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Showing papers on "Adaptive algorithm published in 2012"


Journal ArticleDOI
TL;DR: In this paper, an adaptive control algorithm is proposed to balance the need for power quality (voltage regulation) with the desire to minimize power loss in a radial distribution circuit with a high penetration of photovoltaic cells.
Abstract: We show how an adaptive control algorithm can improve the performance of distributed reactive power control in a radial distribution circuit with a high penetration of photovoltaic (PV) cells. The adaptive algorithm is designed to balance the need for power quality (voltage regulation) with the desire to minimize power loss. The adaptation law determines whether the objective function minimizes power losses or voltage regulation based on whether the voltage at each node remains close enough to the voltage at the substation. The reactive power is controlled through the inverter on the PV cells. The control signals are determined based on local instantaneous measurements of the real and reactive power at each node. We use the example of a single branch radial distribution circuit to demonstrate the ability of the adaptive scheme to effectively reduce voltage variations while simultaneously minimizing the power loss in the studied cases. Simulations verify that the adaptive schemes compares favorably with local and global schemes previously reported in the literature.

390 citations


Journal ArticleDOI
TL;DR: It is proved that the proposed adaptive scheme leads to a sequence of discrete solutions, for which the corresponding error estimators tend to zero, under a saturation assumption for the non-perturbed problem which is observed empirically.

369 citations


Journal ArticleDOI
TL;DR: An online gaming algorithm based on policy iteration to solve the continuoustime (CT) twoplayer zerosum game with infinite horizon cost for nonlinear systems with known dynamics is presented.
Abstract: SUMMARY The two-player zero-sum (ZS) game problem provides the solution to the bounded L2-gain problem and so is important for robust control. However, its solution depends on solving a design Hamilton–Jacobi–Isaacs (HJI) equation, which is generally intractable for nonlinear systems. In this paper, we present an online adaptive learning algorithm based on policy iteration to solve the continuous-time two-player ZS game with infinite horizon cost for nonlinear systems with known dynamics. That is, the algorithm learns online in real time an approximate local solution to the game HJI equation. This method finds, in real time, suitable approximations of the optimal value and the saddle point feedback control policy and disturbance policy, while also guaranteeing closed-loop stability. The adaptive algorithm is implemented as an actor/critic/disturbance structure that involves simultaneous continuous-time adaptation of critic, actor, and disturbance neural networks. We call this online gaming algorithm ‘synchronous’ ZS game policy iteration. A persistence of excitation condition is shown to guarantee convergence of the critic to the actual optimal value function. Novel tuning algorithms are given for critic, actor, and disturbance networks. The convergence to the optimal saddle point solution is proven, and stability of the system is also guaranteed. Simulation examples show the effectiveness of the new algorithm in solving the HJI equation online for a linear system and a complex nonlinear system. Copyright © 2011 John Wiley & Sons, Ltd.

145 citations


Journal ArticleDOI
TL;DR: Novel l1-regularized space-time adaptive processing algorithms with a generalized sidelobe canceler architecture for airborne radar applications with a sparse regularization to the minimum variance criterion are proposed.
Abstract: In this paper, we propose novel l1-regularized space-time adaptive processing (STAP) algorithms with a generalized sidelobe canceler architecture for airborne radar applications. The proposed methods suppose that a number of samples at the output of the blocking process are not needed for sidelobe canceling, which leads to the sparsity of the STAP filter weight vector. The core idea is to impose a sparse regularization (l1-norm type) to the minimum variance criterion. By solving this optimization problem, an l1-regularized recursive least squares (l1-based RLS) adaptive algorithm is developed. We also discuss the SINR steady-state performance and the penalty parameter setting of the proposed algorithm. To adaptively set the penalty parameter, two switched schemes are proposed for l1-based RLS algorithms. The computational complexity analysis shows that the proposed algorithms have the same complexity level as the conventional RLS algorithm (O((NM)2)), where NM is the filter weight vector length), but a significantly lower complexity level than the loaded sample covariance matrix inversion algorithm (O((NM)3)) and the compressive sensing STAP algorithm (O((NsNd)3), where N8Nd >; NM is the angle-Doppler plane size). The simulation results show that the proposed STAP algorithms converge rapidly and provide a SINR improvement using a small number of snapshots.

