraction mechanism based on wavelet transform, and sent a limited number of labeled samples and a large number of unlabeled samples to the GAN model to achieve fault diagnosis of high-precision gearboxes.

From the results of the above studies, GAN shows some advantages in fault diagnosis, especially applied to unlabeled and small-sample machinery fault diagnosis.¹⁴ However, in the actual training process, there are some problems, among which, the more prominent is that GAN is prone to training instability and generator crash during the actual training process leading to a decline in the quality of the generated data.¹⁵ To address this problem, this paper utilizes the soft-threshold residual attention mechanism in combination with residual networks and employs multiple generators to improve the GAN in order to prevent the model from crashing, instability and other problems.¹⁶

In this paper, an improved generative adversarial network (IGAN) combined with SR technique is proposed to detect the fault signals of the needle selector actuator to accomplish the fault diagnosis scheme of the needle selector tip. The main contents are organized as follows: Firstly the basic theoretical knowledge of SR and IGAN is introduced in detail. Secondly, the formulas for the characteristic parameters of the signals are provided as well as the implementation process of the adaptive SR based on IGAN. Finally the results of fault diagnosis are presented, the influence of the number of feature parameters on the diagnostic accuracy is analyzed, and the superiority of the proposed IGAN model over other GANs as well as the stability under the influence of different environments are investigated.

Theoretical background

Piezoelectric needle selector working principle and failure form

Piezoelectric needle selector uses the inverse piezoelectric effect of piezoelectric ceramics, under the action of the voltage signal, the piezoelectric cantilever beam end bending, driven by the needle selector head swing, control jacquard needles to participate in the knitting, so as to realize the jacquard knitting control. Piezoelectric needle selector is characterized by rapid response, low heat generation and small volume, which is suitable for multi-way needle selector and fast response requirements, and therefore is widely used in jacquard knitting of various circular weft machines.

In the piezoelectric needle selector, the oscillation of the piezoelectric ceramic sheet up and down the cantilever beam is controlled by adjusting the loading of the electrodes to drive the cutter head to complete the jacquard action. As shown in Figure 1(a) is an actual photograph of the needle selector in a circular weft machine. However, in practice, due to the high frequency of the piezoelectric needle selector, it is prone to weak failure characteristics such as aging of the crystals and peeling of the adhesive layer of the piezoelectric ceramic sheet as shown in Figure 1(b). The gradual accumulation of these failure problems may lead to the needle selector head swinging out of place, reduced jacquard force, reduced operating frequency and unstable operation, which in turn causes quality problems such as flower needle, wrong flower and fabric holes in the fabric.

Figure 1.

Piezoelectric needle selector (a) Needle selector in circular weft machine (b) Needle selector damage and aging schematic diagram.

The piezoelectric crystal of the driver is aging due to long time working, the middle cement layer is peeling off, the cutter head is stuck, and the swing is not in place, etc. In Figure 2(a), ① shows the motion sketch of the needle selector in the normal state, In normal operation, the cutter head of the needle selector drive swings up and down and the cutter head is able to strike the appropriate position, and ② shows the situation that the cutter head is not in place due to the aging of the piezoelectric wafer of the piezoelectric selector, and the corresponding time-frequency diagram of the sampled electrical signals is shown in Figure 2(b)①②, and the blue line represents the characteristic spectrum of the electrical signal in the normal state, but the specific frequency magnitude is the same in the frequency domain. The blue line in the figure represents the characteristic spectrum of the electrical signal under the state of head swing not in place, and the red line represents the characteristic spectrum of the electrical signal under the normal state, the overall trend of the spectrum in the frequency domain of the two states is the same, but the size of the specific frequency is different, the characteristic frequency of the electrical signal generated by the equivalent circuit under the asymptotic failure state is relatively small, and the amplitude of the signal generated by the impact of an external force and the characteristic frequency is slightly reduced. Therefore, it is difficult to distinguish whether or not a failure occurs by the electrical signal in this weak failure state.

Figure 2.

(a) Schematic diagram of the fault characteristics of the needle selector (b) Signal waveforms of the driver for different fault conditions.

Figure 2(a)③ shows the dislodgement of the needle selector drive member, and its corresponding time domain diagram is Figure 2(b)③, which does not have a sudden change in the electrical signal generated by the impact in the time domain.

Figure 2(a)④ shows a Situation where the cutter head is jammed. Its corresponding time domain diagram is shown in Figure 2(b)④. When the cutterhead of the piezoelectric needle selector is stuck between the teeth and grooves of the baffle plate or the free end of the driver and the hinged part of the cutterhead assembly are stuck, the cutterhead and the baffle plate will not collide at this time, and therefore, there is no sudden electrical signal generated by the impact in the time domain. As can be seen from Figure 2(b)④, when the cutter head is stuck between the teeth of the baffle plate, the amplitude of the oscillation of the piezoelectric ceramic internal signal is small.

