Enhancing Sustainability Through Drilling Machine Efficiency: A Comparative Analysis of TOPSIS and VIKOR Methods for Energy Optimization

Figure 1 provides a visual representation of the architectural layout for optimizing drilling machines.

The implementation of the recommended model involves four key stages:

a) Data collection: In this initial stage, data is gathered by measuring values for each parameter from the testing platform. This data serves as the foundation for the subsequent optimization process. To gain a comprehensive understanding and to ensure the reproducibility of our findings, it is necessary to detail the experimental conditions under which the data were collected. Measurements of parameters such as drilling speed, torque were obtained using torque sensors, speedometers. The data were collected over several sessions, with each session consisting of a full week of trials to ensure accuracy and mitigate any variations. Environmental conditions, including temperature and humidity, were strictly monitored and recorded, due to their potential impact on drilling performance.

b) Weight calculation using entropy method: The second stage involves the calculation of risk factor weights using the entropy method. This step helps assign appropriate importance to each parameter, considering their relative significance in the decision-making process.

c) Integrated MCDM approach with VIKOR and TOPSIS: The third stage proposes an integrated Multi-Criteria Decision Making (MCDM) approach, combining VIKOR and TOPSIS methods. This integration allows for a more comprehensive evaluation of alternatives based on multiple criteria.

d) Comparison of methods: The final stage involves comparing the outcomes of the two methods. This comparison is achieved by assessing the coefficient of ranking similarity, using specific experimental results as a reference point. It helps determine the extent to which VIKOR and TOPSIS align with each other and with the experimental data.

1.png

Figure 1. Illustration of the proposed drilling machine

This architectural layout provides a structured framework for optimizing drilling machines, offering a systematic approach that encompasses data collection, weight determination, multi-criteria decision-making, and method comparison to ensure a well-informed and reliable decision-making process.

2.1 Data collection

To facilitate the reproducibility of the experimental setup, it is crucial to clarify the specific configurations used during testing. Drilling experiments were conducted with rock samples of granitic composition. Drilling parameters were set to speed, feed rate, with selection based on preliminary tests to determine optimal conditions. Included setup also has a fluid circulation system, designed to simulate the operating environment as closely as possible.

A detailed drawing in Figure 2 illustrates a sophisticated drilling rig centered on two robust low-speed electrical systems. These systems include the hoist drive responsible for lifting and lowering the drill string and drill bit, and the top-drive that powers the drilling motor for rotary motion. The drill-string setup consists of the following parts:

2.png

Figure 2. Illustration of the proposed drilling machine optimization technique

(i) The drill-bit and sturdy, thick-walled pipes known as drill collars collectively form what's referred to as the bottom-hole assembly (BHA).

(ii) Heavy-weight drill pipes (HWDP) serve the purpose of providing a seamless connection between the rigid drill collars and the more flexible drill pipes. This transition helps prevent fatigue-related concerns that could occur with standard drill pipes close to the bottom-hole assembly.

(iii) The main body of the drill-string primarily consists of standard drill pipes with relatively thinner walls compared to the heavy, thick-walled pipes.

The drilling process relies on the coordinated rotation of the top-drive electrical motor and the draw-works hoist electrical drive. The top-drive imparts torque to the drill-bit through the drill-string, while the draw-works hoist facilitates the longitudinal movement of the drill-string and drill-bit, creating the necessary downward force on the bit (Weight-on-Bit), indirectly measured using a hook-load sensor. During this process, the drill-bit pulverizes the rock bed material, which is then removed by drilling fluid (mud) circulated by mud pumps (not depicted in Figure 2).

Both the draw-works hoist and rotary high-power electrical drives usually operate within a cascade control system. Here, the overarching speed controller governs the inner current/torque control loop. These variable speed drives (VSDs) include embedded control features that allow for the implementation of advanced drilling control functions like the active damping system for drill-string torsional vibrations. They also have the capability to receive commands from supervisory control systems.

To ensure operational safety, these drives incorporate high transmission ratio gearboxes, enabling high-torque/low-speed operation-typical for standard drilling procedures. Moreover, they exhibit notable compliance and friction effects within their working mechanisms.

For safety and operational integrity:

(i) The torque exerted during rotary drive drilling (i.e., drill-string torsional torque) must not surpass predefined limits to prevent structural issues with the drill-pipe.

(ii) If the drill-bit (BHA) or drill-string becomes lodged in the borehole, the rotary drive must safely stop, and the torsional tension on the drill-string should be gradually released in a controlled manner.

