# Bayesian Uncertainty Inferencing for Fault Diagnosis of Intelligent Instruments in IoT Systems
## 2 Overview of Information Uncertainties in Fault Diagnosis Using Bayesian Networks  
Fault diagnosis in industrial scenarios typically requires inferences and reasoning by using structured variables and uncertain information. The probability graph model is a graphical causal model that describes causal relationships among variables. BNs were proposed by [PERSON] [5] in 1988, as a type of probability graph model. BNs use [PERSON] belief concept and (directed acyclic graph) structure to represent probabilistic relationships among variables and execute inferences or predictions. They are applicable in cases in which all problems can be summarized as the probability or degree of interconnection between variables [6]. Therefore, this approach is widely employed in decision making when there are many uncertainties. Among the various approaches to fault diagnosis, BNs function as a combination of data-driven and knowledge-driven approaches and can handle causal relationships and uncertainties with multiple faults, multiple causes, and multiple models. They have been extensively researched and used in a variety of industrial fault diagnosis scenarios [7; 8]. For example, [PERSON] et al. [9] used fuzzy rules to calculate the fuzzy probability of each mode in a BN fault in a gas-monitoring system. [PERSON] et al. [10] dealt with operational uncertainties in evidence and historical information. In their study, the evidence was used as the basis for reasoning, and historical information was used for parameter estimation. The uncertainty mainly originated from the refusing operation rate and incorrect operation rate, which were used in the Monte Carlo simulation to obtain various failure rates. Faults are identified in the on-site monitoring of a manufacturing process or in the operation of equipment due to the growth of the IoT. Hierarchical BN models and the BN model fusion approach are frequently used in large-scale or more complicated systems in which the likelihood of many faults is significantly increased. [PERSON] et al. [11] developed a hierarchical BN for large-scale process monitoring and decision making, to cope with the increasing amount of process knowledge and the massive divergent variables in large-scale processes. Small-scale local units were monitored using the basic layer, and global monitoring was executed in the functional layer. The basic layer was used for local monitoring and the transfer of raw monitoring results into statistical indices. The functional layer formed the BN structure and integrated the basic layer input. A top-down fault method was used to identify the fault units and most responsible variables. A BN can also be utilized to address the issues of incomplete data and data overload problems in multisensory data collection. [PERSON] et al. [12] considered sensor data overload and confusion when using a BN for fault diagnosis. They focused on a situation in which a parameter is measured by multiple sensors; it was established that these multiple sensors would generate too many data inputs and lead to information overload, and at the same time, they also needed to consider incomplete sensor data due to sensor hardware failures or data acquisition system malfunctions. In their method, PCA was used to remove the malfunctioning sensor data. Not all equipment monitoring information is quantifiable, and many failure models are only available as qualitative data. BN data fusion merges various types of data from several sources [13] to increase the effectiveness of BN diagnosis. [PERSON] et al. [14] established a combined BN model for fault diagnosis by using fused numerical and textual data. First, they developed a data fusion method for quantitative sensor data, metrology data, qualitative maintenance data logs, and corrective and preventive action reports. They then constructed a fused BN model with two individual BN models: a text-data BN model, and a numerical-data BN model. Each was constructed using a BN structure algorithm or a heuristic search method.