In summary, the weak periodic signal in the gradual failure operating state of the piezoelectric needle selector is not easy to detect. Since there are few measurement points to monitor the vibration of the needle selector drive in the needle selector drive monitoring, and these gradual failure failure characteristics are gradually accumulated over time, it is usually difficult to timely and solve. Therefore, there is an urgent need for an effective and stable detection method to detect these weak cyclic signals to complete the fault diagnosis of the needle selector driver.

IGAN-based stochastic resonance method

Aiming at the problem that the weak periodic signals of the piezoelectric needle selector asymptotic failure are difficult to detect, which leads to some of its fault characteristics being difficult to be found, it is proposed to use the stochastic resonance method to strengthen the weak fault signals.

Stochastic resonance

In stochastic resonance systems, the principle is to enhance the weak periodic signal by noise, thus improving the detection performance of weak fault features and thus enabling fault diagnosis.¹⁷ The dynamics of a nonlinear system can be described by the Brownian equation of motion as in equation (1). A bistable system consisting of weak periodic signals and Gaussian white noise excitations constitutes an overdamped stochastic resonance model.¹⁸

{\begin{cases} \frac{d x}{d t} = - U^{'} (x) + S (t) + n (t) \\ 〈 n (t) 〉 = 0, 〈 n (t) n (t^{'}) 〉 = M δ (t) \end{cases}

(1)

x denotes the output signal of the system, is the signal to be measured, is the added noise signal, M is the sound intensity. δ(t) denotes Gaussian white noise, and t denotes time. Where U(x) is the potential function, denoted as , a₁,b₁ are the potential well parameters. When the noise, signal and nonlinear system reach synergy, the Brownian particle accumulates energy with the help of noise and realizes the leap between potential wells.¹⁹ Different shapes of bistable potential functions can be obtained by adjusting the parameters a₁ and b₁ as well as the noise intensity M. Therefore, the values of these parameters play a decisive role in determining whether or not resonance phenomena can occur in the system.²⁰ Since it is difficult to obtain the optimal SR response by the traditional SR parameter selection method, this study utilizes the IGAN neural network method to determine the optimal dominant barriers for the parameters a₁,b₁,M, so as to realize the optimal output of the SR system.

Generative adversarial network

The basic block diagram of GAN is shown in Figure 3, GAN consists of two neural networks, generator (G-Net) and discriminator (D-Net), using random noise as the input to the generator, random samples similar to the real samples are generated by the G-Net, and then the D-Net receives the data generated by the G-Net to discriminate, and if the D-Net correctly determines the data, then the G-Net needs to be adjusted If D-Net judges correctly, it needs to adjust the parameters of G-Net to make the fake data more real, and if D-Net judges incorrectly, it needs to adjust the parameters of D-Net to enhance the accuracy of its judgment and prevent the same error from occurring next time.²¹ Thus these two neural networks form an antagonistic process, which ultimately makes the fake data generated by G-Net more realistic and difficult to discriminate, while D-Net is able to distinguish between real and fake data more accurately.²²

Figure 3.

Schematic diagram of generative adversarial network structure.

The training of a GAN can be reflected by an optimization equation as equation (2).

\min_{G} \max_{D} V (D, G) = E_{x \sim P_{data} (x)} [\log (D (x))] + E_{q \sim P q (q)} [\log (1 - D (G (q)))]

(2)

However, the GAN model is prone to training instability, generator crash and other problems that lead to degradation of the quality of the generated data in the process of practical application, by reviewing the relevant literature, this paper introduces the residual attention mechanism based on soft threshold and residual network, which is described in detail in detail below.

Improved generative adversarial network (IGAN)

To improve the performance and stability of the model, we introduce a residual attention mechanism based on soft thresholding.²³ Soft thresholding is a nonlinear transformation method used in signal processing, which works by applying a threshold to the signal that has been softened to remove the unwanted parts and retain the desired parts.²⁴ This method maintains the important features of the signal and at the same time reduces the noise in the signal. The self-learning process of thresholding is shown in Figure 4.

Figure 4.

Soft threshold residual attention mechanism self-learning process.

In order to solve this problem that GAN neural networks are prone to gradient vanishing and gradient collapse during training, the use of residual learning is proposed to simplify the training of deep networks.

The basic formula for the residual network is expressed as equation (3).

H (x) = F (x) + x

(3)

Where x denotes the input signal data, F(x) denotes the output of the convolution operation and H(x) denotes the output of the residual block.

Conventional convolutional neural networks are first convolved and then batch normalization (BN) and activation functions are added.²⁵ In order to enhance the training efficiency and performance of the residual network, a pre-activation module is introduced, and in this study, full pre-activation of the residual connections is considered, and the basic module of the residual network is shown²⁶ in Figure 5

Figure 5.

Basic modules of residual networks.

