In current studies of the belief rule base (BRB) model, the attributes are assumed to be fully reliable and the observation data are directly used as input. However, in engineering practice, the observation data may be affected by some disturbance factors including the quality of the sensors and noise in the environment. Then the reliability of observation data may be affected and the modeling accuracy of BRB is influenced. As such, a new BRB model with attribute reliability (BRB-r) is proposed in this paper. In particular, a calculation method of attribute reliability is given based on the statistical method. Moreover, to integrate the attribute reliability into BRB-r, a new calculation method of matching degree is developed. The model's overall reliability denotes its ability to provide the correct result, and when the attributes are unreliable, the overall reliability of BRB-r is degraded. Thus, a calculation method for the overall reliability of BRB-r is developed to support decision making in engineering practice. A case study of the safety assessment of diesel engine is conducted to demonstrate the efficiency of the proposed BRB-r model.

Evidential reasoning (ER) rule has been widely used in dealing with uncertainty. As an important parameter to measure the inherent property of evidence, the evidence reliability makes the ER rule constitute a generalized reasoning framework. In current research of the ER rule, the evidence reliability tends to be expressed in the form of quantitative value by certain methods or expert knowledge. The single quantitative value lacks the ability to describe the statistical property of reliability, which leads to unreasonable results. In this article, a new ER rule with continuous probability distribution of reliability denoted by ERr-CR is proposed. The combination of two pieces of evidence is discussed in detail, where the reliability is profiled as random variables with specific probability distribution. To characterize the output of ERr-CR, a novel concept of expectation of the expected utility is proposed. In addition, the ERr-CR is expanded to multiple pieces of evidence to show its universality. Further, the basic performances of the ERr-CR are explored to illustrate the rationality. Moreover, a case study of safety assessment of natural gas storage tanks (NGSTs) is conducted to show the potential applications of ERr-CR, which makes the proposed method more practical.

Project to latent structure (PLS) is a well-known data-driven method, which has been widely used in process monitoring. Several dynamic PLS algorithms have been proposed and applied in the dynamic process. However, the oblique decomposition induced by the PLS-based methods leads to redundant information in quality-related space, which results in missing alarms and false alarms. To cope with this problem, an orthogonal multi-block dynamic PLS (OMDPLS) algorithm is proposed. In the proposed method, a modified PLS (MDPLS) model is first built to provide an explicit inner dynamic model, which describes the relationship of latent variables between quality variables and time-delay inputs. Furthermore, based on the proposed MDPLS model, the orthogonal projection operator is constructed for each time-delay multi-block input matrix to reduce the quality-unrelated information in principal space. Afterward, the vector auto-regressive model is constructed to separate the dynamic interaction of the current sample to reflect the true state. Then, a completely dynamic process monitoring strategy is developed for quality-related faults. Finally, two experiments including a numerical simulation and the Tennessee Eastman process (TEP) are performed to demonstrate the effectiveness of the proposed method. Note to Practitioners —Controlling and measuring the quality state is challenging for advance industrial processes due to the dynamic correlation in the states. To ensure safe operation in the dynamic processes, avoiding false alarms of quality indicators has become a crucial task in modern industrial plants. This paper develops a novel dynamic process monitoring method, which reduces the false alarms caused by quality-unrelated faults and has good fault detection capability. The key advantage of OMDPLS is that the orthogonality in the sample space and the orthogonal decomposition in the variable space can be guaranteed. As a result, the latent variables extracted from the input are unrelated to the residuals, and the quality-related space and the quality-unrelated space are mutually exclusive. Driven by OMDPLS, the impact of quality-unrelated faults on the monitoring of key indicators will be reduced with fewer false alarms. In this way, unnecessary maintenance can be avoided. Therefore, the proposed method can be applied to processes with high requirements for low false alarms, such as large-scale process industries (metallurgy, steel rolling, chemical, and more). Meanwhile, the proposed method is purely data-driven and does not require complex process knowledge, which can supply more information for the monitoring needs of engineers. Two case studies show that the process monitoring strategy delivers more comprehensive performance than other methods.

Deep learning has become a promising tool for processing the massive data and attracted an increasing attention in the fields of degradation modeling and remaining useful life (RUL) prediction. The existing deep-learning-based methods are generally faced with the two aspects of problems. On the one hand, the prediction results are represented by the point estimates instead of the probabilistic distribution and, thus, the prognostic uncertainty in RUL prediction cannot be characterized. On the other hand, there exist plenty of the engineering assets without the label data related to lifetime, posing a great challenge for training the deep learning network. Toward this end, we propose a prognostic model under the framework of Bayesian deep learning for equipment lacking the label data related to lifetime. First, the monitoring data of the historical equipment and the historical data of field equipment in the database are preprocessed to generate the samples regarding degradation information as a label. Second, the bidirectional recurrent neural network (RNN) is employed as the candidate network for the advantages in handling the sequential monitoring data. On the basis of this, the idea of Bayesian deep learning is incorporated into the bidirectional RNN; thus, we can characterize the uncertainty of the predicted degradation level at any future time via utilizing the variational inference technique in the Bayesian neural networks. Furthermore, the failure probability for the concerned equipment at any time can be determined, by which the degradation uncertainty can be converted into the RUL uncertainty from the point of the reliability theory. Finally, we provide the case study associated with lithium-ion batteries to verify the proposed prognostic model.