PTS-FNN-Based Health Prediction Method for Flexible Photoelectric Film Material Processing Equipment

Roll-to-Roll (R2R) processing is a common processing method for ﬂexible photoelectric ﬁlm materials. Due to the physical properties of the materials, the change in the performance of the R2R processing equipment can easily cause deformation of the ﬂexible ﬁlm material, it is particularly important to predict the performance degradation of the processing equipment. Based on the accuracy and real-time requirements of performance degradation prediction, a PTS-FNN model for performance degradation prediction was proposed in this paper, which combines the Possibilistic C-Means (PCM) fuzzy clustering and Takagi–Sugeno Fuzzy Neural Network (TS-FNN). We also studied the PCM classiﬁcation algorithm of input data of PTS-FNN model, the predecessor network of TS-FNN prediction model and the construction method of postcomponent network. Finally, the implementation process of PCM classiﬁcation algorithm and TS-FNN prediction model were given. The R2R processing equipment health prediction experiment system was built and the PTS-FNN model experiment was carried out. The experimental results showed that the training time of PTS-FNN model was 50.37% less than the standard TS-FNN prediction model. The prediction accuracy increased by 5.48%, and the PTS-FNN had no error in the judgment of state 1 and state 4.


Introduction
Currently, Roll-to-Roll (R2R) processing technique is the most widespread processing method for a series of flexible thin film materials internationally, for it can maintain the enhancement its productivity while automatizing the mechanical equipment to the greatest extent. R2R processing is a common processing method for flexible photoelectric thin film materials, and the performance deterioration of the R2R processing device is the primal problem the mass manufacturing of flexible photoelectric thin film materials faces. In recent years, the technology of equipment health prognosis has become a research hotspot [1,2]. In 2017, Lee et al. [3] proposed a prognosis algorithm that boosts material removal rate (MRR) based on integrated models and data-driven approach. e method proposed combines the influences of physical mechanism and nearest neighbors, extracts the relating characteristics. ese characteristics are inputted to build multiple regression models which will be integrated so as to obtain the final prognosis. Rapid development and extensive applications in deep learning have been achieved in the last few years. In the field of industry, the researcher applies deep learning to the analysis of industrial data. University of Michigan's Ni Xia [4] developed an operating load based real-time rolling Grey forecasting technique, so as to provide efficient accurate machine health prognosis, as well as analyzed the influencing factors. Deng et al. [5] (2018) combined the quality control chart and SoV, proposing a fault diagnosis approach of the flexible material R2R manufacturing system. Based on the relativity between the source of fault and product quality during manufacturing as well as statistical distribution pattern of the feature vector of processing quality and the source of fault, this approach utilized SoV model under controlled or uncontrolled state and mathematical model of probability distribution to deduce the statistical measurement of quality characteristic variables. e consequent quality control chart can pinpoint the fault location in the system quickly and easily. Zhao and Ouyang [6] (2016) applied Multi-Agent Genetic Algorithms (MAGA) to the prognosis of the state of avionic devices, which overcomes the flaw of the Baum-Welch algorithm easily falling into locally optimal solutions, greatly enhancing the prognosis accuracy, speed, and stability.
In application, the health prognosis model for R2R processing device has advanced instantaneity requirement; therefore, it is particularly vital to study how to enhance the instantaneity of the prognosis model. Because the Fuzzy C-Means (FCM) clustering algorithm is based on fuzzy theory to describe the uncertainty of sample generics, the fuzzy membership value of each classification point is obtained by optimizing the objective function. Although FCM is widely used in clustering algorithms, it has the problem of being sensitive to noise data. e PCM clustering algorithm can make up for the shortcomings of the above-mentioned FCM algorithm by relaxing the constraint of membership degree without normalizing the data. Because the neural network modeling has the characteristics to deal with the nonlinear approximation problem well, the PCM clustering method can well divide the data with irregular boundaries. For that reasons, the following content will be binding the PCM clustering analyzing method and the Takagi-Sugeno Fuzzy Neural Network (TS-FNN) to discuss the health state prognosis modeling of the R2R processing device.

