Mathematical Problems in Engineering

Research Article

A Novel Intelligent Method for Predicting the Penetration Rate of the Tunnel Boring Machine in Rocks

Table 1

Review of several TBM performance prediction models using the dataset from the Queens Water Tunnel .


Reference	Model	Main factors	Predicted value	Evaluation parameter

Yagiz [13]	SA	UCS, BTS, BI, DPW, α, FN	FPI	R², r
Gholamnejad and Tayarani [18]	ANN	DPW, UCS, RQD	PR	MSE, R²
Mahdevari et al. [19]	SVM	UCS, BTS, BI, DPW, α, SE, TF, CP, CT	PR	MSE, R²
Yagiz et al. [23]	ANN	DPW, UCS, BI, α	PR	RMSE, VAF, r
Mikaeil et al. [24]	FIS	DPW, UCS, BTS, α, PSI	PR	DPDO
Wen et al. [25]	BP-ANN	UCS, BTS, SWP, PSI, α	PR	MRE
Yagiz and Karahan [26]	PSO	UCS, BTS, BI, DPW, α	PR	MSE
Ghasemi et al. [27]	FIS	UCS, BI, DPW, α	PR	VAF, RMSE
Yagiz and Karahan [28]	DE, HS-BFGS, GWO	DPW, UCS, BI, α	PR	MSE
Mikaeil et al. [29]	EMFE	UCS, PSI, DPW, α	PR	R²
Naghadehi et al. [30]	GEP	UCS, BTS, BI, DPW, α	PR, FPI	R², RMSE, MAPE
Naghadehi et al. [31]	ICA, CART, GEP	UCS, BTS, DPW, BI, α	PR	R², RMSE, MAPE
Naghadehi et al. [32]	GEP, ICA	UCS, BTS, DPW, BI, α	PR	R², RMSE, MAPE

Nomenclature in this table: brittleness index (BI); Brazilian tensile strength (BTS); classification and regression tree (CART); cutterhead power (CP); cutterhead torque (CT); differential evolution (DE); Dubois–Prade decision operator (DPDO); distance between planes of weakness (DPW); extended multifactorial fuzzy evaluation (EMFE); field penetration index (FPI); gene expression programming (GEP); grey wolf optimizer (GWO); hybrid harmony search (HS-BFGS); imperialist competitive algorithm (ICA); individual cutter force (FN); mean absolute percentage error (MAPE); mean relative error (MRE); mean squared error (MSE); penetration rate (PR); peak slope index (PSI); coefficient of correlation (R²); root mean square error (RMSE); rock quality designation (RQD); coefficient of the cross correlation (r); statistical analysis (SA); specific energy (SE); the spacing between the weakness planes (SWP); thrust force (TF); uniaxial compressive strength of intact rock (UCS); variance accounted for (VAF); angle between the longitudinal tunnel axis and the plane of weakness (α).