138 citations


Journal ArticleDOI
TL;DR: Experimental results proved that the proposed adaptive contrast enhancement algorithm can effectively enhance the contrast of infrared images, especially the details of infrared image.

131 citations


01 Jan 2012
TL;DR: An efficient adaptive algorithm is set up which successively improves the accuracy of the computed solution by construction of locally refined meshes for time and space discretizations of parabolic optimization problems.
Abstract: In this paper we derive a posteriori error estimates for space-time finite element discretizations of parabolic optimization problems. The provided error estimates assess the discretization error with respect to a given quantity of interest and separate the influences of different parts of the discretization (time, space, and control discretization). This allows us to set up an efficient adaptive algorithm which successively improves the accuracy of the computed solution by construction of locally refined meshes for time and space discretizations.

126 citations


Journal ArticleDOI
TL;DR: An adaptive algorithm is derived for an automatic adjustment of the coupling phase such that a desired state can be selected from an otherwise multistable regime of delay-coupled Stuart-Landau oscillators.
Abstract: We consider networks of delay-coupled Stuart-Landau oscillators. In these systems, the coupling phase has been found to be a crucial control parameter. By proper choice of this parameter one can switch between different synchronous oscillatory states of the network. Applying the speed-gradient method, we derive an adaptive algorithm for an automatic adjustment of the coupling phase such that a desired state can be selected from an otherwise multistable regime. We propose goal functions based on both the difference of the oscillators and a generalized order parameter and demonstrate that the speed-gradient method allows one to find appropriate coupling phases with which different states of synchronization, e.g., in-phase oscillation, splay, or various cluster states, can be selected.

107 citations


Journal ArticleDOI
TL;DR: A sparsity promoting adaptive algorithm for distributed learning in diffusion networks is developed following the set-theoretic estimation rationale and enjoys monotonicity, asymptotic optimality and strong convergence to a point that lies in the consensus subspace.
Abstract: In this paper, a sparsity promoting adaptive algorithm for distributed learning in diffusion networks is developed. The algorithm follows the set-theoretic estimation rationale. At each time instance and at each node of the network, a closed convex set, known as property set, is constructed based on the received measurements; this defines the region in which the solution is searched for. In this paper, the property sets take the form of hyperslabs. The goal is to find a point that belongs to the intersection of these hyperslabs. To this end, sparsity encouraging variable metric projections onto the hyperslabs have been adopted. In addition, sparsity is also imposed by employing variable metric projections onto weighted l1 balls. A combine adapt cooperation strategy is adopted. Under some mild assumptions, the scheme enjoys monotonicity, asymptotic optimality and strong convergence to a point that lies in the consensus subspace. Finally, numerical examples verify the validity of the proposed scheme compared to other algorithms, which have been developed in the context of sparse adaptive learning.

95 citations


Journal ArticleDOI
TL;DR: This paper describes an Adaptive Mesh and Algorithm Refinement (AMAR) methodology for multi-scale simulations of gas flows and the challenges associated with extending this methodology for simulations of weakly ionized plasmas and describes fluid plasma models with AMR capabilities.