(iii) Limitations on the draw-works drive speed downwards are crucial to prevent hazardous unwinding of the steel-wire rope from the winch drum. Simultaneously, precise control over the bit's normal force is essential to prevent damage.

This methodical approach allowed for a comprehensive evaluation of the drill's performance under various conditions and provided a reliable set of data for further analysis and decision-making in the study.

2.2 Determine the weights of risk factors using entropy method

The entropy approach is employed to determine the weight or significance of various elements or criteria in a specific condition. It utilizes a decision matrix that is constructed based on a set of data associated with these elements. This decision matrix is created to represent the importance or contribution of each element to the decision-making process, and it typically involves assigning values or weights to each element based on their characteristics or attributes. According to the information theory's criteria for the amount of uncertainty that a discrete probability distribution conveys [26], there is general agreement that a broad distribution signals more uncertainty than one that is closely packed. For the jth criterion, the entropy of the set of normalized results is given by:

$\begin{gathered}E_j=-\frac{\left[\sum_{i=1}^m P_{i j} \ln \left(P_{i j}\right)\right]}{\ln (m)} \\ j=1,2 \ldots, n \text { and } i=1,2 \ldots, m\end{gathered}$                  (1)

The normalized decision matrix provides the P_ij, which is:

$P_{i j}=\frac{r_{i j}}{\sum_i^m r_{i j}}$      (2)

where, $r_{ij}$ is an element of the decision matrix, E_j  as the information entropy value for j^th criteria. Hence, the criteria weights, W_j  is obtained using the following expression:

$\begin{gathered}W_j=\frac{1-E_j}{\sum\left(1-E_j\right)} \\ j=1,2 \ldots, n \text { and } i=1,2 \ldots, m\end{gathered}$                  (3)

where, (1-E_j) is the level of information diversity involved in the jth criterion's results.

2.3 Determine the weights of risk factors using entropy method

2.3.1 VIKOR approach

VIKOR, which stands for "Multi-Criteria Optimization and Compromise Solution" in its abbreviated form, is a multi-criteria decision-making (MCDM) method used to evaluate and rank alternatives when multiple criteria are involved. The VIKOR approach provides a systematic framework for determining the most suitable alternative in a decision-making context.

The VIKOR method assumes that decision-making is a process of compromising rather than finding optimal solutions, especially in scenarios with conflicting criteria. It seeks a solution that is closest to the ideal and provides maximum group utility for the majority and a minimum of individual regret for the opponent. The choice of VIKOR for this study is motivated by its adaptability in dealing with uncertain and imprecise data, often encountered in the evaluation of drilling machine performance.

The VIKOR Method's steps are:

Step 1: Normalize the decision matrix

To normalize, apply the following formula:

$\begin{gathered}f_{i j}(\mathrm{x})=\frac{x_{i j}}{\sqrt{\sum_{i=1}^m x_{i j}^2}} \\ j=1,2 \ldots, n \text { and } i=1,2 \ldots, m\end{gathered}$                 (4)

Step 2: Determine the best and worst benefits of each criterion

The best and worst benefits can be determined by the following formula:

If the criterion is positive, then:

$\begin{gathered}f_j^*=\operatorname{Max}_i f_{i j}, f_j^{-}=\operatorname{Min}_i f_{i j} \\ j=1,2 \ldots, n\end{gathered}$             (5)

If the criterion is negative, then:

$f_j^*=\operatorname{Min}_i f_{i j}, f_j^{-}=\operatorname{Max}_i f_{i j} \\ j=1,2 \ldots, n$              (6)

The positive ideal solution $\left(f^*\right)$and negative ideal solution $\left(f^{-}\right)$ can be expressed as follows:

$f^*=\left\{f_1^*, f_2^*, f_3^*, \ldots, f_n^*\right\}$             (7)

$f^{-}=\left\{f_1^{-}, f_2^{-}, f_3^{-}, \ldots, f_n^{-}\right\}$           (8)

Step 3: Calculate the S_i and R_i values

The values $S_i$ and $R_i$, representing the group utility and individual regret, respectively, can be calculated by the formulas below:

$S_i=\sum_{j=1}^n w_j \frac{\left(f_j^*-f_{i j}\right)}{\left(f_j^*-f_j^{-}\right)}$              (9)

$R_i=\operatorname{Max}_j\left[w_j \frac{\left(f_j^*-f_{i j}\right)}{\left(f_j^*-f_j^{-}\right)}\right]$            (10)

where, $w_j$ denotes the weight of the criteria.

