A study conducted by Saffet Yagiz et al., from the Geological Engineering Department at Pamukkale University in Denizli, Turkey, focuses on predicting the penetration rate of Tunnel Boring Machines (TBMs) in rock mass for the Queens Water Tunnel No. 3 in New York. This research employs various optimization techniques, including Differential Evolution (DE), Hybrid Harmony Search (HS-BFGS), and Grey Wolf Optimizer (GWO).
The construction of the tunnel commenced in 1970, with an anticipated completion date of 2020. Spanning over 93 kilometers, the project is divided into four distinct stages. The current study specifically examines the section between Brooklyn and Queens, which measures approximately 7.5 kilometers in length and has a diameter of 7 meters. This segment was excavated between 1997 and 2000 at an average depth of 200 meters below sea level, utilizing an open TBM. The geological formations encountered in this area are notably complex, comprising a range of metamorphosed igneous rocks, such as Mafic-to-Mesocratic Gneiss, Amphibolite, Schist, Granitoid Gneiss, Orthogneiss, and Rhyodacite dikes, among others.
Several studies have successfully employed machine learning techniques, including artificial neural networks (ANN), particle swarm optimization (PSO), support vector machines (SVM), and fuzzy logic FL), to address complex non-linear challenges in geotechnical projects. However, there has been a notable absence of efforts to predict the penetration rate of tunnel boring machines (TBM) using optimization techniques.
The author developed the database by performing intact rock tests, including uniaxial compressive strength (UCS) and Brazilian tensile strength (BTS), in accordance with the standards set by the American Society for Testing Materials (ASTM). The input parameters utilized in this study comprise uniaxial compressive strength (UCS), brittleness index (BI), distance between planes of weakness (DPW), and alpha angle. The output of this analysis is the rate of penetration. The study involved a systematic division of the collected dataset into five distinct phases along the length of the tunnel in order to develop accurate models. The dataset was categorized into five phases, designated as P1 to P5, spanning from the tunnel’s entrance to its exit. A total of seven models were created, labeled M1 through M7. The distribution of data within each model is as follows:
For M1, Training dataset = P2-P3-P4-P5; Testing dataset = P1
For M2, Training dataset = P1-P3-P4-P5; Testing dataset = P2
For M3, Training dataset = P1-P2-P4-P5; Testing dataset = P3
For M4, Training dataset = P1-P2-P3-P5; Testing dataset = P4
For M5, Training dataset = P1-P2-P3-P4; Testing dataset = P5
For M6, Training dataset = 100% of dataset; Testing dataset = P1
For M7, Training dataset = 80% of dataset; Testing dataset = 20% of all dataset.
The analysis focused on the influence of various rock types on the rate of penetration (ROP), accompanied by their respective percentages. Additionally, several computational algorithms were employed to develop predictive models, specifically Hybrid Harmony Search, Differential Evolution (DE), and Grey Wolf Optimizer (GWO). A detailed examination was conducted on how different epsilon values (ε) affect the accuracy of the developed models through multiple trials. It was observed that lower epsilon values yielded a higher correlation coefficient during the training phase; however, this was associated with a decline in performance during the testing phase. This finding underscores the critical importance of selecting an appropriate epsilon value, with 1.00E-06 identified as optimal for achieving the best results.
Moreover, to ensure effective comparison of results, it is imperative that stopping criteria, objective functions, population sizes, and specific rock parameters remain consistent across all prediction models, including HS-BFGS, DE, and GWO. Each algorithmic procedure was precisely followed to develop the models, and the resultant model equations were generated using weighting parameters identified through the optimal epsilon values for each modelling technique. Models M1 through M7, utilizing a constant epsilon value of 1.00E-06, were executed twenty times to thoroughly assess the accuracy and reliability of the developed models.
A series of models (Model 1 to Model 7) have been developed for the analysis of rock types in tunnel segments. Among these, Model 3 stands out as it incorporates four rock types with comparable percentages, resulting in the most reliable outcomes. It achieves higher correlation coefficients during both the testing and training phases when compared to Models 1, 2, 4, and 5. Model 6 utilizes the full dataset for training; however, its accuracy varies depending on the specific type and percentage of rocks present in the testing phase.
To enhance generalizability, Model 7 was created, utilizing 20% of the dataset for testing and 80% for
training. This approach ensures a more balanced representation of the rock types. Ultimately, the performance, accuracy, and practicality of the best models from each of the seven explored will be evaluated to determine their effectiveness.
Based on thorough analysis, the M7 model for each machine learning algorithm emerged as the most effective for solving optimization problems related to Tunnel Boring Machine (TBM) performance. Algorithms such as HS-BFGS, Differential Evolution (DE), and Grey Wolf Optimizer (GWO) were evaluated based on their CPU time and Number of Function Evaluations (NFE). CPU time measures how long a CPU processes instructions of a program, reflecting algorithm efficiency. Number of Function Evaluations (NFE) indicates how often the clustering algorithm calculates the objective function to find the optimal solution, with a smaller NFE indicating faster convergence. The HS-BFGS algorithm demonstrated exceptional performance, yielding high-quality solutions with the shortest CPU time and the fewest NFEs, making it particularly suitable for practical applications.
Differential Evolution was recognized for its simplicity, whereas the GWO algorithm exhibited relatively
weaker performance, indicating the need for enhancements to reduce NFE and CPU time. The developed models proficiently estimate TBM penetration rates by leveraging rock properties. A performance comparison was conducted using a dataset of 30 samples, affirming the reliability and accuracy of the models, with a notable emphasis on the advantages of HS-BFGS.
In conclusion, these developed models, supported by accessible equations, are sufficiently precise for estimating TBM performance. However, the M7 model based on HS-BFGS stands out as the superior choice, particularly in simulations where computational efficiency and time are critical factors.
Reference
Yagiz, S., & Karahan, H. (2015). Application of various optimization techniques and comparison of their performances for predicting TBM penetration rate in rock mass. International Journal of Rock Mechanics and Mining Sciences, 80, 308-315.