As an emerging research field, physics-informed machine learning and its structural integrity applications may bring new opportunities to the intelligent solution of engineering problems. Pure data-driven approaches have some limitations when solving engineering problems due to lack of interpretability and data hungry applications. Therefore, further unlocking the potential of machine learning will be an important research direction in the future. Knowledge-driven machine learning methods may have a profound impact on future engineering research. The theme of this special issue focuses on more specific physics-informed machine learning methods and case studies. This issue presents a series of practical ideas to demonstrate the huge potential of physics-informed machine learning for solving engineering problems with high precision and efficiency. This article is part of the theme issue \'Physics-informed machine learning and its structural integrity applications (Part 2)\'.

The issue focuses on physics-informed machine learning and its applications for structural integrity and safety assessment of engineering systems/facilities. Data science and data mining are fields in fast development with a high potential in several engineering research communities; in particular, advances in machine learning (ML) are undoubtedly enabling significant breakthroughs. However, purely ML models do not necessarily carry physical meaning, nor do they generalize well to scenarios on which they have not been trained on. This is an emerging field of research that potentially will raise a huge impact in the future for designing new materials and structures, and then for their proper final assessment. This issue aims to update the current research state of the art, incorporating physics into ML models, and providing tools when dealing with material science, fatigue and fracture, including new and sophisticated algorithms based on ML techniques to treat data in real-time with high accuracy and productivity. This article is part of the theme issue \'Physics-informed machine learning and its structural integrity applications (Part 1)\'.

The development of machine learning (ML) provides a promising solution to guarantee the structural integrity of critical components during service period. However, considering the lack of respect for the underlying physical laws, the data hungry nature and poor extrapolation performance, the further application of pure data-driven methods in structural integrity is challenged. An emerging ML paradigm, physics-informed machine learning (PIML), attempts to overcome these limitations by embedding physical information into ML models. This paper discusses different ways of embedding physical information into ML and reviews the developments of PIML in structural integrity including failure mechanism modelling and prognostic and health management (PHM). The exploration of the application of PIML to structural integrity demonstrates the potential of PIML for improving consistency with prior knowledge, extrapolation performance, prediction accuracy, interpretability and computational efficiency and reducing dependence on training data. The analysis and findings of this work outline the limitations at this stage and provide some potential research direction of PIML to develop advanced PIML for ensuring structural integrity of engineering systems/facilities. This article is part of the theme issue \'Physics-informed machine learning and its structural integrity applications (Part 1)\'.

Prognostic and health management technologies are increasingly important in many fields where reducing maintenance costs is critical. Non-destructive testing techniques and the Internet of Things (IoT) can help create accurate, two-sided digital models of specific monitored objects, enabling predictive analysis and avoiding risky situations. This study focuses on a particular application: monitoring an endodontic file during operation to develop a strategy to prevent breakage. To this end, the authors propose an innovative, non-invasive technique for early fault detection based on digital twins and infrared thermography measurements. They developed a digital twin of a NiTi alloy endodontic file that receives measurement data from the real world and generates the expected thermal map of the object under working conditions. By comparing this virtual image with the real one acquired by an IR camera, the authors were able to identify an anomalous trend and avoid breakage. The technique was calibrated and validated using both a professional IR camera and an innovative low-cost IR scanner previously developed by the authors. By using both devices, they could identify a critical condition at least 11 s before the file broke.

A classic problem in prognostic and health management (PHM) is the prediction of the remaining useful life (RUL). However, until now, there has been no algorithm presented to achieve perfect performance in this challenge. This study implements a less explored approach: binary classification of the state of mechanical systems at a given forecast horizon. To prove the effectiveness of the proposed approach, tests were conducted on the C-MAPSS sample dataset. The obtained results demonstrate the achievement of an almost maximal performance threshold. The explainability of artificial intelligence (XAI) using the SHAP (Shapley Additive Explanations) feature contribution estimation method for classification models trained on data with and without a sliding window technique is also investigated.

Resulting from the short production cycle and rapid design technology development, traditional prognostic and health management (PHM) approaches become impractical and fail to match the requirement of systems with structural and functional complexity. Among all PHM designs, testability design and maintainability design face critical difficulties. First, testability design requires much labor and knowledge preparation, and wastes the sensor recording information. Second, maintainability design suffers bad influences by improper testability design. We proposed a test strategy optimization based on soft-sensing and ensemble belief measurements to overcome these problems. Instead of serial PHM design, the proposed method constructs a closed loop between testability and maintenance to generate an adaptive fault diagnostic tree with soft-sensor nodes. The diagnostic tree generated ensures high efficiency and flexibility, taking advantage of extreme learning machine (ELM) and affinity propagation (AP). The experiment results show that our method receives the highest performance with state-of-art methods. Additionally, the proposed method enlarges the diagnostic flexibility and saves much human labor on testability design.

