Preface to the theme issue 'physics-informed machine learning and its structural integrity applications'.

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)'.

Physics-informed machine learning and its structural integrity applications: state of the art.

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)'.

Defect driven physics-informed neural network framework for fatigue life prediction of additively manufactured materials.

Additive manufacturing (AM) has attracted many attentions because of its design freedom and rapid manufacturing; however, it is still limited in actual application due to the existing defects. In particular, various defect features have been proved to affect the fatigue performance of components and lead to fatigue scatter. In order to properly assess the influences of these defect features, a defect driven physics-informed neural network (PiNN) is developed. By embedding the critical defects information into loss functions, the defect driven PiNN is enhanced to capture physical information during training progress. The results of fatigue life prediction for different AM materials show that the proposed PiNN effectively improves the generalization ability under small samples condition. Compared with the fracture mechanics-based PiNN, the proposed PiNN provides physically consistent and higher accuracy without depending on the choice of fracture mechanics-based model. Moreover, this work provides a scalable framework being able to integrate more prior knowledge into the proposed PiNN. This article is part of the theme issue 'Physics-informed machine learning and its structural integrity applications (Part 1)'.

Design of robust superhydrophobic surfaces.

The ability of superhydrophobic surfaces to stay dry, self-clean and avoid biofouling is attractive for applications in biotechnology, medicine and heat transfer1-10. Water droplets that contact these surfaces must have large apparent contact angles (greater than 150 degrees) and small roll-off angles (less than 10 degrees). This can be realized for surfaces that have low-surface-energy chemistry and micro- or nanoscale surface roughness, minimizing contact between the liquid and the solid surface11-17. However, rough surfaces-for which only a small fraction of the overall area is in contact with the liquid-experience high local pressures under mechanical load, making them fragile and highly susceptible to abrasion18. Additionally, abrasion exposes underlying materials and may change the local nature of the surface from hydrophobic to hydrophilic19, resulting in the pinning of water droplets to the surface. It has therefore been assumed that mechanical robustness and water repellency are mutually exclusive surface properties. Here we show that robust superhydrophobicity can be realized by structuring surfaces at two different length scales, with a nanostructure design to provide water repellency and a microstructure design to provide durability. The microstructure is an interconnected surface frame containing 'pockets' that house highly water-repellent and mechanically fragile nanostructures. This surface frame acts as 'armour', preventing the removal of the nanostructures by abradants that are larger than the frame size. We apply this strategy to various substrates-including silicon, ceramic, metal and transparent glass-and show that the water repellency of the resulting superhydrophobic surfaces is preserved even after abrasion by sandpaper and by a sharp steel blade. We suggest that this transparent, mechanically robust, self-cleaning glass could help to negate the dust-contamination issue that leads to a loss of efficiency in solar cells. Our design strategy could also guide the development of other materials that need to retain effective self-cleaning, anti-fouling or heat-transfer abilities in harsh operating environments.

Reliability Analysis of FRP-Confined Concrete at Ultimate using Conjugate Search Direction Method.

In this paper compressive strength and ultimate strain results in the current database of fiber-reinforced polymer (FRP)-confined concrete are used to determine the reliability of their design space. The Lognormal, Normal, Frechet, Gumbel, and Weibull distributions are selected to evaluate the probabilistic characteristics of six FRP material categories. Following this, safety levels of the database are determined based on a probabilistic model. An iterative reliability method is developed with conjugate search direction for evaluating the reliability. The results show that Lognormal and Gumbel distributions provide best probability distribution for model errors of strength and strain enhancement ratios. The developed conjugate reliability method provides improved robustness over the existing reliability methods owing to its faster convergence to stable results. The results reveal that the part of the database containing normal strength concrete (NSC) heavily confined (i.e., actual confinement ratio (flu,a/f'co) > 0.5) by low and normal modulus carbon fibers (i.e., fiber elastic modulus (Ef) ≤ 260 GPa) and moderately confined (i.e., 0.3 ≤ flu,a/f'co ≤ 0.5) by aramid fibers exhibits a very high safety level. The segments of the database with a low and moderate safety level have been identified as i) NSC moderately and heavily confined by higher modulus glass fibers (i.e., Ef > 60 GPa), ii) high strength concrete (HSC) moderately and heavily confined (i.e., flu,a/f'co > 0.3) by glass fibers, iii) HSC lightly confined (i.e., flu,a/f'co ≤ 0.2) by carbon fibers, and iv) HSC lightly confined by aramid fibers. Additional experimental studies are required on these segments of the database before they can be used reliably for design and modeling purposes.

