Number Of Design Points Research Articles

A single-loop reliability sensitivity analysis strategy for time-dependent rare events with both random variables and stochastic processes

To deal with the time-dependent reliability sensitivity (TDRS) analysis of rare events with both random variables and stochastic processes, a single-loop sampling procedure combined with the cross entropy-based importance sampling strategy (CEIS), namely SCEIS, is derived to lighten the computational burden without loss of precision. Firstly, the TDRS indices are derived to make them implementable by a single-loop importance sampling (IS) procedure. Then, the quasi-optimal IS density is obtained through the extension of the cross-entropy method, which is an adaptive procedure that overcomes the challenges of determining the position and number of design points in traditional IS. Furthermore, the SCEIS can be easily implemented to estimate the TDRS indices for problems with small failure probability. Three examples involving numerical and engineering problems are analyzed to demonstrate the performance of the proposed method. The results obtained from comparing with other existing methods reveal that the proposed method provides satisfactory TDRS analysis for rare events while significantly reducing computational costs.

Confidence intervals for multiple isotonic regression and other monotone models

We consider the problem of constructing pointwise confidence intervals in the multiple isotonic regression model. Recently, Han and Zhang (2020) obtained a pointwise limit distribution theory for the so-called block max–min and min–max estimators (Fokianos, Leucht and Neumann (2020); Deng and Zhang (2020)) in this model, but inference remains a difficult problem due to the nuisance parameter in the limit distribution that involves multiple unknown partial derivatives of the true regression function. In this paper, we show that this difficult nuisance parameter can be effectively eliminated by taking advantage of information beyond point estimates in the block max–min and min–max estimators. Formally, let uˆ(x0) (resp. vˆ(x0)) be the maximizing lower-left (resp. minimizing upper-right) vertex in the block max–min (resp. min–max) estimator, and fˆn be the average of the block max–min and min–max estimators. If all (first-order) partial derivatives of f0 are nonvanishing at x0, then the following pivotal limit distribution theory holds: nuˆ,vˆ(x0)(fˆn(x0)−f0(x0))⇝σ·L1d. Here nuˆ,vˆ(x0) is the number of design points in the block [uˆ(x0),vˆ(x0)], σ is the standard deviation of the errors, and L1d is a universal limit distribution free of nuisance parameters. This immediately yields confidence intervals for f0(x0) with asymptotically exact confidence level and oracle length. Notably, the construction of the confidence intervals, even new in the univariate setting, requires no more efforts than performing an isotonic regression once using the block max–min and min–max estimators, and can be easily adapted to other common monotone models including, for example, (i) monotone density estimation, (ii) interval censoring model with current status data, (iii) counting process model with panel count data, and (iv) generalized linear models. Extensive simulations are carried out to support our theory.

Design Analysis of 110kV Double Circuit Narrow-Base Steel Pipe Tower

Secondary bending moment and geometric nonlinearity should be taken into account in pipe tower design. Taking the 110kV double-circuit narrow-base steel pipe tower as an example, the 110 kV double-circuit narrow-base steel pipe tower is compared and analyzed through the tower structure design software and the general finite element software ANSYS. The analysis results show that the narrow-base steel tube tower should adopt a rigid-truss structure model, and the influence of the secondary bending moment of the main material and the geometric nonlinearity should be considered. The secondary bending moment effect accounts for about 10-20% of the strength stress of the steel pipe main material. Through comparative analysis, a number of design points are summarized, which provides a certain practical guiding significance for the design and application of the double-circuit narrow-base steel pipe tower.