The improved GAN model (IGAN), whose structure is shown in Figure 6, uses an independent alternating training pattern to train two network models during the IGAN training process. In this Situation, during the training process of the G network, multiple sub-generators are fed into the original target signal with noise to generate false samples, and these false samples are labeled as real samples, and at the same time, the parameters connecting to the D network are not updated but are used to pass the error information. When the error is passed to the G network, the parameters of the G network are updated to complete the training. After the training is completed, new fake samples are generated based on the new G network and the training of the D network is performed. After the training of D network, its parameters can be shared with the connected D network. By performing this process repeatedly, the independent rotation training mode of IGAN is realized. It is characterized by the fact that D tries to distinguish samples from multiple sub-generators rather than just from a single G. This approach helps alleviate the problem of G collapse and increases the diversity of generated samples.

Figure 6.

Block diagram of the basic structure of IGAN.

A residual network is used instead of the original convolutional layers in the G and D networks to improve network training. This residual network uses a fully pre-activated structure, which is different from other residual networks. The residual network allows the gradient to flow directly between the layers, which alleviates the problem of vanishing gradients, speeds up convergence, and improves the stability of training. In addition, residual networks allow deeper layers to be constructed without compromising performance, which is crucial for GANs, as they often require large and complex networks to generate more realistic signal data.

In addition, introducing soft-threshold residual attention into G and D allows them to capture trustworthy samples from a wide range of different patterns, which speeds up information acquisition and improves the performance of G and D. By introducing soft-threshold residual attention into the network, the learning and representation capabilities of the model can be enhanced and the performance of G and D can be improved, as well as the robustness of the model, its sensitivity to random perturbations can be reduced, its generalization ability can be improved, and its adaptability to new data can be enhanced.

Methods

Calculation of target signal characteristic parameters

In the fault diagnosis system, the appropriate choice of parameters a₁, b₁,M is crucial for generating the SR response. The nonlinear system of parameters a₁, b₁, M inducing SR’s x(t),can be expressed as equation (4).

{\begin{cases} \frac{dx}{d t} = a_{1} z (t) - b_{1} z {(t)}^{3} + y (t) \\ y (t) = S (t) + \sqrt{2 M} δ (t) \end{cases}

(4)

Since it is difficult to obtain the optimal SR response by traditional SR parameter selection methods, the generation of reliable parameters a₁, b₁, M using IGAN is the focus of this study, and in this study we utilize the game process between G-Net and D-Net to train the optimal SR parameters.

Due to the large input scale, it may be difficult to obtain better network accuracy by directly inputting the noisy vibration signal y(t) into G-Net. In this paper, 13 characteristic parameters calculated from the time and frequency domain analysis of the noisy signal y(t) are used as inputs to the G-Net instead of the original vibration sequence. The formulas for these parameters are shown in Table 1 below:

Table 1.

Characteristic parameter calculation table.

Time domain parameters		Frequency domain parameters
Minimum value $X_{\min} = \min {x (t)}$	Root mean square $X_{rms} = \sqrt{\frac{1}{N} \sum_{t = 1}^{N} x^{2} (t)}$	Center of gravity frequency $F C = \frac{\sum_{t = 0}^{N} f_{t} A (f_{t})}{\sum_{t = 0}^{N} A (f_{t})}$
Average value $X_{mean} = \frac{1}{N} \sum_{t = 1}^{N} x (t)$	Skewness $S = \frac{\sum_{n = 1}^{N} {[x (n) - \bar{x}]}^{3}}{(N - 1) σ_{x}^{3}}$	Mean square frequency $F M S = \frac{\sum_{t = 0}^{N} f_{t}^{2} A (f_{t})}{\sum_{t = 0}^{N} A (f_{t})}$
Standard deviation $Var = \frac{1}{N} \sum_{t = 1}^{N} {(x (t) - X_{mean})}^{2}$	Pulse index $I = \frac{\max (z (t)) - \min (z (t))}{\frac{1}{N} \sum_{t = 1}^{N} \| z (t) \|}$	Frequency variance $F V = \frac{\sum_{t = 0}^{N} {(f_{t} - F C)}^{2} A (f_{t})}{\sum_{t = 0}^{N} A (f_{t})}$
Steepness $K = \frac{\sum_{n = 1}^{N} {[x (n) - \bar{x}]}^{4}}{(N - 1) σ_{x}^{4}}$	Square-root amplitude $X_{r} = {(\frac{1}{N} \sum_{t = 1}^{N} \sqrt{\| x (t) \|})}^{2}$	Standard deviation of frequencies $F S D = \sqrt{F V}$
Kurtosis $C = \frac{\max (x (t)) - \min (x (t))}{\sqrt{\frac{1}{N} \sum_{t = 1}^{N} x^{2} (t)}}$

In this paper, we continue the classical signal-to-noise ratio (SNR) metric to evaluate the effect of stochastic resonance, and the signal-to-noise ratio (SNR) can be described as equation (5).²⁷

S N R_{i} = 10 \log_{10} \frac{P_{signal} (S_{i})}{P_{noise} (S_{i})}

(5)

Where P_signal(S_i) denotes the power spectrum value of the i^th target signal and P_noise(S_i) is the same background noise power spectrum value of the i^th target signal.²⁸ Where the power k of the signal has been expressed as equation (6).

