Mixed Integer Linear Programming Based Speed Profile Optimization for Heavy-Haul Trains

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Introduction
Heavy-haul transportation is of great importance for improving transport efciency, increasing economic profts, and lowering transport costs.It has developed rapidly in many countries.Specifcally, the axle load of heavy-haul trains (HHTs) has increased signifcantly to improve the transport capacity, which in turn presents higher requirements for the drivers of HHTs.Moreover, the increase in weight and size of HHTs is also limited by the infrastructure and the hauling capacity of the locomotives.In particular, the application of the automatic train operation (ATO) system for HHTs [1][2][3] has attracted increasing attention from researchers in recent years, compared with the traditional manual operation.
With the increasing demand for iron ore year by year in Australia, the AutoHaul system [2] developed by Rio Tinto has been applied to achieve autonomous heavy-haul train (HHT) operation in 2018.Tere are three main benefts to this endeavour in preference to manual operation.Te frst is to increase productivity by shortening cycle times and eliminating stops for driver changes.Furthermore, operating costs would be reduced with fewer drivers and lower fuel consumption.Te third is to reduce the possibility of driver error, thereby improving the safety of HHT operations.However, the implementation of the ATO system in Chinese HHTs is a challenging open issue due to the diferences in HHT speed control methods between Australia and China.Specifcally, HHTs in Australian railways have achieved automatic operation through the electronically controlled pneumatic (ECP) braking mode, which allows all wagons to receive control commands consistently [4].HHTs in China are still equipped with conventional air brake systems, where control commands are delivered with a transmission delay depending on the speed of the air wave and the length of the HHT.
Although there has been much research on the application of ATO in Chinese urban rail transit [5][6][7].Researchers have mainly focused on the following two critical issues: the speed profle optimization that can be achieved of-line and the train speed controller design with real-time performance.In order to achieve improved performance of train operation, there are still many challenges in the operation of HHTs.Passenger trains, such as urban rail trains and high-speed trains, are mainly controlled by traction and electric braking, which has higher control accuracy and faster response time than air braking; in particular, air braking is only applied when the electric brake force is too small to stop the train at low speed without considering the efect on the next regime.For HHTs, due to their large tractive mass and many sections with long and steep downgrades (LSDs), air braking and electric braking should be applied collaboratively to keep the speed within the given limits, i.e., speed limit and minimum release speed.In particular, we note that the air braking should be applied intermittently for the operation of HHTs on LSDs, as shown in Figure 1.Tis strategy is also known as the cyclic air braking, where the driver should consider when to apply or release the air brakes and the amount of pressure reduction, taking into account the efect on the next brake application or release, until the trains have left the LSDs [8].In addition, electric braking prevents the sharp increase in the speed of HHTs and makes the air-flled times of the train pipes more sufcient.It is noted that the electric brake force should be equal to zero when HHTs are running in a neutral section.
Train speed profle optimization [9,10] is commonly formulated as an optimal control problem aimed at enhancing train operation performance by optimizing the outputs like regime sequences and switching points.Tis study centers on the optimization of strategies aimed at ensuring the safe, efcient, and economical operation of HHTs on LSDs.While various approaches like pontryagin maximum principle (PMP) [11], approximate dynamic programming (ADP) [12,13], quadratic programming (QP) [14,15], mixed integer linear programming (MILP) [16], and heuristic algorithms (HAs) [17][18][19] have been used to develop HHT operation strategies, there exists a notable gap in the discussions pertaining to critical aspects.Specifcally, the time characteristics of air braking, and a constraint within engineering applications where power supply is interrupted while travelling through the neutral section, have not been adequately addressed.Furthermore, the cycle air braking strategy was not taken into consideration in [14,15], warranting further investigation.In addition, the complexity of line conditions makes it challenging for the PMP to yield optimal solutions, while the results obtained from both ADP and HAs are approximate solutions.On the other hand, mathematical programming methods like QP and MILP beneft from mature commercial solvers that ensure the identifcation of globally optimal solutions [20,21].Tis study was conducted building upon the aforementioned discussion.Te main contributions of this paper are summarized as follows: (1) A formula is developed to calculate air brake force, considering time characteristics for the frst time.Subsequently, a discrete-time-based MILP model is presented to optimize the HHT speed profle.In this model, the total running time is divided into multiple intervals.
(2) Real-world line conditions and operational constraints, including slopes, neutral sections, and airflled times, are considered.To facilitate approximate linearization, the big-M approach and binary variables are introduced.(3) A hybrid scheme that integrates coarse-grained and fne-grained models is devised to strike a balance between computation efciency and accuracy.Ten this complex challenge is tackled by using the wellknown solver CPLEX.Moreover, a series of experiments are conducted to demonstrate the solutions achieved.
Te remainder of this paper is organized as follows.Section 2 delves into the existing literature concerning the optimization of HHT operation strategies.Section 3 outlines the model of the HHT running on LSDs integrating a neutral section.Moving forward, the discrete-time-based MILP approach is given in Section 4. Te efectiveness and fexibility of the proposed approach are validated through simulation experiments in Section 5. Finally, conclusions are drawn in Section 6.

