Development of multidisciplinary design optimization computing environment based on HLA for heavy machinery

Abstract

To solve the global optimization problem in heavy machinery, a multidisciplinary design optimization (MDO) computing environment is developed based on high level architecture (HLA). The computing environment encapsulates the analysis optimization tools in relevant disciplinary fields to seek global optimization design based on a single disciplinary optimization. The goal of a minimum discrepancy between the subsystem-level design variables and system-level target values is reached by establishing multidisciplinary consistency constraints. The HLA-compliant optimization model realizes collaboration and interoperation between the disciplines through mapping the coupled state variables to corresponding published or subscribed attributes of an object class according to the rules of HLA. Finally, an example application of designing a hydraulic-powered support is presented to demonstrate the effectiveness of the optimization environment.

Keywords

Multidisciplinary design optimization high level architecture consistency constraint hydraulic-powered support

1. Introduction

As a method for solving complex system optimization designs, multidisciplinary design optimization (MDO) has been primarily applied in the aerospace field including large aircraft [1, 2, 3] and carrier rockets [4, 5] firstly. It has versatile areas of application in civil machinery in the past 20 years. Heavy machinery such as coal-mine machinery involves multiple disciplines. Its design process must be optimized due to the long design cycle, high consumption of steel, and increasing requirements for accuracy and reliability. However, its design optimization tends to be limited to a single discipline [6] and it is difficult to achieve overall optimization because the large-scale design problem involving multiple disciplines may be cumbersome to manage. What needs to be further explained is that MDO can enhance system design by exploiting synergies among different disciplines [7].

There are currently two main types of computing environments for multidisciplinary optimization design. One is based on Unified Modeling Language [8], but there is little mature commercial simulation software for support. The other is based on the interfaces between simulation software for different disciplines [9]. This widely used method is currently supported by many kinds of commercial simulation software. However, the interfaces of simulation software in various disciplines lack standards and are not open. High level architecture (HLA) [10, 11] is applied in collaborative simulation, as it supports heterogeneous combinations and interoperation between distributed optimization simulation models in various disciplines.

In this paper, the MDO computing environment based on HLA for designing a type of coal heavy machinery is developed and presented. Its primary contribution is to collaborate the optimization of subsystems which are decomposed along disciplinary boundaries from a complex system. The problem of multidisciplinary interaction is solved with use of the publish-and-subscribe mechanism provided by HLA for passing messages between disciplines.

The remainder of this paper is organized as follows. The next section discusses individual discipline optimization. Section 3 details our approach for model using the collaborative optimization computing environment based on HLA. Finally, an example application of the design process of a type of hydraulic-powered support with experiment results and conclusions are given in Sections 4 and 5, separately.

2. Individual discipline optimization model

The mathematical model of typical nonlinear individual discipline optimization is

$\displaystyle\min f(\bm{x},\bm{p})\bm{x}=[x_{1}\ldots x_{n}]^{T},\bm{p}=[p_{1}% \ldots p_{n}]^{T}x_{i,LB}\leqslant x_{i}\leqslant x_{i,UB},i=1,2,\ldots,n$ (1) $\displaystyle\textit{s.t.}g(\bm{x},\bm{p})<0,h(\bm{x},\bm{p})=0$

where $f(\bm{x},\bm{p})$ is the objective function; $\bm{x}$ is the design vector with $n$ dimensions; $\bm{p}$ is the system constant vector with $m$ dimensions; $x_{i,LB}$ and $x_{i,UB}$ are respectively the lower and upper limits of the design variable; and $g(\bm{x},\bm{p})$ and $h(\bm{x},\bm{p})$ are inequality and equality constraints, respectively. The schematic diagram for the appropriate individual discipline iterative loops is shown in Fig. 1.

The optimizer is a mathematical model that seeks the optimal solution using the iteration of the objective function $f(\bm{x},\bm{p})$ under the inequality constraint $g(\bm{x},\bm{p})$ or equality constraint $h(\bm{x},\bm{p})$ , based on individual discipline optimization with the process result $\bm{x}^{k}$ of the analysis module as the input variable.

Figure 1.

Diagram of iterative loops of individual disciplines.

The analysis module seeks the optimal solution $\bm{x}^{\ast}$ of the state variable with the design variable as the initial input. The analysis methods include analytical, experimental, and finite element. The state variables which reflect the performance or characteristics of a single discipline are the important information for designers to make engineering decisions. For example, the state variables of the structural discipline may be ultimate loads, strain, stress, etc.

