Sensor selection for model-based real-time optimization: relating design of experiments and design cost

Real-time optimization systems have become a common tool, in the continuous manufacturing industries, for improving process performance. Typically, these are on-line, steady-state, model-based optimization systems, whose effectiveness depends on a large number of design decisions. The work presented here addresses one of these design decisions and proposes a systematic approach to the selection of sensors to be used by the RTO system. This paper develops a sensor system selection metric based on a trade-off between two approaches to the design of experiments, which is shown to be consistent with the design cost approach of Forbes and Marlin [Computers Chem Eng 20 (1996) 7/7]. The resulting design metric is incorporated into a systematic procedure for RTO sensor selection problem. Finally, the proposed RTO sensor selection procedure is illustrated with a case study using the Williams–Otto [AIEE Trans 79 (1960), 458] plant.     

Interdigitation for effective design space exploration using iSIGHT

Optimization studies for nonlinear constrained problems (i.e. most complex engineering design problems) have repeatedly shown that (i) no single optimization technique performs best for all design problems, and (ii) in most cases, a mix of techniques perform better than a single technique for a given design problem. iSIGHT^TM is a generic software framework for integration, automation, and optimization of design processes that has been developed on the foundation of interdigitation: the strategy of combining multiple optimization algorithms to exploit their desirable aspects for solving complex problems. With the recent paradigm shift from traditional optimization to design space exploration for evaluating “what-if” scenarios and trade-off studies, iSIGHT has grown from an optimization software system to a complete design exploration environment, providing a suite of design exploration tools including a collection of optimization techniques, design of experiments techniques, approximation methods, and probabilistic quality engineering methods. Likewise, the interdigitation design methodology embodied in iSIGHT has grown to support the interdigitation of all design exploration tools for effective design space exploration. In this paper we present an overview of iSIGHT, past and present, of the interdigitation design methodology and its implementation for multiple design exploration tools, and of an industrial case study for which elements of this methodology have been applied. Received December 30, 2000     

Integration of topology and shape optimization for design of structural components

This paper presents an integrated approach that supports the topology optimization and CAD-based shape optimization. The main contribution of the paper is using the geometric reconstruction technique that is mathematically sound and error bounded for creating solid models of the topologically optimized structures with smooth geometric boundary. This geometric reconstruction method extends the integration to 3-D applications. In addition, commercial Computer-Aided Design (CAD), finite element analysis (FEA), optimization, and application software tools are incorporated to support the integrated optimization process. The integration is carried out by first converting the geometry of the topologically optimized structure into smooth and parametric B-spline curves and surfaces. The B-spline curves and surfaces are then imported into a parametric CAD environment to build solid models of the structure. The control point movements of the B-spline curves or surfaces are defined as design variables for shape optimization, in which CAD-based design velocity field computations, design sensitivity analysis (DSA), and nonlinear programming are performed. Both 2-D plane stress and 3-D solid examples are presented to demonstrate the proposed approach. Received January 27, 2000 Communicated by J. Sobieski     

Control system design for parametric uncertainty

This paper introduces some recently developed frequency-domain design techniques that are effective in the design of control systems that are required to be robust under parametric uncertainty. We have extended the well-known classical control tools (i.e., Nyquist plot, Bode plot, and Nichols chart) developed for a fixed plant to the domain of families of plants where the uncertain parameter varies in intervals. Using this new family of plots, classical control design techniques can be used to design robust control systems. The technique is illustrated by examples.     

