3。4。 Optimization algorithm: hybrid Taguchi-random coordinate search algorithm
To find the optimal value of each step, an optimization algorithm is required。 The objective function used in this paper is com- posed of an obvious equation, but it is too complex to analyze the function analytically。 This type of function is treated as a black- box function [20]。 To optimize the black-box function, derivative-free optimization (DFO) algorithms such as genetic algorithms (GA), simulated annealing (SA), or pattern search optimization (PSO) are applied [21]。 However, these methodologies are limited in that they sometimes cannot find global optimal points。 Rios and Sahinidis [21] suggest that a better solution to this kind of problem may be a combination of two algorithms。 Thus, the hybrid Taguchi-random coordinate search algorithm (HTRCA) is ap- plied [22]。 HTRCA combines the Taguchi method (TM) with the random coordinate search algorithm (RCA) to find the optimal solution of the objective functions。
4。 Case studies
This section analyzes a number of cases that were investigated with the developed algorithm to validate the method。 For a performance comparison, the conventional method that minimizes tracking error is used。 The input data set of the given points and their intervals is controlled for unprejudiced comparison。 The method minimizes the tracking error of the given data set and finds the optimal mechanism。 Moreover, the method developed in this paper derives the optimal mechanism to minimize the objective function with the reference slope and its change in angle of slope, which are estimated from the given data set。
4。1。 Case 1–1: type-I (equal intervals)
The desired trajectory of the first case is a mathematical ellipse described as follows:
1000 coupler points were chosen to identify the optimal solution that can trace an ellipse with a = 100 and b = 50。 Because the purpose of this case study is to find the shape and size of the trajectory, the position variables x0 and y0 are not needed。 Therefore, for this problem,
Target curve:
Cx;D ¼ 100 cos θ ð11Þ
Cy;D ¼ 50 sin θ ð12Þ
θ ¼ i=1000; i ¼ 1; …; 1000
Constraint conditions: Desired shape: Type-I
Xsize ∈ ð 0; 500 ]
½ l2 l3 l4 ]=l1 ∈ ð 0; 10 ]
。 lcx lcy 。=l1 ∈ ½—10; 10]
4。2。 Case 1–2: type-I (variable intervals)
This case is also an ellipse described by Eq。 (10)。 In some real situations, the velocity of each section needs to be considered。 Therefore, the velocity profile of the coupler points is modified from the first case。 The other conditions are the same。 For this problem,
Target curve:
Constraint conditions: Desired shape: Type-I
Xsize ∈ ð 0; 500 ]
½ l2 l3 l4 ]=l1 ∈ ð 0; 10 ]
。 lcx lcy 。=l1 ∈ ½—10; 10]
4。3。 Case 2–1: type-III (equal interval)
The desired trajectory of case 2 looks like a crescent, as shown in Fig。 7 (A)。 The desired velocity in all sectors is constant。 For this problem, the target curve and constraint conditions are as follows。
Target curve:
The value of parameter composing the shape of the desired trajectory is demonstrated in Fig。 7(A)。 1000 coupler points in total are positioned equidistantly。 曲柄摇杆机构英文文献和中文翻译(7):http://www.youerw.com/fanyi/lunwen_82614.html