Literature Review
Te optimization of train operation has been aptly described as an optimal control problem, as noted in [5].Various optimization methods have been employed to improve the operation performance of long HHTs. 2

Journal of Advanced Transportation
In early years, the researchers from the Scheduling and Control Group (SCG) of the University of South Australia developed the FreightMiser system to reduce fuel consumption for long-haul trains, and optimal speed profles for relatively simple scenarios, such as isolated steep uphill or downhill sections, were obtained using PMP [22].Subsequently, another PMP-based approach was proposed in [11] for the purpose of energy saving, which considered the operation requirements of a Chinese HHT.However, the pursuit of rigorous mathematical solutions led to model simplifcation, ignoring factors such as changing slopes and air braking characteristics.With the improvement of computing power, recent years have witnessed a multistage decision process to determine the control sequence for HHTs running on LSDs, where lookuptable-based [12] and value-iteration-based [13] ADP were used to yield safety-centric, cost-efective, and operationally efcient driving strategies.Te advent of deep Q-network (DQN) [23] mitigated the challenge of high-dimensional spaces by approximating action-value functions with neural networks.Furthermore, a QP-based approach was developed to address the multiobjective trajectory optimization problem in the context of HHTs.Tis approach encompassed considerations of key constraints, including line resistance, neutral section, as well as traction and electric braking, as highlighted in [14].Moreover, a purposeful selection scheme was designed to obtain the optimal weighting factors [15].Notably, these investigations were conducted on railway scenarios characterized by less intricate line conditions and the absence of LSDs.In addition, HAs fnd predominant application in resolving the HHT operation strategy on LSDs due to their less stringent model requirements.For instance, to ensure safety and improve efciency during operations, methods like particle swarm optimization (PSO) [17], genetic algorithm (GA) [18], and artifcial bee colony (ABC) [19] have been embraced.Tese algorithms enable the identifcation of optimized switching points for air brake application and release.In the realm of optimizing train speed profles, MILP has established itself as a widely recognized and efective method.Its utility spans across urban rail trains [24][25][26], high-speed trains [27,28], and medium-speed maglev trains [29].Notably, it has recently been employed in the domain of HHT [16], where the linearization description of the air brake force and the air-flled time constraint is not well treated and still full of challenges.
However, in the aforementioned studies, when addressing air braking, the force was calculated using empirical formulas on the assumption of instantaneous characteristics due to the complex working principle of the air brake system, and the delay of air brake application or release, as well as the progression of air brake force alteration were overlooked.Moreover, real constraints such as the neutral section were not given due consideration.To highlight achievements and gaps in existing research, a brief comparison of the most relevant literature is presented in Table 1.

Model Formulation
3.1.Assumptions.In this paper, we make the following assumptions: (1) Te pressure reduction for brake control typically ranges from 50 to 140 kPa in intervals of 10 kPa.On lines with LSDs, a pressure reduction of 50 kPa can be employed to control the speed of the HHT.It is important to note that routine stops and stops resulting from suboptimal control are not taken into account.
(2) Te output for electric brake control is expressed as a ratio of the characteristic curve.

Notations.
For a better understanding of the paper, Table 2 lists the notations used in this section.