P = \frac{\sum_{n = 0}^{N - 1} x {(n)}^{2}}{N}

(6)

Where x(n) is the signal sequence and N is the length of the signal sequence.

Fault diagnosis of IGAN based stochastic resonance methods

After calculating the feature parameters of the real sample and inputting them into G-Net, G-Net will produce three outputs, that is, the bistable system parameters a₁ , b₁ and the noise intensity M, which interact with the noisy vibration signals y(t) corresponding to the 10 input feature parameters to form the SR phenomenon according to equation (1) and realize the fault feature extraction.

The fault diagnosis process of the adaptive SR method realized by IGAN is shown in Figure 7. Firstly, the vibration signal data of the needle selector tip is collected, and in order to grasp the characteristics of the signal data, the time-domain and frequency-domain parameters of each vibration signal data are calculated, and then Gaussian noise sequences are added to the vibration signal data, and each set of data is processed by the SR system, and the optimal SR parameters (a₁ , b₁ , and M) are calculated, and the (SNR, K, C, and I) are calculated accordingly. Combining the optimal SR parameters (a₁, b₁, and M), each noisy simulated data corresponds to 14 characteristic parameters as shown in equation (7).

X_{real} = {a_{1}, b_{1}, M, S N R, K, C, I, X_{mean}, Var, α, F C, F M S, F V, F S D}_{i = 1}^{K}

(7)

Figure 7.

Block diagram of SR-IGAN structure.

The data is divided into two parts, one as a training set and the other as a test set. At this point, the real samples for inputting into the IGAN network are made. All the samples are normalized before training, and then the training set is input into the IGAN network for training. After completing the IGAN training, the test set is input into the generated network weight file, and the G-Net can adaptively generate a set of SR parameters in response to the noisy signals, so as to stimulate the nonlinear system to produce SR phenomena for periodic extraction and fault diagnosis.

In order to better evaluate the performance of the proposed method, the binary cross entropy is used as the loss function, denoted as equation (8).

Loss = \frac{1}{P} \sum_{n = 1}^{P} - ω_{n} [y_{n} \log x_{n} + (1 - y_{n}) \log (1 - x_{n})]

(8)

Where P is the batch size. ω denotes the loss weight of the components in each batch. x and y are the predicted and measured values respectively. The G-Net and D networks are trained using the Adam optimizer.

Results and discussion

The vibration health detection based on the inverse piezoelectric effect in textile machinery is currently in the exploratory stage, there is no relevant dataset, in order to analyze the feasibility and accuracy of the proposed method in the diagnosis of the needle selector head fault, A needle selector failure test platform was built, as shown in Figure 8, for obtaining the original fault signal data. Specific steps are as follows: first of all, through the signal generator to generate a square wave signal, the output of the square wave through the power amplifier output 250 V, 100 Hz signal, and then use the signal to drive the failure of the needle selector drive work, and finally through the oscilloscope to observe the piezoelectric ceramic piece of the inverse piezoelectric effect generated by the voltage signal.²⁹

Figure 8.

Needle selector failure test Bench.

The time-frequency diagram of the vibration signal is shown in Figure 9(a), and the vibration data are generated by the electrical signal inside the vibration of the piezoelectric needle selector. The vibration signal may have strong coupling characteristics between components and large vibration noise, in order to better analyze the effectiveness of the proposed method in fault diagnosis, Gaussian white noise with intensity 1 is added to the simulation data, and the time and frequency domain results of the mixed signal are shown in Figure 9(b). The strong noise completely drowns out the periodic fault characteristics.³⁰ This vibration data is used as the target signal to be processed in this section.

Figure 9.

Normal time-frequency diagram of the needle selector (a) Time-frequency diagram of the original vibration electrical signal (b) Time-frequency diagram of the vibration electrical signal mixed with noise.

Effect of sample feature parameters on SR response

In the real fault diagnosis application of the pinpoint selector, in order to obtain the optimal SR parameters by IGAN, some real samples are firstly applied to input the IGAN adversarial network for training, and in this study, 13 feature parameters of the mixed noise in Figure 9(b) are selected to create the real samples. Therefore, the SR response of the model will be affected by the input samples, and the effect of the number of feature parameters of the original noise signal on the SR response will be investigated in this section. The effect of the time-domain parameters of the original noise on the SR response is investigated first; followed by the effect of the frequency-domain parameters and the combination of frequency-domain and time-domain parameters on the SR response.

The a₁, b₁ and M are the key parameters that generate the SR phenomenon. We combine the SR parameters to analyze the effect of different sample parameters on the network accuracy, as shown in Table 2. From the table, it can be seen that the SNR decreases by 1.90 dB from Situation 1 to Situation 2, while Situation 3 has the highest SNR of 7.79 dB, which is an increase of 1.38 dB from the SNR of Situation 1. By further analyzing the results, the signal to noise ratio using only time domain parameters is 42.12% higher than the results using only frequency domain parameters and if the combination of frequency domain parameters and time domain parameters is used, the signal to noise ratio of the results is higher by a larger amount of 72.72% as compared to the frequency domain parameters only and 21.52% higher than the results of the time domain parameters only. Thus, we find that the highest accuracy is obtained using a combination of time domain parameters and frequency domain parameters, and the accuracy of time domain parameters is higher when either of the parameters is used alone.

