Transformer‐Based Remaining Fatigue Life Prediction for Steel Springs of Urban Train via Data‐Driven

In the present and the next chapter, an approach is developed to account the stress gradient effect on fatigue life of springs. The applied method of the analytical description is based on two steps. The first step provides the description of fatigue life of the homogeneously stressed material subjected to the cyclic load. This problem is studied in this chapter. Common methods for the estimation of fatigue life, based on Goodman and Haigh diagrams, stress-life and strain-life approaches, are briefly summarized. More attention is paid to different method of fatigue analysis, which is describes the crack growths per cycle. The expressions for spring length over the number of cycles are derived. The second step uses the weak-link concept for the non-homogeneously loaded structural elements. The estimation of the fatigue life utilizes the closed-form solutions for fatigue crack propagation from this chapter. The weak-link is applied for the evaluation of fatigue life of helical spring in Chap. 9.

Article history: Received 6 January, 2015 Accepted 10 May 2015 Available online 12 May 2015 There are literally several studies accomplished to predict the fatigue life of leaf springs but estimation of fatigue life of a parabolic leaf spring by using CAE tools has not yet been executed in the past. Parabolic spring is an important component in a vehicle suspension system. It needs to have excellent fatigue life and in today’s scenario manufacturers rely on constant loading fatigue analysis. The objective of this work is to perform the fatigue analysis of parabolic leaf spring by three different methods where CAE analysis is performed to observe the distribution of stress fatigue life and damage using Goodman approach. In this work, fatigue life of the parabolic leaf spring is determined as per SAE spring design manual and experimentally by testing on full scale fatigue testing machine. ANSYS is used for CAE solution for the prediction of leaf springs fatigue life considering stress theory. The fatigue life estimated by all three modes is then compared for the purpose of validation. The methodology used in this paper brings a practical approach to the professionals in the industries who are engaged for design of mechanical components. © 2015 Growing Science Ltd. All rights reserved.

This study presents establishment of multiple input prediction model for automotive coil spring fatigue life estimation to shorten automotive suspension design process. Automotive suspension design is a lengthy work where any changes of the design lead to repetition of the entire process. It was hypothesised that the established model could be used to predict the spring design fatigue life without using any strain measurements. To initiate this model establishment, five sets of strain and acceleration measurement across different road conditions were collected and used for validations. To include spring stiffness as a parameter, a quarter car model was generated to obtain the force time histories from spring and vertical vibration of vehicle mass. In addition, artificial road profiles of road classes “A” to “D” were also generated for the quarter car simulation. Through adjusting the spring stiffness in the quarter car model, the spring and vehicle responses were varied. The simulated force time histories were used to predict springs’ fatigue life while acceleration time histories were used to calculate ISO 2631 ride-related vertical vibration. Subsequently, multiple linear regression approach was applied to determine the relationship between vehicle body frequency, ISO 2631 ride-related vertical vibration and spring fatigue life. The obtained regression had shown significance to the spring fatigue life with coefficient of determination of 0.8320. Reciprocally, multiple linear regression models were also used to predict the ISO 2631 ride-related vertical vibration with a coefficient of determination at 0.8810 and mean squared error values below 0.3430. To optimise the prediction results, artificial neural network was trained for the fatigue and vibration prediction purposes. The architectures of the artificial neural network were designed in terms of number of neurons and hidden layers to achieve a higher coefficient of determination of 0.9926 and lower mean squared error of 0.0824. For vibration prediction, the vehicle body frequency and spring fatigue life has shown a significant coefficient of determination to the ISO 2631 weighted vertical vibration, reaching 0.9579 with mean squared error of 0.0004. Based on the experimental strain and acceleration results, the predicted fatigue lives of multiple linear regression models were correlated well with the experimental results with coefficient of determination value of 0.9275. Meanwhile, the maximum difference of vibration prediction to experimental value using multiple linear regression models was only 18%. For artificial neural network predictions, the fatigue lives were mostly distributed within 1:2 or 2:1 life correlation and vibration prediction results were within 12%. For a good prediction, the target correlation value was above 0.80 to demonstrate a good fitted curve and the difference below 20%. The trained artificial neural network has shown outstanding capability in fatigue life or ride-related vertical vibration predictions. In this research, the main novelty was the trained artificial neural network for spring fatigue life or ride-related vertical vibration predictions which serve to reduce some procedures of automotive suspension design. The outcome of this study can be used to provide a new knowledge towards the field of fatigue research as well as vehicle ride dynamics. This research contributes to automotive industries especially in suspension spring design where the analysis of fatigue and ride-related vibration are provided.

