A method for optimizing bolt layout for special-shaped structures

Abstract

The present invention provides a method for optimizing the bolt layout for special-shaped structures, comprising the following steps: S1: Read the design area information given by the user, generate the design area boundary, and then generate a bolt hole layout area that meets the margin requirements; S2: Convert the positions of the bolts into design parameters, batch model and simulate based on the sampling parameters to obtain a data set; S3: After obtaining the bolt loads corresponding to each sample in S2, establish a training surrogate model; S4: Optimize the surrogate model according to the model established in S3 and check the results; S5: Add new samples based on the optimization results in S4; S6: When the optimization results meet the requirements or the total number of samples reaches the set upper limit, stop the calculation. If not, go to S4. The method for optimizing the bolt layout for special-shaped structures according to the present invention improves the automation degree of optimizing the bolt hole positions, is simple to use, has a high applicable range, and has a wide range of application values.

Description

Technical Field

[0001] The present invention belongs to the field of bolts, and particularly relates to a method for optimizing the bolt layout for special-shaped structures. Background Art

[0002] As an important fastening connection method, bolt connection is widely used in the fields of aviation, aerospace, machinery, etc. due to its simple structure and convenient disassembly and assembly. In traditional structural design, bolts are usually selected according to previous experience to determine the hole positions, and then appropriate bolts are selected according to the load conditions to ensure that the bolts can be within the safe load range during the operation of the structure. However, the distribution positions of bolts often have an important impact on the bolt loads. Reasonable bolt distribution positions can effectively reduce the bolt loads, thereby improving the safety of bolt connections and reducing costs. Therefore, optimizing the bolt connection positions is of great significance for structural design and analysis.

[0003] Currently, the bolt position optimization method mainly aims at specific structures. After determining the optimization variables and optimization objectives, corresponding programs are written for optimization. However, such optimization programs are generally only applicable to the same type of structures. When the structure changes, a series of adjustments are often required to the programs to be applicable to the optimization of other structures. Thus, it can be seen that the current bolt position optimization methods still have great limitations and are difficult to meet the engineering requirements. Summary of the Invention

[0004] In view of this, the present invention aims to propose a method for optimizing the bolt layout for special-shaped structures to solve the problems that the bolt position optimization methods have great limitations and are difficult to meet the engineering requirements.

[0005] To achieve the above object, the technical solution of the present invention is realized as follows:

[0006] Step 1: Read the design area information given by the user and generate the design area boundary

[0007] Execute the parametric script, export the node and mesh data of the design area to a text file. Read this file to obtain the node and mesh data, and use the difference in the number of meshes to which the boundary nodes and internal nodes of the area belong to distinguish and obtain the boundary node set.

[0008] Taking a region evenly divided by triangular meshes as an example, its internal nodes generally belong to 6 elements, while the boundary nodes belong to 3 elements. Using the node data and element data, the number of elements to which each node belongs can be statistically obtained, and the boundary node set can be obtained with 3 as the threshold.

[0009] Determine the boundary polyline information. Calculate the average of the boundary node set to obtain a center point. Calculate the distance and radian of all boundary nodes relative to this center point, and the polar coordinate representation of all boundary nodes can be given. Sort all boundary nodes according to the radian size and connect the boundary nodes into a polyline in this order to obtain the polyline representation of the boundary nodes.

[0010] Step 2: Generate a bolt hole layout area that meets the margin requirements

[0011] After obtaining the polyline representation of the area boundary, translation operations can be sequentially performed on two line segments connected to a vertex of the polyline to obtain a new intersection point of the two line segments. The principle is as Figure 1 shown;

[0012] As shown in the figure above, when the intersection point of two line segments is P, the two straight lines are respectively indented inward by a distance L along the normal direction to obtain a new intersection point Q. It can be regarded as moving point P along vector V 1 and then along vector V 2 to obtain the new intersection point which is Q. It can be expressed as

[0013] Q = P + V 1 + V 2 (1)

[0014] Here, vectors V 1 and V 2 are of equal length, and the length

[0015] |V 1 | = |V 2 | = L / sinθ (2)

[0016] where θ is the included angle between the two line segments.