3. Collaborative optimization computing environment based on HLA

Multidisciplinary design optimization emphasizes the interdisciplinary coupling effect rather than simply superposing optimization results in single discipline. A major goal of the HLA is to support interoperability between distributed models and reuse of simulations. The variables requiring interactions are mapped as federation member object class attributes according to the HLA standard, thus achieving interdisciplinary interactions. Below we explain how to establish a collaborative optimization computing environment based on HLA followed by an analysis of the collaborative optimization model.

3.1 Multidisciplinary collaborative optimization model

The collaborative optimization method involves approaches to system decomposition and interdisciplinary communication. The complex system design problems are divided into several subsystem problems (which may correspond to one discipline). With the use of subsystem optimizers, each discipline is given control over its own set of design variables and is charged with satisfying its own disciplinary constraints. The system optimizer utilizes the consistency constraints to coordinate subsystem-level optimization results and target values of the system-level design variables and to update the system-level design variable. It finally obtains the global optimal solution which satisfies the consistency constraints.

The general model of system optimization can be stated as

$\displaystyle\mathop{\min}_{j=1,2,\ldots,q}F\left(f_{1}(\bm{x}_{1},\bm{y}_{j1}% ,\bm{p}_{1}),f_{2}(\bm{x}_{2},\bm{y}_{j2},\bm{p}_{2}),\ldots,f_{q}(\bm{x}_{q},% \bm{y}_{jq},\bm{p}_{q})\right)\mathop{\bm{x}_{i}}_{1\leqslant i\leqslant q}=[x% _{1}\ldots x_{n}]^{T}\mathop{\bm{p}_{i}}_{1\leqslant i\leqslant q}=[p_{1}% \ldots p_{n}]^{T}\mathop{\bm{y}_{ji}}_{i,j=1,2,\ldots,q;i\neq j}=[y_{1i}\ldots y% _{ki}]^{T}$ (2) $\displaystyle\textit{s.t.}H_{i}(\bm{x}_{i})=\|\bm{x}_{i}^{t+1}-\bm{x}_{i}^{t}% \|\leqslant\varepsilon,i=1,2,\ldots,q$

where $F()$ is the objective function of global optimization, $f()$ is the objective function of subsystem-level optimization, $\bm{x}_{i}$ is the $n$ -dimensional subsystem-level design variable, $\bm{p}_{i}$ is the subsystem-level constant variable with m dimensions, $\bm{y}_{ji}$ represents the coupling state variable from subsystem $j$ to subsystem $i$ , $q$ is the number of subsystem or disciplines. $\bm{x}_{i}^{t}$ is the target value of the design variable computed and transferred to the $i$ th subsystem at the system-level (including the inter-subsystem coupling state variable), and $\bm{x}_{i}^{t+1}$ is the new target generated by Eq. (2). As the consistency constraint of multidisciplinary collaborative optimization, $H()$ is the objective function of the $i$ th subsystem optimizer. $\varepsilon$ which is referred to as a relaxation factor is a very small positive number to improve the iteration efficiency of optimization.

The optimization model of the $i$ th subsystem is

$\displaystyle\min H_{i}(\bm{x}_{i})=\|\bm{x}_{i}^{k}-\bm{x}_{i}^{t}\|$ $\displaystyle\textit{s.t.}g_{i}(\bm{x}_{i},\bm{y}_{ji},\bm{p}_{i})<0h_{i}(\bm{% x}_{i},\bm{y}_{ji},\bm{p}_{i})=0$ (3)

where $g_{i}()$ and $h_{i}()$ are the inequality and equality constraints required by the corresponding discipline respectively. $\bm{x}_{i}^{k}$ is the optimized local design variable and is charged with satisfying its own disciplinary constraints. The subsystem optimizer minimizes the discrepancy between the subsystem-level optimization result and the target value of these variables computed by the system-level optimizer.

Accordingly, an optimization model involving two disciplines or subsystems is shown in Fig. 2. In this model, a complex system is hierarchically decomposed along disciplinary boundaries into two subsystems. The upper part illustrates a system-level optimization model which provides coordination and minimizes the overall objective. The lower part illustrates an optimization model involving two subsystems.

Figure 2.

Model of multidisciplinary optimization.

