Abstract: To address the limitations of deep neural networks in terms of interpretability and the inability of current interpretable networks to perform cross-domain diagnosis tasks, this paper proposes an interpretable triple feature extractor transfer network(ITFETN). For the interpretability challenge, a multi-layer sparse coding model is established, and its iterative solving algorithm is derived. By unrolling the fast iterative soft thresholding algorithm, an equivalent network form of the sparse coding model soving algorithm is obtained. This equivalent network then serves as a feature extractor, forming an interpretable algorithm-structure-equivalent network. To tackle the problem of cross-domain tranfer diagnosis, a triple feature extractor strategy is constructed. This strategy is designed to extract the shared features from the source and target domains, as well as their respective private features. Based on the concept of feature adversarial learning, a loss function for the transfer diagnosis task is designed for the effective training of ITFETN. This effectively extracts shared features with minimized distance between the source and target domains for cross-domain diagnosis, thereby achieving interpretable transfer diagnosis tasks. Experimental results demonstrate that ITFETN exhibits improved average accuracy and robustness in two case studies compared to benchmark methods. This confirms its effectiveness in achieving interpretable cross-domain diagnosis.