Sampling-based Monte Carlo Methods Research Articles

Creating interior support structures with Lightweight Voronoi Scaffold

Nowadays product designers have possibilities to design complex geometries, since for instance with additive manufacturing, there is less technological limits then before. However, besides that they have geometric freedom, it is essential to pay attention to engineering aspects, such as efficient material usage, stiffness and so on. This article is dealing with internal support structures and introduces a new lattice, called Lightweight Voronoi Scaffold. The scaffolds as 3-dimensional structures are well known in numerous fields of science. These structures provide mechanical stiffness for bones and place for biomolecules as well. The aim of this research was testing this new structure in case of complex geometry with multiaxial load case. Therefore, the arrangement of Voronoi scaffold is not regular, random sampling-based Monte Carlo method was applied in order to provide proper distribution of generation of geometric instances. Although the random point seed generates a high number of improper geometries, the remaining ones always include notable solutions. Lightweight Voronoi Scaffold was compared to some common regular beam lattices, and results shown that Lightweight Voronoi Scaffold was lighter in each case, that may open new opportunities in the field of additive manufacturing.

Dynamic Robust Reconfiguration of Distribution Network with Low-wind-speed Wind Turbine Integrated

For distribution systems where wind sources are poor, low-wind-speed wind turbines (LWTG) plays an important role in improving the security, economy and reliability of the system. However, the stochastic volatility of LWTG output and loads poses a challenge to the technology of distribution network reconfiguration. Considering the uncertainty of LWTG output, photovoltaic output and changes of load in multiple continuous periods, a dynamic robust reconfiguration model is established. The optimization target is to minimize the three-phase current unbalance and network loss. The model solving process combines the Latin hypercube sampling-based Monte Carlo method, the Semi-invariant method and the compound differential evolution algorithm. The influence of LWTG on the reconfiguration results is explored based on the modified IEEE34-node simulation system, and the performance of the proposed dynamic robust reconfiguration method is then verified.

A Bayesian Monte Carlo-based algorithm for the estimation of small failure probabilities of systems affected by uncertainties

The estimation of system failure probabilities in presence of uncertainties may be a difficult task when the values involved are very small, so that sampling-based Monte Carlo methods may become computationally impractical, especially if the computer codes used to model the system response require large computational efforts, both in terms of time and memory. In this work, we propose to exploit the Bayesian Monte Carlo (BMC) approach to the estimation of definite integrals for developing a new, efficient algorithm for estimating small failure probabilities. The Bayesian framework allows an effective use of all the information available, i.e. the computer code evaluations and the input uncertainty distributions, and, at the same time, the analytical formulation of the Bayesian estimator guarantees the construction of a computationally lean algorithm. The proposed method is first satisfactorily tested with reference to an analytic, two-dimensional case study of literature, offering satisfactory results; then, it is applied to a realistic case study of a natural convection-based cooling system of a gas-cooled fast reactor, operating under a post-loss-of-coolant accident (LOCA), showing performances comparable to those of other efficient alternative methods of literature.

Improved metamodel-based importance sampling for the performance assessment of radioactive waste repositories

In the context of a probabilistic performance assessment of a radioactive waste repository, the estimation of the probability of exceeding the dose threshold set by a regulatory body is a fundamental task. This may become difficult when the probabilities involved are very small, since the classically used sampling-based Monte Carlo methods may become computationally impractical. This issue is further complicated by the fact that the computer codes typically adopted in this context requires large computational efforts, both in terms of time and memory. This work proposes an original use of a Monte Carlo-based algorithm for (small) failure probability estimation in the context of the performance assessment of a near surface radioactive waste repository. The algorithm, developed within the context of structural reliability, makes use of an estimated optimal importance density and a surrogate, kriging-based metamodel approximating the system response. On the basis of an accurate analytic analysis of the algorithm, a modification is proposed which allows further reducing the computational efforts by a more effective training of the metamodel.

An improved adaptive kriging-based importance technique for sampling multiple failure regions of low probability

The estimation of system failure probabilities may be a difficult task when the values involved are very small, so that sampling-based Monte Carlo methods may become computationally impractical, especially if the computer codes used to model the system response require large computational efforts, both in terms of time and memory. This paper proposes a modification of an algorithm proposed in literature for the efficient estimation of small failure probabilities, which combines FORM to an adaptive kriging-based importance sampling strategy (AK-IS). The modification allows overcoming an important limitation of the original AK-IS in that it provides the algorithm with the flexibility to deal with multiple failure regions characterized by complex, non-linear limit states. The modified algorithm is shown to offer satisfactory results with reference to four case studies of literature, outperforming in general several other alternative methods of literature.