Multimaterial design of physically nonlinear structures

A theoretical consideration of optimization problems for physically nonlinear hyperelastic structures is carried out. The structures are subjected to a single static “dead” loading and a multimaterial design approach is analysed. Structural materials are assumed to be isotropic, with stress-strain relations being weakly concave. The problems considered are mass minimization with prescribed structural stiffness, stiffness maximization with prescribed structural mass, and mass minimization with constrained stresses. Optimality conditions for the problems are analysed. Generalizations of Maxwell’s and Michell’s theorems for the considered structures are proved. Some regularities inherent in the third problem are analysed using the analytical example of a three-rod physically nonlinear truss made of two materials. An algorithm for compliance decreasing in the case of prescribed structural mass is proposed. The monotonicity property of the algorithm is proved. Numerical examples (bi-material beam and airframe) are presented and corresponding results are analysed on a basis of the theoretical approaches developed. Received November 3, 1999     

CAD系统的二次开发在飞机构型优化中的应用

飞机概念设计优化目前存在的主要问题是分析对象的几何描述过于简单、描述不统一和修改困难,造成分析计算可信度不高而且不同学科分析模块间信息很难转换。从建立一个三维运输机参数模型入手,通过CAD系统的二次开发,将模型集成到设计优化框架中,应用高信度的计算流体方法（CFD）,以飞机起飞重量最小为目标完成构型优化。     

仪器设备网络开放系统的设计

在传统的管理模式下,高校和社会企业之间的仪器设备资源没有得到充分的信息共享,本文基于Web网络技术,采用B/S开发模式,提供了构建仪器设备网络开放系统的解决方案,并给出了系统数据库设计图、系统功能模块设计图和仪器预约流程设计图。     

A mutual energy formulation for optimal structural design

This paper presents a variational formulation for the design of elastic structures where the function to be minimized by the optimal design, i.e. the objective, is expressed in abstract form. The resulting statement of necessary conditions is uniformly applicable for all admissible objectives. Both state and adjoint state variables appear directly in the problem statement, and all objectives and the arguments of constraints are scalars. The adjoint pair of state variables appear in symmetric roles via the expression termed “mutual energy". Application of the generalized formulation is demonstrated by treatment of the following examples: design to minimize the maximum value of displacement or to minimize a global measure of stress, design for generalized compliance, design where self-weight is taken into account, and multicriterion design. Received April 28, 2000     

Analytical derivatives technology for structural shape design

The ability to perform and evaluate the effect of shape changes on the stress and modal responses of components is an important ingredient in the “design” of aircraft engine components. The classical design of experiments (DOE)-based approach that is motivated from statistics (for physical experiments) is one of the possible approaches for the evaluation of the component response with respect to design parameters [Myers, Montgomery. Response surface methodology, process and product optimization using design of experiments. John Wiley and Sons, NY (1995)]. As the underlying physical model used for the component response is deterministic and understood through a computer simulation model, one needs to re-think the use of the classical DOE techniques for this class of problems. In this paper, we explore an alternate sensitivity-analysis-based technique where a deterministic parametric response is constructed using exact derivatives of the complex finite-element (FE)-based computer models to design parameters. The method is based on a discrete sensitivity analysis formulation using semi-automatic differentiation (Griewank, SIAM (2000), ADIFOR, Automatic Differentiation of FORTRAN codes ) to compute the Taylor series or its Pade equivalent for finite-element-based responses. Shape design or optimization in the context of finite element modeling is challenging because the evaluation of the response for different shape requires the need for a meshing consistent with the new geometry. This paper examines the differences in the nature and performance (accuracy and efficiency) of the analytical derivatives approach against other existing approaches with validation on several benchmark structural applications. The use of analytical derivatives for parametric analysis is demonstrated to have accuracy benefits on certain classes of shape applications.     

Parameterization and optimization strategies for the automated design of uPVC profile extrusion dies

Optimization strategies for use within an automated optimization framework for PVC profile extrusion dies are presented. The methods are designed to work in an industrial environment and must therefore account for the specific design and manufacturing techniques for these profile dies. The complex three-dimensional die geometry will be represented through a series of two-dimensional so-called die-slices. The purpose of the presented optimization cycle is to find the optimal shape of the die cross-section of the die-slices. Each die-slice geometry is optimized by a computerized optimization loop using a finite element (FE) analysis of the polymer flow through the die. Simple data representation of the complex die geometry allows an efficient parameterization. Several optimization strategies are compared regarding the achieved quality of the optimization, the computational costs, the required user interaction and the robustness in industrial applications. The strategies are (i) a global scheme in which all design variables (DVs) are dealt with simultaneously, (ii) a sequential optimization in which DVs are addressed one after each other, (iii) employing a height approximation type method in which the new values for the DVs are found using assumptions of the flow between two parallel plates, and (iv) a global scheme in which the DVs are decoupled taking advantage of the particular FE analysis applied.     

