## 2 Multimodal Learning Techniques for Fault Diagnosis  
### Deep Learning Approaches  
Deep learning has truly revolutionized fault diagnosis by providing powerful, scalable solutions for detecting faults in complex systems. What sets deep learning apart is its ability to automatically learn patterns directly from raw data, making it highly effective, especially when handling unstructured data such as images, sounds, and time-series signals. Traditional manual extraction of features can be labor-intensive and prone to errors, but deep learning navigates these challenges effortlessly [12].  
In fault diagnosis, convolutional neural networks (CNNs) are frequently the preferred option due to their proficiency in processing spatial data, such as images from thermal cameras or visual inspections. What's particularly remarkable is that CNNs need minimal preprocessing [12]. Conversely, recurrent neural networks (RNNs), particularly long short-term memory (LSTM) networks, excel at handling sequential data, such as sensor readings over time, models like You Only Look Once (YOLO) and Single Shot Detector (SSD) have proven to be highly effective in detecting structural defects, surface cracks, and other anomalies in industrial visual data [13, 14]. These models effectively identify temporal patterns that may signal an impending fault [15]. A typical deep learning model used in fault diagnosis might look like this:  
\[\hat{y}=f(X;\theta) \tag{1}\]  
In Equation (1), \(\hat{y}\) stands for the predicted fault type (or output class), \(X\) represents the input data (such as sensor readings or images), and \(\theta\) refers to the model parameters, which are adjusted during the training process.  
To train the model, an optimization algorithm such as stochastic gradient descent (SGD) is employed to minimize the loss function:  
\[L(\theta)=\frac{1}{N}\sum_{i=1}^{N}\ell(f(X_{i};\theta),y_{i}) \tag{2}\]  
Equation (2) represents the loss function \(L(\theta)\), where \(\ell\) is the chosen loss metric (such as cross-entropy), \(X_{i}\) is the input for the \(i\)-th training example, \(y_{i}\) is the corresponding true label, and \(N\) is the total number of samples in the dataset. The objective is to minimize this loss over the parameter space.  
Although deep learning has demonstrated remarkable success in fault diagnosis, it is not without challenges. One of the primary obstacles is the requirement for large, labeled datasets to train these models effectively, which can be challenging in industrial settings where faults are often infrequent. Additionally, deep learning models can be computationally demanding, necessitating powerful hardware for both training and real-time implementation.  
For example, in agricultural systems, especially in fish farming, deep learning is exerting a great impact on how we monitor and maintain fish health. By connecting various sensors and data sources, these systems can provide real-time updates on things like water quality, fish behavior, and overall health. For example, deep learning models like CNNs can analyze images of fish to spot early signs of illness or stress, while other models, like RNNs, can track changes in behavior or environmental conditions over time. These tools also use data like temperature, pH levels, and oxygen content to predict potential health problems or optimize feeding. This interconnected approach not only boosts efficiency and sustainability in fish farming but also helps catch issues early, reducing the chances of disease outbreaks and improving overall management.  
Looking to the future, several exciting directions exist for enhancing deep learning in fault diagnosis. A key area is improving the interpretability of these models, where explainable AI techniques come into play [16]. Additionally, there is significant potential in enhancing these models' abilities to manage smaller datasets. Techniques such as transfer learning and data augmentation can significantly enhance the performance of deep learning models, even when labeled data are limited [17].