Digital twin modeling for loaded contact pattern-based grinding of spiral bevel gears

To distinguish with the conventional tooth flank grinding only considering geometric accuracy, an innovative digital twin modeling is proposed for loaded contact pattern based grinding of spiral bevel gears. Where, data-driven grinding simulation, sensitivity analysis strategy, adaptive decision and control are developed. Focusing on loaded contact pattern optimization, numerical loaded tooth contact analysis (NLTCA) considering noncentrosymmetric problem and tooth flank roughness is developed for data-driven relationship establishment. Then, an adaptive data-driven tooth flank grinding decision and control model is established. Where, the universal motion concept (UMC) machine settings is selected as the optimal design variable. It is actually an infinite approximation to the target tooth flank in form of an adaptive control system. Moreover, with point-to-point material removal distribution, the different optimization strategies are proposed for accurate tooth flank grinding. In particular, the overcutting problem on the tooth flank grinding programming is investigated. Finally, Levenberg-Marquardt method is applied to solve the established nonlinear lease square model for the accurate machine tool settings having modification variations. Thus, this accurate data-driven digital twin modeling can achieve loaded contact pattern-based grinding. The provided numerical and test instances can verify the proposed digital twin modeling.     

Optimal finite-precision controller realization of sampled-data systems

We investigate the sensitivity of closed-loop stability with respect to finite word length (FWL) effects in the implementation of digital controller coefficients. The optimal realization of digital controller structures with finite precision consideration is formulated as the solution of a constrained nonlinear optimization problem. A sophisticated optimization strategy involving the adaptive simulated annealing (ASA) optimizer is developed to provide an efficient computational method for searching the optimal FWL controller realization with maximum stability bound and minimum bit length requirement. A numerical simulation example is presented to illustrate the effectiveness of the proposed strategy.     

Optimal digital simulations for random linear systems with integration constraints

A generalized approach involving concepts from optimization theory is developed for realizing optimal digital simulations for linear, time-varying, continuous dynamical systems having random inputs by modifying discrete input signal variances. The minimization of a cost functional based on the state covariance matrices of the continuous system and its discrete model leads to a two-point boundary value problem which can be solved by known numerical techniques. The result is a systematic procedure for determining optimal digital simulations under the constraints that the numerical integration formula and integration step size have been specified in advance. An example is presented to illustrate the procedure, including a verification using Monte Carlo simulation runs.     

Optimization of digital holographic setup by a fuzzy logic prediction system

In this study, the optimization of the digital holography setup is achieved by a using fuzzy logic prediction system. In fact, when this optimization process is experimentally performed, some parameters are changed in the setup. These parameters affect directly the obtained image quality after a reconstruction process, which is determined by normalized root mean square. The aim of this study is to achieve the optimization of digital holographic setup by using both experimental and fuzzy logic prediction systems. Furthermore, the required time during the experimental optimization can be lowered by using a numerical method like the fuzzy logic prediction system. Here, the experimental optimization results and the optimization results obtained by the fuzzy logic prediction system are compared. It is offered that the designed experimental system can be optimized by using an artificial intelligent tool. The applied fuzzy logic prediction model is used the first time for optimization of hologram recording setup. As a result, it is reached a conclusion that the optimization of digital holographic setup can be numerically performed by the fuzzy logic prediction system. Moreover, while digital holographic setup is experimentally designed, the required time for optimization is reduced, as well.     

The optimum shape of cooling towers

Numerous computer optimization techniques have been developed and applied primarily to the design of structures composed of discrete elements. Continuous surface structures have been optimized primarily by methods based upon the differential or integral calculus (e.g. the calculus of variations). However, the determination of the optimal shape of continuous surface structures can also be approached by algebraic methods more suitable for digital computation. If the coordinates of the middle surface of a shell are expressed by a finite polynomial series, an optimization problem in a finite set of discrete variables results. In the present work, this method is applied to a particular example of a shell of revolution: a natural draft cooling tower. A simple preliminary design model is formulated in order to evaluate the potential savings due to numerical optimization, and the resulting nonlinear programming problem is solved by iterated linear programming. The results indicate that the method is feasible and that significant savings might be attainable by computerized shape optimization.     

Electronic design automation using a unified optimization framework

This work proposes an object-oriented unified optimization framework (UOF) for general problem optimization. Based on biological inspired techniques, numerical deterministic methods, and C++ objective design, the UOF itself has significant potential to perform optimization operations on various problems. The UOF provides basic interfaces to define a general problem and generic solver, enabling these two different research fields to be bridged. The components of the UOF can be separated into problem and solver components. These two parts work independently allowing high-level code to be reused, and rapidly adapted to new problems and solvers. The UOF is customized to deal with several optimization problems. The first experiment involves a well-known discrete combinational problem, wihle the second one studies the robustness for the reverse modeling problem, which is in high demanded by device manufacturing companies. Additionally, experiments are undertaken to determine the capability of the proposed methods in both analog and digital circuit design automation. The final experiment designs antenna for rapidly growing wireless communication. Most experiments are categorized as simulation-based optimization tasks in the microelectronics industry. The results confirm that UOF has excellent flexibility and extensibility to solve these problems successfully. The developed open-source project is publicly available.     

