Optimal design of computer experiments for surrogate models with dimensionless variables

This paper presents a method for constructing optimal design of experiments (DoE) intended for building surrogate models using dimensionless (or non-dimensional) variables. In order to increase the fidelity of the model obtained by regression, the DoE needs to optimally cover the dimensionless space. However, in order to generate the data for the regression, one still needs a DoE for the physical variables, in order to carry out the simulations. Thus, there exist two spaces, each one needing a DoE. Since the dimensionless space is always smaller than the physical one, the challenge for building a DoE is that the relation between the two spaces is not bijective. Moreover, each space usually has its own domain constraints, which renders them not-surjective. This means that it is impossible to design the DoE in one space and then automatically generate the corresponding DoE in the other space while satisfying the constraints from both spaces. The solution proposed in the paper transforms the computation of the DoE into an optimization problem formulated in terms of a space-filling criterion (maximizing the minimum distance between neighboring points). An approach is proposed for efficiently solving this optimization problem in a two steps procedure. The method is particularly well suited for building surrogates in terms of dimensionless variables spanning several orders of magnitude (e.g. power laws). The paper also proposes some variations of the method; one when more control is needed on the number of levels on each non-dimensional variable and another one when a good distribution of the DoE is desired in the logarithmic scale. The DoE construction method is illustrated on three case studies. A purely numerical case illustrates each step of the method and two other, mechanical and thermal, case studies illustrate the results in different configurations and different practical aspects.     

Optimal design of sandwich and laminated composite plates based on the planning of experiments

Optimal design problems of sandwich plates with soft core and laminated composite face layers, and multilayered composite plates are investigated. The optimal design problems are solved by using the method of the planning of experiments. The optimization procedure is divided into the following stages: choice of control parameters and establishment of the domain of search, elaboration of plans of experiment for the chosen number of reference points, execution of the experiment, determination of simple mathematical models from the experimental data, design of the structure on the basis of the mathematical models discovered, and finally verification experiments at the point of the optimal solution. Vibration and damping analysis is performed by using a sandwich plate finite elements based on a broken line model. Damping properties of the core and face layers of the plate are taken into account in the optimal design. Modal loss factors are computed using the method of complex eigenvalues or the energy method. Frequencies and modal loss factors of the plate are constraints in the optimal design problem. There are also constraints on geometrical parameters and the bending stiffness of the plate. The mass of the plate is the objective function. Design parameters are the thickness of the plate layers. In the points of experiments computer simulation using FEM is carried out. Using this information, simple mathematical models for frequencies and modal loss factors for the plate are determined. These simple mathematical functions are used as constraints in the nonlinear programming problem, which is solved by random search and the penalty function method. Numerical examples of the optimal design of clamped sandwich and simply supported laminated composite plates are presented. A significant improvement of damping properties of a sandwich plate is observed in comparison with a simple plate of equal natural frequencies.     

Optimal designs for conjoint experiments

In conjoint experiments, each respondent receives a set of profiles to rate. Sometimes, the profiles are expensive prototypes that respondents have to test before rating them. Designing these experiments involves determining how many and which profiles each respondent has to rate and how many respondents are needed. To that end, the set of profiles offered to a respondent is treated as a separate block in the design and a random respondent effect is used in the model because profile ratings from the same respondent are correlated. Optimal conjoint designs are then obtained by means of an adapted version of an algorithm for finding D-optimal split-plot designs. A key feature of the design construction algorithm is that it returns the optimal number of respondents and the optimal number of profiles each respondent has to evaluate for a given number of profiles. The properties of the optimal designs are described in detail and some practical recommendations are given.     

Bayesian models for two-sample time-course microarray experiments

A truly functional Bayesian method for detecting temporally differentially expressed genes between two experimental conditions is presented. The method distinguishes between two biologically different set ups, one in which the two samples are interchangeable, and one in which the second sample is a modification of the first, i.e. the two samples are non-interchangeable. This distinction leads to two different Bayesian models, which allow more flexibility in modeling gene expression profiles. The method allows one to identify differentially expressed genes, to rank them and to estimate their expression profiles. The proposed procedure successfully deals with various technical difficulties which arise in microarray time-course experiments, such as small number of observations, non-uniform sampling intervals and presence of missing data or repeated measurements. The procedure allows one to account for various types of error, thus offering a good compromise between nonparametric and normality assumption based techniques. In addition, all evaluations are carried out using analytic expressions, hence the entire procedure requires very little computational effort. The performance of the procedure is studied using simulated and real data.     

