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Neural network approaches for real-time fatigue life estimation by Surrogating the rainflow counting method

INTERNATIONAL JOURNAL OF FATIGUE 2025年 197卷

作者： Guo, Yiwen Li, Liangxing Gui, Jiabin Hu, Shurui Xi An Jiao Tong Univ State Key Lab Multiphase Flow Power Engn Xian 710049 Peoples R China

Fatigue life estimation is critical for ensuring the safety and reliability of systems under cyclic loading. Traditional rainflow counting methods require exhaustive traversal of load histories, making them computationally expensive for real-time applications. To address this issue, this present study leverages the increasing demand for efficient high-cycle fatigue (HCF) life estimation methods, combining neural network surrogate modeling with physical principles to enhance both accuracy and computational speed. The Euler neural network (ENN) and the Runge-Kutta 4th-order neural network (RK4NN) for fatigue life estimation are proposed. These approaches are validated by comparing the results of rainflow counting with wind turbine damage ratios, demonstrating the accuracy achieves errors within 15 % for over 74 % of cases in the numerical stability range. Moreover, the RK4NN displayed superior generalization and fitting capacities across varied load conditions, effectively capturing early-stage damage growth while avoiding overfitting with the mean squared error 1.99 x 10- 36. Additionally, the ENN and the RK4NN achieved the acceleration ratio of 19.53 x and 19.38 x respectively in comparison with the modified rainflow counting method (RCM). These findings underscore the practical value of the surrogate models in improving the real-time responsiveness and computational efficiency of fatigue life estimation frameworks, particularly in digital twin applications for industrial systems.

关键词： Fatigue life estimation rainflow counting method Neural network Euler iteration Runge-Kutta method

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Fatigue life prediction of the aluminum box for aircraft parts turnover based on the rainflow counting method

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JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY 2025年第5期39卷 2651-2662页

作者： Li, Guang Guo, Danfeng Deng, Yulin Zhang, Xinyu Tianjin Univ Sci & Technol Coll Light Ind Sci & Engn Tianjin 300457 Peoples R China

Aircraft parts are typically transported in metal aluminum boxes, which require a time-consuming fatigue life test to determine if their service life can meet the actual needs. However, direct prediction of the fatigue life of these boxes is challenging and costly due to their large sizes. Accordingly, an economical and intuitive fatigue life analysis method for large packaging boxes must be proposed. This study proposed an accelerated fatigue life prediction method to improve the excitation level of aircraft parts for turnover aluminum boxes. First, the stress changes at the most hazardous point of the aluminum box for aircraft parts turnover is obtained through kinetic analysis. Second, the rainflow counting method is used to count the load time course, analyze the distribution of the amplitude of stress and mean, and create the load spectra. Third, the modified P-S-N curve of the turnover aluminum box is obtained, considering the structural parameters and fatigue limit value of the turnover aluminum box. Finally, the Palmgren-Miner linear cumulative damage theory is applied to forecast the fatigue life of aluminum boxes used for airplane parts turnover. Results show that, under the 0.05 significance level, the amplitude and the mean of the stress are independent of each other, and the stress amplitude is Weibull distributed with a shape parameter of 1.04 and a scale parameter of 7.26. The average stress value has a mean of 0.06 and a standard deviation of 2.39, which is normally distributed. The Miner's rule of the fatigue life of the turnover aluminum box is predicted to be 16.4 years. The research in this study can provide an analytical method for fatigue life prediction under different transportation environments and provide a reference basis for judging the cycle life of metal packaging boxes.