Longitudinal Dynamics of the HHT.
In this paper, the HHT is regarded as a rigid multimass model when running on the line, as in [30], to reduce unnecessary complexity.
When the HHT with n cars runs on LSDs, n � n l + n w , n l is the number of locomotives and n w is the number of wagons.M t �  n i�1 m i , i is the index of cars and m i is the mass of car i.Te continuous-time model of the HHT moving along the track is expressed as follows: where s is the position of the HHT, M t and v are the mass and speed of the HHT, t is the time of the HHTrunning, F e is the electric brake force provided by the locomotives, F a is the air brake force acting on all cars, and F b and F l are the basic and line resistances.

3.3.1.
Resistance.Te basic resistance [31], related to the speed of the train, can be expressed as follows: where and c 1 are positive coefcients related to the type of car.g denotes the gravity constant.As the number of locomotives is much smaller than that of wagons, it can be assumed that the unit basic resistance of a locomotive is the same as that of a wagon.Te line resistances [31] composed by the slope and curve resistances can be computed as follows: where D is the empirical coefcient.
For the position of the car i, the gradient is measured by I i ‰ and the curve resistance can be calculated by the curve radius C i , which can be described by the following piecewise linear functions: where x i is the position of car i, l i−1,i is the physical length between cars i − 1 and i, and s n g are the starting and ending positions of slopes, I 1 ′ , I 2 ′ , • • • , I n g ′ are the gradient of slopes; ′ are the starting and ending positions of curves, and ′ are the radius of curves.

Electric Brake Force.
Te electric brake force [31] can be formulated as follows: where u e is the output ratio and F e,max is the maximum electric brake force that can be achieved according to the characteristics of a locomotive.

Air Brake Force.
Te air brake force [31] is generated by compressed air, and it can be calculated as follows: where for car i, K i is the pressure acting on each brake shoe, and φ i is the brake shoe friction coefcient.n s is the number of brake shoes equipped on a car.
where d b is the diameter of the brake cylinder, η b is the transmission efciency of the braking device, c b is the braking leverage, and n b is the number of brake cylinders equipped on a car.In equation (7a 4n s is a constant for a given brake system.Terefore, the description of the brake cylinder pressure P a i is the key to calculating the air brake force.Based on the function proposed in [33] and test data, the mathematical formulations are as follows: where P b,i and P r,i are the pressure of the brake cylinder of car i during air brake application and release, u b and u r are the binary variables indicating the application and release of the air brake, Δp denotes the amount of pressure reduction, t b a and t r a are the timing of the air brake application and release, and t b,i and t r,i are the delay times for car i at which the pressure begins to rise and fall, depending on the propagation speed of the wave.t b max and t r min are the times required for the pressure to change to the maximum value P a,max and zero, and f b a and f r a are the functions that describe the processes of air brake application (pressure rise) and air brake release (pressure fall) for each car.Objective.Given a specifc running time, the pursuit of enhanced operation efciency necessitates a higher average speed, thereby maximizing the covered distance.Besides, to mitigate the wear of brake shoes caused by elevated temperatures and reduce maintenance cost, the duration of air brake application must be minimized.Te running distance S and the air brake application time T b can be calculated by Te objective function can be written as follows: where w 1 and w 2 are weight coefcients, w 1 + w 2 � 1. S max is the running distance when the HHT runs at maximum speed (see below "speed limit").T is the given running time of the HHT.

Constraints.
Train dynamic constraint: Te movement of the HHT should follow equations (1a) and (1b).Speed constraints: For safety, trains cannot run above the speed limit v lim or below the minimum release speed v r .When the speed is lower than v r , the in-train force will increase and the coupler may even break.
Electric brake constraint: Generally, 0 ≤ F e ≤ F e,max , that is, the output of the electric brake force should not be greater than the maximum electric brake force.So in this paper, the following set should be satisfed.
Air brake constraints: "u b � 1" denotes application and "u r � 1" denotes release, the relationship between them can be described as follows: Te rated pressure of the brake pipe is set at 500 or 600 kPa, with a chosen output of 50 kPa when the HHT is navigating on lines with LSDs.
Δp � 50 kPa. ( Besides, to allow sufcient time for the train pipe to be flled, a release interval between adjacent air brake applications must be at least as long as the air-flled time.
where t r is the air brake release time, and t f is the airflled time.
Neutral section constraint: For the neutral section of the electric railway, the output of the electric brake force equates to zero, which can be rewritten as follows: where s b and s e are the starting position and ending position of a neutral section, respectively.