[0017]

[0018] Therefore, the intersection point Q can be re-expressed as

[0019]

[0020] Take L equal to the margin and perform the above operations on the line segments connected pairwise of the polyline respectively, then the set of contour points of the indented hole layout area can be obtained.

[0021] After obtaining the information of the contour points of the hole layout area, re-give the polar coordinates r and θ of these points, and use piecewise linear interpolation to fit these points to obtain the contour line of the complete hole layout area.

[0022] Step 3: Parameterize the bolt hole layout area

[0023] In order to better collect samples within the drillable hole regions, it is necessary to parametrically represent the drillable hole regions and convert the positions of bolts in several drillable hole regions into a series of design parameters. In Step 2, we obtained the polar coordinate representation of the drillable hole regions. Therefore, each drillable hole region is represented by the distance r from the center of the circle and the radian θ in the polar coordinate system. For M drillable hole regions, the number of design variables is 2M. It should be noted that the contour of the drillable hole region is not a standard circle. The solution adopted here is to use a sampling method, such as the Latin Hypercube Sampling (LHS) method, to sample within the minimum circumscribed circle of the region and exclude the sampling points outside the region. A basic requirement is to ensure that the samples collected within the drillable hole region are evenly distributed within the region.

[0024] Taking Latin Hypercube Sampling as an example, if the distance r from the center of the circle and the radian θ are directly sampled according to a uniform distribution, the obtained sampling points will be more distributed near the center of the circle. Therefore, it is converted into a mathematical problem: randomly throw a point within a circle with a radius of R, and this point is equally likely to fall at any position within the circle. Then, the distribution function of the distance r of this point from the center of the circle is:

[0025]

[0026] By performing Latin Hypercube Sampling on the distribution function F(r) of the distance r from the center of the circle and the uniform distribution function of the radian θ, relatively uniform sampling can be achieved within the circle with a radius R.

[0027] Next, it is necessary to exclude the samples within the circle that do not belong to the drillable hole region. The specific process is as follows: for any sampling point within the circle, calculate its distance r from the center of the circle and the radian θ. According to θ, the corresponding distance r of the drillable hole region contour can be determined. b When r < r b , this point is within the drillable hole region; otherwise, it is outside the boundary.

[0028] Step 4: Batch Modeling and Simulation Based on Sampling Parameters

[0029] After sampling a sufficient number of samples, convert the design parameters of the samples into Cartesian coordinates within each drillable hole region, automatically call the structural simulation software for automatic hole layout and finite element simulation, calculate the loads at the bolt hole layout positions corresponding to each sample, and obtain a data set.

[0030] Step 5: Training the Surrogate Model

[0031] After obtaining the bolt loads corresponding to each sample in the previous step, pair them one by one to construct a data set for training the surrogate model. Then, various regression methods can be used to construct the surrogate model. The methods that can be used here include, but are not limited to, neural networks, support vector regression, Gaussian process regression, polynomial regression, etc.

[0032] The function fitted by the surrogate model can be expressed as

[0033] P = M(r, θ) (6)

[0034] where P = {P 1 , P 2 , …, P M} represents the set of bolt loads, r = {r 1 , r 2 , …, r M} represents the set of distances of each bolt position from the corresponding center of the circle, and θ = {θ 1 , θ 2 , …, θ M} represents the set of angles in radians of each bolt position relative to the corresponding center of the circle.

[0035] The trained surrogate model can quickly predict the bolt load according to the optimized parameters of the input bolt positions

[0036] Step 6: Optimization based on the surrogate model

[0037] For the bolt position optimization problem, there are problems such as many optimization variables, a heterogeneous design space of variables, and difficulty in calculating the gradient information of the optimization variables. It is difficult to use traditional gradient-based methods, such as the gradient descent method, to optimize the bolt hole positions. The swarm / evolutionary algorithms have low requirements for the mathematical properties of the objective and constraints, such as convexity, continuity, or explicit definition, etc. They are a good choice for solving some heterogeneous optimization problems. The algorithms that can be used include but are not limited to genetic algorithms, example ant colony algorithms, ant colony algorithms, artificial bee colony algorithms, spider monkey algorithms, etc.