Step 4: Comprehensive evaluation score (Q)

Compute the comprehensive evaluation score for each alternative by combining the utility values and considering the weights assigned to criteria. The value Q, representing the VIKOR index for each alternative can be calculated by the following formula:

$Q_i=\gamma \frac{\left(S_i-S^*\right)}{\left(S^{-}-S^*\right)}+(1-\gamma) \frac{\left(R_i-R^*\right)}{\left(R^{-}-R^*\right)}$                 (11)

where,

$\begin{gathered}S^*=\operatorname{Min}_i\left\{S_i\right\} ; S^{-}=\operatorname{Max}_i\left\{S_i\right\} \\ R^*=\operatorname{Min}_i\left\{R_i\right\} ; R^{-}=\operatorname{Max}_i\left\{R_i\right\} .\end{gathered}$

And $\gamma$ is the maximum group utility represented by value 0.5.

Step 5: Rank the alternatives, sorting by the S, R and Q values

Alternatives are ranked by sorting the S, R, and Q, values in decreasing order such that the best rank is assigned to the alternative with the smallest VIKOR value. The results are three ranking lists.

VIKOR is particularly useful when decision-makers are looking for a compromise solution that takes into account both the best and worst-case scenarios for each criterion. It balances the need to maximize benefits and minimize drawbacks, making it a valuable tool in various decision-making scenarios, including project selection, supplier evaluation, and product design.

2.3.2 TOPSIS approach

The TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) approach is a Multi-Criteria Decision Making (MCDM) method used for ranking and selecting the best alternative from a set of options based on multiple criteria. It is a systematic and structured technique that helps decision-makers make informed choices. Here's TOPSIS Steps [27], To further clarify the TOPSIS methodology, it is based on the principle that the chosen alternative should have the shortest Euclidean distance from the Positive Ideal Solution (PIS) and the furthest Euclidean distance from the Negative Ideal Solution (NIS). This presupposes a perfectly compensatory decision-making model in which high scores on some criteria can offset low scores on others. TOPSIS was chosen because it is good at handling both qualitative and quantitative data, which makes it a good choice for making the complicated, multi-criteria decisions that are needed to improve drilling processes:

Step 1: Create a normalized matrix

$f_{i j}(\mathrm{x})=\frac{x_{i j}}{\sqrt{\sum_{i=1}^m x_{i j}^2}}$             (12)

Step 2: Determine the weighted normalized matrix

$V_{i j}=r_{i j} \times W_j$       (13)

where, W_j  is the weights of criteria and given by entropy method.

Step 3: Obtain the maximum z⁺ and minimum scores z^- for each column

$Z^{+}=\underbrace{\max }_n\left\{V_{i j}\right\}=\left\{Z_1^{+}, Z_2^{+}, Z_3^{+}\right\}$            (14)

$Z^{-}=\underbrace{\min }_n\left\{V_{i j}\right\}=\left\{Z_1^{-}, Z_2^{-}, Z_3^{-}\right\}$         (15)

$\alpha_n^{+}=\sqrt{\left(V_{i 1}-Z_1^{+}\right)^2+\left(V_{i 2}-Z_2^{+}\right)^2+\left(V_{i 3}-Z_3^{+}\right)^2}$       (16)

$\begin{gathered}\boldsymbol{\alpha}_n^{-}=\sqrt{\left(V_{i 1}-Z_1^{-}\right)^2+\left(V_{i 2}-Z_2^{-}\right)^2+\left(V_{i 3}-Z_3^{-}\right)^2} \\ i=1,2 \ldots, n\end{gathered}$        (17)

Step 4: The final ranking index should be created

The FRIn [28] is a credible ranking index that defines the basis for the ultimate ranking. For MCDM techniques, we take into account the separation distance, which may be stated as follows, between the positive ideal solution and the negative ideal solution for the ranking index in the suggested model.

$\begin{aligned} F R I_n= & \left(\frac{\boldsymbol{\alpha}_n^{-}}{\sum_{n=1}^m \alpha_n^{-}}\right)-\left(\frac{\boldsymbol{\alpha}_n^{+}}{\sum_{n=1}^m \alpha_n^{+}}\right) \\ & -1 \leq F R I_n \leq 1\end{aligned}$                  (18)