Neural Network Model for Health
Prediction of Roll-To-Roll Processing Equipment e standard TS-FNN [7] was first proposed by Japanese scholars Takagi and Sugeno; it is a specific method for identifying fuzzy models of nonlinear dynamic systems. TS-FNN can be divided into antecedent networks and consequent network according to different structural functions ( Figure 1). e antecedent network is used to match the fuzzy rules, that is, to calculate the adaptability of each fuzzy rule. e antecedent network is composed of four layers of neural networks: the first layer is the input layer, the second layer is the membership layer (Gaussian function), the third layer is to calculate the adaptability (a j � min u 11 , . . . u 1j , . . . u nj , a j is the j -th fuzzy rule adaptability, n represents the number of inputs), the fourth layer is to perform normalized processing, the adaptability is normalized (a j � (a j / m b�1 a b ), m represents the number of nodes in the fourth layer of antecedent network), and {a 1 , a 2 , . . . a m } is the output to the antecedent network. e consequent network is to generate fuzzy rules, it consists of three layers of networks. e first layer is the input layer, and the second layer is the rule computing layer (y gj � n i�0 p r ji x i , j � 1, 2, . . . m; g � 1, 2, . . . r; p r ji is the linear parameter of the consequent network). e third layer is the system output layer. e system output {y 1 , y 2 , . . . y r } is obtained by adding the weights of {a 1 , a 2 , . . . a m } as the connection weights, where y r � m j�1 a j y rj , y r ∈ Y, y rj is the output of the j -th fuzzy rule. e standard T-S fuzzy neural network model requires to linearize the input data, which will make the input space and fuzzy rules difficult to optimize and extract, and this will lead to more problems, for instance, the system structure should be planned in advance. erefore, when dealing with the multi-input nonlinear space, the PCM fuzzy clustering is used as the antecedent model extraction method, to realize the expected purpose of improving the training efficiency and recognition effect of the model. e PCM algorithm can adjust the clustering center, radius, and number of clusters of the input space; rationally divide the ambiguity of the input data; and determine the membership function of the data points and the rule adaptability; therefore, this PCM algorithm achieves basic elimination of the low quality samples to participate in the antecedent networks calculation, and model training speed and accuracy can be greatly improved. According to the above analysis and reference [8], the performance regression evaluation model PTS-FNN of R2R processing equipment based on PCM and TS-FNN shown in Figure 2 is proposed. e model combines the advantages of the PCM method, the T-S fuzzy inference model, and the fuzzy neural network modeling method. e PTS-FNN model includes an antecedent network and a consequent network. e antecedent network matches the standard T-S fuzzy rules, and the antecedent network concludes the fuzzy rules. After the weighted calculation of the antecedent and consequent network, the PCA parameter of each station roller axis performance X � {x 1 , x 2 , . . . x n } and the nonlinear modeling of equipment health status S � {s 1 , s 2 , . . . s r } are established [9].

PCM Classification Method for Input Data of Health State Prediction Model of Roll-To-Roll Processing Equipment
Instead of normalizing the input data, Possibilistic C-Means Clustering Algorithm relaxes the constraints of the membership function during the division of data, which is an advantage of Possibilistic C-Means Clustering Algorithm, thus enhancing the sensitivity to noisy data [10,11].

Mathematical Problems in Engineering
In order to avoid null solution in the target function, introducing the regularization term f (U) of the possibility partition matrix (shown in equation (4)), provides a larger penalty value when u ik ⟶ 0 + .
As mentioned in the previous chapters and sections, for the sake of dividing the fuzzy level of the input data of the health prognosis artificial neural network model for R2R processing device precisely, the front end of the PTS-FNN model is classified by PCM first. Combining equations (1)-(4), the calculating formulas of the possibility partition matrix U and the clustering center V is shown as equations (5) and (6), respectively. Figure 3 provides the process of the PCM algorithm: ① Set clustering category to c, set the fuzzy weight to α (normally α � 2), set the iteration thresholding to q (normally between 0.001 and 0.01), set the iteration count to t, initialize the possibility partition matrix U (s) and the clustering prototype V (s) (s � 0) ② Estimate η i base on U (s) and V (s) as well as equation (3) ③ Update the division of the matrix U (s+1) and the clustering prototype V (s+1) in accordance with equations (5) and (6) ④ Reestimate η i , repeat ③ ⑤ Determining threshold: according to the given threshold q, if ||V (s+1) -V (s) ||≤q, stop the iteration; otherwise, t � t + 1 and Jump to ② Figure 2 shows that the health status prognosis TS-FNN model for R2R processing device includes determining the structural parameter of the antecedent network and the consequent network. e following content focus on introducing the deduction of the antecedent network's the membership function and the rule compatibility, as well as the weight between each node of the consequent network can be obtained using the Error Back Propagation Algorithm [8].