[0038] In the use of the optimization algorithm, first set the optimization objectives and constraints. The optimization objectives include but are not limited to minimizing the standard deviation of the bolt loads and minimizing the maximum load among the bolts. The constraints include but are not limited to the maximum and minimum limits of the edge distance and spacing of the bolts. Take the parameters determined in Step 4 as the optimization variables, set the parameter ranges, and perform optimization through the optimization algorithm. During the optimization process, embed the surrogate model constructed in Step 5 into the fitness calculation function of the optimization algorithm, quickly calculate all bolt loads according to the optimization variables, and calculate the objective function value according to the selected optimization objective. Set the termination conditions for the optimization to obtain the optimal bolt hole positions under the current conditions.

[0039] Step 7: Verification of the optimization results of the surrogate model

[0040] After obtaining the optimization result in step 6, it is necessary to check the result. Input the optimal variables obtained after optimization into the parametric modeling and simulation program to obtain the calculated value of the bolt load. Compare it with the prediction result of the surrogate model. If the difference between the two is large, it indicates that the accuracy of the surrogate model is poor, and the obtained optimization result is unreliable. It is necessary to further increase the samples by means of adaptive sampling and go to step 8; if the result is good, it indicates that the surrogate model is accurate and the optimization result is credible, and go to step 9.

[0041] Step 8: Add new samples based on the optimization result

[0042] Based on the verification result of the optimization based on the surrogate model, adding new samples to the sample set can improve the accuracy of the surrogate model training. Here, a feasible sample addition strategy is given, but it is not limited to this strategy.

[0043] The added samples are divided into three types:

[0044] The first type: Samples after re-simulation calculation of the optimization result of the previous step.

[0045] The second type: Neighborhood development: Search for parameter combinations near the optimal sample in the existing sample set, which can be called development. Apply local perturbations to the existing optimal sample to obtain several new samples and add them to the sample set.

[0046] The third type: Space exploration: Randomly sample and generate several samples within the feasible parameter space and add them to the sample set.

[0047] Add these three types of samples to the sample set to obtain a new sample set, and then go back to step 6.

[0048] Step 9: Judgment of the optimization result

[0049] When the optimization result meets the requirements or the total number of samples reaches the set upper limit, stop the calculation. If not, go to step 8.

[0050] Compared with the existing technology, the bolt layout optimization method for special-shaped structures described in the present invention has the following beneficial effects:

[0051] The present invention proposes a bolt position optimization method applicable to any special-shaped structure. By obtaining the bolt hole layout design area determined by the user, automatically identifying the area boundary, and determining the feasible hole layout area that meets these requirements according to the design requirements such as the bolt edge distance and spacing given by the user. By automatically collecting samples in the area, establishing a surrogate model, and using an intelligent optimization algorithm to optimize the bolt hole position based on the surrogate model. This method improves the automation degree of bolt hole position optimization, is simple to use, has a high applicable range, and has a wide application value. Brief description of the drawings

[0052] The accompanying drawings, which form a part of the present invention, are used to provide a further understanding of the present invention. The schematic embodiments and descriptions thereof of the present invention are used to explain the present invention and do not constitute an improper limitation to the present invention. In the drawings:

[0053] Figure 1 It is a flowchart of a method for optimizing bolt layout for special-shaped structures according to an embodiment of the present invention;

[0054] Figure 2 It is a schematic diagram of obtaining point Q by shrinking the boundary of point P according to the edge distance;

[0055] Figure 3 It is an isometric view of the hexagonal structure in Embodiment 1;

[0056] Figure 4 It is a top view of the hexagonal structure in Embodiment 1;

[0057] Figure 5 It is the discrete node information of a certain area inside the hexagonal structure;

[0058] Figure 6 It is the boundary of the drillable hole area obtained by shrinking inward from the boundary of the design area;

[0059] Figure 7 It is a sample generated based on the parameters of the drillable hole area;

[0060] Figure 8 It is an image of sampling points in six areas;

[0061] Figure 9 It is the difference between the optimization result and the verification result in Embodiment 1;

[0062] Figure 10 It is the optimization result of the bolt hole layout scheme in Embodiment 1;

[0063] Figure 11 It is the comparison of the bolt positions before and after optimization in Embodiment 1;

[0064] Figure 12 It is a schematic diagram of an irregular quadrilateral in Embodiment 2;

[0065] Figure 13 It is the relationship between the objective function value and the number of samples during the optimization process in Embodiment 2;

[0066] Figure 14 It is the bolt positions before and after optimization in Embodiment 2;

[0067] Figure 15 It is the relationship between the difference between the optimization result and the verification result and the number of samples during the optimization process in Embodiment 2; Specific Embodiments

[0068] It should be noted that, without conflict, the embodiments in the present invention and the features in the embodiments can be combined with each other.

