희소 센서 데이터 기반 비선형 구조물의 동적 응답 업데이트 기법 개발 및 검증에 관한 연구 = A Study on the Development and Validation of a Dynamic Response Updating Method for Nonlinear Structures Using Sparse Sensor Data

다국어 초록 (Multilingual Abstract)

Accurate prediction of nonlinear structural responses is important for structural design, performance evaluation, and structural health management. Although reduced-order and data-driven models can reduce the computational cost associated with high-fidelity finite element analysis, prediction errors may persist because of model mismatch and approximation errors. This study proposes non-intrusive response correction procedures that directly correct previously generated full-field dynamic responses using sparse sensor data without modifying the governing equations, system matrices, or internal parameters of the underlying prediction models.
Three correction procedures are developed in this study. First, a method based on the System Equivalent Reduction Expansion Process （SEREP） expands limited sensor responses to the full degree-of-freedom space to construct full-field residuals and estimates a full-field correction operator from the relationship between the residuals and the predicted reduced coordinates. Second, a sensor-residual-based reduced-space method transforms sensor residuals into low-dimensional correction coefficients, estimates a reduced-space correction operator from the relationship between the correction coefficients and the predicted reduced coordinates, and then reconstructs a full-field correction using a correction basis. Third, the reduced-space method is extended to sequential interval-wise correction. The entire prediction interval is divided into consecutive update intervals, and a correction operator is independently estimated using only the sensor data acquired within each interval, thereby enabling block-wise quasi-real-time correction.
The proposed procedures are validated using a two-dimensional cantilever beam and a three-dimensional box-shaped cantilever beam exhibiting geometrically nonlinear behavior. High-fidelity nonlinear finite element responses are used as reference responses, and displacement responses at selected locations are treated as virtual sensor measurements. Correction performance is evaluated in terms of full-field relative error, displacement time histories, deformed shapes, and robustness to sensor noise.
For the SEREP-based method, the relative errors of the two-dimensional and three-dimensional examples decrease from 33.1% and 27.7% to 0.012% and 0.71%, respectively. The sensor-residual-based reduced-space method reduces the relative error of the three-dimensional example from 22.1% to 0.58%. For the sequential correction method, the relative errors of the two-dimensional and three-dimensional examples decrease from 81.0% and 106.2% to approximately 0.0049% and 1.2%, respectively. The average correction times per update interval are approximately 0.03 s and 0.16 s, which are shorter than the corresponding update-interval lengths of 1.0 s and 0.2 s. Although increasing sensor noise reduces correction accuracy, the corrected responses remain more accurate than the original predictions under all examined noise conditions.
These results demonstrate that sparse local sensor measurements can be transformed into full-field correction information for unmeasured degrees of freedom. The proposed non-intrusive output correction procedures improve the accuracy of predicted nonlinear structural responses without modifying the underlying prediction models or repeatedly performing nonlinear finite element analyses and are applicable to interval-wise quasi-real-time response correction.

목차 (Table of Contents)

• 제1장 서 론 1
• 제1절 연구 배경 1
• 제2절 모델 및 응답 불일치 보정을 위한 기존 연구와 한계 4
• 제3절 연구 목적 및 구성 9
• 제2장 이론적 배경 12
• 제1절 저차원 구조 응답 표현 12
• 제2절 센서 기반 전장 응답 추정 13
• 제3절 센서 기반 예측 응답 보정 15
• 제3장 SEREP 기반 전장 잔차 보정 방법 17
• 제1절 연구 방법 19
• 1. POD 기반 축소 모델의 구성 19
• 2. 트랜스포머 시계열 예측 모델 22
• 3. 전장 잔차 기반 보정 연산자 추정 26
• 제2절 수치 예제 31
• 1. 2차원 외팔보 32
• 2. 3차원 박스형 외팔보 41
• 제3절 소결 50
• 제4장 센서 잔차 기반 축소 공간 보정 방법 52
• 제1절 연구 방법 53
• 1. 이차 비선형 시스템 기반 응답 예측 53
• 2. 센서 잔차 기반 응답 보정 연산자 추정 56
• 제2절 수치 예제 61
• 1. 2차원 외팔보 62
• 2. 3차원 박스형 외팔보 71
• 제3절 소결 81
• 제5장 센서 잔차 기반 준실시간 응답 보정 방법 83
• 제1절 연구 방법 84
• 1. 센서 잔차 기반 순차적 보정 연산자 추정 84
• 제2절 수치 예제 90
• 1. 2차원 외팔보 91
• 2. 3차원 박스형 외팔보 102
• 제3절 소결 112
• 제6장 결 론 114
• 참 고 문 헌 117
• ABSTRACT 129