# Sensor-Data-Driven Prognosis Approach of Liquefied Natural Gas Satellite Plant
## 5 Application to Predictive Maintenance of LNG Tank Refilling by Means of Trucks
### Prognosis of Remaining Time to Refill Tank Using FIR Methodology  
Weather (mainly temperature) is one of the most important factors that influences daily urban gas consumption. Using the FIR methodology described in Section 4.2.1, we obtained a model for simulating gas consumption per operation-tank cycle using mean annual temperature. In a satellite plant, temperature is an important parameter related with its safety. For this purpose, the plant is equipped with several temperature sensors. There is a temperature sensor for detecting tank depressurization (or venting emissions); in normal operation, this sensor measures ambient temperature. Figure 6 shows in the cyan line the data of this sensor during 2018. Mean ambient temperature (\(T_{m}\)) of the whole period is approximated by Fourier series representation  
\[T_{m}(t)=a0+a1\cos(wt)+b1\sin(wt), \tag{10}\]  
in which the parameters are fitted to the data using a nonlinear least-squares algorithm. Figure 6 shows the values of \(T_{m}\) in red line, with estimate parameters \(a0=15.26\), \(a1=-6.789\), \(b1=-7.321\), and \(w=0.019\). Figure 5: XY plot of LNG level in tank (NVT) and accumulated NG consumption (m\({}^{3}\)). In order to obtain FIR models, it is necessary to define two parameters: the first is related to the fuzzification process of the variables (number of classes per variable) and the membership function, as was described in Section 4.2.1. In our case, there were two variables, \(u(k)\) is the temporal series given by Equation (10), and \(y(k)\) is the accumulated consumption given by Equation (8). Data were divided into 84 datasets corresponding with the time intervals between refilling; Figure 7 shows three of them. In this application, variables were discretized into three classes, and the equal-frequency-partition method was used to determine the membership function of the classes. The proposed candidate mask is displayed in Table 2. The two columns are associated with variables, \(T_{m}\) and \(Q_{a}\), and the rows with their samples. The proposed mask had a depth of one day, resulting a candidate mask of depth-144, since the variable sequences were sampled every 10 min. In order to reduce the computation complexity and enable fast convergence to an optimal mask, in the \(m-\)input of the candidate mask, only one sample per hour was considered. It can be observed in Table 2, where \(\beta\) is equal to \(-1\) for \(i=6,12,...,138\); otherwise, it is zero. The candidate mask assumed a causal relation between the two variables each hour during one day. The found optimal mask had causal relation \(\hat{Q}_{a}(k)=f(Q_{a}(k-6),Q_{a}(k-78),Q_{a}(k-114),\)\(T_{m}(k-144))\), which means that the consumption prediction at instant \(k\), \(\hat{Q}_{a}(k)\) depends on the consumption of samples 6, 78, and 114 before, which is equivalent to 1, 13, and 19 h, and the temperature of 144 samples (or 24 h) before. The whole available datasets were divided into training and evaluating sets. First, 68 datasets were used for training the model, and the remaining 16 datasets for evaluating the performance of the prediction model. Figure 8 shows the Visual FIR main screen where we can visualize the real output signal (blue), the predicted signal (red dashed line), and the mean square error (MSE2). Figure 6: Ambient temperature during 2018 (cyan) and its prediction (red). Figure 8: Visual-FIR visualization screen with real (blue line) and predicted (red dashed line) result. \begin{table}
\begin{tabular}{c c c} \hline \hline \(k\setminus x\) & \(T_{m}\) & \(Q_{a}\) \\ \hline \(k-144\) & \(-1\) & \(-1\) \\ \(k-i\) & \(\beta\) & \(\beta\) \\ \(k\) & \(-1\) & \(+1\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Candidate mask. Figure 7: Accumulated consumption in three different periods of time corresponding with refilling periods. The estimated model was used recursively for predicting the tank-emptying time.