[0069] In the description of the present invention, it should be understood that the orientation or positional relationship indicated by the terms "center", "longitudinal", "lateral", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc. is based on the orientation or positional relationship shown in the drawings, and is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as a limitation to the present invention. In addition, the terms "first", "second", etc. are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly indicating the quantity of the indicated technical features. Thus, the features defined with "first", "second", etc. may explicitly or implicitly include one or more of such features. In the description of the present invention, unless otherwise specified, the meaning of "a plurality" is two or more.

[0070] In the description of the present invention, it should be noted that, unless otherwise clearly defined and limited, the terms "installed", "connected", "coupled" should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be directly connected or indirectly connected through an intermediate medium, and it can be the communication inside two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood through specific situations.

[0071] The present invention will be described in detail below with reference to the drawings and in combination with embodiments.

[0072] Embodiment 1:

[0073] The overall structure is a hexagonal stiffened structure, and the hole layout design area is six areas divided by the ribs. The structure bears a concentrated load of 10 N in the Z direction. The material is hard aluminum alloy, with an elastic modulus of 70 GPa and a Poisson's ratio of 0.3. It should be noted that the ribs in the structure are not symmetrically distributed here, so the six areas are not the same, and the side of each area close to the center of the structure is an arc, which makes these areas have sufficient irregularity and can well serve as an embodiment of this patent. Among them, the maximum number of samples is set to 1000, and the initial number of samples is 10% of the maximum number of samples. The number of newly added neighborhood development samples each time is 3, and the number of parameter space exploration samples is 3, as Figure 3 、 Figure 4As shown. Step 1: Read the design area information given by the user and generate the design area boundary.

[0074] Process the grid and node data divided for this structure to obtain the node information of one of the regions as shown in the following figure. Among them, the green represents the boundary nodes, and the red represents the internal nodes. Represent all the edge nodes using polar coordinates and sort them according to the radian size to obtain the region edge represented by polar coordinates, as Figure 5 shown.

[0075] Step 2: Generate a bolt hole layout area that meets the margin requirements

[0076] Combine the edge nodes of this region in pairs to form a polyline, and shrink the polyline inward by 2 times the bolt diameter to obtain the shrinkable hole layout area as Figure 6 shown.

[0077] Step 3: Parameterize the bolt hole layout area

[0078] Calculate the maximum radius of the hole layout area, use the distance from the center of the circumscribed circle and the radian as parameters, and use the Latin hypercube sampling method combined with the acceptance-rejection method for sampling to generate several feasible samples. For better display, Figure 7 10,000 samples collected from one region are shown. During the actual operation process, 100 samples are collected for the first time.

[0079] Step 4: Batch modeling and simulation based on the sampling parameters

[0080] As Figure 8 shown, convert the sampling parameters into the bolt hole layout coordinates, call the parametric simulation software, calculate the bolt load corresponding to each sample, and form a data set. The number of samples in the initial data set is 100.

[0081] Step 5: Train the surrogate model

[0082] In this embodiment, use the neural network function of MATLAB software to train the surrogate model. Among them, the input of the neural network is the radii and arc lengths of 6 regions, a total of 12 parameters, and the output is the loads of 6 bolts.

[0083] Step 6: Optimization based on the surrogate model

[0084] Use the spider monkey optimization algorithm to optimize the samples and obtain the optimized results.

[0085] Step 7: Check the optimized results of the surrogate model

[0086] Check the optimized results and find that there is a large difference between the check results and the prediction results of the surrogate model. Go to step 8 to further increase the samples. Figure 9 The differences between the optimized results and the true results each time are shown.