关键词： Aluminum turnover box Fatigue life prediction P-S-N curve rainflow counting method Random load

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Stochastic approach of fatigue vibratory: comparison between Peak-Valley method and rainflow counting method

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REVUE DE METALLURGIE-CAHIERS D INFORMATIONS TECHNIQUES 2012年第4期109卷 217-247页

作者： Colin, B. Nexter Syst Versailles France

Stochastic approach of fatigue vibratory: comparison between Peak-Valley method and rainflow counting method. In the energy and transport industrial sectors, the mechanical structures are subjected to strong levels of dynamic stresses which largely impact the level of durability of these structures. In a context of reduction of the life cycle cost and extension of lifetime, the industrialists are led from now on to controlling well the mechanical reliability of their product. In addition, because of the stochastic nature of the dynamic loadings, the methods used are those of the fatigue vibratory, which models the modal behavior of the structure and the random processes of excitation, in the spectral domain. Of these technical considerations, this article gives a good view on the methods of calculation used in fatigue vibratory. It thus compares the methods of Peak-Valley counting (PV) with those of rainflow counting (RFC), recognized like the least conservative and thus most relevant, in term of prediction of lifetime. With regard to the Peak-Valley methods, the Rice model [S.O. Rice, Bell Systems Technical Journal 23 (1944) 282-332;24 (1945) 46-156] and Miles model [J.W. Miles, J. Aeronautical Sci. 21 (1954) 753-762], developed respectively in 1944 and 1954, are taken as reference and compared with the models rainflow counting of these last years. With this intention, the comparative study will be based in particular on the empirical approaches of Wirsching-Light [P.H. Wirsching, M.C. Light, J. Structural Division ASCE 106 (1980) 1593-1607], and semi-empirical of Dirlik [T. Dirlik, Application of computer in fatigue analysis, Ph.D. thesis, University of Warwick, 1985], developed respectively in 1980 and 1985.

关键词： Fatigue vibratory peak-valley method rainflow counting method Rice and Dirlik models durability of the structures law of Basquin random processes and lifetime

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Improved Data Processing of Loading Spectrum for Applications of rainflow counting method

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Journal of Donghua University(English Edition) 2015年第6期32卷 919-922页

作者：吕志强彭卫文黄洪钟 School of Mechatronics Engineering University of Electronic Science and Technology

The rainflow counting method is a reasonable cyclecounting procedure for fatigue life calculation and simulation testing of *** defines cycles as closed stress /strain hysteresis *** of the rainflow counting method requires a data processing of the loading spectrum,which consists of the elimination of non-peak value data points,load time histories adjustment and loop *** the data processing of the loading spectrum,if a stress point is neither the peak nor the valley,it will be identified and eliminated from the loading ***,the loading process is idealized as a single peak-valley straight *** in actually,there are polylines or nearly straight lines between peaks and valleys which can't be ***,in the process of eliminating such data points,it will produce error in method *** reduce the error produced by the traditional method itself,a new method which can well simplify the polylines in data processing of loading spectrum is proposed in this *** with the original approximation method,the proposed method has higher precision.

关键词： fatigue life rainflow counting method loading spectrum loop peaks and valleys

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A hybrid frequency-time domain life prediction method based on the critical plane theory

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FATIGUE & FRACTURE OF ENGINEERING MATERIALS & STRUCTURES 2024年第7期47卷 2351-2368页

作者： Wang, Yantian Qiu, Yuanying Li, Jing Bai, Jin Xidian Univ Sch Mechatron Engn Xian Peoples R China Xian Aerosp Prop Test Technol Inst Xian Peoples R China Xidian Univ Sch Mechatron Engn 2 South Taibai Rd Xian 710071 Peoples R China

This study proposes a multiaxial rainflow counting method to realize simultaneous counting of four-channel data. The power spectral density (PSD) expressions of stresses and strains in different planes are derived according to multiaxial theories to address the fatigue problems under random vibration loading. This study takes the plane with maximum variance of shear strain PSD as the critical plane and proposes a hybrid frequency-time domain life prediction method for calculating the life under random vibration loading in combination with the proposed new multiaxial rainflow counting method. Both the feasibilities of the proposed multiaxial rainflow counting method and hybrid frequency-time domain life prediction method are verified by using the multiaxial fatigue experimental results of 6061-T6 and 7075-T6 aluminum alloys under random loading. Meanwhile, the calculation results and efficiencies of the proposed life prediction method are summarized, and the prediction effects of the different multiaxial fatigue models are evaluated, and different rainflow counting methods are compared. A novel four-channel multiaxial rainflow counting method is proposed. A novel hybrid frequency-time domain life prediction method is proposed. Validities of the proposed methods are confirmed by the fatigue life prediction cases. Different life prediction methods and multiaxial fatigue models are evaluated.