As a critical issue of diagnostics and health management (PHM), health indicator (HI) construction aims to describe the degradation process of bearings and can provide essential support of domain knowledge for early fault detection and remaining useful life prediction. In recent years, various deep neural networks, with end-to-end modeling capability, have been successfully applied to the HI construction for rolling bearings. In small-sample environment, however, the degradation features would not be extracted well by deep learning techniques, which may raise insufficient tendency and monotonicity characteristics in the obtained HI sequence. To address this concern, this paper proposes a HI construction method based on wavelet scattering network (WSN) and makes an empirical evaluation from frequency perspective. First, degradation features in different frequency bands are extracted from vibration signals by using WSN to expand the feature space with different scales and orientations. Second, the frequency band with the optimal scale and orientation parameters is selected by calculating the dynamic time wrapping (DTW) distance between the feature sequences of each frequency band and the root mean square (RMS) sequence. With the feature subset from the determined frequency band, the HI sequence can be built by means of principal component analysis (PCA). Experimental results on the IEEE PHM Challenge 2012 bearing dataset show that the proposed method can work well with only a small amount of bearing whole-life data in obtaining the HI sequences with high monotonicity and correlation characteristics. More interestingly, the critical frequency band whose information supports decisively the HI construction can be clarified, raising interpretability in a frequency sense and enhancing the credibility of the obtained HI sequence as well.

Rolling bearings are some of the most crucial components in rotating machinery systems. Rolling bearing failure may cause substantial economic losses and even endanger operator lives. Therefore, the accurate remaining useful life (RUL) prediction of rolling bearings is of tremendous research importance. Health indicator (HI) construction is the critical step in the data-driven RUL prediction approach. However, existing HI construction methods often require extraction of time-frequency domain features using prior knowledge while artificially determining the failure threshold and do not make full use of sensor information. To address the above issues, this paper proposes an end-to-end HI construction method called a multi-scale convolutional autoencoder (MSCAE) and uses LSTM neural networks for RUL prediction. MSCAE consists of three convolutional autoencoders with different convolutional kernel sizes in parallel, which can fully exploit the global and local information of the vibration signals. First, the raw vibration data and labels are input into MSCAE, and then, MSCAE is trained by minimizing the composite loss function. After that, the vibration data of the test bearings are fed into the trained MSCAE to extract HI. Finally, RUL prediction is performed using the LSTM neural network. The superiority of the HI extracted by MSCAE was verified using the PHM2012 challenge dataset. Compared to state-of-the-art HI construction methods, RUL prediction using MSCAE-extracted HI has the highest prediction accuracy.

In this study, the board level solder joint reliability analysis and fatigue life prediction of dual-row QFN package are carried out. The effects of solder constitutive model and finite element (FE) model on solder fatigue life are studied. Three different constitutive models of SnAgCu lead-free solder including viscoplastic Anand model, steady-state creep hyperbolic sine model and double power law model are implemented. In addition, three FE models including full 3D-Quarter model, 3D-Quarter/Octant model with constraint equation (CE) technique are used. The volume-averaged method is used for accumulated inelastic strain energy density calculation. Zhu's energy based fatigue model for QFN package is taken to predict fatigue life. The FE modeling results show that the critical solder joint is at the package corner and crack is likely to occur along lead and solder interface. The maximum accumulated inelastic strain energy are located at top layer elements of critical solder joint for all solder constitutive models and FE models. The predicted fatigue life of dual-row QFN package calculated from Anand model is slightly higher than that from the other two models. The predicted fatigue life obtained from different FE models have almost the same value, which indicating FE model with the CE technique can well be applied for fatigue life prediction.

Fatigue phenomenon is one of the main causes of parabolic leaf spring failure. Therefore, fatigue life assessment and prediction represent an important aspect during parabolic leaf spring design stage. Nevertheless, the estimation of fatigue life is usually affected by many inherent uncertainties which must be considered in a fatigue design approach. In this work, a stochastic approach based on Latin hypercube simulation method has been performed to predict the fatigue life of parabolic leaf spring. The strain based approach and Morrow fatigue criterion have been used to compute the number of cycles to failure. The proposed approach has been applied on a finite element and a response surface model of parabolic leaf spring. The dispersion of geometrical dimensions, materials properties and cyclic loading parameters have been taken into consideration. The number of cycles to failure distribution has been presented and characterized. The effects of probabilistic variables on the fatigue life results have been studied in order to enhance the fatigue behavior of parabolic leaf spring.