95 citations


Journal ArticleDOI
TL;DR: In this paper, a novel adaptive algorithm in fractional Fourier transform (FRFT) domain is proposed, which combines statistic-based and FRFT-based detection method, which provides less error and faster convergence.
Abstract: Attention has been focused on the moving target detection in heavy sea clutter. On the basis of detection model of moving target with fluctuant amplitudes, a novel adaptive algorithm in fractional Fourier transform (FRFT) domain is proposed, which combines statistic-based and FRFT-based detection method. FRFT has good energy concentration property on linear frequency modulation (LFM) signal with the optimal transform angle, which is determined by calculating spectral kurtosis (SK) in FRFT domain. Grading iterative search method is used for good accuracy of parameter estimation and fast calculation speed. A novel adaptive line enhancer (ALE) in FRFT domain is proposed to suppress sea clutter and improve signal-to-clutter ratio (SCR), which provides less error and faster convergence. Leakage factor is introduced into the update equation of weight vector to reduce `memory effect` and step size is normalised by the power of input signal with better convergence characteristic. In the end, both X-band and S-band real sea clutter is used for verification and the results present that the proposed algorithm has good convergence property and small mean square error (MSE). Weak moving target in low SCR environment (SCR = -6 dB) can be well detected and estimated, which indicates the effectiveness of the algorithm.

94 citations


Book ChapterDOI
17 Jun 2012
TL;DR: A new task scheduling model is proposed, and a Particle Swarm Optimization (PSO) based algorithm is proposed that improves the standard PSO, and introduces a simple mutation mechanism and a self-adapting inertia weight method by classifying the fitness values.
Abstract: It is possible for IT service providers to provide computing resources in an pay-per-use way in Cloud Computing environments. At the same time, terminal users can also get satisfying services conveniently. But if we take only execution time into consideration when scheduling the cloud resources, it may occur serious load imbalance problem between Virtual Machines (VMs) in Cloud Computing environments. In addition to solve this problem, a new task scheduling model is proposed in this paper. In the model, we optimize the task execution time in view of both the task running time and the system resource utilization. Based on the model, a Particle Swarm Optimization (PSO) --- based algorithm is proposed. In our algorithm, we improved the standard PSO, and introduce a simple mutation mechanism and a self-adapting inertia weight method by classifying the fitness values. In the end of this paper, the global search performance and convergence rate of our adaptive algorithm are validated by the results of the comparative experiments.

Journal ArticleDOI
TL;DR: A fast direct algorithm for solutions to linear systems arising from 2D elliptic equations using the multifrontal method with hierarchical matrices and an adaptive decomposition procedure for general meshes is presented.

Journal ArticleDOI
TL;DR: A new adaptive algorithm for frequency-domain identification is presented, based on an adaptive decomposition algorithm previously proposed for decomposing the Hardy space functions, in which a greedy sequence is obtained according to the maximal selection criterion.

Journal ArticleDOI
TL;DR: A nonparametric, adaptive, and high resolution technique, known as the time-recursive iterative adaptive approach, is presented as a tool for the extraction of the electric network frequency (ENF) from digital audio recordings and results show that the adaptive algorithm improves the ENF estimation accuracy in the presence of interference from other signals.
Abstract: A novel forensic tool used for assessing the authenticity of digital audio recordings is known as the electric network frequency (ENF) criterion. It involves extracting the embedded power line (utility) frequency from said recordings and matching it to a known database to verify the time the recording was made, and its authenticity. In this paper, a nonparametric, adaptive, and high resolution technique, known as the time-recursive iterative adaptive approach, is presented as a tool for the extraction of the ENF from digital audio recordings. A comparison is made between this data dependent (adaptive) filter and the conventional short-time Fourier transform (STFT). Results show that the adaptive algorithm improves the ENF estimation accuracy in the presence of interference from other signals. To further enhance the ENF estimation accuracy, a frequency tracking method based on dynamic programming will be proposed. The algorithm uses the knowledge that the ENF is varying slowly with time to estimate with high accuracy the frequency present in the recording.