In the model, $t$ represents the number of system-level iterations and $k$ represents the number of subsystem-level iterations. The objective of each subsystem optimizer is to minimize the discrepancy between the subset of subsystem variables $\bm{x}_{i}^{k}$ and the target values of the system-level design variables $\bm{x}_{i}^{t}$ which initial value is $\bm{x}_{i}^{0}$ . The optimization results $\bm{x}_{i}^{k}$ of respective disciplines are obtained according to their respective optimization conditions. The optimization results $\bm{x}_{i}^{k}$ of different disciplines are input into the system-level optimizer. New target values are generated following optimization, and they are input to the subsystem-level optimizer for further optimization iteration cycles. Finally, the system-level optimization result $\bm{x}_{s}^{\ast}$ is obtained.

3.2 Federation design with collaborative optimization based on HLA

The high level architecture is a distributed system architecture. It achieves interoperability between models while improving the reusability, scalability, real-time capability, and cooperation of the simulation models in different fields.

The models developed by commercial simulation software in different disciplinary fields are first divided into federation members. Then, as for the coupling state variables, the publication/subscription attributes of object classes are developed according to the run time infrastructure (RTI) interface specification. A federation member sends an interaction, registers a new instance of an object class, and updates its attributes. Other members subscribe and receive the interaction as required, identify new object instances, and reflect the new attribute value of an object instance, thus achieving interactions between coupling state variables in different disciplinary fields.

To establish the multidisciplinary collaborative optimization model, two classes and four federations are designed based on the HLA rules, object model template (OMT), and interface specification.

One type of member is the collaborative design optimization computation federation, including two federation members:

1)
System-level optimization federation members are meant to achieve the system-level optimization algorithm, and to finally obtain the optimal solution of the system $\bm{x}_{s}^{\ast}$ . In addition, they continuously give the system-level target values during iterations. The system-level target value $\bm{x}_{i}^{t}$ is designed as the attribute of the object class published by the system-level federation member. The optimization result $\bm{x}_{i}^{k}$ published by the subsystem-level federation member object class is subscribed by the system-level federation member.
2)
Subsystem-level optimization federation members are intended to obtain the subsystem-level optimization results $\bm{x}_{i}^{k}$ during iteration. The optimization results $\bm{x}_{i}^{k}$ are designed as the corresponding object class attributes published by the federation member of the subsystem. The coupling state variables produced by some subsystems are designed as the published attributes and subscribed by the federation members of other subsystems. For instance, $\bm{y}_{ji}$ represents the coupling state variable from subsystem $j$ to subsystem $i$ . According to the RTI interface specification, it is the object class attribute published by the federation member encapsulated by the $j$ th subsystem on the one hand, on the other hand it is the object class attribute subscribed by the federation member encapsulated by the $i$ th subsystem.

The other type of member is to manage optimization simulation, also including two types of federation members.

3)
Optimization process monitoring members are responsible for monitoring the state of the entire optimization computation. To improve system efficiency and reduce network-data redundancy, optimization process monitoring members only subscribe the target values of the system-level design variables $\bm{x}_{i}^{t}$ to monitor the system optimization process and terminate any nonconvergent iteration process.
4)
Optimization-data collection members are responsible for collecting the data generated in the optimization computation for post analysis. These mainly involve system-level design variables $\bm{x}_{i}^{t}$ and subsystem-level optimization results $\bm{x}_{i}^{k}$ .

4. Application to hydraulic-powered support design

We present a case study in product development of a type of hydraulic-powered support (ZY3500/ 12/26) to demonstrate the multidisciplinary collaborative optimization computing environment as well as show how it can be established based on HLA.

This case study is a typical multidisciplinary design optimization problem involving two disciplines, structural mechanics and kinematics. As the major stressed component of the hydraulic-powered support, the shield-beam is subjected to the coalseam pressure together with the top beam. Structural optimization design of the shield-beam is carried out to determine the length and sectional dimensions, which involves the fields of structural mechanics. On the other hand, the shield-beam, foundation, and front and back linkages form a four-bar mechanism. The optimization objective of the four-bar mechanism is to control and optimize the trajectory of the endpoint A shown in Fig. 3 when the support is operating, which involves the fields of kinematics. The length of the shield-beam and the position of the hinge point can be designed as coupling state variables as they can influence the optimization of two subsystems.

Figure 3.

Geometric parameters of the four-bar mechanism.

Figure 4.

Cross-section parameters of the shield-beam.

4.1 Kinematic optimization of the four-bar subsystem

As shown in Fig. 3, the range of the motion trajectory of endpoint A of the top beam should be no larger than 70 mm. $l_{0},l_{1},l_{2},l_{3},l_{4},l_{5}$ are the lengths of the six bars of the four-bar mechanism to be optimized, respectively. $l_{0}$ is the horizontal distance between the foundation hinge point of the front and back linkages. $l_{1}$ and $l_{4}$ determine the height of the hinge point of the back and front linkage, respectively. $l_{2}$ determines the position of the hinge point of the front linkage and the shield-beam. $l_{3}$ is the length of the front linkage. $l_{5}$ is the overall length of the shield-beam.