Decision models for designing and planning private communication networks

We consider the recently developed reconfigurable digital data networks consisting of T1/T3 circuits and Digital Crossconnect Systems (DCSs). A DCS is a device to patch base channels electronically from one T1/T3 circuit to another with a negligible queuing delay at the connecting node. We present new decision models for the design and circuit leasing policies of such digital backbone networks. Our model takes advantage of the special capabilities of the DCS technology and is likely to result in remarkable economic gains for the private network users. The formulation and analyses presented here simultaneously address the following problems: physical link and capacity selection, logical network configuration and channel assignment, and traffic routing on the logical network. The problem formulation results in a large-scale non-linear mixed integer program, and we propose an efficient solution methodology employing Lagrangean relaxation and subgradient optimization. Several numerical results illustrate the utility of our approach for these complex problems. We show that the economies of scale built into the tariff structure of these digital networks can be successfully exploited, and that the inherent flexibility of DCSs leads to logical networks that are dramatically different from their underlying physical topologies.     

浅谈MATLAB在化工计算中的应用

ＭＡＴＬＡＢ是Ｍａｔｈｗｏｒｋｓ公司推出的适用于科学和工程计算的数学软件系统,可高效地解决数值线性代数、微分方程数值解、数值逼近、最优化、数值积分等科学和工程问题,且具有数值稳定性好,使用方便等特点本文对化工中的４个典型计算为例,讨论了ＭＡＴＬＡＢ在化工计算中的应用。     

有限字长数字控制器的实稳定半径最优实现

主要讨论了有限字长(FWL)数字控制器的一种最优实现问题,考察了一个典型的采样反馈系统,将实有理稳定半径测度应用到有限字长数字控制器的实现问题中,对实稳定半径测度进行优化,并由此得到控制器的最优状态变换矩阵和最优结构及最小字长.数值算例验证了优化的结果是有效的,优化后较小字长的控制器就可以使系统取得较大的稳定半径.     

Optimal realizations of fixed-point implemented digital controllers with the smallest dynamic range

A novel approach is proposed to design optimal finite word length (FWL) realizations of digital controllers implemented in fixed-point arithmetic. A minimax-based search procedure is first formulated to obtain an optimal controller realization that optimizes an FWL closed-loop stability measure. Since this FWL closed-loop stability measure is solely linked to the fractional part or precision of fixed-point format, the resulting realization may not have the smallest dynamic range. A measure is then derived to indicate the dynamic range of fixed-point implemented realization. By choosing an appropriate orthogonal transformation of this dynamic range measure of the optimal precision controller realization, a numerical optimization method is developed to make the controller realization having the smallest dynamic range without sacrificing FWL closed-loop stability robustness. The proposed approach is more efficient than a direct optimization of some combined FWL closed-loop stability and dynamic range measure via a numerical means. The proposed approach is established within a unified framework that includes both the shift and delta operator parameterizations, which makes it possible to compare the closed-loop stability characteristics of the optimal FWL controller realizations using shift and delta operators, respectively. Through analysing the simulation results of a design example, some useful insights and understandings are obtained regarding the FWL controller realizations based on shift and delta operators.     

The steady-state region of attraction under linear feedback control: A numerical approach

In this paper, a numerical approach to operability analysis is developed. Based on the concept of the steady-state region of attraction, which indicates the initial operating conditions that can be driven to a given setpoint, this analysis helps design engineers assess whether a process can be effectively controlled by linear control systems. Using steady-state operating data that are generated with process simulators (such as ASPEN PLUS^®), the steady-state region of attraction are calculated by solving the proposed constrained nonlinear optimization problem. The objective function for the optimization problem is developed using the ellipsoid theory while the constraint functions are formulated from the complement set of the initially defined constraint set and the boundary of the available input space (AIS). Furthermore, as the solution of a nonlinear optimization problem generally depends on the initial starting point, a method of generating a set of ellipsoids in the hyperspace to start the calculation is also developed. The proposed constrained nonlinear optimization problem can be solved using numerical tools such as MATLAB^®. This analysis can be performed based on process flowsheets with process simulators and thus is useful in early stages of process design. The use of the proposed numerical framework is illustrated by a case study of a methyl acetate reactive distillation column.     

基于VC++6.0与Fortran混合编程的斜井螺杆泵优化设计

针对某斜井螺杆泵优化设计软件进行大型数值计算时效率很低的问题,应用VC+ + 6.0与Fortran语言混合编程的方法编制斜井螺杆泵优化设计软件. 该方法用VC+ + 6.0制作界面,用Fortran语言编写主运算程序,用VC+ + 6.0调用Fortran生成的动态链接库. 对于斜井螺杆泵的优化设计,采用Fortran编写优化设计程序,用ANSYS对整个抽油杆系统进行非线性大变形有限元分析﹑静力分析和疲劳分析. 工程实例表明,该软件计算效率较高,可以提高人机交互性和可操作性,同时验证混合编程在大型数值运算软件设计中的可行性、实用性以及有效性.     

