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Research Article

Component-Wise NNLS Aggregation for Bridge Defect-Index Reconstruction and Extrapolation-Oriented Evaluation

부재별 NNLS 통합 기반 교량 결함도지수 외삽 평가 프로토콜 검토 및 데이터 보강 기법 검정

Chaemin Lee1
,
Yangrok Choi2
,
Jung Sik Kong3*
이 채민1
,
최 양록2
,
공 정식3*
1MS Student, School of Civil, Environmental and Architectural Engineering, Korea University, Seoul 02841, Korea
2Post-Doctoral Researcher, School of Civil, Environmental and Architectural Engineering, Korea University, Seoul 02841, Korea
3Professor, School of Civil, Environmental and Architectural Engineering, Korea University, Seoul 02841, Korea
1고려대학교 건축사회환경공학부 석사과정
2고려대학교 건축사회환경공학부 박사후연구원
3고려대학교 건축사회환경공학부 교수
*Corresponding Author
30 June 2026. pp. 13-26
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Abstract

High-defect cases are scarce in Korean highway-bridge inspection records: of 7,327 inspection rows from Korea Expressway Corporation precision-inspection data, only two exceed the grade-D defect-index threshold of 0.49, so the overall index cannot be regressed directly in the extrapolation region. We instead predict ten component defect indices with a multi-target network and combine them into the overall index using non-negative least squares (NNLS) weights fitted on the training data alone. Applied to observed components, these fixed weights reconstruct the overall index with correlation 0.886 to 0.965 across the validation, test, and extrapolation hold-out splits, their sum (0.982) matching the guideline's aggregation structure. This result represents aggregation validity rather than end-to-end prediction accuracy: once the components are themselves network-predicted, the extrapolation correlation falls to 0.68 (MAE 0.024). In facility-clustered bootstrap tests with Bonferroni correction, none of four augmentation methods reliably improved extrapolation, though a guideline-constrained diffusion model (GC-TabDDPM) showed a limited but statistically unconfirmed improvement trend.

Keywords
bridge defect index
defect-index reconstruction
extrapolation-oriented evaluation
component-wise multi-target learning
non-negative least squares
facility-level cluster bootstrap

본 연구는 한국도로공사 정밀점검･진단 데이터 7,327건으로 교량 결함도지수(Defect Index, DI)의 고결함 표본이 희소한 조건에서 부재별 재구성 및 외삽 지향 평가 문제를 다루었다. D등급 임계값(DI ≥ 0.49) 표본이 2건에 불과해 직접 회귀가 식별되기 어려우므로, 전체 1개와 부재별 10개의 총 11개 타깃을 동시 모형화한 뒤 비음수 최소제곱(Non-negative Least Squares, NNLS) 가중평균으로 전체 지수를 합성하는 부재별 분해-통합 프레임워크를 제안하였다. 훈련 데이터로만 적합한 NNLS 통합식은 검증･테스트에서 상관계수 0.886–0.952, 외삽 평가에서 0.965의 재구성 정합성을 보였으며, 가중치 합 0.982로 세부지침 가중합 구조와 정합하였다. 시설물 단위 군집 부트스트랩과 Bonferroni 다중비교 보정(유의수준 0.05/4) 하의 4종 보강 기법 검정에서 가우시안 노이즈 증강은 사전 가설과 반대로 노이즈 미적용 조건이 유의 우세였고(R2 차이 +0.194, 단측 p < 0.001), TDL과 신뢰도 기반 자기 학습 역시 가설을 지지하지 않았으며, GC-TabDDPM은 5개 시드 모두 일관된 개선 방향(Wilcoxon 단측 p = 0.03125)을 보였으나 보정 임계치 미통과로 제한적 개선 경향으로 해석하였다. 본 재구성 결과는 전 구간 외삽 예측 정확도의 직접 증거라기보다 부재-전체 결함도지수 간 통합식의 전이성과 평가 가능성을 검토한 결과로 해석되어야 한다. 동일한 NNLS 가중치를 신경망 예측 부재값에 적용한 전 구간(end-to-end) 경로의 외삽 평가 데이터 상관계수는 0.68(MAE 0.024)로, 통합식의 정합성과 예측 단계의 정확도 사이에 분명한 간극이 존재한다. 본 연구의 기여는 부재 단위 외삽을 통한 평가 경로 확보, NNLS 분해-통합 프레임워크, 시설물 단위 누설 통제 평가 프로토콜, 그리고 4종 보강 기법의 보수적 통계 검정으로 요약된다.

키워드
교량 결함도지수
결함도지수 재구성
외삽 지향 평가
부재별 다중 타깃 학습
비음수 최소제곱법
시설물 단위 군집 부트스트랩
데이터 희소성
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Information
  • Publisher :Korean Institute of Bridge and Structural Engineers
  • Publisher(Ko) :한국교량및구조공학회
  • Journal Title :Journal of Structure Research and Practice
  • Journal Title(Ko) :한국교량및구조공학회 논문집
  • Volume : 4
  • No :1
  • Pages :13-26
  • Received Date : 2026-06-17
  • Accepted Date : 2026-06-26
  • DOI :https://doi.org/10.22725/JSRP.2026.4.1.13
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