Bayesian network (BN) and probabilistic principal component analysis (PPCA) are powerful tools in artificial intelligence. In this study, two intelligent soft sensors, designed based on BN and PPCA, were proposed for fault detection and data prediction in chemical processes. A gas sweetening process was considered as a case study in which the existing data for H 2 S concentration in sweet gas stream were incomplete. In order to detect faults during the operation, a soft sensor was designed using BN and PPCA for predicting H 2 S concentration in the sweet gas stream. Then, another soft sensor was developed based on the BN for fault detection, considering the Gaussian mixture model with hidden nodes. The Tennessee-Eastman challenge process was used to assess the efficiency of the fault detection method. Results showed that the predicted values of the soft sensors are very close to real data. The fault occurring in this process was detected in early stages, demonstrating the good performance of the proposed fault detection system. It was also shown that the performance of the BN is better than the PPCA in prediction of incomplete data. Moreover, the confidence interval can be evaluated for the predicted values when using the BN. An uncertainty analysis was performed to assess the quality of predicted data, and it was observed that the error magnitude of predicted data is smaller when using the BN compared with the PPCA. In particular, the results showed that the BN model is capable of estimating H 2 S concentration with nearly 96.1% accuracy, whereas the accuracy of the PCA-based method was 93.2%. K E Y W O R D SBayesian network, fault detection, gas sweetening process, probabilistic principal component analysis, soft sensor, Tennessee-Eastman challenge process

In this study, a shell-and-tube heat exchanger (STHX) design based on seven continuous independent design variables is proposed. Delayed Rejection Adaptive Metropolis hasting (DRAM) was utilized as a powerful tool in the Markov chain Monte Carlo (MCMC) sampling method. This Reverse Sampling (RS) method was used to find the probability distribution of design variables of the shell and tube heat exchanger. Thanks to this probability distribution, an uncertainty analysis was also performed to find the quality of these variables. In addition, a decision-making strategy based on confidence intervals of design variables and on the Total Annual Cost (TAC) provides the final selection of design variables. Results indicated high (R. Zarghami).2 accuracies for the estimation of design variables which leads to marginally improved performance compared to commonly used optimization methods. In order to verify the capability of the proposed method, a case of study is also presented, it shows that a significant cost reduction is feasible with respect to multi-objective and single-objective optimization methods. Furthermore, the selected variables have good quality (in terms of probability distribution) and a lower TAC was also achieved. Results show that the costs of the proposed design are lower than those obtained from optimization method reported in previous studies. The algorithm was also used to determine the impact of using probability values for the design variables rather than single values to obtain the best heat transfer area and pumping power. In particular, a reduction of the TAC up to 3.5% was achieved in the case considered.

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