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Health Indices (HIs) summarize degradation from operational data and support diagnostic and prognostic tasks in Prognostics and Health Management (PHM). Their usefulness depends on capturing degradation and interpreting system condition. Autoencoders learn such representations from unlabelled monitoring data; however, when training is driven only by reconstruction, the physical meaning of latent variables remains undefined, limiting their interpretation and diagnostic value. This work proposes a physics-constrained autoencoder that embeds system knowledge as an inductive bias in the decoder architecture and as a learning bias in the loss function. The decoder contains differentiable physical equations that receive latent variables and operating conditions as inputs, structurally guiding each latent variable to represent a predefined physical quantity and enabling component-level analysis before aggregation into a system-level HI.The methodology is benchmarked on the N-CMAPSS dataset against alternative representations. Reconstruction reaches an $R^2$ of 0.9993 and an MAE of 0.0036, comparable to fully data-driven models. After operating-condition correction, the inferred physical quantities track degradation, and their aggregation produces an HI with a Spearman correlation of 0.9791 with the ground truth, an RMSE of 0.0286, and an MAE of 0.0233. The methodology is further evaluated using a single model trained across four datasets representing distinct degradation scenarios. This model preserves component-level signatures that distinguish compression-side from expansion-side degradation without diagnostic labels.Finally, the proposed framework enables degradation trends to be visualized on component maps, providing a health representation in a form familiar to engine operators and domain experts.

Fault diagnosis in complex systems requires linking observed changes in physical quantities to the failure mechanisms that produce them. Experienced engineers perform this task by combining sensor information with knowledge of system behavior and fault propagation. Large Language Models (LLMs) can support this process, but their diagnostic reasoning depends on the availability of asset-specific engineering knowledge and on how this knowledge is represented and used during inference. This work introduces Chain of Physics (CoP), an LLM-based fault-diagnosis framework built around a Constrained Knowledge Graph (CKG) generated automatically from asset-specific reference documentation. CoP addresses failure-sensor association from textual engineering knowledge. The CKG stores diagnostic chains connecting failure modes, changes in physical quantities, and monitoring sensors. During inference, semantically similar graph paths are retrieved for each question and used as both information and in-context examples for the reasoning process. Candidate failure modes are extracted from the question and analysed independently through dedicated LLM calls, which generate plausible failure-to-observation chains. A final decision module compares these chains with the available answer choices. CoP is evaluated on the FailureSensorIQ benchmark across four industrial asset classes and three LLMs. Compared with direct prompting and conventional Retrieval-Augmented Generation (RAG), CoP improves diagnostic accuracy across all evaluated models, with gains ranging from 7.8 to 19.6 percentage points and from 11.7 to 18.2 percentage points, respectively. The results show that structured engineering knowledge can improve LLM-based diagnostic reasoning when graph retrieval is combined with in-context examples of fault propagation.