关键词： critical plane method life prediction multiaxial fatigue power spectral density rainflow counting method

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DESIGN EVALUATION method FOR RANDOM FATIGUE BASED ON SPECTRUM CHARACTERISTICS

DESIGN EVALUATION METHOD FOR RANDOM FATIGUE BASED ON SPECTRU...

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Pressure Vessels and Piping Conference of the American-Society-of-Mechanical-Engineers

作者： Sakai, Shinsuke Okajima, Satoshi Izumi, Satoshi Kasahara, Naoto Univ Tokyo Tokyo 1138654 Japan

ISBN: (纸本)9780791843666

This paper shows the new design approach for random fatigue evaluation based on spectral characteristics. Fatigue damage under random loading is usually evaluated according to the following steps: I. decomposition of random wave to stress amplitude using the rainflow cycle counting method (RFC) 2. evaluation of fatigue damage using Palmgren-Miner's linear summation rule. In design process, the fluctuation of load is usually characterized through power spectral density (PSD). Therefore, the design process is expected to be generalized if the fatigue damage is directly evaluated from the PSD together with S-N diagram of the material. In fact many properties related to fatigue damage, such as distribution of extreme values, can be derived theoretically from geometrical properties of PSD. However, concerning the distribution of stress amplitude counted by RFC, it is rather difficult to derive it theoretically due to its complicated procedure. In this paper, upper bound of stress amplitude distribution is confirmed for many random waves generated by numerical simulation for many types of PSD. Expressing the upper bound distribution by closed form function using PSD characteristics leads us to the direct evaluation of fatigue damage with safety margin if the fatigue damage by particular stress amplitude is approximated using some series expansion form. Simple approximation procedure of high cycle fatigue damage for austenitic stainless steel and ferritic steel will be proposed in the paper. Finally, design evaluation procedure for the fatigue damage evaluation from PSD together with S-N diagram is summarized.

关键词： Fatigue damage Random loads Power spectral density Spectral based design rainflow counting method Level crossing counting method

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Nonlinear fatigue damage constrained topology optimization

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COMPUTER methodS IN APPLIED MECHANICS AND ENGINEERING 2024年 429卷

作者： Gu, Jinyu Chen, Zhuo Long, Kai Wang, Yingjun South China Univ Technol Natl Engn Res Ctr Novel Equipment Polymer Proc Key Lab Polymer Proc Engn Minist EducGuangdong Prov Key Lab Tech & Equipmen Guangzhou 510641 Guangdong Peoples R China South China Univ Technol Sch Mech & Automot Engn Guangzhou 510640 Peoples R China North China Elect Power Univ State Key Lab Alternate Elect Power Syst Renewable Beijing 102206 Peoples R China

In engineering applications, plenty of components are subjected to variable-amplitude cyclic loading, resulting in fatigue damage, which is one of the main forms of structural damage. While the linear damage rule has long served as a fundamental approach, its limitations necessitate advancements for more accurate fatigue life predictions. Hence, this paper introduces a pioneering method termed nonlinear fatigue damage constrained topology optimization (NFDCTO). This method integrates several key components: the rainflow counting method to evaluate the non-proportional cyclic load levels, Basquin's equation to describe the S-N curve, and Morrow's plastic work interaction rule to calculate the nonlinear cumulative damage of the structure. Consequently, we establish a mathematical model for the NFDCTO method based on these components. The incorporation of penalized damage aggregation with the P-Normal function is used to address significant constraints and singularity challenges. Furthermore, by employing the adjoint method, we derive sensitivity equations for both the objective function and fatigue constraint function concerning the design variables. Subsequently, the superiority of the NFDCTO method over traditional linear fatigue damage method were verified applying 2D L-shaped beam and simply supported structures as examples. Concurrently, bridge structures were employed to investigate the effect of the sensitivity index of the material to the history of variable amplitude stresses on the optimization results. In addition, the influence of the fatigue penalty factor on the topology optimization results was assessed using a 2D cantilever beam. Finaly, we verify the