To improve the accuracy of our previous bearing ensemble remaining useful life (RUL) prediction model using the genetic algorithm (GA), support vector regression, and the Weibull proportional hazard model (WPHM) (see Qiu et al (2020 Measurement 150 107097)), we proposed a more practical health indicator (HI) construction methodology for bearing ensemble RUL prediction. A weighted coefficient determination method for four prognostic metrics-monotonicity, robustness, trendability, and consistency-was proposed to select sensitive health features accurately using the analytic hierarchy process. The selected sensitive health features were fused through isometric feature mapping (ISOMAP), and differential evolution (DE) was employed to replace GA for computing the optimal weight coefficients of each input fused feature. One-dimensional HI was constructed by multiplying each input fused feature with the corresponding optimal weight coefficient, and RUL prediction was implemented through an extreme learning machine (ELM) and WPHM. The accuracy and effectiveness of the proposed method were validated by a bearing experiment. The results show that HI construction with ISOMAP-DE has achieved the best performance, and the proposed ELM-WPHM model is compared with BP-WPHM, SVM-WPHM, LSTM-WPHM, and DLSTM-WPHM in terms of RMSE criteria. The minimum error and training time appear in ELM-WPHM, indicating the superiority of the proposed bearing ensemble RUL prediction model.

Unsupervised health indicator construction by a new Gaussian-student’s t-distribution mixture model and its application

This paper proposes a new technique for the construction of a concrete-beam health indicator based on the Kullback–Leibler divergence (KLD) and deep learning. Health indicator (HI) construction is a vital part of remaining useful lifetime (RUL) approaches for monitoring the health of concrete structures. Through the construction of a HI, the deterioration process can be processed and portrayed so that it can be forwarded to a prediction module for RUL prognosis. The degradation progression and failure can be identified by predicting the RUL based on the situation of the current specimen; as a result, maintenance can be planned to reduce safety risks, reduce financial costs, and prolong the specimen’s useful lifetime. The portrayal of deterioration through HI construction from raw acoustic emission (AE) data is performed using a deep neural network (DNN), whose parameters are obtained by pretraining and fine tuning using a stack autoencoder (SAE). Kullback–Leibler divergence, which is calculated between a reference normal-conditioned signal and a current unknown signal, was used to represent the deterioration process of concrete structures, which has not been investigated for the concrete beams so far. The DNN-based constructor then learns to generate HI from raw data with KLD values as the training label. The HI construction result was evaluated with run-to-fail test data of concrete specimens with two measurements: fitness analysis of the construction result and RUL prognosis. The results confirm the reliability of KLD in portraying the deterioration process, showing a large improvement in comparison to other methods. In addition, this method requires no adept knowledge of the nature of the AE or the system fault, which is more favorable than model-based approaches where this level of expertise is compulsory. Furthermore, AE offers in-service monitoring, allowing the RUL prognosis task to be performed without disrupting the specimen’s work.

A health indicator enabling both first predicting time detection and remaining useful life prediction: Application to rotating machinery

While the fatigue behaviours (including fatigue life predictions) of lead-free solder joints have been extensively researched in the last 15 years, these are not adequately compared and benchmarked for different lead-free solders that are being used. As more and more fatigue properties of lead-free solders are becoming available, it is also critical to know how fatigue behaviours differ under different mathematical models. This paper addresses the challenges and presents a comparative study of fatigue behaviours of various mainstream lead-free Sn-Ag-Cu (SAC) solders and benchmarked those with lead-based eutectic solder. Creep-induced fatigue and fatigue life of lead-based eutectic Sn63Pb37 and four lead-free SAC solder alloys: SAC305, SAC387, SAC396 and SAC405 are analysed through simulation studies. The Anand model is used to simulate the inelastic deformation behaviour of the solder joints under accelerated thermal cycling (ATC). It unifies the creep and rate-independent plastic behaviour and it is used to predict the complex stress-strain relationship of solders under different temperatures and strain rates, which are required in the prediction of fatigue life using the fatigue life models such as Engelmaier, Coffin-Mason and Solomon as the basis of our comparison. The ATC was carried out using temperature range from -40°C to 150°C. The fatigue damage propagation is determined with finite element (FE) simulation, which allows virtual prototyping in the design process of electronics devices. The simulation was carried out on a BGA (36 balls, 6 × 6 matrix) mounted onto Cu padded substrate. Results are analysed for plastic strain, Von mises stress, strain energy density, and stress-strain hysteresis loop. The simulation results show that the fatigue behaviours of lead-based eutectic Sn63Pb37 solder is comparable to those of lead-free SAC solders. Among the four SAC solders, SAC387 consistently produced higher plastic strain, strain energy and stress than the other solders. The fatigue life's estimation of the solder joint was investigated using Engelmaier, Coffin-Manson, and Solomon models. Results obtained show that SAC405 has the highest fatigue life (25.7, 21.1 and 19.2 years) followed by SAC396 (18.7, 20.3 and 17.9 years) and SAC305 (15.2, 13.6 and 16.2 years) solder alloys respectively. Predicting the fatigue life of these solder joints averts problems in electronics design for reliability and quality, which if not taken care of, may result in lost revenue. Predictive fatigue analysis can also considerably reduce premature failure, and modern analysis technique such as one used in this research is progressively helping to provide comprehensive product life expectancy data.

