유전자 프로그래밍과 개체군집최적화를 이용한 픽 커터의 절삭비에너지 예측모델

Prediction Model for Specific Cutting Energy of Pick Cutters Based on Gene Expression Programming and Particle Swarm Optimization

Abstract

본 연구에서는 유전자 프로그래밍과 개체군집최적화기법을 이용하여 픽 커터의 비에너지를 예측하기 위한 모델을 제안하였다. 기계굴착장비의 굴진성능을 평가하는 것은 터널의 설계 초기 단계에서 매우 중요하며, 비에너지를 이용한 기계 굴착장비의 굴진성능평가방법은 모든 기계굴착공법에 적용될 수 있는 표준화된 방법이다. 본 연구에서는 코니컬형상의 픽 커터가 암석을 절삭할 때 요구되는 비에너지와 암석의 강도특성, 절삭조건 간의 상관관계를 분석하고자 하였으며, 선행연구를 통해 총46개의 선형절삭시험 결과를 수집하여 분석에 활용하였다. 본 연구에서 제안한 예측모델을 이용하여 산정된 픽 커터의 비에너지는 다중선형회귀분석에 비해 작은 평균제곱오차를 나타내었으며, 결정계수 또한 본 연구에서 제안한 모델이 다중선형회귀분석에 비해 우수한 예측결과를 나타내는 것을 확인할 수 있었다.

This study suggests the prediction model to estimate the specific energy of a pick cutter using a gene expression programming (GEP) and particle swarm optimization (PSO). Estimating the performance of mechanical excavators is of crucial importance in early design stage of tunnelling projects, and the specific energy (SE) based approach serves as a standard performance prediction procedure that is applicable to all excavation machines. The purpose of this research, is to investigate the relationship between UCS and BTS, penetration depth, cut spacing, and SE. A total of 46 full-scale linear cutting test results using pick cutters and different values of depth of cut and cut spacing on various rock types was collected from the previous study for the analysis. The Mean Squared Error (MSE) associated with the conventional Multiple Linear Regression (MLR) method is more than two times larger than the MSE generated by GEP-PSO algorithm. The $R^2$ value associated with the GEP-PSO algorithm, is about 0.13 higher than the $R^2$ associated with MLR.

Fig. 1. Effect of line spacing and depth of cut on specific energy (Bilgin et al., 2013)

Fig. 2. The distribution of UCS values used in this study and their corresponding rock type. The highlighted part is the range of application for pick cutters according to Copur et al. (2012)

Fig. 3. A schematic view of a chromosome with two genes

Fig. 4. Expression tree and mathematical expression of the genes shown in Figure 3; “a” is a numerical value.

Fig. 5. An example for mutation in a gene

Fig. 6. An example of inversion operation in a gene

Fig. 7. An example for transposition of insertion sequence elements operation. Please note that the part highlighted in light grey is the selected insertion sequence and the part highlighted in dark grey is removed at the end of the head

Fig. 8. An example for transposition of root insertion sequence elements operation. Please note that the part highlighted in light grey is the selected sequence and the part highlighted in dark grey is removed at the end of the head

Fig. 9. An example for gene transposition

Fig. 10. An example of one-point recombination. The parts highlighted in grey are exchanged between chromosomes

Fig. 11. An example of two-point recombination. The parts highlighted in grey are exchanged between chromosomes

Fig. 12. An example of gene recombination. The genes highlighted in grey are exchanged between chromosomes

Fig. 13. The standard flowchart of GEP algorithm (Ferreira, 2006)

Fig. 14. Random distribution of particles or candidate solutions (P1-P10) over A-B plane

Fig. 15. The standard flowchart for Particle Swarm Optimization algorithm

Fig. 16. The hybrid GEP-PSO algorithm used in this study

Fig. 17. An example of the difference between the outputs of the chromosomes with dynamic and static linking functions

Fig. 18. Prediction results of specific energy by (a) MLR and (b) GEP-PSO models

Fig. 19. Definitions for Tip (Φ), Attack (α), Tilt (φ), and Skew (θ) angles (Jeong and Jeon, 2018)

Table 1. Descriptive statistics for the data base used in this study

Table 2. The setting used in GEP-PSO code

Table 3. The results generated by MLR and the GEP-PSO code