Journal ArticleDOI
TL;DR: An adaptive algorithm is proposed in this paper to integrate a higher level image classification task and a lower level super-resolution process, in which it incorporate reconstruction-based super- resolution algorithms, single-image enhancement, and image/video classification into a single comprehensive framework.
Abstract: Super-resolution technology provides an effective way to increase image resolution by incorporating additional information from successive input images or training samples. Various super-resolution algorithms have been proposed based on different assumptions, and their relative performances can differ in regions of different characteristics within a single image. Based on this observation, an adaptive algorithm is proposed in this paper to integrate a higher level image classification task and a lower level super-resolution process, in which we incorporate reconstruction-based super-resolution algorithms, single-image enhancement, and image/video classification into a single comprehensive framework. The target high-resolution image plane is divided into adaptive-sized blocks, and different suitable super-resolution algorithms are automatically selected for the blocks. Then, a deblocking process is applied to reduce block edge artifacts. A new benchmark is also utilized to measure the performance of super-resolution algorithms. Experimental results with real-life videos indicate encouraging improvements with our method.

Journal ArticleDOI
TL;DR: A new state space model for estimate and track the frequency of such nonstationary signals and an EKF frequency tracker that only uses one tuning parameter is proposed, which allows an easier and more transparent tuning of the EKf tracking behaviour.

Book ChapterDOI
01 Jan 2012
TL;DR: An adaptive hierarchy of non uniform time discretizations, generated by an adaptive algorithm introduced in AnnaDzougoutov et al.
Abstract: This work generalizes a multilevel forward Euler Monte Carlo method introduced in Michael B. Giles. (Michael Giles. Oper. Res. 56(3):607–617, 2008.) for the approximation of expected values depending on the solution to an Ito stochastic differential equation. The work (Michael Giles. Oper. Res. 56(3):607– 617, 2008.) proposed and analyzed a forward Euler multilevelMonte Carlo method based on a hierarchy of uniform time discretizations and control variates to reduce the computational effort required by a standard, single level, Forward Euler Monte Carlo method. This work introduces an adaptive hierarchy of non uniform time discretizations, generated by an adaptive algorithmintroduced in (AnnaDzougoutov et al. Raul Tempone. Adaptive Monte Carlo algorithms for stopped diffusion. In Multiscale methods in science and engineering, volume 44 of Lect. Notes Comput. Sci. Eng., pages 59–88. Springer, Berlin, 2005; Kyoung-Sook Moon et al. Stoch. Anal. Appl. 23(3):511–558, 2005; Kyoung-Sook Moon et al. An adaptive algorithm for ordinary, stochastic and partial differential equations. In Recent advances in adaptive computation, volume 383 of Contemp. Math., pages 325–343. Amer. Math. Soc., Providence, RI, 2005.). This form of the adaptive algorithm generates stochastic, path dependent, time steps and is based on a posteriori error expansions first developed in (Anders Szepessy et al. Comm. Pure Appl. Math. 54(10):1169– 1214, 2001). Our numerical results for a stopped diffusion problem, exhibit savings in the computational cost to achieve an accuracy of \( \vartheta{\rm(TOL),\, from\,(TOL^{-3})}\), from using a single level version of the adaptive algorithm to \( \vartheta\left( \begin{array}{lll}\left({(TOL^{-1})\,log(TOL)}\right)^2\end{array}\right).\)

Journal ArticleDOI
TL;DR: The proposed PSO algorithm outperforms, in most cases, other existing attempts to solve the same problem as shown by experimental results.
Abstract: A new adaptive algorithm based on particle swarm optimization (PSO) is designed, developed and applied to the high school timetabling problem. The proposed PSO algorithm is used in order to create feasible and very efficient timetables for high schools in Greece. Experiments with real-world data coming from many different high schools have been conducted in order to show the efficiency of the proposed PSO algorithm. As well as that, the algorithm has been compared with four other effective techniques found in the literature in order to demonstrate its efficiency and superior performance. The proposed PSO algorithm outperforms, in most cases, other existing attempts to solve the same problem as shown by experimental results.