[0087] Step 8: Add new samples based on the optimization results

[0088] Add the verified optimization results to the sample set. Meanwhile, add 3 neighborhood development samples and 3 space exploration samples respectively, and continue to execute Step 6.

[0089] Step 9: Judgment of the optimization results

[0090] In this embodiment, until 1000 samples, the optimization results based on the surrogate model still do not meet the requirements, and the calculation is stopped. The obtained optimization results are as follows Figure 10 、 Figure 11 as shown

[0091] Table 1 Comparison of bolt loads and standard deviations before and after optimization

[0092]

[0093] It can be seen from the table that after optimization, the standard deviation of the bolt load drops from 0.5579 to 0.2406, a decrease of 43.12%, indicating that the optimization has a good effect.

[0094] Example 2:

[0095] The overall structure is an irregular pentagon stiffened structure, and the hole layout design area is four irregular areas divided by the ribs. The structure bears a concentrated load of 1 N in the Y direction. The material is hard aluminum alloy, with an elastic modulus of 70 GPa and a Poisson's ratio of 0.3. It should be noted that, like Example 1, the four areas here are not the same, meeting the definition of a special-shaped structure. Among them, the maximum number of samples is set to 1000, and the initial number of samples is 10% of the maximum number of samples, which is 100. The number of newly added neighborhood development samples each time is 20, and the number of parameter space exploration samples is 20.

[0096] The implementation steps of the numerical example are the same as those of Example 1.

[0097] After 1000 times, the optimization terminates, and the results are shown in the following table. It can be seen that after the optimization, the loads of the four bolts are basically the same, indicating that the optimization has achieved good results.

[0098] Bolt position 1 2 3 4 Standard deviation After optimization 0.23 0.26 0.38 0.14 0.0991 Before optimization 0.25 0.26 0.25 0.25 0.0050

[0099] Figure 13 shows the relationship between the objective function value and the number of samples during the optimization process. It can be seen that as the number of samples increases, the objective function value continues to decrease.

[0100] Figure 14 shows the bolt positions before and after optimization.

[0101] Figure 15 It shows the relationship between the difference between the optimization result and the verification result during the optimization process and the number of samples. It can be seen that the overall trend is downward, indicating that the accuracy of the surrogate model is gradually improving.

[0102] The above are only two preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for optimizing bolt layout for special-shaped structures, characterized in that: It includes the following steps: S1: Read the design area information given by the user, generate the design area boundary, and then generate a bolt hole layout area that meets the margin requirements; S2: Convert the positions of bolts in several hole layout areas into design parameters, perform batch modeling and simulation based on sampling parameters, and obtain a data set; S3: After obtaining the bolt load corresponding to each sample in S2, establish a training surrogate model; S4: Optimize the surrogate model according to the model established in S3 with the parameters obtained in S2, and then check the optimized results; S5: Add new samples based on the optimization results of S4; S6: When the optimization results meet the requirements or the total number of samples reaches the set upper limit, stop the calculation. If not, go to S5; The bolt hole layout area that meets the margin requirements generated in step S1 is as follows: According to the polyline representation of the area boundary, translation operations are sequentially performed on two line segments connected to one vertex of the polyline to obtain new intersection points of the two line segments connected to the vertex. When the intersection point of the two line segments is P, the two straight lines are respectively indented inward by a distance L along the normal direction to obtain a new intersection point Q. Point P moves along vector V 1 and then moves along vector V 2 . The polar coordinate expression of Q is: P is the polar coordinate of the intersection point of two line segments; L is the distance that two straight lines are indented inward along the normal direction; V 1 and V 2 is the vector for the movement of point P; θ is the included angle between two line segments; Take L equal to the margin, and perform the above operations on each pair of connected line segments of the polyline respectively, then the set of contour points of the hole layout area after indentation can be obtained; after obtaining the information of the contour points of the hole layout area, re-give the polar coordinate representations r and θ of these points, and use piecewise linear interpolation to fit these points to obtain the contour line of the complete hole layout area; The batch modeling and simulation of sampling parameters in step S2 is as follows: After sampling to obtain samples, convert the design parameters of the samples into Cartesian coordinates in each hole layout area, automatically call the structural simulation software for automatic hole layout and finite element simulation, calculate the load at the bolt hole layout position corresponding to each sample, and obtain a data set.