Table 2.

Signal to noise ratio under different feature parameters.

Situations	Characteristic parameters	SNR (dB)(SR evaluation)
Situation 1	a₁,b₁,M,SNR,X_mean, X_rms,Var,S,Xr	6.41
Situation 2	a₁,b₁,M,SNR,FC,FMS,FV,FSD	4.51
Situation 3	a₁,b₁,M,SNR,X_mean, X_rms,Var,S,Xr, FC,FMS,FV,FSD	7.79

Figure 10 shows the corresponding SR waveforms and spectrograms for different parameter Situations, where (a) represents the time-frequency plot of the SR response for parameter Situation 1, with a peak amplitude of 0.225 V; (b) represents the waveform and spectrogram of the SR response for parameter Situation 2, with a peak amplitude of 0.208 V; and (c) represents the time-frequency plot of the SR response for parameter Situation 3, with a peak amplitude of 0.305 V. The results are shown in Figure 10.

Figure 10.

SR waveforms and spectrograms corresponding to different parametric Situations (a) Time-frequency plot of SR response for parametric Situation 1 (b) Time-frequency plot of SR response for parametric Situation 2 (c) Time-frequency plot of SR response for parametric Situation 3.

The results show that the network accuracy is poor when the time-domain parameter (Situation 1) and the frequency-domain feature (Situation 2) are used as inputs to the G-Net, respectively. Compared with the frequency domain feature parameters, the time domain features can improve the network accuracy. The time-domain parameters can well describe the local features of the original vibration signal and better represent the original signal. However, the frequency domain parameters reflect the statistics of the original signal on a longer time scale, so it is difficult to distinguish the local features of the signal. The best prediction results can be obtained by the network after considering both time and frequency domain characteristics (Situation 3).

The results show that only the time or frequency domain features cannot accurately describe the signal with noise, and the optimal SR can only fully extract the noisy signal features to input to the G-Net in order to better extract the fault features and achieve the best fault diagnosis results.

Comparison of the accuracy of SR-IGAN network models

The proposed method will be analyzed and validated by the collision data signal of the needle selector tip with noise in Figure 9(b). In order to prove the effectiveness of the proposed SR-IGAN method compared to other methods in extracting fault features, the SR-BP neural network is used as a comparison to test the effect of different sample sizes on the network accuracy. As shown in Figure 11. The network accuracy is evaluated based on the same validation set, and the accuracy rate is used as a criterion to evaluate the effectiveness of the two methods during the validation process.

Figure 11.

Fault diagnosis accuracy of two methods with different sample sizes.

The network accuracies of SR-IGAN and SR-BP gradually increase with the increase of sample size, and the accuracy of IGAN-based network is significantly higher than that of BP-based network from the overall point of view. IGAN can expand the samples with smaller sample size. IGAN can expand the samples with smaller sample size, although given few real samples, G-Net can generate data close to the real samples, which makes the network training more accurate. However, the smaller the sample size for BP’s network, the lower the prediction accuracy. This shows that IGAN has a clear advantage in obtaining optimal SR parameters with fewer samples. Figure 12 shows the time-domain plot and spectrogram of the optimal SR response based on predicted SR parameters by IGAN and BP networks under 1000 training samples. Figure 12(a) shows the signal plot of the optimal SR response of SR-BP, (b) shows the spectrogram of this signal with a vibration amplitude of 0.301 V; (c) shows the signal plot of the optimal SR response achieved by SR-IGAN, and (d) shows the spectrogram of this signal with a vibration amplitude of 0.325 V. The results show that the SR-IGAN method is more likely to achieve a higher accuracy than the other algorithms with less data, and can take full advantage of the fewer samples. Accuracy and can fully utilize the noise of fewer samples to extract fault features. Therefore, our proposed SR-IGAN method is more suitable for the fault diagnosis of needle selector tips than the SR-BP method.

Figure 12.

Optimal SR response for IGAN and BP implementations (a) Time-frequency plot under optimal SR response for BP implementation (b) Time-frequency plot under optimal SR response for IGAN implementation.

Stability of IGAN compared to other network models

In the actual fault diagnosis work, the stability of the model is crucial, if the model has the problem of unstable collapse, it will have a great impact on the whole needle selector fault diagnosis, therefore, in order to further validate the stability and superiority of the proposed model, a section of a typical dataset is used to validate the superiority of the IGAN model compared to other known GAN variants. From the introductory section, it is clear that generator modal collapse is the main factor for the training instability phenomenon of the GAN network during the training process. Modal collapse refers to the generator not being able to capture all the features or types in the dataset when generating the samples, which leads to a lack of diversity and richness in the generated samples, thus affecting the accuracy of the overall fault diagnosis. If the generator has a modal collapse problem, the number of modalities in the generated samples will be significantly reduced, that is, the generated samples will be relatively homogeneous or lack diversity. The final results generated will become less accurate because there is no guarantee of the diversity of the data generated, which will result in unreliable results for the entire experiment. Therefore, in practical evaluation, by observing the number of recovered modalities in the generated samples, it is possible to determine whether the GAN has a modal collapse potential.

