Rapid fault diagnosis in complex processes of gas refineries is a key challenge in process engineering and control, due to the strategic importance of this equipment and the high maintenance costs. Despite the vast amount of data generated in these processes, the effective exploitation of this data has been limited so far. In data-driven fault detection methods, two main approaches exist: fault detection and classification, and fault diagnosis and fault measurement, with the latter being achievable through regression techniques or accurate models. This paper presents a machine learning-based approach for the regression modeling of industrial systems with outlier and noisy data, tailored for fault diagnosis applications. For fault diagnosis, two regression methods, including Support Vector Machine Regression and Gaussian Process Regression, have been utilized. These models are capable of predicting the behavior of industrial systems and diagnosis faults without the need for precise physical models. The main innovation of this paper is the introduction of a machine learning framework that can perform more accurately and rapidly compared to traditional expert fault diagnosis methods, particularly in scenarios with outlier and noisy data.