A multi-criteria trajectory-based parameter sampling strategy for the screening method of elementary effects

Environmental models are inherently complex and often characterized by high dimensionality. The method of elementary effects (EE) is one of the most widely used parameter screening technique implemented to reduce burden on computational resources required for thorough model evaluation. Due to issues like inefficient screening and excessive sampling time, the development of more effective EE sampling strategies has been a recent research focus. This paper presents a new sampling strategy - Sampling for Uniformity (SU) – based on the principles of meeting close-to-theoretical parameter distributions and maximizing trajectory spread. The performance of the SU relative to existing strategies was evaluated using a number of criteria including generated parameter distributions' uniformity, time efficiency, trajectory spread, and screening efficiency. The SU performed better than some trajectory-based benchmark strategies across the evaluation criteria, underlining the effectiveness of multi-criteria based sampling and the need to focus future efforts on exploring other combinations of sampling criteria.     

A divide-and-conquer direct differentiation approach for multibody system sensitivity analysis

In the design and analysis of multibody dynamics systems, sensitivity analysis is a critical tool for good design decisions. Unless efficient algorithms are used, sensitivity analysis can be computationally expensive, and hence, limited in its efficacy. Traditional direct differentiation methods can be computationally expensive with complexity as large as O(n ⁴+n ² m ²+nm ³), where n is the number of generalized coordinates in the system and m is the number of algebraic constraints. In this paper, a direct differentiation divide-and-conquer approach is presented for efficient sensitivity analysis of multibody systems with general topologies. This approach uses a binary tree structure to traverse the topology of the system and recursively generate the sensitivity data in linear and logarithmic complexities for serial and parallel implementations, respectively. This method works concurrently with the forward dynamics problem, and hence, requires minimal data storage. The differentiation required in this algorithm is minimum as compared to traditional methods, and is generated locally on each body as a preprocessing step. The method provides sensitivity values accurately up to integration tolerance and is insensitive to perturbations in design parameter values. This approach is a good alternative to existing methodologies, as it is fairly simple to implement for general topologies and is computationally efficient.     

Analytical approach to sensitivity analysis of flutter speed in bridges considering variable deck mass

Design techniques based upon sensitivity analysis are not usual in the current design of suspension bridges. However, sensitivity analysis has been proved to be a useful tool in the car and aircraft industries. Evaluation of sensitivity analysis is a mandatory step in the way towards an efficient automated optimum design process which would represent a huge jump in the conception of long span bridges. Some of the authors of this paper were pioneers in establishing a methodology for obtaining the sensitivity analysis of flutter speed in suspension bridges a few years ago. That approach was completely analytical and required the evaluation of many matrices related to the phenomenon. In those works the total mass of the deck was considered as constant and such a circumstance supposed a limitation of the method. In the present paper the complete analytical formulation of the sensitivity analysis problem in bridges considering variable deck mass is presented, as well as its application to the design problem of the Great Belt Bridge. Analytical evaluation of sensitivities is a time demanding task, and in order to avoid excessive computation times, distributed computing strategies have been implemented which can be considered as an additional benefit of this approach. For the application example, it has been found that deck cross-section area and torsional inertia are the structural properties with the greatest influence on the flutter performance.     

A variational method in design optimization and sensitivity analysis for aerodynamic applications

Variational method is applied to the state equations in order to derive the costate equations and their boundary conditions. Thereafter, the analyses of the eigenvalues of the state and costate equations are performed. It is shown that the eigenvalues of the Jacobean matrices of the state and the transposed Jacobean matrices of the costate equations are analytically and numerically the same. Based on the eigenvalue analysis, the costate equations with their boundary conditions are numerically integrated. Numerical results of the eigenvalues problems of the state and costate equations and of a maximization problem are finally presented.     

A unified approach to optimal feature selection

The optimum finite set of linear observables for discriminating two Gaussian stochastic processes is derived using classical methods and distribution function theory. The results offer a new, accurate information-theoretic strategy and are superior to well-known conventional methods using statistical distance measures.     

A new approach to visualizing time-varying sensitivity indices for environmental model diagnostics across evaluation time-scales

Assessing the time-varying sensitivity of environmental models has become a common approach to understand both the value of different data periods for estimating specific parameters, and as part of a diagnostic analysis of the model structure itself (i.e. whether dominant processes are emerging in the model at the right times and over the appropriate time periods). It is not straightforward to visualize these results though, given that the window size over which the time-varying sensitivity is best integrated generally varies for different parameters. In this short communication we present a new approach to visualizing such time-varying sensitivity across time scales of integration. As a case study, we estimate first order sensitivity indices with the FAST (Fourier Amplitude Sensitivity Test) method for a typical conceptual rainfall–runoff model. The resulting plots can guide data selection for model calibration, support diagnostic model evaluation and help to define the timing and length of spot gauging campaigns in places where long-term calibration data are not yet available.     