In this study, the proposed IGAN is compared with three GAN variants, DCGAN, WGAN, and InfoGAN. A fixed number of samples are used for the experiments, and the whole dataset consists of 400 training samples and 100 test samples, which are sequentially put into these network training models, and the recovered modal counts of the final outputs are used as the judgment criteria. The results are shown in Table 3.

Table 3.

The number of restored modes for different models under the same conditions.

Method	Sample size	Modal recovery number
SR-DCGAN	400	212
SR-WGAN	400	324
SR-InfoGAN	400	304
SR-IGAN	400	378

The results show that under the same training samples, the performance of SR-DCGAN is more unstable, and the number of recovered modalities reaches only 212, while SR-WGAN and SR-InfoGAN are more stable, and the number of recovered modalities reaches 324 and 304, respectively. The proposed SR-IGAN method performs the best, and the number of recovered modalities reaches a high level of 378 under the condition of 400 training samples. The proposed method is therefore superior to the above methods. In this experiment, these results clearly demonstrate that IGAN effectively mitigates the modal collapse problem of the model. In order to make the experimental results more intuitive and obvious, a histogram comparing the recovered modal counts of different GANs under the same condition samples is produced, and the results are shown in Figure 13. Therefore, compared with other network models, the SR-IGAN model has better stability and is more suitable for use in fault diagnosis in real factory production.

Figure 13.

Modal recovery number for different network models.

Environmental noise is an important factor that affects the stability of network models, and in order to investigate the stability of SR-IGAN networks in environments with different signal-to-noise ratios, a set of experiments was designed in this study. The SR-IGAN model was trained in environments with different degrees of signal-to-noise ratios and evaluated for the quality of the generated samples as well as the model stability. The signal-to-noise ratio is set to - 4 dB, - 2 dB, 0 dB, 2 dB and 4 dB, and the performance of the proposed model is compared under these five signal-to-noise ratio environments.

Table 4 gives the results of the tests in different signal-to-noise ratio environments. It can be seen more intuitively through Figure 14 that the accuracy of the model increases as the strength of the S/N ratio continues to diminish, where the accuracy of the SR-WGAN model reaches only 71.25% at a lower S/N ratio (S/N ratio = −4 dB), while the other two models reach an accuracy of about 80%, respectively, and the proposed SR-IGAN model can still reach 86.57%. When the signal-to-noise ratio = 0 dB, the accuracy of SR-WGAN as well as its improved model (SR-WGAN-GP) is still lower than 90%, SR-DCGAN performs better with an accuracy of 93.52%, but the SR-IGAN model achieves an even better 96.57%. When the signal-to-noise ratio = 4 dB, all the models have higher accuracies, reaching more than 90%, and the SR-IGAN model reaches a higher 99.32%. Through comparison, it is found that the accuracy of the proposed SR-IGAN model is higher than the other models in different SNR environments, and it also shows that the proposed IGAN network model has strong performance in different fixed-value SNR environments, which reflects the excellent environmental adaptability.

Table 4.

Performance of different network models in different noise environments.

Method	SNR(dB)−4	−2	0	2	4
SR-DCGAN	83.74	89.94	93.52	96.17	98.95
SR-WGAN	71.25	75.21	86.21	89.12	94.17
SR-WGAN-GP	80.17	84.51	89.47	92.59	96.13
SR-IGAN	86.57	92.71	96.57	97.71	99.32

Figure 14.

Performance of different network models in different noise environments.

Since the SNR values in the working environment of the workshop are not fixed in the actual factory tests, in order to more realistically test the stability and accuracy of the proposed model in the actual factory production environment, we selected the SNR band of −4 dB ∼ 4 dB as the base frequency, and simulated a SNR environment with changing values through the random noise generated by equation (9) to train the model.

x = μ + σ \cdot N (0, 1)

(9)

Where μ is the mean of the noise, σ is the standard deviation of the noise, and N(0,1) is a standard normally distributed random number with mean 0 and variance 1.