Quantifying design quality through design experiments

The authors present a model for design quality metrics, discuss its relevance, and give some examples of use. Design experiments demonstrate error data extraction and analysis. Using a model of the design process for electronic products that emphasizes the resulting quality of the design, the authors demonstrated that they can quantify design quality. They can best express the probability of an error-free design in terms of the quality of the synthesis process and the quality of the verification procedure     

Designing optimal sequential experiments for a Bayesian classifier

As computing power has grown, the trend in experimental design has been from techniques requiring little computation towards techniques providing better, more general results at the cost of additional computation. This paper continues this trend presenting three new methods for designing experiments. A summary of previous work in experimental design is provided and used to show how these new methods generalize previous criteria and provide a more accurate analysis than prior methods. The first method generates experimental designs by maximizing the uncertainty of the experiment's result, while the remaining two methods minimize an approximation of the variance of a function of the parameters. The third method uses a computationally expensive discrete approximation to determine the variance. The methods are tested and compared using the logistic model and a Bayesian classifier. The results show that at the expense of greater computation, experimental designs more effective at reducing the uncertainty of the decision boundary of the Bayesian classifier can be generated     

直接数字频率合成器DDS的优化设计

在深入理解DDS基本原理的基础上,采用多级流水线控制技术对DDS的VHDL语言实现进行了优化,并进行了异步接口的同步化设计,给出了DDS系统的时序仿真结果及其在FPGA中的资源占有率。     

Optimal design of arch-networks

Optimality criteria for minimum volume design are derived for a class of arch-networks comprising of pin-supported arches contained in vertical planes. The supports lie in a horizontal plane and the loads are applied vertically. It is assumed that the arches transmit loads by axial compression and the interaction among arches at intersections is by vertical reactions. It is shown that in the optimal arch-network, the centroids of all arches lie on a single surface and each individual arch is of an optimal form. An iterative numerical procedure to obtain the optimal solution for a given layout plan of arches and the loading on it is presented. Two examples are provided for the purpose of illustration.     

Sequential optimal design of neurophysiology experiments

Adaptively optimizing experiments has the potential to significantly reduce the number of trials needed to build parametric statistical models of neural systems. However, application of adaptive methods to neurophysiology has been limited by severe computational challenges. Since most neurons are high-dimensional systems, optimizing neurophysiology experiments requires computing high-dimensional integrations and optimizations in real time. Here we present a fast algorithm for choosing the most informative stimulus by maximizing the mutual information between the data and the unknown parameters of a generalized linear model (GLM) that we want to fit to the neuron's activity. We rely on important log concavity and asymptotic normality properties of the posterior to facilitate the required computations. Our algorithm requires only low-rank matrix manipulations and a two-dimensional search to choose the optimal stimulus. The average running time of these operations scales quadratically with the dimensionality of the GLM, making real-time adaptive experimental design feasible even for high-dimensional stimulus and parameter spaces. For example, we require roughly 10 milliseconds on a desktop computer to optimize a 100-dimensional stimulus. Despite using some approximations to make the algorithm efficient, our algorithm asymptotically decreases the uncertainty about the model parameters at a rate equal to the maximum rate predicted by an asymptotic analysis. Simulation results show that picking stimuli by maximizing the mutual information can speed up convergence to the optimal values of the parameters by an order of magnitude compared to using random (nonadaptive) stimuli. Finally, applying our design procedure to real neurophysiology experiments requires addressing the nonstationarities that we would expect to see in neural responses; our algorithm can efficiently handle both fast adaptation due to spike history effects and slow, nonsystematic drifts in a neuron's activity.     

Optimal design of cylindrical shells

In this paper, two types of problems of the optimal design of cylindrical shells with arbitrary axisymmetrical boundary conditions and distributed load, under the condition of the volume being constant, are discussed. These problems involve the minimax deflection and minimal compliancy of a cylindrical shell. Expressions of the objective function can be obtained by a stepped reduction method. In minimizing the maximum deflection, the position of the maximum deflection from the previous iteration is used as the next one. This procedure converges (Avriel 1976). Several examples are provided to illustrate the method.     

Optimal design of conical springs

Mechanical systems often use springs to store energy though their axial length must sometimes be significantly reduced. This leads to the use of conical springs as they are able to telescope. Designers of mechanical systems can call on a large number of tools to assist them though most of these are merely validation tools requiring concomitant trial and error strategies. Optimization strategies can be applied to provide synthesis assistance tools for which the designer simply specifies his requirement. Thus the tool directly indicates the spring best suited to standards and requirements. Recent advances in the study of constant pitch conical springs have provided analytical expressions of their behavior even in the non-linear phase. Considering this, we have used optimization strategies to provide a synthesis tool for conical spring design. An example of application is presented. The tool introduced here is thus a synthesis assistance tool that can be of considerable interest for designers who require a conical spring in their design.     

