Online Monitoring-Based Prediction Model of Knitting Machine Productivity

In addition, the IoT system was deployed as it is based upon ESP32. It consists of a low-cost and low-power system on a chip microcontroller with built-in Bluetooth and Wi-Fi. ESP32 was used along with MQTT to convey the data to the server and store them for analysis. MQTT is an efficient, reliable and OASIS standard messaging protocol for IoT. It is designed as an extremely lightweight publish/subscribe messaging transport which uses little network traffic and has a small code footprint, making it perfect for connecting faraway devices. The MQTT interacts with HiveMQ, a form of cloud computing that offers a wide range of services through the Internet, including data storage, servers, databases, networking, and applications. IoT devices may be reliably and scalable connected to any cloud platform using the fully managed MQTT platform called HiveMQ. Figure 1 shows the connection of an MQTT broker server where ESP32 is assigned as the MQTT Client which acquires and processes the sensor’s data and then publishes them to the MQTT Broker server. On the other hand, the MQTT Broker must have already subscribed the ESP32 MQTT Client. Moreover, the monitoring device, such as a phone or laptop, plays the role of another MQTT Client [9-11].

Fig. 1.

For data collection of the online monitoring system proposed, the device gathers and populates the data through MQTT. In this work, we used our prototype of the monitoring device designed to gather the machine speed and yarn feeder sensor count. As a result, the production rate was calculated. Figure 2 shows an illustration of the prototype of the monitoring device designed. It shows the circular knitting machine in operation while the monitoring system captures the sensors’ data and stores them in the cloud. This monitoring device consists of proximity sensor and yarn feeder sensor in addition to IoT embedded sensors in order to gather the revolutions of the machine speed and the yarn feeder sensor. As a result, the production rate was calculated. Figure 3 displays the architecture of the data migration process, where the MQTT broker is the interaction between server and machine. It explains the IoT components and how production data are sent from the machine to the server using the ESP32 and MQTT broker. The server then stores and analyses the data and displays them in tables and on graphs. Finally, the server transmits information to the mobile application so that managers can use it to monitor the productivity and control the machine through this application, as well as fix problems and resolve issues.

Fig. 2.

Fig. 3.

This arrangement’s primary objective is to forecast a product or intermediary product performance using the process setup during machine running. It is accomplished by gathering information from all equipment involved and tracking the product. This makes it possible to identify the settings and conditions that a work piece is exposed to inside each phase. It is feasible to create prediction models utilizing ML approaches, such as regression or deep neural networks, by gathering large data sets over time and assessing key performance indicators (KPIs) that measure the performance of the output. More than 6000 data points were recorded using the test system. The statistical data of the machine revolutions, yarn feeder sensor revolutions, stitch length and the production rate are denoted as n₁, n₂, L and P, respectively, as shown in Table 1. Hence, the purpose of this study was to estimate the production rate P based on the online monitoring parameters (n₁, n₂, and L). Indeed, the speed of the yarn feeder sensor stabilizes after three rotations, causing the variations observed, primarily due to sensor speed fluctuations. These fluctuations subsequently influence the standard deviation forn₂. Therefore, the output of the problem is P and the preliminary input dataset is formed from n₁, n₂ and L, where all other production factors, such as the yarn count, machine efficiency, and number of needles and feeders, are constant. The training set is 4000 and the test set - 2000.

A statistical analysis method is used in order to predict the machine production based on the monitoring data. The correlation between the available data sets should be determined to exclude highly correlated variables. The multicollinearity concept is an effective way to detect the correlation between multiple variables. A typical approach to detect the multicollinearity features is using Pearson’s correlation matrix [12]. The correlation matrix is provided in Figure 4, which shows the correlation between the independent variables n₁, n₂ and the L and production rate, where the correlation coefficients (r) determine the degree of correlation. When the r value rises, the features are positively correlated; while on the other hand, the features are negatively correlated when it rises negatively. The results show that the n₂, n₁ and L are correlated with P by (100%, 99% and 2.1%) respectively. In addition, the correlations between the independent variables (n₁ and n₂), (n₁ and L) and (n₂ and L) are (99%, -7.2% and 2.1%) in order.

Fig. 4.

In a multiple regression equation, multicollinearity occurs when one or more independent variables have a high correlation with one another. The statistical significance of an independent variable is affected by the multicollinearity issue, which is a problem. Statistical indicators like R² (coefficient of determination), tolerance, and VIF (Variance Inflation Factors) are used to significantly measure the degree of multicollinearity [13, 14]. These results imply that there is a high correlation between (n₁, n₂). The following equations are used to calculate the degrees of multicollinearity between independent variables: 1Tolerance =1−Ri2$${\rm{Tolerance\;}} = 1 - R_i^2$$ 2VIF=1/(1−Ri2)$${\rm{VIF}} = 1/\left( {1 - R_i^2} \right)$$

According to statistical outcomes shown in Table 2, it is clear that there is a multicollinearity problem between (n₁ and n₂), where the VIF (50.251) value is higher than 10. Furthermore, R² between (n₁ and n₂) is high (0.980) with the lowest tolerance of (0.020), which proves the multicollinearity issue. Conversely, the relation between the other variables is normal, where the lowest R² values (0.005) and (0.000) are found between (L&n₁) and (L&n₂) respectively. In addition, there are high correlation values (0.995) and (1.000) between (L&n₁) and (L&n₂) in order. Besides, the lowest VIF values of (1.005) and (1.000) are found between (L&n₁) and (L&n₂) in series.