The subsystem analysis module is simplified as follows.

$\displaystyle\min e(\bm{l},\bm{p},\bm{\theta})\bm{l}=[\bm{l}_{\textit{local}},% \bm{l}_{\textit{couple}}]=[l_{0},l_{1},l_{3},l_{4},l_{2},l_{5}]^{T}\bm{p}[h_{% \min},h_{\max}]^{T}\bm{l}_{\textit{local}}=[l_{0},l_{1},l_{3},l_{4}]\bm{l}_{% \textit{couple}}=[l_{2},l_{5}]\bm{\theta}=[\alpha,\beta]$ (4)

Where, the objective function $e()$ is the width of the motion trajectory of point A; $\bm{p}$ is the system parameter vector consists of the minimum $h_{\min}$ and maximum $h_{\max}$ of mining height; $\bm{l}_{\textit{local}}$ and $\bm{l}_{\textit{couple}}$ are the subsystem-level design variable and coupling state variable, respectively; and $\bm{\theta}$ is the angle constraint over the four-bar mechanism. As shown in Fig. 3, $\alpha$ and $\beta$ are the elevation angles of back linkage and shield-beam, respectively (see Fig. 3).

The subsystem optimizer can be expressed as

$\displaystyle\min H_{1}(\bm{l}_{\textit{local}},\bm{l}_{\textit{couple}})=\|% \bm{l}_{\textit{local}}^{k}-\bm{l}_{\textit{local}}^{t}\|+\|\bm{l}_{\textit{% couple}}^{k}-\bm{l}_{\textit{couple}}^{t}\|$ (5)

Where, $H_{1}()$ is the objective function of the subsystem optimizer; $\bm{l}_{\textit{local}}^{k}$ and $\bm{l}_{\textit{couple}}^{k}$ are the optimization results of the subsystem-level design variable and coupling state variable; $\bm{l}_{\textit{local}}^{t}$ and $\bm{l}_{\textit{couple}}^{t}$ are the target values computed by system-level optimizer.

The constraint conditions of the analysis module and the optimizer should meet the constraint requirements of the discipline, i.e.

$\displaystyle\alpha_{\min}\leqslant\alpha\leqslant\alpha_{\max}$ (6) $\displaystyle\beta_{\min}\leqslant\beta\leqslant\beta_{\max}$

The parametric modeling function offered by ADAMS/View is used to establish a kinematic model of the four-bar mechanism of the hydraulic powered support. Within the variation range, the design variables are computed and optimized to obtain the optimal design based on the optimization analysis procedures. The optimizer is used to satisfy multidisciplinary consistency constraints according to the description in Eq. (5).

4.2 Optimization of structural parameters of shield-beam

The box-section shield-beam of a hydraulic-powered support has a high capacity to be subjected to combined bending and torsion. A general optimization objective is to optimize the cross-section size and reduce the area of the cross section of the beam, thus reducing the weight of the shield-beam provided that its length is fixed. The example considers the coupling effect of the four-bar linkage parameters for optimization of the cross-section size.

For instance, the cross-section parameters of a three-chamber box section, as shown in Fig. 4, will be optimized by the finite element method with the use of ANSYS Workbench software.

$b$ is the width of the left and right chambers; $\delta$ is the thickness of the upper and lower cover plates of the left and right chambers; $\delta_{1}$ is the thickness of the left and right vertical plates; $\delta_{2}$ is the thickness of the upper and lower cover plates of the middle chamber; $\delta_{3}$ is the thickness of the middle rib plate; $h$ is the cross-section height; and $a$ is the cross-section width.

