Fault diagnosis for a solar assisted heat pump (SAHP) system in the presence of incomplete data and expert knowledge is discussed in this article. A method for parameter learning of Bayesian networks (BNs) from incomplete data based on the back-propagation (BP) neural network and maximum likelihood estimation (MLE), which is called BP-MLE method, is presented. The BP neural network is utilized to impute the missing data and the complete data sets are addressed with MLE to obtain the parameters of BN. A method for parameter estimation under incomplete expert knowledge based on BP neural networks and fuzzy set theory is also presented, which is called BP-FS method. Similarly, the missing information is imputed by the trained BP neural network. Fuzzy set theory is employed to quantify the parameters of BN based on complete qualitative expert knowledge. The presented methods are applied to parameter learning of diagnostic BN for a SAHP system with incomplete simulation data and expert knowledge. The developed BN can perform fault diagnosis with complete or incomplete symptoms. (C) 2015 Elsevier Ltd. All rights reserved.