Solution Approach
Te given running time is divided into N intervals.
T �  N k�1 Δt, and in each interval [t k , t k+1 ], values of the speed limit, the slope resistance, and the curve resistance are constant; we also assume that the traction or braking force is taken as constant.Note that t 1 � t start � 0 and t N � t end � T, t start and t end are the beginning and ending times. 3 presents the decision variables for optimizing the speed profle of the HHT.

MILP Approach.
Inspired by [24], the optimization problem described in Section 3 was solved using the MILP approach.Specifcally, the trajectory optimization problem of passenger trains was studied in [24], and a discrete-spacebased model was obtained, with kinetic energy per unit mass E � 0.5v 2 and time t as state variables, and position s as the independent variable.In this paper, a discrete-time-based model has been established, with speed v and position s as state variables, and time t as the independent variable.In addition, the modelling of the air brake force and the airflled time of the train pipe are the focus, and the neutral section, the gradient and the curve radius are all piecewise functions related to the position.Binary variables must therefore be introduced to achieve linearization.
PWA functions are used to realize the linearization, and the nonlinear function F b (v), equation ( 2), can be written as a piecewise linear function of F b,k , where the values of μ 1,k , μ 2,k , θ 1,k , θ 2,k , and v 1,k are determined by the ftting process.Besides, F e (v), F a (v, t), and F l (s) can be written as the form: F e (v) � F e,k , F a (v, t) � F a,k , and { }, the model in equation (1a) can be rewritten as follows:

Journal of Advanced Transportation
Ten, the zero-order holder and the trapezoidal integration rule are used to obtain the discrete-time dynamic model: where a r,k � e η r,k Δt , b r,k � (e η r,k Δt −1)ξ/η r,k , and c r,k � (e η r,k Δt −1)c r,k /η r,k ; v 1 � v 0 , s 1 � 0, and v 0 are the initial speeds of the HHT.
According to the properties introduced in [34], the PWA model in equation (19a) can be transformed as follows: Here, the auxiliary logical variables δ 1,k , z 1,k , and h 1,k are defned to transform the model Terefore, the following linear constraints should be satisfed: where F e,min and F e,max are the minimum and maximum electric brake force, F a,min and F a,max are the minimum and maximum air brake force, F l,min and F l,max are the minimum and maximum line resistance, and notably, ε is a positive small number.For equations (4a) and (4b), binary variables are introduced to describe these piecewise linear functions: where M 1 is a positive large number, Based on equations ( 6)-(8c), the total air brake force of the HHT can be obtained and expressed as a function of time for the specifc pressure reduction.
where f b and f r are the functions of air brake force and time during brake application and release, respectively.Here, when v ∈[9.72, 20.83]m/s, the value range of (3.6v + 150)/(2 × 3.6v + 150) is from 0.75 to 0.84, which is not large.So, in equation (7b), the average speed v is used for the calculation.Ten, we defne F b a,k � u b,k f b (t) and F r a,k � u r,k f r (t); equation ( 24) can be rewritten as Next, general recursive expressions are proposed to calculate the air brake force, taking into account the time characteristics and the efects of historical regimes: where n b and n r are number of the selected values used in force calculation for air brake application and release.
max , (n r −1)Δt ≤ t r,n + t r min .Take air brake application for example, as shown in Figure 2, Also, these logical conditions should be rewritten as the following linear constraints: For equation (11), that is, where v min,k and v max,k can be calculated based on the minimum release speed v r and the speed limit v lim,k .Two binary variables k b,k and k r,k are also introduced to indicate the timing of air brake application and release, then ensure that the release time is not less than the air-flled time given in equation (15), where M 2 is a positive large number, which is introduced to ensure k2−k1 ≥ t f /Δt when k b,k2 � 1, k r,k1 � 1, and k2 ≥ k1 In addition, the binary variable λ k is introduced to defne the neutral section,
Above all, the speed profle optimization problem of the HHT can be transformed into a MILP model.In this paper, the MILP model is solved using CPLEX.

