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Results show data-only models underperform and linear damage yields limited gains, while the proposed model improves accuracy, applicability, and quantitative tracking of damage evolution versus PINNs based on M-H, Pavlou, and improved M-H models.",{"@graph":14,"@context":72},[15,34,55],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/research-report/","Research & 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to Fatigue Life Prediction Under Multi-Level Loads  \nYou Zhao1 | Zhang Dang1,2  | Guoqian Wei1,2,3 | Huan Xu3 | Dingkang Lyu1,3  \n1Hubei Key Laboratory of Mechanical Transmission and Manufacturing Engineering, Wuhan University of Science and Technology, Wuhan, China | 2Key Laboratory of Metallurgical Equipment and Control Technology, Wuhan University of Science and Technology, Wuhan, China | 3Precision Manufacturing Institute, Wuhan University of Science and Technology, Wuhan, China  \nCorrespondence: Zhang Dang ([dangzhang@wust.edu.cn](dangzhang@wust.edu.cn))  \nReceived: 8 May 2026 | Revised: 25 July 2026 | Accepted: 20 August 2026  \nKeywords: load interactions | multi-level loads | physics-informed neural network | remaining life prediction  \nABSTRACT  \nA fatigue life prediction model under multi-level loading was developed to address reduced prediction accuracy associated with load sequence effects and load interactions. First, an improved nonlinear damage accumulation model was proposed based on the Pavlou damage accumulation framework. It was then embedded in the loss function of an artificial neural network to construct a physics-informed neural network (PINN) for fatigue test data. A data structure termed “Former-Preceding Inheritance/ Load-Zero Padding”(F-PI/L-ZP) was designed for the input layer to accommodate variable numbers of load levels. It was found that purely data-driven models without physical information exhibited poor accuracy, and linear damage models provided only marginal improvements. Trained using fatigue test data under loading sequences with different numbers of levels, the proposed model demonstrated higher prediction accuracy, broader applicability, and a stronger ability to quantitatively describe fatiguedamage evolution than the PINNs based on the M-H, Pavlou, and improved M-H models.  \n1 | Introduction  \nFatigue critically affects the performance and reliability of metallic materials and governs the safety and service life of structures subjected to fluctuating stresses or strains [1–3] . Statistics show that over 80% of engineering structural failures are attributed to fatigue [4], making it a pivotal issue in reliability-based design and safe operation of modern engineering structures.  \nTwo fundamental approaches for fatigue life prediction have been established: the S-N curve-based method and the LEFMbased method. Since engineering structures are frequently subjected to multi-level loading with varying stress levels, fatigue damage accumulation models are required. The most widely used damage-accumulation rule was proposed by Palmgren [5] and later popularized by Miner [6] . It defines fatigue damage as the ratio of the applied number of cycles to the corresponding fatigue life, with the total damage obtained by linear  \nsummation. This model has been adopted by numerous industry standards and design codes, such as BS7608:2014 [7], DNVGLRP-C203:2016 [8], and EN 1993-1-9:2005 [9] . However, the Miner model often yields fatigue life predictions that deviate significantly from experimental results because it neglects loadsequence effects and interactions among loading blocks [10] .  \nThe linear nature of the Miner model limits its handling of load sequencing issues, prompting the development of various nonlinear damage accumulation models, such as the Subramanyan model [11], the M-H model [12], the Aeran model [13], and the Rege model [14] . Recently, Pavlou integrated existing concepts of equivalent damage curves and proposed a general nonlinear damage accumulation framework based on the damage envelope domain [15], which describes damage evolution by tracking damage points within the region bounded by the S-N curve and coordinate axes. With few parameters, ease of implementation, and broad applicability, this framework is regarded as a  \n© 2026 John Wiley & Sons Ltd.  \nAll r","cbCaigIIwfJVaTU0","https://ap.wps.com/l/cbCaigIIwfJVaTU0","pdf",3518976,16,"English","# Introduction\n## Fatigue life prediction background\n## Damage accumulation rules: Miner and nonlinear alternatives\n## Pavlou framework and its limitations\n## Load interaction factor and generalizability","[{\"question\":\"What problem does the proposed model address in fatigue life prediction?\",\"answer\":\"It addresses reduced prediction accuracy caused by load sequence effects and interactions among multi-level loading blocks.\"},{\"question\":\"How is the physics-informed neural network constructed?\",\"answer\":\"An improved nonlinear damage accumulation model based on the Pavlou framework is embedded into the neural network loss function, and the PINN is trained on fatigue test data.\"},{\"question\":\"What is the role of the F-PI/L-ZP input structure?\",\"answer\":\"F-PI/L-ZP is designed for the input layer to accommodate variable numbers of load levels in the loading history.\"}]","A Physics-Informed Neural Network Approach to Fatigue Life Prediction Under Multi-Level Loads | PDF"]