РАСЧЕТНО-ЭКСПЕРИМЕНТАЛЬНЫЙ МЕТОД ИССЛЕДОВАНИЯ ШИРОКОХОРДНОГО ВЕНТИЛЯТОРА АВИАЦИОННОГО ДВИГАТЕЛЯ НА ОТСУТСТВИЕ АВТОКОЛЕБАНИЙ

The main gas-dynamic parameters are considered for studying of the absence of flutter wide-chord fan of aircraft engine. The experimental-rated method is proposed to confirm the absence of flutter on the fan in the entire operating range of the aircraft engine. The method is based on experience in the design and development of aircraft engine fans. The method proposes the limitations of the study area of operation of a wide-chord of the aircraft engine fan. The method shows the boundaries of the possible operation of a wide-chord of the aircraft engine fan, taking into account the limitations of the studied range for the research and development of the testing. The aircraft flight parameters were processed with the control of the absence of flutter using pressure pulsation gauges. The results of processing the studied flight parameters are generalized and systematized. A technique for graphically depicting of the main controlled parameters of the method in a two-dimensional and three-dimensional setting is shown, indicating the boundaries of the possible range of operation, the wide-chord fan of the aircraft engine under study, taking into account the reserves of pressure and temperature. To verify the method, the test points of the fan are graphically showed in a thermal vacuum chamber of a similar sized fan of an aircraft engine, which, as the figures show, lie near the boundaries proposed in the method. It is proposed to use the studied points with a proven absence of flutter for verification of computational models using software systems and methods, for calculating the absence of flutter, taking into account the limits of possible operation defined in the method. The proposed boundaries of the studied ranges will significantly reduce the list of tests at the flying laboratory and the number of design points, which will allow us to make the best option for checking the absence of self-oscillations of the aircraft engine fan by the experimental-rated method in Ukraine without using a thermal pressure vacuum chamber and flying in hot and cold conditions.

Active learning for efficiently training emulators of computationally expensive mathematical models.

An emulator is a fast-to-evaluate statistical approximation of a detailed mathematical model (simulator). When used in lieu of simulators, emulators can expedite tasks that require many repeated evaluations, such as sensitivity analyses, policy optimization, model calibration, and value-of-information analyses. Emulators are developed using the output of simulators at specific input values (design points). Developing an emulator that closely approximates the simulator can require many design points, which becomes computationally expensive. We describe a self-terminating active learning algorithm to efficiently develop emulators tailored to a specific emulation task, and compare it with algorithms that optimize geometric criteria (random latin hypercube sampling and maximum projection designs) and other active learning algorithms (treed Gaussian Processes that optimize typical active learning criteria). We compared the algorithms' root mean square error (RMSE) and maximum absolute deviation from the simulator (MAX) for seven benchmark functions and in a prostate cancer screening model. In the empirical analyses, in simulators with greatly varying smoothness over the input domain, active learning algorithms resulted in emulators with smaller RMSE and MAX for the same number of design points. In all other cases, all algorithms performed comparably. The proposed algorithm attained satisfactory performance in all analyses, had smaller variability than the treed Gaussian Processes, and, on average, had similar or better performance as the treed Gaussian Processes in six out of seven benchmark functions and in the prostate cancer model.

Adaptive experiment design for probabilistic integration

Probabilistic integration is a Bayesian inference technique for numerical integration, and has received much attention in the community of scientific and engineering computations. The most appealing advantages are the ability to improve the integration accuracy by making full use of the spatial correlation information among the design points, and the treatment of discretization error as a source of epistemic uncertainty being explicitly propagated to the integration results. This paper aims to develop an adaptive algorithm for further improving the efficiency and accuracy of the probabilistic integration when it is applied to the time-consuming computer simulators. A learning function is first extracted from the posterior variance of the integration and is shown to be especially useful for identifying the design point, by adding which to the training data set, the most reduction of the posterior variance of integration can be achieved. Based on this learning function, an adaptive experiment design algorithm is then developed for actively producing optimal design points. Results of the experiment tests and engineering application show that, with the same number of design points, the developed design strategy always produce more accurate and robust integration results, than the three kinds of commonly used random sampling design strategies (i.e., Monte Carlo design, Latin-hypercube design and Sobol sequence).

