Optimal control concepts in design sensitivity analysis

A close link is established between open loop optimal control theory and optimal design by noting certain similarities in the gradient calculations. The resulting benefits include a unified approach, together with physical insights in design sensitivity analysis, and an efficient approach for simultaneous optimal control and design. Both matrix displacement and matrix force methods are considered, and results are presented for dynamic systems, structures, and elasticity problems

Exponential approximations in optimal design

One-point and two-point exponential functions have been developed and proved to be very effective approximations of structural response. The exponential has been compared to the linear, reciprocal and quadratic fit methods. Four test problems in structural analysis have been selected. The use of such approximations is attractive in structural optimization to reduce the numbers of exact analyses which involve computationally expensive finite element analysis

Fixed-point iteration based algorithm for a class of nonlinear programming problems

A fixed-point algorithm is presented for a class of singly constrained nonlinear programming (NLP) problems with bounds. Setting the gradient of the Lagrangian equal to zero yields a set of optimality conditions. However, a direct solution on general problems may yield non-KKT points. Under the assumption that the gradient of the objective function is negative while the gradient of the constraint function is positive, and that the variables are positive, it is shown that the fixed-point iterations can converge to a KKT point. An active set strategy is used to handle lower and upper bounds. While fixed-point iteration algorithms can be found in the structural optimization literature, these are presented without clearly stating assumptions under which convergence may be achieved. They are also problem specific as opposed to working with general functions f, g. Here, the algorithm targets general functions which satisfy the stated assumptions. Further, within this general context, the fixed-point variable update formula is given physical significance. Unlike NLP descent methods, no line search is involved to determine step size which involves many function calls or simulations. Thus, the resulting algorithm is vastly superior for the subclass of problems considered. Moreover, the number of function evaluations remains independent of the number of variables allowing the efficient solution of problems with a large number of variables. Applications and numerical examples are presented

An optimization program based on the method of feasible directions: Theory and users guide

The theory and user instructions for an optimization code based on the method of feasible directions are presented. The code was written for wide distribution and ease of attachment to other simulation software. Although the theory of the method of feasible direction was developed in the 1960's, many considerations are involved in its actual implementation as a computer code. Included in the code are a number of features to improve robustness in optimization. The search direction is obtained by solving a quadratic program using an interior method based on Karmarkar's algorithm. The theory is discussed focusing on the important and often overlooked role played by the various parameters guiding the iterations within the program. Also discussed is a robust approach for handling infeasible starting points. The code was validated by solving a variety of structural optimization test problems that have known solutions obtained by other optimization codes. It has been observed that this code is robust: it has solved a variety of problems from different starting points. However, the code is inefficient in that it takes considerable CPU time as compared with certain other available codes. Further work is required to improve its efficiency while retaining its robustness

The Machine that Changed the World: The Story of Lean Production

Nomenclature A = area E b = black body emission per unit area Fij or F sj = shape factor between surfaces i and j (including; = (') or between gas and surface j q = heat transfer m = mass flow rate N = number of surface elements on the wall and the solid T = temperature Az = size of each axial segment of the kil

Daylight adaptive smart indoor lighting control method using artificial neural networks

Accurate and efficient adjustment of maintained illuminance and illuminance uniformity in indoor environments with daylight variations is a tremendous challenge, mainly due to the nonlinear and time-variant nature of lighting control systems. In this paper, we propose a smart lighting control method for indoor environments with both dimmable (controllable) and uncontrollable external light sources. Targeting an indoor environment with multiple zones, each requiring a different lighting condition and equipped with an unequal number of photodetectors and dimmable light sources, this paper presents a novel control mechanism that determines the output flux of each luminary in such a way that each zone (1) receives the required maintained illuminance, (2) illuminance uniformity conditions are met inside each zone, and (3) the power consumption is optimized. This method uses a neural network to learn the impact of each luminary on the maintained illuminance of each zone and adjust the dimming level of the luminaries to establish the required illuminance in the zones. We also rely on photodetectors to measure the daylight illuminance continuously and use it as the bias value for the neural network. The new priority value allows losing some illuminance accuracy (by allowing lager difference between the actual and required maintained illuminance values) for low-priority zones to reduce power consumption. The method has been evaluated in different test cases by chaining the widely-used DIALux tool and some MATLAB toolboxes. The evaluation results show that the method can achieve considerable accuracy by yielding an average Mean Square Error of 1.2 between the demanded and sensed illuminance values. Furthermore, when all sensors except one reference sensor are removed from each zone (to increase user comfort or reduce cost), the mean square error is less than 25.4 across all considered test cases

Application of structural topology optimisation to perforated steel beams

This paper focuses on the application of structural topology optimisation technique to design steel perforated I-sections as a first attempt to replace the traditional cellular beams and better understand the mechanisms involved when subjected to bending and shear actions. An optimum web opening configuration is suggested based on the results of parametric studies. A FE analysis is further employed to determine the performance of the optimised beam in comparison to the conventional widely used cellular type beam. It is found that the optimised beam overperforms in terms of load carrying capacities, deformations, and stress intensities. Barriers to the implementation of the topology optimisation technique to the routine design of beam web are highlighted

A new scheme for efficient and direct shape optimization of complex structures represented by polygonal meshes

In this paper, a new shape optimization approach is proposed to provide an efficient optimization solution of complex structures represented by polygonal meshes. Our approach consists of three main steps: (1) surface partitioning of polygonal meshes; (2) generation of shape design variables on the basis of partitioned surface patches; and (3) gradient-based shape optimization of the structures by reducing a weighted compliance among all load cases. The main contributions of this paper include (i) that our approach can be directly applied on polygonal meshes with the reduction of design variables or decision variables by 10 to 1000 times, compared to the conventional design variable scheme of using each mesh node; (ii) our perturbation scheme is mathematically proven with respect to maintaining the smoothness of each surface patch, except on its boundary; and (iii) overall, our approach can be used to automate time-consuming shape optimization of polygonal meshes to a greater extent. Numerical experiments have been conducted and the results indicate the effectiveness of the approach. Copyright © 2003 John Wiley & Sons, Ltd.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/34539/1/859_ftp.pd