一类参数线性系统辨识的最优输入设计

对未知参数进行估计时,得到的结果与激励系统所选用的输入信号有较大的关系.针对一类参数可线性化系统,本文提出了一种利用多维同步正交信号和直接配点法设计最优输入信号的方法.首先根据最小二乘原理,利用法矩阵构造Mayer型性能指标函数.然后利用不同频率的正弦基函数构造相互正交的多维输入,通过添加幅值与相位的等式约束,使得输入信号在初/末时刻取值均为零.之后采用直接配点法离散状态变量,将动态的最优输入问题转化为静态的非线性规划问题.最后采用从可行解到优化解的串行优化策略进行求解,不仅提高了寻优效率,还确保了优化结果为原问题的可行解.仿真结果表明,与工程上常用的输入信号相比,本文方法获取的最优输入信号可以提高参数估计精度并加快收敛速率.     

Formulation of the Audze-Eglais uniform Latin hypercube design of experiments for constrained design spaces

Optimal Latin Hypercubes (OLH) created in a constrained design space might produce Design of Experiments (DoE) containing infeasible points if the underlying formulation disregards the constraints. Simply omitting these infeasible points leads to a DoE with fewer experiments than desired and to a set of points that is not optimally distributed. By using the same number of points a better mapping of the feasible space can be achieved. This paper describes the development of a procedure that creates OLHs for constrained design spaces. An existing formulation is extended to meet this requirement. Here, the OLH is found by minimizing the Audze-Eglais potential energy of the points using a permutation genetic algorithm. Examples validate the procedure and demonstrate its capabilities in finding space-filling Latin Hypercubes in arbitrarily shaped design spaces.     

Dynamic problems of shape optimal design for shallow curved plates

The problem of optimal structural design of shallow thin-walled elements such as curved rectangular plates are formulated and solved for dynamic conditions. The distribution of the initial curvature of shallow plates in a nonstrained state is taken as the control function. Dynamic compliance is considered as the minimized performance functional. Optimality conditions are derived for the distributed parameter system considered and applied for the construction of the analytical solution. The rigorous analysis of extremum conditions and behavioural equations shows that the initial optimization problem is decomposed into several problems of classical structural analysis, which can be successfully solved analytically. Some optimal designs obtained for rectangular plates under stretching and bending, and a plate lying on an elastic foundation and subjected to lateral forces are presented. Received: November 27, 1998     

Untangling parameters: A formalized framework for identifying overlapping design parameters between two disciplines for creating an interdisciplinary parametric model

Employing an interdisciplinary approach in design is an important part of the future of architecture. Therefore, taking a step toward better understanding the overlaps between disciplines, and formalizing the process of integration between disciplines accelerates progress in the field. In examining an interdisciplinary design approach using computational design and simulation tools, while considering shell structures as a special case for spanning large-span roofs, structural and daylighting discipline are considered. The aim is to understand what are the design parameters that co-exist in the structural and daylighting design disciplines, and how may these parameters be implemented in a parametric model created by designers. The parametric model that includes discipline specific parameters can later be used for interdisciplinary performance-based design. Implementing design parameters calls for an understanding of the ways in which parameters affect design and performance. This research considers the application of parametric design methods at the early stages of design for designing high-performance buildings.     