Optimal design of hydraulic support

This paper describes a procedure for optimal determination of two groups of parameters of a hydraulic support employed in the mining industry. The procedure is based on mathematical programming methods. In the first step, the optimal values of some parameters of the leading four-bar mechanism are found in order to ensure the desired motion of the support with minimal transversal displacements. In the second step, maximal tolerances of the optimal values of the leading four-bar mechanism are calculated, so the response of hydraulic support will be satisfying. Received April 13, 1999     

Optimal design of controlled structures

A formulation that finds the optimal design of a controlled structure is proposed. To achieve this goal, a composite objective composed of structural and control objectives is introduced to be optimized, and the effect of the control weighting is examined. A feedback control law is defined before the structural optimization and then the composite objective will only become a function of structural design variables. As a result, optimal structural design and control forces in steady state are obtained.Part of this paper was presented at WCSMO1 (First World Congress of Structural and Multidisciplinary Optimization), held in Goslar, Germany, May 28–June 2, 1995     

Optimal design of PID regulators

Tuning of three-term controllers, a widely popular device for process control, has always been accomplished by semi-empirical rules. The aim of this paper is to establish a link between PID regulators and optimal feedback design for linear systems. After showing how the optimal control theory can be tailored to the design of optimal regulators, the results are extended to the discrete-time case and the feasibility of a microprocessor implementation is assessed with the aid of benchmark tests     

Optimal planning of robot calibration experiments by genetic algorithms

In this article, techniques developed in the science of genetic computing are applied to solve the problem of optimally selecting robot measurement configurations, which is an important element in successfully completing a robot calibration experiment. Genetic algorithms are customized for a type of robot measurement configuration selection problem in which the robot workspace constraints are defined in terms of robot joint limits. Simulation studies are conducted to examine the effectiveness of the genetic algorithms for the application. ©1997 John Wiley & Sons, Inc.     

A Bayesian support tool for morphological design

Dynamic computer based support tools for the conceptual design phase have provided a long-standing challenge to develop. This is largely due to the ‘fluid’ nature of the conceptual design phase. Design evaluation methods, which form the basis of most computer design support tools, provide poor support for multiple outcomes. This research proposes a stochastic-based support tool that addresses this problem. A Bayesian Belief Network (BBN) is used to represent the causal links between design variables. Included in this research is an efficient method for learning a design domain network from previous design data in the structure of a morphological design chart. This induction algorithm is based on information content. A user interface is proposed to support dynamically searching the conceptual design space, based on a partial design specification. This support tool is empirically compared against a more traditional search process. While no compelling evidence is produced to support the stochastic-based approach, an interesting broader design search behaviour emerges from observations of the use of the stochastic design support tool.     

Optimal mean-square-error calibration of classifier error estimators under Bayesian models

A recently proposed Bayesian modeling framework for classification facilitates both the analysis and optimization of error estimation performance. The Bayesian error estimator is then defined to have optimal mean-square error performance, but in many situations closed-form representations are unavailable and approximations may not be feasible. To address this, we present a method to optimally calibrate arbitrary error estimators for minimum mean-square error performance within a supposed Bayesian framework. Assuming a fixed sample size, classification rule and error estimation rule, as well as a fixed Bayesian model, the calibration is done by first computing a calibration function that maps error estimates to their optimally calibrated values off-line. Once found, this calibration function may be easily applied to error estimates on the fly whenever the assumptions apply. We demonstrate that calibrated error estimators offer significant improvement in performance relative to classical error estimators under Bayesian models with both linear and non-linear classification rules.     

Application portfolio management: a decision-oriented view of enterprise architecture

Today large companies operate 100s of computer-based information systems (IS), also called applications, to support their businesses. Enterprise Architecture (EA) is regarded as a promising concept to cope with the complexity caused by large application portfolios (AP). This article focuses on senior IT managers’ decision-making with regard to their AP, and EA’s role therein. Through multiple case studies in large companies, we found that these managers consider and balance a set of aspects, each of which is supported by partial EA models maintained by specific groups within their IT departments. These models are, however, not sufficiently integrated. Based on the empirical findings, we propose indicators for each of the partial EA models to aggregate the AP-relevant characteristics per application, which are then integrated into an AP dashboard to support senior IT managers’ holistic AP management. Consequently, a decision-oriented view is created of the overall EA, which the managers of the case studies companies deemed to be very helpful for steering their AP.     

入侵检测中贝叶斯分类器的改进和设计

针对入侵检测系统在实时检测能力和自适应能力方面的不足,提出了一个改进的贝叶斯分类器,通过引入滑动窗口技术改善入侵检测的实时性.同时通过所设计的性能调节器对贝叶斯分类器中参数的动态设置,实现了入侵检测系统的自适应性.改进后的贝叶斯分类器有效地实现了入侵检测的实时性、主动性和自适应性.