Based on the analysis in Reference [12], optimization of the cross-section size, i.e. the analysis module of the discipline can be stated as

$\displaystyle\left\{\begin{array}[]{l}\min\sigma_{eqV_{\max}}=\sigma(\bm{v},% \bm{l}_{\textit{couple}})\\ \min S(\bm{v},\bm{l}_{\textit{couple}})\end{array}\right.\quad(\bm{v}=b,\delta% ,\delta_{1},\delta_{2},\delta_{3},h)$ (7)

The subsystem optimization can be stated as

$\displaystyle\min H_{2}(\bm{v})=\|\bm{v}^{k}-\bm{v}^{t}\|$ (8)

The constraint conditions of the analysis module and optimizer of the subsystem should also meet the constraint requirements of the discipline, i.e.,

$\displaystyle\textit{s.t. }0<b<a/2\delta\geqslant\delta_{\min}(h,[\sigma])% \delta_{1}\geqslant\delta_{1\min}(h,\delta,[\tau])0<\delta_{2}\leqslant\delta 0% <\delta_{3}\leqslant\delta_{1}0<h<a$ (9)

where $\sigma_{eqV_{\max}}$ is the maximum equivalent stress of the box-section structure, $S(\bm{v})$ is the volume of the box-section structure, and $\bm{l}_{\textit{couple}}$ is the optimization result of the coupling state variable of the four-bar linkage subsystem. Some of the constraint conditions are stated as follows: $\delta\geqslant$ the minimum value when the bending stresses of the upper and lower plate reach the yield point; $\delta_{1}\geqslant$ the minimum value when the shearing stresses of four vertical plate reach the limit shearing stress. $\bm{v}^{t}$ is the target value of the design variable computed and transferred to the subsystem by the system-level, and $\bm{v}^{k}$ is the optimization result of the subsystem-level design variable.

4.3 System-level optimization

The objective of the system-level optimization design is to optimize the structure and cross-section size parameters of the shield-beam and reduce the weight of various components while satisfying strength requirements and achieving economical design.

As mentioned above, the length of the shield-beam and the position of the hinge point would influence the optimization result of the cross-section size. Therefore, the lengths of $l_{5}$ and $l_{2}$ that determine the position of the hinge point between the front linkage and the shield-beam are designed as the coupling state variables for optimization of two subsystems. The system-level optimization and the consistency constraint are as follows:

$\displaystyle\min F(e,\sigma_{eqV_{\max}},S)$ $\displaystyle\textit{s.t. }H_{1}(\bm{l})=\|\bm{l}^{k}-\bm{l}^{t}\|\leqslant% \varepsilon H_{2}(\bm{v})=\|\bm{v}^{k}-\bm{v}^{t}\|\leqslant\varepsilon$ (10)

where $\bm{l}=[\bm{l}_{\textit{local}},\bm{l}_{\textit{couple}}]$ .

4.4 Federation design based on HLA

This study omits the optimization simulation management members and only describes the collaborative design optimization computation federation members. These include a system-level federation member FedSystem, and two subsystem-level federation members, Fed4BarL-Adams and FedShieldB-Ansys. The former encapsulates the four-bar linkage optimization model created by the Adams software and the latter encapsulates the parameter optimization model of the shield-beam created by the Ansys software. The principles are shown in Fig. 5.

Table 1
Optimization result of four-bar linkage parameters

Design variables	$l_{0}$ /mm	$l_{1}$ /mm	$l_{3}$ /mm	$l_{4}$ /mm	$l_{2}$ /mm	$l_{5}$ /mm
Original parameters	420	983	995	360	295	1340
Optimization result	475	991	1105	270	265	1150

Table 2

Optimization result of the cross-section dimension of the shield-beam

Design variables	$b$ /mm	$\delta$ /mm	$\delta_{1}$ /mm	$\delta_{2}$ /mm	$\delta_{3}$ /mm	$h$ /mm
Original parameters	430	30	25	30	25	430
Optimization result	390	32	26	29	24	415

Figure 5.

Federation design based on HLA.

Vector $\bm{l}_{\textit{couple}}=[l_{2},l_{5}]$ is the coupling state variable of the optimization model between two subsystems. It can be considered as the output of the former and the input of the latter. According to the HLA standard which provides a publish-and-subscribe mechanism for passing messages, vector $\bm{l}_{\textit{couple}}$ corresponds to the published attribute of the four-bar linkage optimization model and the subscribed attribute of the shield-beam optimization model $\bm{l}_{\textit{local}}^{k}$ , $\bm{l}_{\textit{couple}}^{k}$ and $\bm{v}^{k}$ are the optimization results of each iteration of the four-bar linkage optimization model and the shield-beam optimization model, respectively. They are designed as published attributes of the corresponding federation member object class and mapped to the subscribed attributes of the system-level federation member FedSystem. $\bm{l}_{\textit{local}}^{t}$ $\bm{l}_{\textit{couple}}^{t}$ and $\bm{v}^{t}$ are the target values computed and transferred to the subsystem from the system. They are designed as the published attributes of the system-level federation member FedSystem and mapped to the subscribed attributes of the federation members of two subsystems.

