지반공학 분야에 대한 차분진화 알고리즘 적용성 분석

Analysis for Applicability of Differential Evolution Algorithm to Geotechnical Engineering Field

Abstract

역해석 수행 시 상대적으로 복잡한 공간 및 목표 설계 변수가 많은 경우, 지반공학 분야에 적용하기 위한 연구를 수행하였다. 지반공학 다변수 문제에 대한 모델로 터널 분야 및 흙막이벽체에 대해서 Sharan 공식 및 Blum 방법을 사용하였다. 최적화 방법은 크게 결정론적인 방법 및 확률론적인 방법으로 구분된다. 본 연구에서는 전자 중 모의강화법(SA), 후자 중 차분진화 알고리즘(DEA), 입자 군집 최적화 알고리즘(PSO)을 선택하여 다변수 모델을 적용해서 비교하였다. 지반공학 다변수 역해석 문제에서 결정론적인 방법은 문제가 있음을 확인하였고, 차분진화 알고리즘의 우수성을 확인하였다. DEA는 Sharan의 이론 해에 대한 문제에서 평균 3.12%, Blum 문제에 대해서 평균 2.23% 오차율을 보였고, 반복 탐색 회수도 가장 작은 것으로 파악되었다. DEA 대비해서 SA는 117.39~167.13배, PSO는 2.43~6.91배의 탐색시간이 소요되었다. 지반공학 문제의 다변수 역해석에 차분진화 알고리즘을 적용하면, 계산속도 및 정확도가 향상될 것으로 기대된다.

This study confirmed the applicability to the field of geotechnical engineering for relatively complicated space and many target design variables in back analysis. The Sharan's equation and the Blum's method were used for the tunnel field and the retaining wall as a model for the multi-variate problem of geotechnical engineering. Optimization methods are generally divided into a deterministic method and a stochastic method. In this study, Simulated Annealing Method (SA) was selected as a deterministic method and Differential Evolution Algorithm (DEA) and Particle Swarm Optimization Method (PSO) were selected as stochastic methods. The three selected optimization methods were compared by applying a multi-variate model. The problem of deterministic method has been confirmed in the multi-variate back analysis of geotechnical engineering, and the superiority of DEA can be confirmed. DEA showed an average error rate of 3.12% for Sharan's solution and 2.23% for Blum's problem. The iteration number of DEA was confirmed to be smaller than the other two optimization methods. SA was confirmed to be 117.39~167.13 times higher than DEA and PSO was confirmed to be 2.43~6.91 times higher than DEA. Applying a DEA to the multi-variate back analysis of geotechnical problems can be expected to improve computational speed and accuracy.

Fig. 1. Prediction of theoretical displacement solution on tunnel excavation surface for rock mass (Sharan, 2003)

Fig. 2. Blum’s schematization (Verruijt, 2001)

Fig. 3. Flowchart for using three different optimization methods for back analysis

Fig. 4. The comparison between error rate number of target variables for PSO, SA and DEA (Sharan’s solution)

Fig. 5. The comparison between number of iteration and target variables for PSO, SA and DEA (Sharan’s solution)

Fig. 6. The comparison between error rate and number of target variables for PSO, SA and DEA (Blum’s method)

Fig. 7. The comparison between number of iteration and target variables for PSO, SA and DEA (Blum’s method)

Table 1. Input parameter and range of targets for Sharan’s equation

Table 2. Input parameter and range of targets for Blum’s equation

Table 3. Results of the error rates for PSO, SA and DEA (Sharan’s equation)

Table 4. Results of the error rates for PSO, SA and DEA (Blum’s equation)

Table 5. Results of the number of iteration for PSO, SA and DEA