Journal ArticleDOI
TL;DR: A new adaptive fuzzy sliding mode (AFSM) observer is proposed which can be used for a class of MIMO nonlinear systems and the performance of the observer shows its effectiveness in the real world.
Abstract: In this paper, a new adaptive fuzzy sliding mode (AFSM) observer is proposed which can be used for a class of MIMO nonlinear systems. In the proposed algorithm, the zero-input dynamics of the plant could be unknown. In this method, a fuzzy system is designed to estimate the nonlinear behavior of the observer. The output of fuzzy rules are tuned adaptively, based on the observer error. The output connection matrix is used to combine the observer errors of individual subsystems. A robust term, which is designed based on the sliding mode theory, is added to the observer to compensate the fuzzy estimation error. The estimation error bound is adjusted by an adaptive law. The main advantage of the proposed observer is that, unlike many of the previous works, the measured outputs is not limited to the first entries of a canonical-form state vector. The proposed observer estimates the closed-loop state tracking error asymptotically, provided that the output gain matrix includes Hurwitz coefficients. The chattering is eliminated by using boundary layers around the sliding surfaces and the observer convergence is proved using a Lyapunov-based approach. The proposed method is applied on a real multilink robot manipulator. The performance of the observer shows its effectiveness in the real world.

Journal ArticleDOI
TL;DR: The approach gives a first mathematical justification for the proposed steering of anisotropic mesh-refinements, which is mandatory for optimal convergence behavior in 3D boundary element computations, and proves estimator convergence in the sense that the adaptive algorithm drives the underlying error estimator to zero.

Journal ArticleDOI
TL;DR: A comparison between the MsD TM and the adaptive MsDTM reveals that the proposed approach is an efficiency tool for solving the considered equations using fewer time steps.

Journal ArticleDOI
TL;DR: The proposed GAAL method is applied to a number of constrained test problems taken from the evolutionary algorithms (EAs) literature and is found to be accurate, computationally fast, and reliable over multiple runs.
Abstract: Among the penalty based approaches for constrained optimization, augmented Lagrangian (AL) methods are better in at least three ways: (i) they have theoretical convergence properties, (ii) they distort the original objective function minimally, thereby providing a better function landscape for search, and (iii) they can result in computing optimal Lagrange multiplier for each constraint as a by-product. Instead of keeping a constant penalty parameter throughout the optimization process, these algorithms update the parameters (called multipliers) adaptively so that the corresponding penalized function dynamically changes its optimum from the unconstrained minimum point to the constrained minimum point with iterations. However, the flip side of these algorithms is that the overall algorithm requires a serial application of a number of unconstrained optimization tasks, a process that is usually time-consuming and tend to be computationally expensive. In this paper, we devise a genetic algorithm based parameter update strategy to a particular AL method. The proposed strategy updates critical parameters in an adaptive manner based on population statistics. Occasionally, a classical optimization method is used to improve the GA-obtained solution, thereby providing the resulting hybrid procedure its theoretical convergence property. The GAAL method is applied to a number of constrained test problems taken from the evolutionary algorithms (EAs) literature. The number of function evaluations required by GAAL in most problems is found to be smaller than that needed by a number of existing evolutionary based constraint handling methods. GAAL method is found to be accurate, computationally fast, and reliable over multiple runs. Besides solving the problems, the proposed GAAL method is also able to find the optimal Lagrange multiplier associated with each constraint for the test problems as an added benefit--a matter that is important for a sensitivity analysis of the obtained optimized solution, but has not yet been paid adequate attention in the past evolutionary constrained optimization studies.