Development of Bolted Flange Design Tool Based on Artificial Neural Network

Finite element analysis (FEA) of bolted flange connections is the common methodology for the analysis of bolted flange connections. However, it requires high computational power for model preparation and nonlinear analysis due to contact definitions used between the mating parts. Design of an optimum bolted flange connection requires many costly finite element analyses to be performed to decide on the optimum bolt configuration and minimum flange and casing thicknesses. In this study, very fast responding and accurate artificial neural network-based bolted flange design tool is developed. Artificial neural network is established using the database which is generated by the results of more than 10,000 nonlinear finite element analyses of the bolted flange connection of a typical aircraft engine. The FEA database is created by taking permutations of the parametric geometric design variables of the bolted flange connection and input load parameters. In order to decrease the number of FEA points, the significance of each design variable is evaluated by performing a parameter correlation study beforehand, and the number of design points between the lower and upper and bounds of the design variables is decided accordingly. The prediction of the artificial neural network based design tool is then compared with the FEA results. The results show excellent agreement between the artificial neural network-based design tool and the nonlinear FEA results within the training limits of the artificial neural network.

Construction of Two Level Super-saturated Designs Using PBIBDs

Experimenter has to minimize the number of design points in a design by identifying the effects of active factor combinations for efficient utilization of resources. Super-saturated design is a factorial design having the more number of factors than the number of design points. Several researchers have provided the constructions of supersaturated designs. In this paper, we construct a series of two level E( $$\hbox {s}^{2}$$ )-optimal super-saturated designs using partially balanced incomplete block designs.

Construction of Super-Saturated Designs

A design which is having more number of factors than the number of design points is called a Super-saturated Design. In this paper, an attempt is made to propose two new series of constructions of super-saturated designs using mutual orthogonal Latin squares and balanced incomplete block designs and the methods are illustrated with suitable examples.

Pairwise Meta-Modeling of Multivariate Output Computer Models Using Nonseparable Covariance Function

Gaussian process (GP) is a popular method for emulating deterministic computer simulation models. Its natural extension to computer models with multivariate outputs employs a multivariate Gaussian process (MGP) framework. Nevertheless, with significant increase in the number of design points and the number of model parameters, building an MGP model is a very challenging task. Under a general MGP model framework with nonseparable covariance functions, we propose an efficient meta-modeling approach featuring a pairwise model building scheme. The proposed method has excellent scalability even for a large number of output levels. Some properties of the proposed method have been investigated and its performance has been demonstrated through several numerical examples. Supplementary materials for this article are available online.

Exploring Multilevel Cache Hierarchies in Application Specific MPSoCs

Multiprocessor systems make use of multilevel cache hierarchies to improve overall memory access speed. Embedded systems typically use configurable processors, where the caches in the system can be customized for a given application or a set of applications. Finding the optimal or a near-optimal set size, block size, and associativity of each of the caches in a multilevel cache hierarchy is a challenging task due to the presence of billions or even trillions of design points. This paper presents an iterative exploration method to find suitable configurations for all the caches in the hierarchy of an application specific multiprocessor system-on-chip, to improve memory access speed. We propose an algorithm and combine it with the use of specialized hardware for parallel cache simulation to enable multiple back-and-forth iterations through the cache levels. In every iteration, our algorithm explores selected portions of the entire design space to quickly converge upon the final design point. We demonstrate our methodology on two- and three-level cache hierarchies with private and shared caches in a quad-core system, respectively, consisting of 5.4 billion and 10.4 trillion design points. Our method was able to find design points with up to 18.9% lower average memory access time while reducing total cache size by up to 74.15%, compared to a state-of-the-art noniterative method. The number of design points explored was $ {4\times }$ higher in our method, which is still a mere $ {3.6\times 10}^{ {-5}}$ % of the entire design space, and took 6.08 h.