4.5 Collaborative optimization result

In the example, the minimum mining height is $h_{\min}=$ 1200 mm and the maximum mining height is $h_{\max}=$ 2600 mm. To prevent the back linkage from being stuck by the collapsed rock in the back of the support, the angle constraints are as follows, $\alpha_{\min}=$ 25 ${}^{\circ}$ , $\alpha_{\max}=$ 85 ${}^{\circ}$ , $\beta_{\min}=$ 118 ${}^{\circ}$ and $\beta_{\max}=$ 155 ${}^{\circ}$ . The value of the consistency constraint $\varepsilon$ is 10 ${}^{-4}$ . The optimization process terminates after 14 iteration cycles.

Figure 6.

Cross-section parameters of the shield-beam.

Tables 1 and 2 present the optimization results of the two subsystems while considering the coupling effect, respectively. Figure 6 describes the iteration curve under the condition of the consistency constraint. From the results shown in Tables 1, 2 and Fig. 6, it is clear that the sizes compared with original parameters are reduced, meanwhile, the consistency constraint is gradually being met.

5. Conclusion

It is a challenging problem to solve the global optimization problem in complex system especially for large-scale, distributed analysis applications. In this paper, an MDO computing environment was developed to solve the global optimization problem of a complex system which is hierarchically decomposed along disciplinary boundaries into numerous subsystems. The problem of interdisciplinary communication was solved based on HLA. In addition, the process of collaborative optimization which is easily parallelized on heterogenous applications was simplified through the consistency constraints. The computing environment was successfully applied to designing of heavy machinery. It was demonstrated that this method is well-suited for MDO.

Footnotes

Acknowledgments

This work was supported by the Research Award Fund for Outstanding Young and Middle-aged Scientists of Shandong Province (No. BS2011ZZ018).

References

Zhu

La Rocca

and van Tooren

M.J.L.

, A methodology to enable automatic 3D routing of aircraft electrical wiring interconnection system, CEAS Aeronautical Journal 8 (2017), 287–302.

Lambe

A.B.

and Martins

J.R.R.A.

, Matrix-free aerostructural optimization of aircraft wings, Structural and Multidisciplinary Optimization 53 (2016), 589–603.

Ghoman

S.S.

Kapania

R.K.

Chen

P.C.

et al., Multifidelity, multistrategy and multidisciplinary design optimization environment, Journal of Aircraft 49 (2012), 1255–1270.

Jin

Duan

Chen

et al., A robust global optimization approach to solving CO problems — enhanced design space decrease collaborative optimization, Structural and Multidisciplinary Optimization 55 (2017), 2305–2322.

Zhao

Huang

Chen

et al., Numerical simulations and surrogate-based optimization of cavitation performance for an aviation fuel pump, Journal of Mechanical Science and Technology 31 (2017), 705–716.

Lee

Kim

Seo

et al., Four-bar linkage-based automatic tool changer: Dynamic modeling and torque optimization, Journal of Mechanical Science and Technology 31 (2017), 2407–2413.

Yao

Chen

Ouyang

et al., A surrogate based multistage-multilevel optimization procedure for multidisciplinary design optimization, Structural and Multidisciplinary Optimization 45 (2012), 559–574.

Misbhauddin

and Alshayeb

, UML model refactoring: A systematic literature review, Empirical Software Engineering 20 (2015), 206–251.

Renzi

, A genetic algorithm-based integrated design environment for the preliminary design and optimization of aeronautical piston engine components, The International Journal of Advanced Manufacturing Technology 86 (2016), 3365–3381.

10.

Junior

J.C.V.S.

Brito

A.V.

Costa

L.F.S.

et al., Testing real-time embedded systems using high level architecture, Design Automation for Embedded Systems 20 (2016), 289–309.

11.

Zacharewicz

and Chen

, A federated approach to develop enterprise interoperability, Journal of Intelligent Manufacturing 27 (2016), 11–31.

12.

Ren

Wang

and Fan

, Geometric parameters optimization of box cross section structure in hydraulic powered support based on finite element analysis, Journal of China Coal Society 35 (2010), 680–685.

Development of multidisciplinary design optimization computing environment based on HLA for heavy machinery

Abstract

Keywords

1. Introduction

2. Individual discipline optimization model

3.1 Multidisciplinary collaborative optimization model

Table 1 Optimization result of four-bar linkage parameters

Footnotes

Acknowledgments

References

Table 1
Optimization result of four-bar linkage parameters