All of these outcomes highlight the multicollinearity between independent variables (n₁ and n₂), which affects the accuracy of the prediction model. Hence, the recommended solution to overcome this problem is to delete one of these independent variables.

This is the relation between one or more independent variable (predictors or regressors) and a dependent (response) variable. In this case, the output variable P and the predictors are (n₁, n₂ and L).Figure 5 shows the relation between the production rate and measured parameters, where Figure 5 (a, b) shows a strong correlation between the production rate and (n₁ and n₂) in series, which is presented in a straight line. Furthermore, both figures show the best fit of the data set, which indicates that the production rate increases with the rising of (n₁ and n₂). Conversely, Figure 5 (c) shows a weak correlation between the production rate and stitch length in a certain range of the data set.

Fig. 5.

The linear regression method of ML is adopted, which fits a straight line reducing the outcome error between observed and expected values. There are simple linear regression calculators that use a “least squares” method to discover the best-fit line for a set of paired data. A typical linear regression model output is shown in equation (3) [15, 16]. 3Yi=f(Xi,β)+ei$${Y_i} = f\left( {{X_i},\beta } \right) + {e_i}$$ Where X_i, β and e_i are the independent variable, unknown parameters and error terms, respectively.

Prediction results of the recommended solutions to overcome the multicollinearity problem in estimating the production rate are obtainedin two ways. The first procedure is deleting n₂ and the prediction of the production rate using n₁ and L, which is represented by the linear regression equation of the model (4).The second procedure is deleting n₁ and the prediction of production rate using n₂ and L, which is represented by the model’s linear regression equation (5). 4P1=0.345(n1)+1.5525(L)−3.224$${{\rm{P}}_1} = 0.345\left( {{n_1}} \right) + 1.5525(L) - 3.224$$ 5P2=0.005(n2)−(7.44E−16)∗(L)−(4.09E−14)$${{\rm{P}}_2} = 0.005\left( {{n_2}} \right) - (7.44{\rm{E}} - 16) * (L) - (4.09{\rm{E}} - 14)$$

Figure 6 shows the regression hyper-plane of the dataset after training. The count of the machine revolution n₁ and the stitch length L are on the x-axis and y-axis, respectively. The production rate is on the z-axis. The coefficients of n₁ and L are 0.345 and 1.5525, respectively. The intercept of the hyper-plane is -3.224. The intercept is the y-axis anticipated mean value when all the x-axis is equal to 0. The model creates a regression equation with the x-axis as the only predictor to begin with. The predicted mean value of the y-axis at that value is the intercept in the event that the x-axis occasionally equals 0, which has significance.

Fig. 6.

Figure 7 shows the regression hyper-plane of the dataset after training. The count of the machine revolution n₂ and the stitch length L are on the x-axis and y-axis, respectively. The production rate is on the z-axis. The coefficients of n₂ and L are 0.005 and (7.44E-16), respectively. The intercept of the hyper-plane is -(4.09E-14). The intercept is the y-axis anticipated mean value when all the x-axis is equal to 0. The model creates a regression equation with the x-axis as the only predictor to begin with. The predicted mean value of the y-axis at that value is the intercept in the event that the x-axis occasionally equals 0, which has significance.

Fig. 7.

After that, model evaluation is made through statistical indicators such as the mean absolute error (MAE) and mean absolute percentage error (MAPE), as well as the accuracy of the test data. Results of prediction precision are shown in Tables (3 and 4) for prediction using (n₁ and L) and using (n₂ and L), respectively. Table 3 shows precision results which represent a high level of accuracy of predicting the production rate (kg/h). The findings show that the accuracy reaches 99.73 % with an MAE of 0.029 and standard deviation of 0.002. The least value of MAPE is 0.65 %. In addition, Table 4 shows precision results which represent a high level of accuracy of predicting the production rate (kg/h). The findings show that the accuracy reaches 100% with an MAE of 0 and standard deviation of 0. The least value of MAPE is 0 %. Thus, this prediction model for determining the production rate using (n₂ and L) introduces a novel formula in the knitting industry. Thus, it is recommended to calculate the production rate (kg/hr) using predictors (n₂ and L) or (n₁ and L) due to high precision results.