Design of experiments for interpolation-based metamodels

A metamodel is a simplified mathematical description of a simulation model that represents the system’s input–output relationship with a function. In many situations, we may not need a single formula to describe the systems being simulated. Interpolation-based metamodels are useful for providing simple estimates at non-design points to communicate the input–output relationship. This paper proposes a new approach to select an experimental design for interpolation-based metamodels. The algorithm dynamically increases the sample size and the number of design points so that the estimates obtained via the metamodel satisfy the pre-specified precision. An experimental performance evaluation demonstrates the validity of interpolation-based metamodels.

An adaptive response surface method for crashworthiness optimization

Response surface-based design optimization has been commonly used for optimizing large-scale design problems in the automotive industry. However, most response surface models are built by a limited number of design points without considering data uncertainty. In addition, the selection of a response surface in the literature is often arbitrary. This article uses a Bayesian metric to systematically select the best available response surface among several candidates in a library while considering data uncertainty. An adaptive, efficient response surface strategy, which minimizes the number of computationally intensive simulations, was developed for design optimization of large-scale complex problems. This methodology was demonstrated by a crashworthiness optimization example.

Optimizing Latin hypercube designs by particle swarm

Latin hypercube designs (LHDs) are widely used in many applications. As the number of design points or factors becomes large, the total number of LHDs grows exponentially. The large number of feasible designs makes the search for optimal LHDs a difficult discrete optimization problem. To tackle this problem, we propose a new population-based algorithm named LaPSO that is adapted from the standard particle swarm optimization (PSO) and customized for LHD. Moreover, we accelerate LaPSO via a graphic processing unit (GPU). According to extensive comparisons, the proposed LaPSO is more stable than existing approaches and is capable of improving known results.

OSCAR: An Optimization Methodology Exploiting Spatial Correlation in Multicore Design Spaces

This paper presents OSCAR, an optimization methodology exploiting spatial correlation of multicore design spaces. This paper builds upon the observation that power consumption and performance metrics of spatially close design configurations (or points) are statistically correlated. We propose to exploit the correlation by using a response surface model (RSM), i.e., a closed-form expression suitable for predicting the quality of nonsimulated design points. This model is useful during the design space exploration (DSE) phase to quickly converge to the Pareto set of the multiobjective problem without executing lengthy simulations. To this end, we introduce a multiobjective optimization heuristic which iteratively updates and queries the RSM to identify the design points with the highest expected improvement. The RSM allows to consolidate the Pareto set by reducing the number of simulations required, thus speeding up the exploration process. We compare the proposed heuristic with state-of-the-art approaches [conventional, RSM-based, and structured design of experiments (DoEs)]. Experimental results show that OSCAR is a faster heuristic with respect to state-of-the-art techniques such as response-surface Pareto iterative refinement ReSPIR and nondominated-sorting genetic algorithm NSGA-II. In fact, OSCAR used a lower number of simulations to produce a similar solution, i.e., an average of 150 simulations instead of 320 simulations (NSGA-II) and 178 simulations (ReSPIR). When the number of design points is fixed to an average of 300, OSCAR achieves less than 0.6% in terms of average distance with respect to the reference solution while NSGA-II achieves 3.4%. Reported results also show that OSCAR can significantly improve structured DoE approaches by slightly increasing the number of experiments.

Using the Canonical Design Space to Obtain c-optimal Designs for the Quadratic Logistic Model

c-optimal designs for estimating the model parameters of the quadratic logistic regression model are considered. The designs are constructed via the canonical design space. It is shown that the number of design points varies between 1 and 4 depending on the parameter being estimated. Furthermore, formulae for finding the design points along with the corresponding design weights are derived.