Unified Approach for Developing EfficientAlgorithmic Programs

A unified approach called partition-and-recur for developing efficient and correct algorithmic programs is presented.An algorithm(represented by recurrence and initiation)is separated from program,and special attention is paid to algorithm manipulation rather than proram calculus.An algorithm is exactly a set of mathematical formulae.It is easier for formal erivation and proof.After getting efficient and correct algorithm,a trivial transformation is used to get a final rogram,The approach covers several known algorithm design techniques,e.g.dynamic programming,greedy,divide-and-conquer and enumeration,etc.The techniques of partition and recurrence are not new.Partition is a general approach for dealing with complicated objects and is typically used in divide-and-conquer approach.Recurrence is used in algorithm analysis,in developing loop invariants and dynamic programming approach.The main contribution is combining two techniques used in typical algorithm development into a unified and systematic approach to develop general efficient algorithmic programs and presenting a new representation of algorithm that is easier for understanding and demonstrating the correctness and ingenuity of algorithmicprograms.     

Numeric sensitivity analysis applied to feedforward neural networks

During the last 10 years different interpretative methods for analysing the effect or importance of input variables on the output of a feedforward neural network have been proposed. These methods can be grouped into two sets: analysis based on the magnitude of weights; and sensitivity analysis. However, as described throughout this study, these methods present a series of limitations. We have defined and validated a new method, called Numeric Sensitivity Analysis (NSA), that overcomes these limitations, proving to be the procedure that, in general terms, best describes the effect or importance of the input variables on the output, independently of the nature (quantitative or discrete) of the variables included. The interpretative methods used in this study are implemented in the software program Sensitivity Neural Network 1.0, created by our team.     

A sensitivity analysis of powder forging processes

The purpose of this paper is to analyze the sensitivity problems in metal forming of rigid-visco-poroplastic materials. A repressing powder forging process is analyzed. Parameter sensitivity, material derivative, and control volume approaches to shape sensitivity analysis are presented, analyzed, and compared. Discretization of the continuum expressions is presented. The numerical solutions for parameter sensitivity in forging problems have been described. Numerical examples concerning simple compression test of cylindrical porous specimen are presented.     

A unified approach to Markov decision problems and performance sensitivity analysis with discounted and average criteria: multichain cases

We propose a unified framework to Markov decision problems and performance sensitivity analysis for multichain Markov processes with both discounted and average-cost performance criteria. With the fundamental concept of performance potentials, we derive both performance-gradient and performance-difference formulas, which play the central role in performance optimization. The standard policy iteration algorithms for both discounted- and average-reward MDPs can be established using the performance-difference formulas in a simple and intuitive way; and the performance-gradient formulas together with stochastic approximation may lead to new optimization schemes. This sensitivity-based point of view of performance optimization provides some insights that link perturbation analysis, Markov decision processes, and reinforcement learning together. The research is an extension of the previous work on ergodic Markov chains (Cao, Automatica 36 (2000) 771).     

A specification-based approach to concurrency analysis

The behavior of a concurrent program often depends on the arbitrary interleaving of computations performed by asynchronous processes. The resulting non-determinism can lead to such phenomena as deadlock and starvation, making program development extremely difficult, and consequently making the development of tools for formal analysis highly desirable.A specification-based approach to concurrency analysis is a particularly promising way of addressing some of the difficulties inherent in concurrent program development. According to this approach, a programmer first writes a specification describing the interprocess communication behavior of a concurrent program. A set of formal analysis techniques are then applied in an effort to determine whether the specification can be fully satisfied. If the analysis is successful, target code is generated automatically that conforms to the specification.This approach has a variety of benefits. While such properties as safety and liveness are rather difficult to discern in actual code, they are actually easy to include as part of a specification. Moreover, state spaces induced by specifications tend to be smaller and more manageable than state spaces of actual code, and this leads to more effective analysis techniques. Finally, the generation of interprocess communication code from formal specifications is accomplished in a relatively straightforward manner.Research partially supported by NSF grant CCR-9109231.     

Extending a global sensitivity analysis technique to models with correlated parameters

The identification and representation of uncertainty is recognized as an essential component in model applications. One important approach in the identification of uncertainty is sensitivity analysis. Sensitivity analysis evaluates how the variations in the model output can be apportioned to variations in model parameters. One of the most popular sensitivity analysis techniques is Fourier amplitude sensitivity test (FAST). The main mechanism of FAST is to assign each parameter with a distinct integer frequency (characteristic frequency) through a periodic sampling function. Then, for a specific parameter, the variance contribution can be singled out of the model output by the characteristic frequency based on a Fourier transformation. One limitation of FAST is that it can only be applied for models with independent parameters. However, in many cases, the parameters are correlated with one another. In this study, we propose to extend FAST to models with correlated parameters. The extension is based on the reordering of the independent sample in the traditional FAST. We apply the improved FAST to linear, nonlinear, nonmonotonic and real application models. The results show that the sensitivity indices derived by FAST are in a good agreement with those from the correlation ratio sensitivity method, which is a nonparametric method for models with correlated parameters.     

A unified approach to shaft calculations using a microcomputer

This paper describes a program written for a microcomputer which allows shaft (or beam) calculations to be made for a wide range of geometrical, loading and support conditions. Expressions for generalized support conditions are developed including support flexibility and unloaded support misalignment. The program, occupying 6100 bytes of memory without problem data statements, is shown applied to a simple flexible support problem and to a complex paper-making machine shaft mounted on 21 supports.     

