The burgeoning development of supervised machine learning (ML) has led to its widespread applications in chemical and energy processes, such as fault detection. However, in some scenarios, collecting labelled data can be costly, hazardous, or impossible. Moreover, data of the same process can follow varying distributions due to changes in, for example, devices and environment, causing ML models to be ineffective. These challenges pose a domain adaptation task, necessitating the refinement of existing ML models to tackle issues from related applications. This study proposes a domain adaptation approach to address label scarcity and data distribution variation. The method has three stages: data distribution modelling (knowledge discovery), adaptation of target domain samples to source domains (knowledge transformation), and classifier ensemble for fault detection (knowledge fusion). Gamma, Weibull, and lognormal distributions are applied for data modelling and domain adaptation. The effectiveness of the method is validated on synthetic datasets and then applied to identify anomalies in coal mine pressure data and detect faults in the Tennessee Eastman (TE) process.