This comprehensive new ASTM publication examines state-of-the-art multiaxial testing techniques and methods for characterizing the fatigue and deformation behaviors of engineering materials. 25 analytical, peer-reviewed papers, written by experts from academia, industry, and government, are divided into the following sections: Multiaxial Strength of Materials--addresses multiaxial strength, stress, and failure modes of materials. Multiaxial Deformation of Materials--investigates constitutive relationships and deformation behavior of materials under multiaxial loading conditions. Fatigue Life Prediction under Generic Multiaxial Loads--examines the challenging task of estimating fatigue life under general multiaxial loads. Fatigue Life Prediction under Specific Multiaxial Loads--describes biaxial and multiaxial fatigue and life estimation under combinations of cyclic loading conditions, such as axial tension/compression, bending, and torsion. Multiaxial Fatigue Life and Crack Growth Estimation--covers crack growth monitoring under cyclic mulitaxial loading conditions and determination of fatigue life. Multiaxial Experimental Techniques--explores state-of-the-art experimental methods to generate mulitaxial deformation and fatigue data to develop and verify both constitutive models used to describe the flow behavior of materials and fatigue life estimation models. The International Standards contained in the Handbook set out the practical methodology which a user requires in order to be able to process and interpret, statistically, testing and inspection results whenever goods are assessed from a sample. This fifth edition of the ISO Standards Handbook Statistical Methods for Quality Control is published in two volumes: Volume 1 includes standards on vocabulary and symbols, and the two basic tools used in sampling throughout the world -- sampling by attributes and by variables. Volume 2 presents interpretation of statistical data, process control charts, the newly revised and expanded standards on the precision of measurement methods. The volumes compliment the ISO 9000 Compendium, containing International Standards for quality management, and ISO/IEC Compendium of Conformity Assessment Documents, containing guides on the testing, inspection and certification of products, processes and services, and on the assessment of quality systems, testing laboratories, inspection bodies, certification bodies and their operation and acceptance.

Description This comprehensive new ASTM publication examines state-of-the-art multiaxial testing techniques and methods for characterizing the fatigue and deformation behaviors of engineering materials. 25 analytical, peer-reviewed papers, written by experts from academia, industry, and government, are divided into the following sections: Multiaxial Strength of Materials--addresses multiaxial strength, stress, and failure modes of materials. Multiaxial Deformation of Materials--investigates constitutive relationships and deformation behavior of materials under multiaxial loading conditions. Fatigue Life Prediction under Generic Multiaxial Loads--examines the challenging task of estimating fatigue life under general multiaxial loads. Fatigue Life Prediction under Specific Multiaxial Loads--describes biaxial and multiaxial fatigue and life estimation under combinations of cyclic loading conditions, such as axial tension/compression, bending, and torsion. Multiaxial Fatigue Life and Crack Growth Estimation--covers crack growth monitoring under cyclic mulitaxial loading conditions and determination of fatigue life. Multiaxial Experimental Techniques--explores state-of-the-art experimental methods to generate mulitaxial deformation and fatigue data to develop and verify both constitutive models used to describe the flow behavior of materials and fatigue life estimation models.

Effective health indicator (HI) construction can help equipment managers detect the abnormal state of rotating machinery quickly. However, although the current deep learning-based HI construction methods have good life prediction value, most of them lose the ability to detect device anomalies and little work has been done on model interpretability. Therefore, an interpretable HI construction method based on semi-supervised autoencoder (AE) latent space variance maximization (SSALSVM) was proposed to monitor the health status of bearings. In order to fully excavate degradation features inside the device and make the model focus on the encoding process, a deep convolutional neural network (DCNN) is used as the encoding layer, while only a layer of fully-connected layer is used as the decoding layer. In addition, to enable the latent space to capture the device early degradation point (EDP) successfully, an auxiliary layer is added to the output of the encoder layer. Simultaneously, for improving the sensitivity of the indicator to capture equipment abnormal state and highlight the difference between equipment health state and degradation state, the constraint of variance maximization is added into the latent space. The model optimizing process was presented by observing the projected variance of the test set in latent space of each epoch model. The validity of the proposed HI was verified by comparison experiments on two datasets.