A sensitivity analysis method for driving the Artificial Bee Colony algorithm's search process

In this paper, we improve D. Karaboga's Artificial Bee Colony (ABC) optimization algorithm, by using the sensitivity analysis method described by Morris. Many improvements of the ABC algorithm have been made, with effective results. In this paper, we propose a new approach of random selection in neighborhood search. As the algorithm is running, we apply a sensitivity analysis method, Morris’ OAT (One-At-Time) method, to orientate the random choice selection of a dimension to shift. Morris’ method detects which dimensions have a high influence on the objective function result and promotes the search following these dimensions. The result of this analysis drives the ABC algorithm towards significant dimensions of the search space to improve the discovery of the global optimum. We also demonstrate that this method is fruitful for more recent improvements of ABC algorithm, such as GABC, MeABC and qABC.     

A unified approach to LMI-based reduced order self-scheduling control synthesis

We consider a reduced order controller synthesis for a general class of control specifications for linear parameter-varying (LPV) systems, when some of state variables are exactly available. The class is defined in an abstract manner so that it uniformly deals with many significant specifications. A necessary and sufficient condition for the existence of a reduced order controller is given in terms of linear matrix inequalities (LMIs). We also show that the order of the controller can be reduced by the number of the state variables exactly available in the measurements. Moreover, in the case of linear time invariant (LTI) systems, a parameterization of all desirable reduced order LTI controllers is given by means of solutions of LMIs. The results in this paper generalize the class of control specifications in which a reduced order controller exists, making it possible to synthesize a reduced order controller based on LMIs for multi-objective control specifications. Furthermore, these results uniformly describe and generalize the existing results on synthesis of a constant state and a full order output feedback controller for LTI and LPV systems such that the specification is given by the existence of a constant positive definite matrix.     

Product platform design through sensitivity analysis and cluster analysis

Scale-based product platform design consists of platform configuration to decide which variables are shared among which product variants, and selection of the optimal values for platform (shared) and non-platform variables for all product variants. The configuration step plays a vital role in determining two important aspects of a product family: efficiency (cost savings due to commonality) and effectiveness (capability to satisfy performance requirements). Many existing product platform design methods ignore it, assuming a given platform configuration. Most approaches, whether or not they consider the configuration step, are single-platform methods, in which design variables are either shared across all product variants or not shared at all. In multiple-platform design, design variables may be shared among variants in any possible combination of subsets, offering opportunities for superior overall design but presenting a more difficult computational problem. In this work, sensitivity analysis and cluster analysis are used to improve both efficiency and effectiveness of a scale-based product family through multiple-platform product family design. Sensitivity analysis is performed on each design variable to help select candidate platform design variables and to provide guidance for cluster analysis. Cluster analysis, using performance loss due to commonization as the clustering criterion, is employed to determine platform configuration. An illustrative example is used to demonstrate the merits of the proposed method, and the results are compared with existing results from the literature.     

Reliability-based design sensitivity by efficient simulation

Reliability-based design sensitivity analysis involves studying the dependence of the failure probability on design parameters. Conventionally, this requires repeated evaluations of the failure probability for different values of the design parameters, which is a direct but computationally expensive task. An efficient simulation approach is presented to perform reliability-based design sensitivity analysis using only one simulation run. The approach is based on consideration of an ‘augmented reliability problem’ where the design parameters are artificially considered as uncertain. It is shown that the desired information about reliability sensitivity can be extracted through failure analysis of the augmented problem. The required computational effort is relatively insensitive to the number of uncertain parameters but generally grows exponentially with the number of design parameters whose sensitivity is to be studied. The latter implies that the proposed approach is applicable for studying the sensitivity of a small number of design parameters, say, less than 3, although this drawback appears unavoidable whenever multi-dimensional information is sought. Examples are presented to illustrate applications of the approach to reliability-based retrofit of structures.     

Assessing cellular automata model behaviour using a sensitivity analysis approach

Rapid advances in computer and geospatial technology have made it increasingly possible to design and develop urban models to efficiently simulate spatial growth patterns. An approach commonly used in geography and urban growth modelling is based on cellular automata theory and the GIS framework. However, the behaviour of cellular automaton (CA) models is affected by uncertainties arising from the interaction between model elements, structures, and the quality of data sources used as model input. The uncertainty of CA models has not been sufficiently addressed in the research literature. The objective of this study is to analyze the behaviour of a GIS-based CA urban growth model using sensitivity analysis (SA). The proposed SA approach has both qualitative and quantitative components. These components were operationalized using the cross-tabulation map, KAPPA index with coincidence matrices, and spatial metrics. The research focus was on the impacts of CA neighbourhood size and type on the model outcomes. A total of 432 simulations were generated and the results suggest that CA neighbourhood size and type configurations have a significant influence on the CA model output. This study provides insights about the limitations of CA model behaviour and contributes to enhancing existing spatial urban growth modelling procedures.