Selection strategies in a structural design support system

This paper presents two selection strategies for the process of establishing a structural design support system. The distinct difference between the strategies is the point of time when the decision maker participates in the design process. The first strategy is called the pre-selection strategy in which the designer tries to grasp the intention or preference of the decision maker at an early stage of the design, and the second one is called the post-selection strategy in which the designer prepares all design information as much as possible, and then the decision maker selects the final design solution. Based on these two strategies, the shared and essential processes of the structural design support system will be explicated in advance, and then the characteristics of these two strategies will be compared. The crucial parts of the structural design support system are common design process that is shared in the two strategies and the alternative based design approach. The common design process means the basic sequences of the design process, such as problem specification, concept design, preliminary design and selection of the final design solution, that are used conventionally in the general design process. These design processes are carried out with the screened region of the design alternatives, which is efficient and effective for the selection of the final design solution. With these concepts, the structural design support system especially the grid-like type structures will be examined and the usefulness of our design methodology will be confirmed. Received October 14, 1999     

PIGMOD: parametric and interactive geometric modeller for mechanical design

The paper describes the implementation of a geometric modelling system named PIGMOD with a parametric design capability based on non-manifold geometric modelling. The basic idea is that a set of modelling operations can be so defined that there are correspondences between the geometric constraints and the modelling operations. The geometric relations are represented internally in terms of the modelling operation sequence. The modelling operations are implemented as manipulations on a non-manifold geometric model. The methods for modifying the geometric model automatically and consistently in accordance with changed or added dimensions are implemented in a simple and unified way.     

A novel data reduction method for Takagi–Sugeno fuzzy system design based on statistical design of experiment

This paper introduces a simple, systematic and effective method for designing Takagi–Sugeno (T–S) fuzzy systems utilizing a significantly smaller training data set versus existing methods. Creating proper training data is usually not an easy task and requires spending considerable time and resources. The proposed method first uses a three-level factorial design to partition the output space. Next the least square technique is used to estimate each of the partitioned output spaces. The membership functions are introduced with only three variables (min, max and number of membership functions). Fuzzy rules are generated with respect to the partitioned output surfaces and the membership functions. The proposed method is applied to two benchmark problems, controlling an inverted pendulum as well as modeling a nonlinear function. In the case of the inverted pendulum simulation results demonstrate significant improvement. In the case of nonlinear function modeling we demonstrated sufficient accuracy with only 9 training data, which represents 98% reduction in the number of training data compare to other method. Additionally, the proposed method offers extremely low computation time allowing it to be used with adaptive type systems.     

桥式起重机智能定制与报价系统开发

通过长期对桥式起重机结构和企业需求的分析研究,将快速智能设计与智能报价两者相结合。以VB6.0为编程工具,Access为数据支撑,运用模块化与参数化技术,二次开发技术以及基于混沌遗传算法的主梁优化设计等关键技术。开发了桥式起重机智能快速定制与报价系统。该系统可根据用户定制参数进行设计计算、优化设计以及快速报价,为企业快速响应用户需求、缩短产品设计周期、降低企业设计成本奠定了技术基础,其对桥式起重机的长期发展具有深远影响。     

An open platform of shape design optimization for shell structure

A general platform built on a computer-aided design (CAD) system is developed for parameterized shape design optimization of shell structure. Within the platform, parameterized surface modeling and computer-aided engineering (CAE) applications are embedded and seamlessly integrated with the CAD system through its application programming interface (API). Firstly, instead of the CAD system inherent surface modeling, a parameterized surface modeling for shell structure is fulfilled through integrating with parametric solid modeling of the CAD system. Thus, any dimensions for parametric solid modeling can be used to control shape modification of shell structure and serve as design variables for shape design optimization. Secondly, seamless integration of geometry modeling and finite-element modeling for shell structure is implemented. Finally, with integrated procedures of finite-element analysis and optimization algorithms, a general platform for parameterized shape optimization of shell structure is realized. Numerical examples are presented, and the results validate the effectiveness and efficiency of the platform. A shorten version of this paper was presented to the 7th World Congress of Computation Mechanics (WCCM 2006), July 16–22, 2006, Los Angeles, CA, USA.