SVR-RSM: a hybrid heuristic method for modeling monthly pan evaporation.

In the present study, a hybrid intelligent model called SVR_RSM, which was extracted using response surface method (RSM) combined by the support vector regression (SVR) approaches was applied for predicting monthly pan evaporation (Epan). This method is established based on two basic calibrating process using RSM and SVR. In the first process, an input data group with two different input variables are used to calibrate the RSM; hence, the calibrating data by RSM in the first process are applied as input database for calibrating the SVR in the second process. Results obtained using the proposed SVR_RSM was compared with those obtained using the RSM, SVR, and the well-known multilayer perceptron neural network (MLPNN) models. Climatic variables including maximum and minimum temperatures (Tmax, Tmin), wind speed (U2), and relative humidity (H%), and the periodicity represented by the month number (α) were selected for predicting the monthly Epan measured with the standard class A evaporation pan. Data was collected at six climatic stations located at the northern East of Algeria. The performances of the proposed models were compared using the RMSE, MAE, modified index of agreement (d), coefficient of correlation (R), and modified Nash and Sutcliffe efficiency (NSE). Using various input combination, the results show that the hybrid SVR_RSM model performed better than all the proposed models. Overall, better accuracy was observed when the model contained the periodicity (α), and it was demonstrated that the best accuracy was obtained using only Tmax and Tmin, coupled with the periodicity.

PSO-BP Neural Network-Based Strain Prediction of Wind Turbine Blades.

The full-scale static testing of wind turbine blades is an effective means to verify the accuracy and rationality of the blade design, and it is an indispensable part in the blade certification process. In the full-scale static experiments, the strain of the wind turbine blade is related to the applied loads, loading positions, stiffness, deflection, and other factors. At present, researches focus on the analysis of blade failure causes, blade load-bearing capacity, and parameter measurement methods in addition to the correlation analysis between the strain and the applied loads primarily. However, they neglect the loading positions and blade displacements. The correlation among the strain and applied loads, loading positions, displacements, etc. is nonlinear; besides that, the number of design variables is numerous, and thus the calculation and prediction of the blade strain are quite complicated and difficult using traditional numerical methods. Moreover, in full-scale static testing, the number of measuring points and strain gauges are limited, so the test data have insufficient significance to the calibration of the blade design. This paper has performed a study on the new strain prediction method by introducing intelligent algorithms. Back propagation neural network (BPNN) improved by Particle Swarm Optimization (PSO) has significant advantages in dealing with non-linear fitting and multi-input parameters. Models based on BPNN improved by PSO (PSO-BPNN) have better robustness and accuracy. Based on the advantages of the neural network in dealing with complex problems, a strain-predictive PSO-BPNN model for full-scale static experiment of a certain wind turbine blade was established. In addition, the strain values for the unmeasured points were predicted. The accuracy of the PSO-BPNN prediction model was verified by comparing with the BPNN model and the simulation test. Both the applicability and usability of strain-predictive neural network models were verified by comparing the prediction results with simulation outcomes. The comparison results show that PSO-BPNN can be utilized to predict the strain of unmeasured points of wind turbine blades during static testing, and this provides more data for characteristic structural parameters calculation.

Advanced Simulation Tools Applied to Materials Development and Design Predictions.

This thematic issue on advanced simulation tools applied to materials development and design predictions gathers selected extended papers related to power generation systems, presented at the XIX International Colloquium on Mechanical Fatigue of Metals (ICMFM XIX) organized at University of Porto, Portugal, in 2018. Guest editors express special thanks to all contributors for the success of this special issue-authors, reviewers, and journal staff.

A New Energy-Critical Plane Damage Parameter for Multiaxial Fatigue Life Prediction of Turbine Blades.

