Global identifiability analysis using algorithms for detecting connected semi-algebraic components

An accurate forecast of runoff is very significant so that there is ample time for the pertinent authority to issue a forewarning of the impending flood. Due to the highly dimension and nonlinear, the calibration of hydrological model become very complex, so the unique “best” parameter set can not be obtained easily. In this study, an MCMC sampler entitled the Shuffled Complex Evolution Metropolis algorithm(SCEM-UA) is presented, which is well suited to infer the posterior distribution of hydrologic model parameters. This algorithm operates by merging the strengths of the Metropolis algorithm, controlled random search, competitive evolution, and complex shuffling in order to continuously update the proposal distribution and evolve the sampler to the posterior target distribution. Therefore, SCEM-UA is applied in this study to calibrate a lumped Xinanjiang hydrological model having 16 parameters. Three types of data were used for Xinanjiang model: rainfall, evaporation and discharge. One years’ data were used for calibration and one years’ data were used for testing. The criterion used to measure the fitness of the calculated against the observed discharges was the Deterministic Coefficient (DC) and Root Mean Square Error(RMSE). The calibration processes included first of all defining the feasible domains of the model parameters, and initialize the parameters in the feasible domains, then the model parameters were iteratively evaluated and updated, until the terminal condition was satisfied. In order to test the efficiency of the SCEM-UA, Genetic algorithm (GA) is also employed for comparison. The results showed that both calibration and testing results are satisfactory: the DC values of SCEM-UA for the calibration period is 0.79, which is much higher than that of GA, 0.73, and the DC for the testing period is 0.81, which is also better than GA, the same as the RMSE. Visual examinations shows in the high peak flood event, the simulated runoff by SCEM-UA is much better than that by GA.

Crystal structure of hypothetical protein PH0642 from Pyrococcus horikoshii at 1.6A resolution.

Sensitivity analyses are frequently used during the design of engineering systems to qualify and quantify the effect of parametric variation in the performance of a system. Two primary types of sensitivity analyses are generally used: local and global. Local analyses, generally involving derivative-based measures, have a significantly lower computational burden than global analyses but only provide measures of sensitivity around a nominal point. Global analyses, generally performed with a Monte Carlo sampling approach, and variation-based measures provide a complete description of sensitivity but incur a large computational burden and require information regarding the distributions of the design parameters in a concept. Local analyses are generally suited to the early stages of design when parametric information is limited, and a large number of concepts must be evaluated (necessitating a light computational burden). Global analyses are more suited to the later stages of design when more information about parametric distributions is available and fewer concepts are under consideration. Current derivative-based local approaches provide a different and incompatible set of measures than a global variation-based analysis. This makes a direct comparison of local to global measures ill posed. To reconcile local and global sensitivity analyses, a hybrid local variation-based sensitivity (HyVar) approach is presented. This approach has a similar computational burden to a local approach but produces measures or percentage contributions. The HyVar approach is directly comparable to global variation-based approaches. In this paper, the HyVar sensitivity analysis method is developed in the context of a functional based behavioral modeling framework. An example application of the method is presented along with a summary of results produced from a more comprehensive example.

A deterministic method for continuous global optimization using a dense curve

The global minimization of large-scale partially separable non-convex problems over a bounded polyhedral set using a parallel branch and bound approach is considered. The objective function consists of a separable concave part, an unseparated convex part, and a strictly linear part, which are all coupled by the linear constraints. These large-scale problems are characterized by having the number of linear variables much greater than the number of nonlinear variables. An important special class of problems which can be reduced to this form are the synomial global minimization problems. Such problems often arise in engineering design, and previous computational methods for such problems have been limited to the convex posynomial case. In the current work, a convex underestimating function to the objective function is easily constructed and minimized over the feasible domain to get both upper and lower bounds on the global minimum function value. At each minor iteration of the algorithm, the feasible domain is divided into subregions and convex underestimating problems over each subregion are solved in parallel. Branch and bound techniques can then be used to eliminate parts of the feasible domain from consideration and improve the upper and lower bounds. It is shown that the algorithm guarantees that a solution is obtained to within any specified tolerance in a finite number of steps. Computational results obtained on the four processor Cray 2, both sequentially and in parallel on all four processors, are also presented.