4.3.
Balancing the Efciency and Accuracy.However, the selection of the time interval signifcantly afects the computation efciency and accuracy.Smaller intervals enhance solution accuracy at the cost of increased computation time, while larger intervals yield the reverse efect.Specifcally, smaller intervals could enable a more detailed consideration of air braking characteristics.As illustrated in Figure 2, assuming 2Δt 2 � Δt 1 , additional data points from the air brake force curve are employed for modelling.Terefore, this paper proposes a hybrid scheme that combines coarse-grained and fne-grained models to optimize operation strategies.Firstly, the speed profle of HHT running is acquired using a larger time interval, constituting a coarse-grained model.Ten, leveraging the calculated solution, a fne-grained model is constructed with a shorter time interval.Tis sequential refnement leads to improved solutions without signifcantly prolonging computational time.
Assuming the initial solution with T � Finally, the solution will be obtained.

Case Study
In this section, we employ a 10, 988-tonne HHT with 116 wagons as the subject of our numerical experiments.Te partial line information of the actual railway is shown in Figure 3.Other relevant details are given in Tables 4 and 5. Te experiments are then carried out on a computer with 3.20 GHz Intel i7 CPU and 16 GB RAM, and CPLEX 12.9.0 is used to solve the proposed model.Also, the computation time is denoted by T c .Remark 1.For the sake of simplicity, we defne two schemes for the following discussion.Scheme I entails the use of a coarse-grained model or a fne-grained model, while Scheme II involves the combination of coarse-grained and fne-grained models.
Remark 2. Due to the gradual variation in slope gradient and the limited impact of curve resistance, we opt to calculate the line resistance for the entire HHT based on the gradient and curve radius of the foremost position, the frst car.

Air brake force (kN)
Air brake application time (s) Figure 2: Diagram of air brake force during air brake application.
Remark 3. Our primary focus is on scenarios, where the HHT traverses a neutral section with an ongoing air brake application regime, necessitating adherence to the relevant constraint, i.e., λ k + u b,k ≥ 1.
We then delve into an analysis of the impact of linearization approximation, presenting the average errors between the approximated and true values of both basic resistance and the air brake force in Table 6.Here, we defne that error � |val t −val a |/val t , where val a and val t denote the approximate value and the true value, respectively.
From Table 6, it becomes evident that the linearization methods proposed in this paper yield results that closely approximate the true values.Te average approximation errors for basic resistance and air brake force are 1% and 8.9%, respectively.Notably, the 8.9% error is obtained at a time interval of 5 seconds during the air brake application, as an illustration.
5.1.Case 1: Efectiveness Verifcation.In this case, w 1 � 0.7 and w 2 � 0.3, and the initial speeds are defned as 13.89 m/s and 19.44 m/s, respectively.Initially, Scheme I is employed to elucidate the impact of the time interval on the HHT operation performance and computation time.In this context, the time intervals are set to 30, 20, 10, and 5 seconds, respectively.Scheme II is then introduced to demonstrate that there is an improvement in efciency.Te experimental results are shown in Tables 7 and 8.
Noticeably, in Scheme I, as the time interval decreases, the number of intervals increases, resulting in performance improvements, including increased running distances and reduced air brake application times.Tis implies that the use of the fne-grained model in conjunction with MILP leads to improved performance.However, this comes at the cost of escalated computation times, surging from 11.29 and 6.55 seconds to over 5000 seconds.Transitioning to Scheme II brings about 91.59% (v 0 is 13.89 m/s) and 91.67% (v 0 is 19.44 m/s) reduction in computation time compared to Scheme I when the time interval is 10 seconds, while preserving performance levels.In particular, when the time interval is 5 seconds, Scheme I struggles to provide solutions within the 5000-second time; with Scheme II, the average time taken is 515.89 seconds.To strike a balanced compromise between operation performance and computation time, a time interval of 5 seconds proves to be optimal for further discussions in Scheme II.
Moving on, Figure 4 shows the relationship between the number of intervals, the objective function, and the computation time for the two initial speeds.Applying Scheme I with a fnely tuned time interval results in a marginal improvement in the objective function relative to the substantial increase in computation time.Also, the application of Scheme II improves this situation.

