## 1 Introduction  
With the rapid development of industrial production and smart manufacturing, energy consumption has become a key indicator of product quality. Normal energy consumption reflects the stability of production processes, resource utilization efficiency, and environmental sustainability [1, 2, 3, 4, 5]. In the heating process of medium and heavy plates, various complex operations are involved. To accurately predict the consumption of different energy types, multiple factors must be considered. Firstly, real-time measurement data from sensors, including critical parameters such as temperature, need to be collected during the heating process. Additionally, process parameters of the batch billets, such as heating temperature, heating rate, and furnace atmosphere, along with spatial step size, are also crucial factors influencing energy consumption. To effectively analyze these intricate relationships, machine learning methods based on neural networks can be employed to develop precise predictive models in a multi-dimensional data space, thereby enabling accurate prediction and optimization of energy consumption [6, 7]. However, due to the complexity of production processes and the diversity of equipment operations, energy consumption data are often influenced by various factors such as equipment malfunctions and operational anomalies, leading to irregular fluctuations in energy levels. Therefore, detecting anomalies in energy consumption data promptly and accurately, and tracing their root causes, has become a critical challenge in improving energy efficiency management. Anomaly detection and root cause analysis are not only essential for ensuring process stability but also play a significant role in optimizing resource allocation, reducing energy consumption, and enhancing production efficiency [8; 9; 10; 11]. Anomaly detection methods can be broadly categorized into statistical model-based approaches, similarity-based methods, and machine learning techniques, among others. Statistical model-based methods, such as Autoreg-Ressive Integrated Moving Average (ARIMA) and Generalized Autoreg-Ressive Conditional Heteroskedasticity (GARCH) [12; 13], assume that the distribution of the data is known in advance, and they rely on prior knowledge to identify anomalies in the data. Similarity-based methods, such as K-Means and DBSCAN [14; 15], are distance-based algorithms that are easy to implement and compare. However, their accuracy tends to decline as the dimensionality of the data increases or when the data quality is inconsistent. Machine learning approaches have also been proposed to address anomaly detection challenges. For instance, ref. [16] introduced new Gaussian Mixture Models (GMM) combined with Optimal Principal Component (OPC) methods for fault detection. Additionally, ref. [17] proposed an improved monitoring strategy based on a modified Discriminative Locality Preserving Projection (DLPP) algorithm and stationary testing. This approach is designed for nonlinear, multivariate process monitoring and is aimed at analyzing both within-mode and cross-mode information. Root cause analysis methods often rely on Granger causality analysis, which determines the causal relationships between variables by solving Granger causality coefficients. This method ultimately identifies the causal propagation paths between variables [18; 19]. Ref. [20] applied Gaussian process regression to GC to solve the limitations of traditional GC for nonlinear systems. Ref. [21] employed Recurrent Neural Networks (RNNs) to automatically capture long-term dependencies between sequences. By incorporating a sparsity-inducing penalty on weights, the study introduced a neural Granger causality approach. Experimental results demonstrated that this method outperforms existing nonlinear Granger causality methods.