2. A method for optimizing bolt layout for special-shaped structures according to claim 1, characterized in that: The reading of the design area information given by the user in step S1 is as follows: Execute the parametric script, export the node and mesh data of the design area to a text file; read this file to obtain the node and mesh data, and use the difference in the number of meshes to which the boundary nodes and internal nodes of the area belong to distinguish and obtain the boundary node set.

3. A method for optimizing bolt layout for special-shaped structures according to claim 1, characterized in that: The generation of the design area boundary in step 1 is as follows: Determine the boundary polyline information, average the boundary node set to obtain a center point, calculate the distance and radian of all boundary nodes relative to this center point, give the polar coordinate system representation of all boundary nodes, sort all boundary nodes according to the radian size, and connect the boundary nodes into a polyline in the order of radian size to obtain the polyline representation of the boundary nodes.

4. A method for optimizing bolt layout for special-shaped structures according to claim 1, characterized in that: The conversion of the positions of bolts in several hole layout areas into design parameters in step S2 is as follows: According to the polar coordinates obtained in S1, each hole layout area is represented by the distance r from the center of the circle and the radian θ in the polar coordinate system. For M hole layout areas, the number of design variables is 2M. Sampling methods are adopted within the minimum circumscribed circle of the area, and sampling points outside the area are excluded.

5. A method for optimizing bolt layout for special-shaped structures according to claim 1, characterized in that: After calculating and corresponding each sample with the corresponding bolt load in step S2, a data set for surrogate model training is constructed, and a surrogate model is constructed using regression methods, and the regression methods include neural network, support vector regression, Gaussian process regression, and polynomial regression; The function fitted by this surrogate model is expressed as: P = M(r,θ) Among them, P = {P 1 , P 2 , …, P M} represents the bolt load set; r = {r 1 , r 2 , …, r M} represents the set of distances of each bolt position relative to the corresponding center of the circle; θ = {θ 1 , θ 2 , …, θ M} represents the set of the radian of each bolt position relative to the corresponding center of the circle; The trained surrogate model quickly predicts the bolt load according to the input bolt position optimization parameters.

6. A method for optimizing bolt layout for special-shaped structures according to claim 1, characterized in that: The algorithms for optimizing the surrogate model according to the parameters obtained in S2 in step S4 based on the model established in S3 include genetic algorithm, ant colony algorithm, artificial bee colony algorithm, and spider monkey algorithm; In the use of the optimization algorithm, first set the optimization objectives and constraints. The optimization objectives include but are not limited to the minimum standard deviation of bolt loads and the minimum maximum load in bolts. The constraints include the maximum and minimum limits of the edge distance and spacing of bolts; Take the parameters in step S2 as optimization variables, set the parameter range, and optimize through the optimization algorithm. During the optimization process, embed the surrogate model constructed in step S3 into the fitness calculation function of the optimization algorithm, quickly calculate all bolt loads according to the optimization variables, and calculate the objective function value according to the selected optimization objective; Set the termination condition of the optimization to obtain the optimal bolt hole layout position under the current conditions.

7. A method for optimizing bolt layout for special-shaped structures according to claim 1, characterized in that: After obtaining the optimization result in step S4, input the optimized optimal variables into the parametric modeling and simulation program to obtain the calculated value of the bolt load, and compare it with the prediction result of the surrogate model. If the difference between the two is large, it means that the accuracy of the surrogate model is poor and the obtained optimization result is unreliable, and it is necessary to further increase the samples by means of adaptive sampling and go to S5; if the result is good, it means that the surrogate model is accurate and the optimization result is credible, and go to S6.

8. A method for optimizing bolt layout for special-shaped structures according to claim 1, characterized in that: The increased samples in S5 are divided into 3 categories: The first category: samples after re-simulation calculation of the previous optimization result; The second category: neighborhood exploitation: finding the parameter combinations near the optimal sample in the existing sample set is called exploitation; applying local perturbations to the existing optimal sample to obtain several new samples and adding them to the sample set; The third category: space exploration: randomly sampling and generating several samples within the feasible parameter space and adding them to the sample set.

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