关键词： Topology optimization Nonlinear fatigue damage rainflow counting method Non -proportional cyclic load P -normal function

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A neural network approach to the simulation of load histories by considering the influence of a sequence of rainflow load cycles

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INTERNATIONAL JOURNAL OF FATIGUE 2002年第11期24卷 1109-1125页

作者： Klemenc, J Fajdiga, M Univ Ljubljana Fac Mech Engn SI-1000 Ljubljana Slovenia

A modeller was developed that simulates random load histories by considering a statistical distribution and a sequence of load cycles that correspond to a rainflow algorithm. The random load histories are generated stepwise by putting together series of load cycles, successively predicted by the modeller. The core of the modeller is a conditional probability density function of load cycles, which is modelled by a multilayer perceptron. The theoretical foundations of the modeller and three examples of its application for the simulation of random load histories are presented in the paper. We concluded from the examples that it is possible to simulate new random load histories on the basis of the load cycles, extracted from the original load history with the rainflow method, so that the statistical distribution and the sequence of load cycles from the original load history are preserved in simulated load histories. (C) 2002 Elsevier Science Ltd. All rights reserved.

关键词： modelling of load histories rainflow counting method sequence of load cycles conditional probability density function mixture of multivariate Gaussian functions multilayer perceptron

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Fatigue life estimation under variable amplitude bending using the non-local damage parameter and multisurface plasticity model

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INTERNATIONAL JOURNAL OF FATIGUE 2011年第10期33卷 1376-1383页

作者： Karolczuk, A. Blacha, L. Opole Univ Technol PL-45271 Opole Poland

The paper presents a non-local damage parameter successfully applied to fatigue life assessment of the smooth specimens subjected to variable amplitude bending. The parameter is based on averaging the stresses over the critical plane in the material using weight function in the exponential form. Parameter of the considered weight function is identified using fatigue lives of specimens subjected to sinusoidal plane bending. The stress fields in specimens are computed taking into account non-linear kinematic hardening of the material implemented in Matlab-based algorithm. It is shown that the kinematic hardening of the material has considerable influence on the histograms of stress amplitudes under the analyzed variable loading. The stress field on the critical plane is reduced to effective stress (the non-local damage parameter) for every time variable t by the weighted averaging process. The computed history of effective stress is used by the well known damage accumulation algorithm along with two damage accumulation hypotheses (Palmgren-Miner and Serensen-Kogayev) to estimate fatigue lives. For comparison purposes, the local concept is also applied for which the calculated fatigue lives are underestimated. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Variable amplitude bending Elastic-plastic strain Kinematic hardening model of material rainflow counting method Non-local stress concept

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PRACTICAL COMPUTATION OF STATISTICAL PROPERTIES OF rainflow COUNTS

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INTERNATIONAL JOURNAL OF FATIGUE 1994年第5期16卷 306-314页

作者： OLAGNON, M IFREMER Centre de Brest BP 70 29280 Plouzané France

Some mathematical properties of the rainflow counting method were established by Rychlik. They enabled him to propose a new algorithm for rainflow counting. Implementations of this algorithm for signal analysis would show poor speed performance, but it is of utmost interest as it can be used abstractly on the statistical properties of the input sequence. The practical implementation of such derivation is discussed here, and probability density functions (PDFs) for rainflow cycles between level j and level k are derived in the simple case when peaks and troughs are chosen from known PDFs in a completely random succession. Algorithms are provided in a common practice case when the sequence is described as a Markovian process with given transition probability matrix. Sequences for which the statistical properties are inferred from the power spectral densities are also discussed. Application is made to some standard sequences from the offshore and automotive industry.

关键词： rainflow counting method rainflow COUNTS ALGORITHM FOR rainflow counting

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