In order to avoid the abnormal vibration behavior of the high temperature superconductor (HTS) flux pinned magnetic levitation (maglev) train at high velocity (reach up to more than 500 km/h) due to the external interference from the suspension frame system, the vibration characteristics of suspension frame system are studied. Firstly, the levitation force between the HTS combination and the permanent magnet guideway (PMG) is measured by way of the quasi-static test platform, and the empirical formula of levitation force is obtained. Then, the nonlinear vibration differential equation of the suspension frame system under the track irregularity harmonic excitation is established. The first approximate solution is obtained based on the multiscale method, which is verified by way of the numerical solution. Finally, the amplitude-frequency response equation of the suspension frame system under the primary resonance is derived, thus the influence of running velocity, track irregularity wavelength and amplitude on the steady-state amplitude is studied. An analytical method for determining the feasible domain of track irregularity parameters under different running velocity is proposed based on the safety standard of maglev train. The effective domain of track irregularity parameters can be obtained. The methodology and results of this manuscript provide a theoretical foundation for constructing PMG of HTS flux pinned maglev train.

Development of closed-form solutions and algorithms for constructing sub-surface swept profiles (SWP) of toroidal and conical bodies is presented in this paper. While the problem of identifying the entire SWP of such surfaces has been extensively investigated in extant studies, construction of subsurface SWPs has rarely been addressed despite the subject being of great significance to machining process employing nonstandard-shaped NC tools. Torus shapes considered in extant literature are restricted to the fourth quadrant of a tube cross section. In industrial applications, however, profile cutters contain different regions of a toroidal surface. To identify SWP elements in the proposed study, a single analytical expression in one variable has been deduced using two moving frames. The basic idea behind such a formulation is to employ the one-to-many strategy, which greatly reduces the computational cost and effort. Algorithms to identify feasible domains of SWP parameters at each level cut, where toroidal and conical surfaces meet, have also been proposed in this study. This is important, since cutting a tool surfaces along the rotation axis divides SWP-parameter domains into non overlapping sets of intervals that must be addressed for each tool posture. In addition, this study demonstrates that for certain tool postures, while C1 continuity between sub-surfaces is satisfied, the SWP connectivity is lost at some points. To locate these so called singular-characteristic points, some precomputation steps have been performed. Lastly, several factors affecting the smoothness of SWPs have been identified and discussed. Highlights Closed form solutions have been derived for constructing the sub-swept profiles of toroidal tools. Three algorithms have been presented to identify the feasible domains of swept profile parameters. In order to locate the singular-characteristic points some precomputation steps have been carried out. Finally, several factors, affecting the smoothness of the swept profiles, have been identified.

In this paper, the feasibility of the application of a dual mass flywheel (DMF) for heavy-duty truck drivetrain systems was studied. The third engine order vibration harmonic was in the focus of analysis as one of the most significant contributions to the oscillatory response in the drivetrain systems of heavy-duty trucks. Global sensitivity analysis (GSA) and Pareto optimization were used for designing torsional vibration absorbers in an operating engine speed range of 600–2000 rpm. The optimization method attempted both to minimize the oscillations of the torque at the transmission input shaft and to maximize the energy efficiency of the vibration absorber. The GSA enabled the appropriate scanning of the domain of design parameters by varying all the parameters at the same time. It provided deep insight into the design process and increased the computational efficiency of the optimization. The results obtained show the following: the solution of the bi-objective optimization problem for torsional vibration absorbers does exist; Pareto fronts were obtained and analyzed for the DMF, presenting a trade-off between the measure of the attenuation of the oscillations of the torque at the transmission input shaft and the measure of the energy efficiency of the absorber; the optimized mass inertia, stiffness and damping parameters of a DMF do exist, providing the best attenuation of the torque oscillations; the performance of a DMF was further enhanced by incorporating a torsional tuned mass damper with appropriate optimized parameters. Finally, the results show evidence of the feasibility of the application of dual mass flywheels in heavy-duty truck drivetrain systems.