Static Displacement Reanalysis of Modified Structures Using Epsilon Algorithm

I N THE optimization of structural systems, it is very important to compute the static displacements of the structures when the parameters of the structures are changed.One of themain obstacles is the high computational cost involved in the solution of large-scale problems. Therefore, the reanalysis problems excite the interest of many researchers and both approximate and exact reanalysis methods have been reported and reviewed [1]. In general, the following factors are considered in choosing an approximate behavior model for a specific optimal design problem [2]. 1) the accuracy of the calculations or the quality of the approximations; 2) the computational effort involved or the efficiency of the method, and 3) the ease of implementation. At present, the various approximations have been developed. Barthelemy, Kirsch, and Haftka et al. [3–5] developed the global approximation (also called multipoint approximations), such as polynomial fitting or reduced basis methods. These approximations are obtained by analyzing the structure at a number of design points, and they are valid for the whole design space. Local approximation is called single-point approximations, such as the Taylor series expansion or the binomial series expansion about a given point in the design space. Local approximations are based on information calculated at a single point. Thesemethods are effective only in cases of small changes in parameters of the structures. For large changes in the design, the accuracy of the approximations often deteriorates, and they may become meaningless [6]. Kirsch [7–12] discussed the combined approximations, which attempt to give global qualities to local approximations. Recently, the Pade approximation and Shanks transformation were used to improve the accuracy of the reanalysis [13,14]. It is shown that it can significantly improve the domain of convergence. In this study, we use the epsilon algorithm [15–17] to deal with the static displacement reanalysis. The main objectives are to preserve the ease of implementation and to improve significantly the domain of convergence and the quality of the results, such that the method can be used in problems with very large changes in the structural parameters. A numerical example is demonstrated and the method is compared with the Kirsch combined approximation.

Predicting product parameters of fly ash–cement–sand bricks

This paper discusses models with ternary systems of fly ash, cement and sand by using simplex lattice and simplex centroid designs for building bricks. A statistical design with upper and lower bounds of three component mixtures was adopted to select the mixture proportions of experimental points required for prediction of the product parameters, namely compressive strength, bulk density and water absorption of cement fly ash bricks. The experimental points include the process parameters such as percentages of fly ash, cement and sand and the corresponding product parameters at different curing periods. Regression models of various orders for the above design methods are developed. Various tables and graphs are incorporated to give the results and comparisons among experimental and theoretical models. The developed model may be useful for direct prediction of product parameters using a smaller and fixed number of design points.

Efficient procedures for repeated calculations of structural sensitivities

Procedures for sensitivity analysis of large-scale structures are presented. Analytical derivatives are evaluated for multiple modified designs where the exact response is unknown. Approximation concepts are used to improve the efficiency and the ease-of-implementation of the calculations. The procedures presented are based on explicit approximations of the response and the combined approximations approach, which is further developed to improve the efficiency of the calculations and the accuracy of the results. Considering sensitivities of static problems and eigenproblems, basis vectors are calculated for a limited number of design points, and then used to evaluate sensitivities for various modified designs. The procedures presented are compared with exact analytical sensitivities. It is shown that accurate results can be achieved with significant reductions in the computational effort.

Optimal sample length for efficient cache simulation

Architectural simulations of microprocessors are extremely time-consuming nowadays due to the ever increasing complexity of current applications. In order to get realistic workloads on current hardware, benchmarks need to be constructed with huge dynamic instruction counts. For example, SPEC released the CPU2000 benchmark suite containing benchmarks that have a dynamic instruction count of several hundreds of billions of instructions. This is beneficial for real hardware evaluation. However, simulating these workloads is impractical if not impossible if we take into account that many simulation runs are needed in order to evaluate a large number of design points. Trace sampling is often used as a practical solution for this problem. In trace sampling, several representative samples are chosen from a real program trace. Since the sampled trace is much shorter than the original trace, a significant simulation speedup is obtained. In this paper, we study what is the optimal sample size to achieve a given level of accuracy while maximizing the total simulation speedup. From various experiments using SPEC CPU2000, we conclude that the optimal sample length (i) is not fixed over benchmarks, and (ii) increases with increasing warmup lengths. As such, we propose an algorithm that determines the optimal sample length per benchmark under different warmup scenarios. This is done within the context of sampled cache simulation.