Prognostic and Health Management (PHM) systems are some of the main protagonists of the Industry 4.0 revolution. Efficiently detecting whether an industrial component has deviated from its normal operating condition or predicting when a fault will occur are the main challenges these systems aim at addressing. Efficient PHM methods promise to decrease the probability of extreme failure events, thus improving the safety level of industrial machines. Furthermore, they could potentially drastically reduce the often conspicuous costs associated with scheduled maintenance operations. The increasing availability of data and the stunning progress of Machine Learning (ML) and Deep Learning (DL) techniques over the last decade represent two strong motivating factors for the development of data-driven PHM systems. On the other hand, the black-box nature of DL models significantly hinders their level of interpretability, de facto limiting their application to real-world scenarios. In this work, we explore the intersection of Artificial Intelligence (AI) methods and PHM applications. We present a thorough review of existing works both in the contexts of fault diagnosis and fault prognosis, highlighting the benefits and the drawbacks introduced by the adoption of AI techniques. Our goal is to highlight potentially fruitful research directions along with characterizing the main challenges that need to be addressed in order to realize the promises of AI-based PHM systems.

Proton exchange membrane fuel cell (PEMFC) has been widely used in diverse applications. However, degradation and durability problem is one of the biggest barriers to take PEMFCs into extensive commercial use. Prognostics and health management is an effective solution to this problem. In this study, we focus on its core technology prognostics and propose an individual difference conscious prediction method for PEMFC using a hybrid transfer learning approach to get higher accuracy. Firstly, a time-scale self-optimization local weighted regression method is designed to adaptively smooth the raw data to prominent the performance degradation trend. Then, to obtain a more similar curve to the predicted fuel cell as the training data of the prediction model, a transferability measurement method using cosine-distance selects the most similar historical test data. Furtherly, it is utilized to generate a more similar curve by a data transfer method combining a deep learning model named stacked autoencoder and a hybrid transfer learning strategy. Two types of transfer learning approaches are fused to maximally mine available information from historical data and previous models to help improve the similarity of the generated curve. In this process, the common degradation information of all cells and individual information of the predicted cells are considered to improve generation quality. Finally, a prediction model using stacked Long-short Term Memory(LSTM) having a significant advantage in modeling series relation is trained by the generated samples cut with variable width sliding windows and estimates remaining useful life(RUL) the target fuel cell. Experimental validation data are employed to verify the effectiveness of the proposed algorithm. Satisfying results are also obtained by accuracy comparison under different smoothing scales, numbers of transferable samples, and prediction methods.

With the development of the internet of things (IoTs), big data, smart sensing technology, and cloud technology, the industry has entered a new stage of revolution. Traditional manufacturing enterprises are transforming into service-oriented manufacturing based on prognostic and health management (PHM). However, there is a lack of a systematic and comprehensive framework of PHM to create more added value. In this paper, the authors proposed an integrative framework to systematically solve the problem from three levels: Strategic level of PHM to create added value, tactical level of PHM to make the implementation route, and operational level of PHM in a detailed application. At the strategic level, the authors provided the innovative business model to create added value through the big data. Moreover, to monitor the equipment status, the health index (HI) based on a condition-based maintenance (CBM) method was proposed. At the tactical level, the authors provided the implementation route in application integration, analysis service, and visual management to satisfy the different stakeholders\' functional requirements through a convolutional neural network (CNN). At the operational level, the authors constructed a self-sensing network based on anti-inference and self-organizing Zigbee to capture the real-time data from the equipment group. Finally, the authors verified the feasibility of the framework in a real case from China.

The cementing manufacturing process of ferrite phase shifters has the defect that cementing strength is insufficient and fractures always appear. A detection method of these defects was studied utilizing the multi-sensors Prognostic and Health Management (PHM) theory. Aiming at these process defects, the reasons that lead to defects are analyzed in this paper. In the meanwhile, the key process parameters were determined and Differential Scanning Calorimetry (DSC) tests during the cure process of resin cementing were carried out. At the same time, in order to get data on changing cementing strength, multiple-group cementing process tests of different key process parameters were designed and conducted. A relational model of cementing strength and cure temperature, time and pressure was established, by combining data of DSC and process tests as well as based on the Avrami formula. Through sensitivity analysis for three process parameters, the on-line detection decision criterion and the process parameters which have obvious impact on cementing strength were determined. A PHM system with multiple temperature and pressure sensors was established on this basis, and then, on-line detection, diagnosis and control for ferrite phase shifter cementing process defects were realized. It was verified by subsequent process that the on-line detection system improved the reliability of the ferrite phase shifter cementing process and reduced the incidence of insufficient cementing strength defects.