## 1 Introduction
However, the linear assumptions underlying this approach can result in the loss of important coefficients when applied to nonlinear systems, potentially leading to causal relationships that do not accurately reflect the true underlying causality. In addition, Bayesian networks [22] are commonly used to provide probabilistic interpretations of faults. These networks update the probability of specific events based on known evidence and prior probabilities, using [PERSON] theorem. One study [23] addressed the phenomenon of performance degradation in complex electronic systems over time by proposing a fault diagnosis method based on Dynamic Bayesian Networks (DBN). Their approach uses Markov chains to model the state transition relationships of an electronic system, considering four distinct system states. Another study [24] proposed a Bayesian Recurrent Neural Network (BRNN) with variational dropout, which introduces uncertainty estimation into the model. This approach enables simultaneous fault detection, fault identification, and fault propagation analysis in chemical processes. Anomaly detection and root cause analysis of energy consumption in medium and heavy plate production face numerous challenges, primarily due to the diversity of energy consumption media and the complexity of underlying factors. On one hand, energy consumption involves various media, such as natural gas, electricity, water, and nitrogen. Each medium exhibits distinct consumption characteristics, operational mechanisms, and anomaly patterns, which complicate anomaly detection. On the other hand, the factorsleading to energy consumption anomalies span multiple areas, including equipment, production processes, and operations, each with their own complexity and variability. For example, equipment issues may involve wear, malfunctions, or efficiency declines; production factors may include fluctuations in billet quality or adjustments in process parameters; and operational factors may arise from habitual practices or execution deviations. Furthermore, the production processes in medium and heavy plate manufacturing are highly coupled, meaning that anomalies in one process can propagate through complex pathways, affecting other stages. The primary challenge addressed in this paper is achieving accurate anomaly detection and root cause analysis in this complex environment. To overcome these challenges and analyze the underlying abnormal problem, this paper proposes a hierarchical diagnostic approach, dividing the diagnostic process into three layers: the manifestation layer, the process variable layer, and the underlying factors layer. This layered approach allows for systematic refinement and traceability in identifying the root causes of anomalies. At the manifestation layer, the box plot mechanism is used to detect anomalies from energy consumption data, and potential anomaly propagation paths are initially identified. In the process variable layer, a weighted nonlinear Granger causality analysis method is proposed to further find the abnormal propagation path. Finally, at the underlying factors layer, domain knowledge is integrated to build a Bayesian Neural Network, enabling a comprehensive analysis of the abnormal paths and identifying the root causes of the anomalies. In this study, prior knowledge derived from historical data and domain expertise were used to construct the priors in the Bayesian model. For instance, a Gaussian prior was assumed for the model parameters based on observed data characteristics, allowing the data to primarily drive the posterior inference. The structure of the remaining content of this paper is as follows: Section 2 first applies the box plot analysis method to detect anomalous data; then, it introduces a weighted Granger causality analysis method based on LSTM and, finally, presents the root cause tracing algorithm using an Adam-based variational inference Bayesian neural network. Section 3 provides experimental validation of the proposed methods. Section 4 concludes the paper and outlines directions for future work.