An algorithm for clustering based on non-smooth optimization techniques

The problem of cluster analysis is formulated as a problem of non‐smooth, non‐convex optimization, and an algorithm for solving the cluster analysis problem based on non‐smooth optimization techniques is developed. We discuss applications of this algorithm in large databases. Results of numerical experiments are presented to demonstrate the effectiveness of this algorithm.     

平面全柔性3-DOF过驱动并联机构的最优综合

以设计全柔性多自由度过驱动并联机构为目标，研究了平面3-DOF 4RRR过驱动并联机构的最优综合问题．从一般四分支3-DOF平面并联机构出发，建立了机构的运动学模型；给出了机构的4种可能拓扑结构分类，对不同拓扑结构类型机构的运动学和力学性能进行了分析比较．建立了并联机构全工作空间操作性改善优化模型，采用遗传算法进行优化设计并给出了实例，根据优化实例的结果设计制造了平面全柔性三自由度过驱动并联机构．以上方法对其它全柔性并联机构的优化设计具有参考价值．     

Shape optimization with computational fluid dynamics

In many product design and development applications, computational fluid dynamics CFD has become a useful analytical simulation tool. CFD simulations are quite useful in predicting several response parameters for a given design condition. However, like any analysis tool CFD simulations provide limited insight into the design space and the changes needed to find the optimum design parameters.This paper deals with the shape optimization of fluid flows using CFD and numerical optimization techniques. By integrating a commercial optimization code with a CFD code, a CFD shape optimization tool was developed. To study the effectiveness of the developed tool and its ability to produce results with reasonable CPU time, the shape optimization of an airfoil and S-shaped duct are studied with different numbers of design variables. The developed shape optimization tool along with the optimization and CPU time results are discussed.     

Adaptive FE-procedures in shape optimization

In structural optimization the quality of the optimization result strongly depends on the reliability of the underlying structural analysis. This comprises the quality and range of the mechanical model, e.g. linear elastic or geometrically and materially nonlinear, as well as the accuracy of the numerical model, e.g. the discretization error of the FE-model. The latter aspect is addressed in the present contribution. In order to guarantee the quality of the numerical results the discretization error of the finite element solution is controlled and the finite element discretization is adaptively refined during the optimization process. Conventionally, so-called global error estimates are applied in structural optimization which estimate the error of the total strain energy. In the present paper local error estimates are introduced in shape optimization which allow to control directly the discretization error of local optimization criteria. In general, the adaptive refinement of the finite element discretization by remeshing affects the convergence of the optimization process if a gradient-based optimization algorithm is applied. In order to reduce this effect the sensitivity of the discretization error must also be restricted. Suitable refinement indicators are developed for globally and locally adaptive procedures. Finally, the potential of two techniques, which may improve the numerical efficiency of adaptive FE-procedures within the optimization process, is studied. The proposed methods and procedures are verified by 2-D shape optimization examples. Received June 3, 1999     

Optimization formulations for the maximum nonlinear buckling load of composite structures

This paper focuses on criterion functions for gradient based optimization of the buckling load of laminated composite structures considering different types of buckling behaviour. A local criterion is developed, and is, together with a range of local and global criterion functions from literature, benchmarked on a number of numerical examples of laminated composite structures for the maximization of the buckling load considering fiber angle design variables. The optimization formulations are based on either linear or geometrically nonlinear analysis and formulated as mathematical programming problems solved using gradient based techniques. The developed local criterion is formulated such it captures nonlinear effects upon loading and proves useful for both analysis purposes and as a criterion for use in nonlinear buckling optimization.     

Design Optimization of Multibody Systems by Sequential Approximation

Design optimization of multibody systems is usually established by a direct coupling of multibody system analysis and mathematical programming algorithms. However, a direct coupling is hindered by the transient and computationally complex behavior of many multibody systems. In structural optimization often approximation concepts are used instead to interface numerical analysis and optimization. This paper shows that such an approach is valuable for the optimization of multibody systems as well. A design optimization tool has been developed for multibody systems that generates a sequence of approximate optimization problems. The approach is illustrated by three examples: an impact absorber, a slider-crank mechanism, and a stress-constrained four-bar mechanism. Furthermore, the consequences for an accurate and efficient accompanying design sensitivity analysis are discussed.     

ε-relaxed approach in structural topology optimization

This paper presents a so-called -relaxed approach for structural topology optimization problems of discrete structures. The distinctive feature of this new approach is that unlike the typical treatment of topology optimization problems based on the ground structure approach, we eliminate the singular optima from the problem formulation and thus unify the sizing and topology optimization within the same framework. As a result, numerical methods developed for sizing optimization problems can be applied directly to the solution of topology optimization problems without any further treatment. The application of the proposed approach and its effectiveness are illustrated with several numerical examples.