Hierarchical finite element method for the prognostic analysis of structural health monitoring
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The structural design of vehicles has become lighter but stronger because of new materials and more precise analysis of structural safety. In aerospace applications for novel lightweight structures, manufacturers design their aircraft to ensure design safety based on regulations of damage tolerance design, which assumes the existence of cracks and the ability to sustain defects until periodic maintenance. However, design regulations guide only the possibility of cracks based on standard history operation regardless of the current condition of individual aircraft. Since the individual aircraft has a unique condition of operation, the study of structural health monitoring suggests identifying any defects early as possible and taking corrective action early to minimize the operation cost and the maintenance cost. The structural health monitoring examines the current state of individual aircraft and simulates the propagation of cracks under various conditions through a computational model referred to as the digital twin, which represents the actual aircraft and plays a key role in a reliable simulation of crack propagation in structural health monitoring. Since defects or crack sizes are minuscule, the finite element of digital twin requires an extremely fine mesh, which requires enormous computation time, then a general finite element method is not suitable for analyzing the behavior of micro cracks. Therefore, this study proposes a new methodology, the hierarchical finite element method (HFEM), to solve the problem of adaptable mesh size and computation time. The HFEM first build a connection of hierarchical models in a pre-processing stage and transfer forces to hierarchical models in a post-processing stage. In the pre-processing stage of the HFEM, classes of finite element model are categorized into three levels: a micro-level, a base-level, and a system-level model. The system-level model is an entire system of a structure with an appropriate element size The HFEM first partitions the various shape and size of the component elements in the system-level model into k clusters using a K-means clustering algorithm. Each cluster center is a candidate for the base-level model, which conducts the crack simulation with fine meshes. Each candidate of the base-level model has a stress distribution map generated by six components of unit loads. In the case of composite materials, the stress map contains additional information, amplification factors, from the micro-level model by applying six components of unit loads on the candidate unit cells, which depend on fiber array types. Post-processing is the simulation of the prognosis for the digital twin with actual aerodynamic loads to predict the remaining life based on the crack propagation analysis. This study focuses on the prognosis related to the crack propagation in the base-level model of HFEM. The constituent element in the base-level model behaves individually with cellular automata rules, an effective way of simulating complex systems without central control. The simulation emerges to a stable or unstable point according to simple local operating rules and neighboring effects. This study investigates local rules and neighboring effects for the crack propagation to employ it into the crack simulation in the HFEM. Crack simulation advances the analysis by regarding an element as a dead cell if the residual strength, calculated based on the fracture mechanics, reaches a critical factor. A mathematical crack-closure model determines critical factors with a size of influence region and the effect of neighboring elements, the former of which determines its life cycle. In the virtual simulation, the digital twin, adopting the cyclic load from virtual sensors, will analyze the remaining life of the aircraft. However, the remaining life is not able to be predicted with currently acquired cyclic loads because it requires future cyclic loads. Therefore, this study proposes an inverse transport wing standard (TWIST) method to forecast the future time-series of cyclic loads based on current loads. TWIST is a spectrum generating method developed to standardize a stress spectrum of transport aircraft by using historical data of fatigue life. In this study, as an opposite way of the TWIST, acquired data from sensors that are samples of standard spectrum generates a predicted historical data. Thus, the digital twin with the stress spectrum of predicted historical data enables the prognosis of remaining life based on accumulated data. The affordability of the HFEM for the prediction of remaining life will be a turning point from inspections based on schedules to inspections based on demand approach. Further, the HFEM enables us to evaluate complex decision making for a damaged aircraft component with reliable information of the current condition.