Construction of TS-FNN Model for Health State Prediction of Roll-To-Roll Processing Equipment
Here are the assumptions that matrix U � [u ik ] is a fuzzy matrix after PCM data division, G i (1 ≤ i ≤ c) represents fuzzy category group of c after division, β represents clustering fuzzy degree weighted index and the category center v iq and the corresponding variance σ 2 iq of G i can be expressed as [7,8] Considering the critical demand of the fuzzy clustering after dividing the input data space, the category data q k of G i and the corresponding variance σ 2 iq of the category component v in+1 , i � 1, 2, . . . c under the clustering center V i � [v i1 , v i2 . . . , v in+1 ] T approximate 0, thus using the minimal value (namely the shortest distance to the category center v iq ) of the category amount q k as the decision function d F (G i ) of the fuzzy clustering d F (G i ),

Mathematical Problems in Engineering
Correspondingly, the membership function Gu(x k ) of G i is expressed as In the equation |v iq − v ' iq | represents the width of the input data's division area, v ' iq represents the nearest cluster center value of cluster center No. i, factor c sets the rate of the membership decrease when the input samples fleeing the cluster center, normally 2 ≤ c ≤ 4. e membership function Gu ji (x kj ) represents the similarity between the input sample x k and a certain fuzzy class G i . ere is a relationship between the two: when x k is far away from the prototype, then Gu ji (x kj ) is close to 0; when x k is close to the prototype, then Gu ji (x kj ) is close to 1.
R i represents a decision rule of certain clustering category , when the multidimensional fuzzy set G i projected onto the entire input data space, the decision rule R i ′ can be expressed as R i ′ : If x 1 ∈ G i1 and x 2 ∈ G i2 and . . . and x n ∈ G in , e compatibility Gα i of the corresponding x k for rule R i ′ is the product of each component's membership Gu ji (x kj ), j � 1, 2..n: Gu ji x kj , i � 1, 2 . . . c.
As shown above, the membership function of the model is calculated by equation (9), the rule compatibility is calculated by equation (11). σ 2 iq manifests the quality of fuzzy division. e larger σ 2 iq is, the worse quality the division is; thus, enter Eσ as the quality index of the fuzzy division. If σ 2 iq > Eσ, c � c + 1, a second fuzzy division is warranted. e relevant fuzzy clustering will not be extracted as the TS-FNN antecedent network until all the categories meet the condition σ 2 iq ≤ Eσ [8].
After the building of the antecedent network is completed, estimates of the consequent network's linear parameter p r ji are required. In this paper, the linear least squares recursive estimation method is used to estimate the parameters of the postnetwork. In this part of the training learning phase, the parameters of the antecedent network need to be fixed first.
Constructing error cost function is as where y r ′ represents the expected output, y r represents the actual output.