Case 2:
Flexibility Verifcation.In this case, to clarify the fexibility of Scheme II, we apply it at a time interval of 5 seconds and investigate the performance of diferent weighting coefcients.
Table 9 presents the optimization results of variable weight coefcients when the initial speeds are set to 13.89 m/ s and 19.44 m/s, the number of intervals N � 276.Solutions are successfully obtained, averaging around 604.38 and 541.54 seconds for the respective initial speeds.Tese values markedly exceed those recorded in the scenario with a time interval of 10 seconds.Tis escalation can be attributed to the signifcant increase in computational complexity as the number of intervals augments and the search space broadens.Furthermore, for identical initial speeds, as w 2 increases, the air brake application time T b when w 1 < w 2 changes signifcantly compared to w 1 > w 2 ; as w 1 increases, the running distance is S when w 1 > w 2 changes signifcantly compared to w 1 < w 2 .
Figure 5 illustrates the speed profles and corresponding forces as aligned with the results presented in Table 9.In Figure 5, the HHT operates within confnes of the speed limit and the minimum release speed.It can be seen that distinct initial regimes manifest with varying initial speeds.However, the infuence of the initial speed on the speed profle is progressively mitigated through the coordinated interplay of air braking and electric braking.Tis trend arises due to the presence of a fxed neutral section around the 20.7 km mark.In accordance with the requirements of operation safety, the HHT control must respect the air brake application regime when traversing the neutral section.
Furthermore, Table 10 provides insights into air brake release times.Notably, a minimum of 180 seconds is allocated for air brake release processes, in compliance with the air-flled time mandate of the train pipe.Noteworthy is the prolonged period required for the initial release of air braking at v 0 � 13.89 m/s, serving the purpose of strategic operation adjustment.
On the basis of the above experiments, it is shown that the proposed MILP approach and Scheme II of combining coarse and fne-grained models can address the problem of speed profle optimization well.

Conclusions
In this paper, the speed profle optimization problem has been investigated for the safe, efcient, and economical operation of heavy-haul trains (HHTs) on a railway with long and steep downgrades (LSDs).Te optimization problem is reformulated as a discrete-time-based mixed integer linear programming (MILP) model, where a set of practical constraints is considered.Specifcally, a number of mathematical formulas have been introduced for the air brake application and release process to obtain a more accurate air brake model.Also, for the neutral section, the regime, i.e., air brake application, adapted to the LSDs has been adopted.Moreover, Scheme II, which combines the coarse-grained model and the fne-grained model, has been presented to balance the efciency and accuracy of the computation.Te computational results suggest that the optimal speed profles of HHTs can be achieved via the mathematical model and solution approach presented.
Te proposed method can be used to obtain the speed profle for automatic train operation, which helps to make the operation strategy more realistic, reduce the work intensity of the drivers, and improve the operation speed of HHTs.While the HHT is passing through the neutral section, where the coasting should be followed, we can modify the constraints to ensure the safe and efcient operation.
We focus mainly on the 10, 000-tonne trains with a single locomotive that make up a large proportion in heavy-haul railway.For the application in 20, 000-tonne trains with "1 + 1" formation, which relies on wireless remote multitraction synchronization control, the model in this paper is no longer applicable.In future work, we will extend this research to more complex train formations, such as 30, 000-tonne trains, and we will consider the characteristics of traction, electric braking and air braking, operation rules, and the coupler force that limit train operation.An efcient algorithm will then be developed to solve the optimization model for long train formations.

Figure 1 :
Figure 1: Diagram of the HHT operation on LSDs.
Number of brake shoes equipped on a car K i Pressure acting on one brake shoe of car i φ i Brake shoe friction coefcient of car i Brake cylinder pressure of car i during air brake application P r,i Brake cylinder pressure of car i during air brake release Δp Amount of pressure reduction u b , u r Binary variable indicating regimes of the application and release of air braking Journal of Advanced Transportation Pressure rise and fall delay times for car i t r min Time required for the pressure to change to zero t b max Time required for the pressure to change to the maximum value P a, max Maximum value of brake cylinder pressure f b a , f r a Functions to describe the rise and fall of brake cylinder pressure for each car T

Figure 3 :
Figure 3: Line information between two stations.

Figure 4 :
Figure 4: Relationship between the number of intervals, the objective function, and the computation time.

Table 1 :
Comparison of relevant publications on method and model.

Table 3 :
Decision variables for speed profle optimization.

Table 4 :
Parameters used in numerical experiments.

Table 5 :
Coefcients of the piecewise linear function of basic resistance.

Table 6 :
Error between the approximated and true values.

Table 7 :
Performance comparison of diferent time intervals with the initial speed 13.89 m/s.

Table 8 :
Performance comparison of diferent time intervals with the initial speed 19.44 m/s.

Table 9 :
Performance comparison of diferent weight coefcients with the time interval 5 seconds.