## 1 Introduction
Machine learning (ML) is a subfield of artificial intelligence (AI) that uses algorithms to analyze data, recognize patterns, and make decisions without explicit instructions. It is based on objective analysis and logical structure. Within the field of ML, artificial neural networks (ANNs) are modeled to simulate the working flow of the human brain and consist of interconnected nodes that mimic neurons. ANNs excel at learning intricate patterns and correlations in data, making them ideal for applications such as image identification, natural language processing, and predictive analytics. The development of deep neural networks has further improved the capability in processing various and complex datasets [17]. ANNs have played a crucial role in image recognition tasks, including object detection, facial recognition, and image classification. This has resulted in significant progress in areas such as self-driving cars, medical imaging, and security systems [18]. Deep learning (DL) differs from traditional ANNs in its ability to automatically learn complex data representations through the use of deep neural networks with many hidden layers. Compared with traditional ML, DL can learn complicated representations of datasets automatically, without the need to manually extract relevant features. It enables more efficient and accurate learning from raw data, automatically uncovering complex patterns and relationships that may not be apparent upon initial analysis. Additionally, it can handle large amounts of data and adapt dynamically to changes, making it particularly suitable for applications with high data complexity and dimensionality [19]. On the other hand, Deep Belief Networks (DBNs) are hierarchically structured ANNs that learn complex representations of input data using probabilistic methods. They have been used successfully in areas such as computer vision, natural language recognition, bioinformatics, and financial data analysis. Recent developments include hybrid architectures that combine DBNs with other deep learning techniques, such as Convolutional Neural Networks (CNNs) for image processing and Recurrent Neural Networks (RNNs) for sequential data processing. This combination improves model performance and increases flexibility when learning data representations. DBNs are increasingly being used on cloud platforms, allowing for more efficient data management and faster neural network training [19]. One of its applications is in smart cities to improve security and efficiency. It enables anomaly detection, data encryption,intrusion detection, behavior analysis, and secure communication with significantly improved overall security by providing effective tools for data protection and cyber threat prevention [20]. Moreover, to enhance the planning and administration of urban tunnel building projects, DBNs are utilized to predict the performance of cantilever roadheaders in challenging terrain. This enables the precise and timely control of factors that affect roadheader performance. The use of DBNs allows one to address issues related to the complexity of geological data and the nonlinear correlations between excavation factors, resulting in more accurate projections that are adaptive to changing ground conditions [21]. High-resolution image processing is crucial in various industries, including medical analysis, satellite image processing, and computer graphics. [PERSON] et al. [22] proposed a cascade approach, where a CNN extracts DNN-based features from input image patches. These features are then fed into the DBN model for high-resolution image quality prediction. This study aims to improve the objective assessment of super-resolution image quality by providing an advanced, accurate approach without reference images. Bayesian neural networks (BNNs) are a type of neural network that treat model weights as random variables with probability distributions, rather than fixed parameters.