Construction of the Health Status Prognosis Model.
In order to verify the efficiency of the health prognosis PTS-FNN model for R2R processing device this paper proposed, the R2R continuous manufacturing device shown in Figure 4 is introduced as the experiment platform, its principle of operation is shown as Figure 5. Use the PCA parameter x 1 , x 2 , x 3 , and x 4 of the roller performance corresponding to workstation 1, 2, 3, and 5 of the R2R manufacturing system as the input of the PTS-FNN model. Divide the thin film processing quality and the health status of the device in accordance with Table 1 and quantify to obtain the health status indicator function y={1, 2, 3, 4} of the device as the output of PTS-FNN.
As shown in Figure 4, the R2R flexible material processing system adopted is mainly composed of a mechanical structure and drive control unit. For the mechanical structure, standard enforced aluminum alloy extrusions was selected as the supporting frame, including the unwinding module, the drive module, the wind-in module, etc. e experiment chose blue PET polyester film with thickness of 0.05 mm, width of 50 mm, elastic modulus of 3495 MPa, density of 1450 kg/m 3 , and Poisson's ratio of 0.3. e vibration data is collected by the AWA5936 vibration measuring instrument. e AWA5936 vibration measuring instrument has good repeatability and can ensure the accuracy of the measurement. e built-in acceleration sensor sensitivity is 1pC/m/s 2 ± 5%, the measurement range of acceleration is 0.03 m/s 2 to 1000 m/s 2 , the piezoelectric sensor frequency response range is 10 Hz to 8 kHz, the measurement error is 5% to 10% (LO : 10 Hz to 1kH; HI: 1 kHz to 8 kHz), and the sampling frequency is 48 kHz.
Principle of operation is shown as Figure 5. Based on different functions of each roll shaft, the R2R processing system is divided into different workstations. As mentioned in the previous content, the vibration workstation 1, 2, 3, 4, and 5 is measured, respectively, and the data is collected and documented every 30 minutes.
Roll shafts of four workstations used to evaluate the performance deterioration of the R2R device are of 4 different stages: excellent condition, prerecession, developing recession, and near expiry. Roll shaft of each stage demonstrates different vibration signals. e vibration signals of workstation1's unwinding roller at different performance stages is shown in Figure 6 (g � 9.8 m/s 2 ).
Collect 20 sets of data from each stage of each of the 4 workstations' roll shafts, 320 in total, as the experiment data of the performance deterioration prognosis PTS-FNN model for the R2R processing device. Based on the building method mentioned in Section 3, make c � 2, Eσ � 1.25, and start the fuzzy division of the input data. When c � 5 and all variance of the fuzzy division categories meet the condition of σ 2 iq ≤ Eσ, the fuzzy division of the input data ends. Table 2 shows the 5 category centers after fuzzy division, which is expressed as V i , i � 1, 2, . . ., 5, and the according width of divides data regions R iq iq indicates the category component of V i , v iq is the clustering center value nearest category center No. i).
Select 240 sets of the 320 sample sets to train the consequent network, the remaining 80 sets of samples are used to inspect the accuracy of the model. Set the initial learning efficiency to 0.55 which decreases successively by 0.05, the minimal expected learning error to 0.005, the amount of training steps to 500. en the linear parameter of the consequent network p r ji is calculated (shown in Table 5). e remaining 80 sets of samples are used to inspect the accuracy of the model. Table 6 shows a part of samples and testing data; the comparison of the accuracy of both models is shown in Table 7.

Model
Comparing the two prediction models of standard TS-FNN and PTS-FNN neural network, it can be concluded that in the training time, the latter is shorter than the training time of the former, which improves the convergence speed of the neural network and reduces the training time; In terms of accuracy, the prediction accuracy of the standard TS-FNN is 91.25%, and the prediction accuracy of the PTS-FNN neural network is 96.25%. e latter is more accurate than the former, and there is no error in the judgment of state 1 and state 4.

Conclusion
Based on the analysis of the health prediction status of flexible photoelectric film processing equipment, this paper proposed a PTS-FNN for flexible material processing equipment health prediction combined with PCM and TS-FNN. e model combined the advantages of PCM method,   Table 3: Membership function of input quantity (x) 1 ∼(x) 4 . And according to equation (11) and Table 3, Gα i can be expressed as the equation given in the table.
Input quantity x 1, x 2 Input quantity x 3, x 4 Serial number Membership function Serial number Membership function 1  T-S fuzzy inference model, and fuzzy neural network modeling method. We also studied the PCM classification algorithm of input data of PTS-FNN model, the antecedent network of TS-FNN prediction model, and the construction method of postcomponent network. Finally, the implementation process of PCM classification algorithm and TS-FNN prediction model was given. e R2R processing equipment health prediction experiment system was built and the PTS-FNN model experiment was carried out. e experimental results showed that the training time of PTS-FNN model was 50.37% less than the standard TS-FNN prediction model. e prediction accuracy increased by 5.48%, and the PTS-FNN had no in the judgment of state 1 and state 4. e proposed PTS-FNN health state prediction model was used for health state prediction of continuous manufacturing systems with time-varying and multistation features such as R2R processing equipment, which improved the real-time and accuracy of the prediction model. e main problem which plagued the large-scale manufacturing of flexible photovoltaic film materials was solved.
Data Availability e data that support the findings of this study are available from the corresponding author on request.

Conflicts of Interest
e authors declare that they have no conflicts of interest.