To enhance the accuracy of advanced constitutive models for soft natural clays, several parameters are necessary, resulting in complexity of numerical modelling. However, the detailed effects of these parameters are not rigorously quantified towards their constitutive relationships. Thus, the aim of the paper is to assess such advanced models in order to determine the most significant parameters over the time series data. Two methods for Global Sensitivity Analysis (GSA), i.e. Experimental Design and the Sobol method, were used and benchmarked to assess the model predictions on a discretised domain in time and space. A rate-dependent Finite Element model using Creep-SCLAY1S and a hydro-mechanically coupled formulation for consolidation was used to study a Constant Rate of Strain (CRS) test. The value of GSA approaches adopted herein was to investigate the model predictions both in the temporal and spatial domain. The temporal analyses indicate three sets of significant model parameters in different portions of the CRS compression curve. Furthermore, the non-stationary nature of sensitivity results is exposed, identifying the parameters that lead to unique solutions for the CRS loading path. The FE implementation enabled the quantification of the most sensitive model parameters in the spatial domain. The spatial results that are governed by the rate-dependent processes in the soil (i.e. consolidation and creep) illustrated that Experimental Design was capable of providing sensitivity maps with satisfactory accuracy similar to the Sobol method. Experimental Design was found to be the most efficient method, concerning execution time and storage costs, to assess rate-dependent problems in Geotechnics.

The random microstructure of heterogeneous materials causes spatial variations in mechanical properties, significantly influencing material behaviour, which cannot be fully captured by deterministic models with fixed input parameters. Contemporary research has increasingly shifted toward stochastic modelling to address two distinct sources of non-determinism: epistemic uncertainty (reducible due to limited knowledge) and aleatory uncertainty (irreducible, reflecting inherent randomness). Stochastic models require a specialised approach to estimate their underlying deterministic material parameters, whereas deterministic models are calibrated by treating their parameters as random variables. Within a probabilistic framework, the identification of random parameters is formulated as a stochastic inverse problem. Its objective is to reproduce the variability observed in experimental data from an ensemble of specimens using a numerical model with random material parameters. To mitigate the computational cost of the numerous model simulations required, two widely used surrogate models polynomial chaos expansions and artificial neural networks are investigated. The preferred polynomial chaos provides analytical statistics of model responses enabling efficient variable transformations and sensitivity analysis, which are critical for uncertainty quantification. This thesis explores advanced methods for identifying aleatory uncertainty, with a particular focus on their application to the calibration of heterogeneous material models. Traditional methods, often based on Bayesian hierarchical modelling, typically assume a prescribed form for the parameter probability density function. The developed stochastic inversion framework derives the parameter distribution directly from the observed data distribution, constrained only by the feasible domain of material parameters to ensure model stability and validity. Both approaches are compared through two case studies involving heterogeneous material models. Additionally, this thesis addresses the calibration of the Lattice Discrete Particle Model for concrete, which necessitates specialised treatment due to its inherent stochasticity arising from the random generation of the material microstructure.

Estimating the functional relation between the probabilistic response of a computational model and the distribution parameters of the model inputs is especially useful for 1) assessing the contribution of the distribution parameters of model inputs to the uncertainty of model output (parametric global sensitivity analysis), and 2) identifying the optimized distribution parameters of model inputs to efficiently and cheaply reduce the uncertainty of model output (parametric optimization). In this paper, the extended Monte Carlo simulation method is developed for this purpose, which provides four benefits to the parametric global sensitivity analysis and parametric optimization problems. First, the extended Monte Carlo simulation method is able to provide an unbiased or progressive unbiased estimate for the model whose behavior is even mainly governed by high nonlinearity or interaction terms. Second, only one set of model input–output samples is needed for implementing the method; thus, the computational burden is free of input dimensionality. Third, the extended Monte Carlo simulation is a derivative-free method. Fourth, the extended Monte Carlo simulation method enables us to solve problems with dependent and non-normally distributed model inputs. Additionally, the R-indices are introduced for conquering the overparameterized problem in the optimization process. An analytical example and two engineering examples are used to demonstrate the power of the proposed methods.