Due to the fluctuating nature of random noise, the model was put into a fluctuating signal-to-noise ratio environment for 10 minutes, and then its accuracy was compared with the generated data, five sets of tests were conducted, and the results are shown in Table 5. It can be seen that in the five sets of tests with the same signal-to-noise ratio environment, the accuracy of the SR-WGAN model is lower, with an accuracy range of about 71%∼75%, its improved model (SR-WGAN-GP) has some improvement relative to it, with an accuracy range of about 77%∼80.5%, and the accuracy of the SR-DCGAN model is higher, with an accuracy of more than 80% in the five tests, with an accuracy range of 81.5∼84.5%, and the proposed SR-IGAN model has higher accuracy, reaching about 90% accuracy. In order to make the experimental results more intuitive, the average of the five groups of results is taken for comparison, and the calculation formula of the proposed SR-IGAN model is shown in equation (10):

\bar{x} = \frac{\sum_{i = 1}^{i_{\max}} x_{i}}{i_{\max}}

(10)

Where i is the number of groups detected and x denotes the accuracy. The results of the experiments are shown in Figure 15, which indicate that the SR-WGAN model has a low accuracy with a mean value of 73.4% in the simulated real plant noise environment varying within a fixed range, the SR-WGAN-GP and SR-DCGAN models have closer average accuracies of 72.766% and 82.766%, respectively, whereas the proposed model, SR-IGAN, achieves a 88.976% high accuracy. Taken together, these results show that the proposed model in this study is more stable and more accurate under the actual factory work noise environment, which is more applicable to the actual production work.

Table 5.

Performance of different network models in simulated noise environment.

Method	Noise Level(dB)	Accuracy(%)A	B	C	D	E
SR-DCGAN	−4∼4	82.46	81.79	82.07	83.29	84.27
SR-WGAN	−4∼4	73.22	71.56	73.15	74.18	74.89
SR-WGAN-GP	−4∼4	78.57	77.47	78.39	79.23	80.17
SR-IGAN	−4∼4	88.57	86.91	88.21	90.14	91.05

Figure 15.

Comparison of the accuracy of different network models in different signal-to-noise ratio environments.

Conclusion

In order to improve the accuracy of needle selector drive part fault diagnosis, an adaptive stochastic resonance method based on improved generative adversarial network is proposed in this paper. The method applies SR technique to extract weak periodic fault features from strong noise, and solves the problem that the optimal SR parameters are difficult to obtain by generative adversarial network, at the same time, in order to solve the problem of unstable operation caused by the collapse of the generator of the GAN during operation, an adaptive SR model based on IGAN is proposed. The stability and superiority of the method are verified through simulation experiments and field data analysis. The main conclusions are as follows.

(1) The experimental results comparing the effects of different numbers of parameters on the model show that the network model works best when the number of time-domain and frequency-domain parameters are considered at the same time, and the SNR of SR output reaches 7.79 dB.

(2) Under the conditions of different numbers of real samples, the proposed adaptive SR-IGAN method has higher accuracy than the traditional algorithm, and the accuracy rate reaches the highest 95.3% when the real samples are 1000. And compared with other models combining GAN and SR, the SR-IGAN model is more stable, and the number of recovered modalities reaches 378 under the condition of 400 training samples. Overall presents the superiority of the SR-IGAN method.

(3) In the environment of different signal-to-noise ratio strengths as well as the fluctuating signal-to-noise ratio environment that simulates the actual working environment of a factory, our model shows strong stability and accuracy when compared with other models. Under the fixed SNR environment, the model achieves an accuracy of 99.32% with a high SNR (SNR = 4 dB) and maintains a high accuracy of 86.57% with a low SNR (SNR = −4 dB); under the fluctuating SNR environment, our model achieves the highest average accuracy of 88.91%.

In conclusion, compared with previous methods, IGAN is faster, more accurate, and more stable, so it can make the fault diagnosis work more efficiently and more stably in the actual textile engineering environment, and can be adapted to different environments. However, our method is only in the laboratory stage, and we have not yet made the actual software that can be applied to the production, in the future work, we will continue to delve into this work, which still needs a lot of experiments and work, including the network to adapt to the operating environment and other aspects still need to be improved.

Footnotes

Acknowledgments

The authors would like to thank the Director, Longgang Research Institute, Zhejiang University of Technology for permission to publish this research work. The authors would also like to thank Yubao Qi, Laihu Peng for their technical support in the research work.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: Special Support Program for High-level Talents in Zhejiang Province, (2023R5212). Zhejiang Province “Sharp Soldier Leader + X” R & D Public Relations Program (2024SJCZX0027).

ORCID iD

Renjie Jin

References

Zhou

Cicone

Zhou

. RRCNN: a novel signal decomposition approach based on recurrent residue convolutional neural network, 2023.

Shi

Zhong

, et al. Incipient fault diagnosis of planetary gearboxes based on an adaptive parameter-induced stochastic resonance method. Appl Acoust 2022; 188: 108587.

Wang

Yang

Guo

, et al. Positive role of bifurcation on stochastic resonance and its application in fault diagnosis under time-varying rotational speed. J Sound Vib 2022; 537: 117210.

L-N

Guo

Y-F

Zhang

, et al. Stochastic resonance in gene transcriptional regulatory system driven by Gaussian noise and Lévy noise. Chaos Solit Fractals 2023; 167: 113096.