Comment on “Energy Aware Iterative Source Localization for Wireless Sensor Networks”

A recent paper [E. Masazade, R. Niu, P. K. Varshney, and M. Keskinoz, “Energy Aware Iterative Source Localization for Wireless Sensor Networks”, IEEE Transactions on Signal Processing, vol. 58, no. 9, pp. 4824–4835, 2010] presents an iterative source localization scheme based on the selection of sensors. An importance sampling based Monte Carlo method was employed at each iteration using the entire received data to approximate the posterior distribution of the source location in the paper. In this note, we propose an alternative sequential importance sampling and resampling algorithm to implement the iterative source localization. The proposed method provides significant performance improvement over the current method via combination of auxiliary particle filtering with kernel smoothing approximation. The superiority of the alternative algorithm is verified by Monte Carlo simulation results.

Interval Analysis of Kinematic Errors in Serial Manipulators Using Product of Exponentials Formula

This paper proposes a methodology for analysis of kinematic errors in robotic manipulators. The approach is based on interval analysis and predicts end-effector pose deviation from its ideal model using the interval bounds on the errors of the individual axes. In contrast to sampling-based Monte Carlo methods, the proposed methodology offers guaranteed bounds for the error that accumulates at the end-effector. The forward kinematics map is extended to intervals using the product of exponentials formulation with interval joint parameters. This is a convenient method that incorporates both analytical and computational techniques and can be used for error analysis, or inversely, for manipulator design. Simulation and experimental results confirm that the calculated interval bounds fully enclose the end-effector error distribution and provide a measure of its volumetric size. An important application of this method is in the design of modular precision manipulators that can be assembled using individual linear and rotary stages.

Energy Aware Iterative Source Localization for Wireless Sensor Networks

In this paper, the source localization problem in wireless sensor networks is investigated where the location of the source is estimated based on the quantized measurements received from sensors in the field. An energy efficient iterative source localization scheme is proposed where the algorithm begins with a coarse location estimate obtained from measurement data from a set of anchor sensors. Based on the available data at each iteration, the posterior probability density function (pdf) of the source location is approximated using an importance sampling based Monte Carlo method and this information is utilized to activate a number of non-anchor sensors. Two sensor selection metrics namely the mutual information and the posterior Cramér-Rao lower bound (PCRLB) are employed and their performance compared. Further, the approximate posterior pdf of the source location is used to compress the quantized data of each activated sensor using distributed data compression techniques. Simulation results show that with significantly less computation, the PCRLB based iterative sensor selection method achieves similar mean squared error (MSE) performance as compared to the state-of-the-art mutual information based sensor selection method. By selecting only the most informative sensors and compressing their data prior to transmission to the fusion center, the iterative source localization method reduces the communication requirements significantly and thereby results in energy savings.

A comparison between the uncertainties in model parameters and in forcing functions: its application to a 3D water-quality model

This paper illustrates the application of both local and global sensitivity analysis techniques to an estimation of the uncertainty in the output of a 3D reaction–diffusion ecological model; the model describes the seasonal dynamics of dissolved Nitrogen and Phosphorous, and those of the phytoplanktonic and zooplanktonic communities in the lagoon of Venice. Two sources of uncertainty were taken into account and compared: (1) uncertainty concerning the parameters of the governing equation; (2) uncertainty concerning the forcing functions. The mean annual concentrations of Dissolved Inorganic Nitrogen (DIN) was regarded as the model output, as it represents the largest fraction of the Total Dissolved Nitrogen, TDN, for which the current Italian legislation sets a quality target in the lagoon of Venice. A local sensitivity analysis was initially used, so as to rank the parameters and provide an initial estimation of the uncertainty, which is a result of an imperfect knowledge of the dynamic of the system. This uncertainty was compared with that induced by an imperfect knowledge of the loads of Nitrogen, which represent the main forcing functions. On the basis of the results of the local analysis, the most important parameters and loads were then taken as the sources of uncertainty, in an attempt to assess their relative contributions. The global uncertainty and sensitivity analyses were carried out by means of a sampling-based Monte Carlo method. The results of the subsequent input–output regression analysis suggest that the variance in the model output could be partitioned among the sources of uncertainty, in accordance with a linear model. Based on this model, 79% of the variance in the mean annual concentration of DIN was accounted for by the uncertainty in the parameters which specify the dynamics of the phytoplankton and zooplankton, and only 5% by the uncertainties in the three main Nitrogen sources.

Gibbs sampler for computing and propagating large covariance matrices

The use of sampling-based Monte Carlo methods for the computation and propagation of large covariance matrices in geodetic applications is investigated. In particular, the so-called Gibbs sampler, and its use in deriving covariance matrices by Monte Carlo integration, and in linear and nonlinear error propagation studies, is discussed. Modifications of this technique are given which improve in efficiency in situations where estimated parameters are highly correlated and normal matrices appear as ill-conditioned. This is a situation frequently encountered in satellite gravity field modelling. A synthetic experiment, where covariance matrices for spherical harmonic coefficients are estimated and propagated to geoid height covariance matrices, is described. In this case, the generated samples correspond to random realizations of errors of a gravity field model.