<p>Human modification of natural systems has typically enhanced provisioning ecosystem services (ES), such as agriculture, at the expense of biodiversity and other types of services. Long-term sustainability requires a balance of ES flows to both maintain human wellbeing, while preserving biodiversity. In river deltas this balance is critical – fertile flat land, well stocked fisheries, and water for use and navigation have promoted rapid population growth and development. Yet the same development degrades the key ES protecting these deltas from hazards and pollution. Many deltas face a critical juncture, at risk or already ‘locked-in’ to the need for engineered solutions to global change problems, unsustainable globally and in the long-term.</p><p>We created a global dataset of 237 deltas and collected indicators of the extent each was modified from its natural state, and its ES supply. Several types of modification to the most important aspects of delta systems were considered – overall human impact (human footprint), pressure and demand on ES (population density), modification of water systems (flow disruption) and modification of natural productivity (human appropriation of net primary productivity); grouping deltas by modification state. The impacts of this human modification on over 50 robust biodiversity and ES indicators were then analysed.</p><p>Firstly, we attempted to create bundles of commonly associated ES in delta areas. Hierarchical clustering highlighted several logical clusters related to crops, fisheries, water, species richness, biodiversity intactness and NPP. Secondly, we examined synergies and trade-offs between different ES. Provisioning services all showed clear correlations with one another, but clear trade-offs with supporting services or biodiversity. There were weaker synergies within and between regulating and supporting ES. Finally, the relationship between each type of modification and the ES was classified using six typologies fitted by applying a decision tree to their LOESS regression curves. Crop indicators typically had an inverted-U relationship, increasing in moderately modified deltas, but decreasing in the most modified, presumably pushed out by other land uses. While many other ES declined with modification, interestingly, species richness and intactness both began to increase again in the most modified deltas. In summary, this global analysis is the first to illustrate how ES vary along a gradient of development in deltas, and highlights the need to balance further modification against these critical services.</p>

In this chapter, following [41], we present a method to interpolate or approximate a given function \(f:{\mathbb G}\rightarrow {\mathbb C}\) (or \(F:{\mathbb H}\rightarrow {\mathbb C}\)) by an AP functions in \({{\mathrm{AP}}}_F({\mathbb G})\), i.e., AP functions whose Fourier transform is supported in a given discrete and finite set \(F\subset \widehat{\mathbb G}\). (See Sect. 2.3.1.) In order to do this, we generalize the well-known decomposition of the 2D Fourier transform on the plane in polar coordinates, via the Fourier-Bessel operator. In the first part of the chapter, exploiting the deep connection between (4.1) and the group of rototranslations SE(2), we generalize the former to \({{\mathrm{AP}}}_F({\mathbb G})\) functions. In particular, we show how a discrete operator that we call the generalized Fourier-Bessel operator plays a crucial role in this generalization. We then consider the problem of interpolating functions \(\psi :{\mathbb G}\rightarrow {\mathbb C}\) on \({\mathbb K}\)-invariant finite sets \(\tilde{E}\subset {\mathbb G}\) via \({{\mathrm{AP}}}_F({\mathbb G})\) functions. The last part of the chapter is devoted to particularize (and slightly generalize) the above results to the relevant case for image processing, i.e., \({\mathbb G}=SE(2,N)\). Indeed we present numerical algorithms for the (exact) evaluation, interpolation, and approximation of \({{\mathrm{AP}}}_F(SE(2,N))\) functions on finite sets of spatial samples \(\tilde{E}\subset {\mathbb R}^2\), invariant under the action of \({\mathbb Z}_N\). This is an instance of a very general problem, and can be seen as a generalization of the discrete Fourier Transform and its inverse, that act on regular square grids, i.e., invariant under the the action of SE(2, 4).

This paper proposes a high level language constituted of only a few primitives and macros for describing recursive maximum likelihood (ML) estimation algorithms. This language is applicable to estimation problems involving linear Gaussian models, or processes taking values in a finite set (only the first case is considered here). The use of high level primitive allows the development of highly modular ML estimation algorithms based on only few numerical blocks. The primitives, which correspond to the combination of different measurements, the extraction of sufficient statistics, and the conversion of the status of a variable from unknown to observed ones, or vice versa, are first defined for linear Gaussian relations specifying mixed deterministic/stochastic information about the system variables. These primitives are used to define other macros, and are illustrated by considering the filtering and smoothing problems for linear descriptor systems, as well as failure detection and isolation. >

In this paper, we consider the l1-clustering problem for a finite data-point set which should be partitioned into k disjoint nonempty subsets. In that case, the objective function does not have to be either convex or differentiable, and generally it may have many local or global minima. Therefore, it becomes a complex global optimization problem. A method of searching for a locally optimal solution is proposed in the paper, the convergence of the corresponding iterative process is proved and the corresponding algorithm is given. The method is illustrated by and compared with some other clustering methods, especially with the l2-clustering method, which is also known in the literature as a smooth k-means method, on a few typical situations, such as the presence of outliers among the data and the clustering of incomplete data. Numerical experiments show in this case that the proposed l1-clustering algorithm is faster and gives significantly better results than the l2-clustering algorithm.