Zhang

Lai

, et al. Stochastic resonance induced weak signal enhancement in a second-order tri-stable system with single-parameter adjusting. Appl Acous 2024; 216: 109753.

Chen

Duan

Chapeau-Blondeau

, et al. Training threshold neural networks by extreme learning machine and adaptive stochastic resonance. Phys Lett 2022; 432: 128008.

Shao

Barras

Kosmas

Detection of extremely weak NQR signals using stochastic resonance and neural network theories. Signal Process 2018; 142: 96–103.

Guo

Wang

Stochastic resonance enhancement of small-world neural networks by hybrid synapses and time delay. Commun Nonlinear Sci Numer Simul 2017; 42: 532–544.

Lei

Han

Lin

, et al. Planetary gearbox fault diagnosis using an adaptive stochastic resonance method. Mech Syst Signal Process 2013; 38: 113–124.

10.

Zhang

Guo

, et al. Research on mud pulse signal detection based on adaptive stochastic resonance. J Petrol Sci Eng 2017; 157: 643–650.

11.

Guo

Liu

RegraphGAN: a graph generative adversarial network model for dynamic network anomaly detection. Neural Netw 2023; 166: 273.

12.

Zhang

Wang

Liang

, et al. Semi-supervised fault diagnosis of gearbox based on feature pre-extraction mechanism and improved generative adversarial networks under limited labeled samples and noise environment. Adv Eng Inform 2023; 58: 102211.

13.

Wang

Jiang

, et al. Adaptive variational autoencoding generative adversarial networks for rolling bearing fault diagnosis. Adv Eng Inform 2023; 56: 102027.

14.

Meng

Kong

, et al. Small sample fault diagnosis method for wind turbine gearbox based on optimized generative adversarial networks. Eng Fail Anal 2022; 140: 106573.

15.

Liu

Jiang

Wang

, et al. A conditional variational autoencoding generative adversarial networks with self-modulation for rolling bearing fault diagnosis. Measurement 2022; 192: 110888.

16.

Wang

Xia

Yin

, et al. An improved generative adversarial network for fault diagnosis of rotating machine in nuclear power plant. Ann Nucl Energy 2023; 180: 109434.

17.

Lin

Adaptive stochastic resonance quantified by a novel evaluation index for rotating machinery fault diagnosis. Measurement 2021; 184: 109920.

18.

Chen

Zhang

, et al. The adaptive bearing fault diagnosis based on optimal regulation of generalized SR behaviors in fluctuating-damping induced harmonic oscillator. Mech Syst Signal Process 2023; 189: 110078.

19.

López

Naranjo

, et al. Hidden markov model based stochastic resonance and its application to bearing fault diagnosis. J Sound Vib 2022; 528: 116890.

20.

Zhou

Huang

Hao

, et al. Vibration-based fault diagnosis of the natural gas compressor using adaptive stochastic resonance realized by Generative Adversarial Networks. Eng Fail Anal 2020; 116: 104759.

21.

Chen

Yang

, et al. Combined with decomposition algorithm and generative adversarial networks on landslide displacement prediction. In: 2022 14th International Conference on Advanced Computational Intelligence (ICACI), Wuhan, China, 15–17 July 2022, 2022.

22.

Woldesellasse

Tesfamariam

. Data augmentation using conditional generative adversarial network (cGAN): application for prediction of corrosion pit depth and testing using neural network. J Pipeline Sci Eng 2023; 3: 100091.

23.

Liu

Zhang

, et al. Deep residual convolutional neural network based on hybrid attention mechanism for ecological monitoring of marine fishery. Ecol Inform 2023; 77: 102204.

24.

Zhang

Wang

Yuan

, et al. Remaining useful life prediction via improved CNN, GRU and residual attention mechanism with soft thresholding. IEEE Sens J 2022; 22: 15178–15190.

25.

Zhu

Jiang

Shen

, et al. Res-HSA: residual hybrid network with self-attention mechanism for RUL prediction of rotating machinery. Eng Appl Artif Intell 2023; 124: 106491.

26.

Feng

Wang

. A fault diagnosis for rolling bearing based on multilevel denoising method and improved deep residual network. Digit Signal Process 2023; 140: 104106.

27.

Park

Kim

Kang

, et al. Dramatically enhanced mechanosensitivity and signal-to-noise ratio of nanoscale crack-based sensors: effect of crack depth. Adv Mater 2016; 28: 8130–8137.

28.

Wang

Chen

, et al. Symmetric cross entropy for robust learning with noisy labels. In: 2019 IEEE/CVF International Conference on Computer Vision (ICCV), Seoul, Korea (South), 27 October–02 November 2019, 2019.

29.

Zhang

Shu

Zhang

Piecewise unsaturated multi-stable stochastic resonance under trichotomous noise and its application in bearing fault diagnosis. Results Phys 2021; 30: 104907.

30.

Shi

Zhang

, et al. Weak signal enhancement for machinery fault diagnosis based on a novel adaptive multi-parameter unsaturated stochastic resonance. Appl Acoust 2022; 189: 108609.