As one of fracture critical components of an aircraft engine, accurate life prediction of a turbine blade to disk attachment is significant for ensuring the engine structural integrity and reliability. Fatigue failure of a turbine blade is often caused under multiaxial cyclic loadings at high temperatures. In this paper, considering different failure types, a new energy-critical plane damage parameter is proposed for multiaxial fatigue life prediction, and no extra fitted material constants will be needed for practical applications. Moreover, three multiaxial models with maximum damage parameters on the critical plane are evaluated under tension-compression and tension-torsion loadings. Experimental data of GH4169 under proportional and non-proportional fatigue loadings and a case study of a turbine disk-blade contact system are introduced for model validation. Results show that model predictions by Wang-Brown (WB) and Fatemi-Socie (FS) models with maximum damage parameters are conservative and acceptable. For the turbine disk-blade contact system, both of the proposed damage parameters and Smith-Watson-Topper (SWT) model show reasonably acceptable correlations with its field number of flight cycles. However, life estimations of the turbine blade reveal that the definition of the maximum damage parameter is not reasonable for the WB model but effective for both the FS and SWT models.

A Combined High and Low Cycle Fatigue Model for Life Prediction of Turbine Blades.

Combined high and low cycle fatigue (CCF) generally induces the failure of aircraft gas turbine attachments. Based on the aero-engine load spectrum, accurate assessment of fatigue damage due to the interaction of high cycle fatigue (HCF) resulting from high frequency vibrations and low cycle fatigue (LCF) from ground-air-ground engine cycles is of critical importance for ensuring structural integrity of engine components, like turbine blades. In this paper, the influence of combined damage accumulation on the expected CCF life are investigated for turbine blades. The CCF behavior of a turbine blade is usually studied by testing with four load-controlled parameters, including high cycle stress amplitude and frequency, and low cycle stress amplitude and frequency. According to this, a new damage accumulation model is proposed based on Miner's rule to consider the coupled damage due to HCF-LCF interaction by introducing the four load parameters. Five experimental datasets of turbine blade alloys and turbine blades were introduced for model validation and comparison between the proposed Miner, Manson-Halford, and Trufyakov-Kovalchuk models. Results show that the proposed model provides more accurate predictions than others with lower mean and standard deviation values of model prediction errors.

Multiaxial Fatigue Damage Parameter and Life Prediction without Any Additional Material Constants.

Based on the critical plane approach, a simple and efficient multiaxial fatigue damage parameter with no additional material constants is proposed for life prediction under uniaxial/multiaxial proportional and/or non-proportional loadings for titanium alloy TC4 and nickel-based superalloy GH4169. Moreover, two modified Ince-Glinka fatigue damage parameters are put forward and evaluated under different load paths. Results show that the generalized strain amplitude model provides less accurate life predictions in the high cycle life regime and is better for life prediction in the low cycle life regime; however, the generalized strain energy model is relatively better for high cycle life prediction and is conservative for low cycle life prediction under multiaxial loadings. In addition, the Fatemi-Socie model is introduced for model comparison and its additional material parameter k is found to not be a constant and its usage is discussed. Finally, model comparison and prediction error analysis are used to illustrate the superiority of the proposed damage parameter in multiaxial fatigue life prediction of the two aviation alloys under various loadings.

A modified nonlinear damage accumulation model for fatigue life prediction considering load interaction effects.

Many structures are subjected to variable amplitude loading in engineering practice. The foundation of fatigue life prediction under variable amplitude loading is how to deal with the fatigue damage accumulation. A nonlinear fatigue damage accumulation model to consider the effects of load sequences was proposed in earlier literature, but the model cannot consider the load interaction effects, and sometimes it makes a major error. A modified nonlinear damage accumulation model is proposed in this paper to account for the load interaction effects. Experimental data of two metallic materials are used to validate the proposed model. The agreement between the model prediction and experimental data is observed, and the predictions by proposed model are more possibly in accordance with experimental data than that by primary model and Miner's rule. Comparison between the predicted cumulative damage by the proposed model and an existing model shows that the proposed model predictions can meet the accuracy requirement of the engineering project and it can be used to predict the fatigue life of welded aluminum alloy joint of Electric Multiple Units (EMU); meanwhile, the accuracy of approximation can be obtained from the proposed model though more simple computing process and less material parameters calling for extensive testing than the existing model.