Proceedings ArticleDOI
10 Dec 2012
TL;DR: An adaptive algorithm, called TAPIOCA (distribuTed and AdaPtive IntersectiOns Control Algorithm), that uses data collected by this sensor network to decide dynamically of the green light sequences, considering three objectives.
Abstract: In this article, we detail and evaluate a distributed algorithm that defines the green lights sequence and duration in a multi-intersection intelligent transportation system (ITS). We expose the architecture of a wireless network of sensors deployed at intersections, which takes local decisions without the help of a central entity. We define an adaptive algorithm, called TAPIOCA (distribuTed and AdaPtive IntersectiOns Control Algorithm), that uses data collected by this sensor network to decide dynamically of the green light sequences, considering three objectives: (i) reducing the users average waiting time while limiting the starvation probability; (ii) selecting in priority the movements that have the best load discharge potential and (iii) synchronizing successive lights, for example to create green waves. Simulation results performed with the SUMO simulator show that TAPIOCA achieves a low average waiting time of vehicles and reacts quickly to traffic load increases, compared to other dynamic strategies and to pre-determined schedules.

Journal ArticleDOI
TL;DR: This work builds an adaptive algorithm for finding online sparse solutions to linear systems and presents simulations showing that, for identifying sparse time-varying FIR channels, this algorithm is consistently better than previous sparse RLS methods based on the -norm regularization of the RLS criterion.
Abstract: Starting from the orthogonal (greedy) least squares method, we build an adaptive algorithm for finding online sparse solutions to linear systems. The algorithm belongs to the exponentially windowed recursive least squares (RLS) family and maintains a partial orthogonal factorization with pivoting of the system matrix. For complexity reasons, the permutations that bring the relevant columns into the first positions are restrained mainly to interchanges between neighbors at each time moment. The storage scheme allows the computation of the exact factorization, implicitly working on indefinitely long vectors. The sparsity level of the solution, i.e., the number of nonzero elements, is estimated using information theoretic criteria, in particular Bayesian information criterion (BIC) and predictive least squares. We present simulations showing that, for identifying sparse time-varying FIR channels, our algorithm is consistently better than previous sparse RLS methods based on the -norm regularization of the RLS criterion. We also use our sparse greedy RLS algorithm for computing linear predictions in a lossless audio coding scheme and obtain better compression than MPEG4 ALS using an RLS-LMS cascade.

Journal ArticleDOI
TL;DR: A new adaptive algorithm which effectively and blindly restores the spectral shape of the desired signal is presented, which has low complexity, does not introduce additional delay in the relay station, and partly compensates for multipath propagation.
Abstract: Although full-duplex relaying schemes are appealing in order to improve spectral efficiency, simultaneous reception and transmission in the same frequency results in self-interference, distorting the retransmitted signal and making the relay prone to oscillation. Current feedback cancellation techniques by means of adaptive filters are hampered by the fact that the useful and interference signals are highly correlated. We present a new adaptive algorithm which effectively and blindly restores the spectral shape of the desired signal. In contrast with previous schemes, the novel adaptive feedback canceller has low complexity, does not introduce additional delay in the relay station, and partly compensates for multipath propagation.

Proceedings Article
26 Jun 2012
TL;DR: A new anytime algorithm that achieves near-optimal regret for any instance of finite stochastic partial monitoring, and is adaptive in the sense that if the opponent strategy is in an "easy region" of the strategy space then the regret grows as if the problem was easy.
Abstract: We present a new anytime algorithm that achieves near-optimal regret for any instance of finite stochastic partial monitoring. In particular, the new algorithm achieves the minimax regret, within logarithmic factors, for both "easy" and "hard" problems. For easy problems, it additionally achieves logarithmic individual regret. Most importantly, the algorithm is adaptive in the sense that if the opponent strategy is in an "easy region" of the strategy space then the regret grows as if the problem was easy. As an implication, we show that under some reasonable additional assumptions, the algorithm enjoys an O(√T) regret in Dynamic Pricing, proven to be hard by Bartok et al. (2011).

Journal ArticleDOI
TL;DR: The parallel mesh adaptivity method introduced in this paper focuses on dynamic load balancing in response to the local refinement and coarsening of the mesh, which is dominated by the cost of the sequential adaptive mesh procedure.

Journal ArticleDOI
TL;DR: This paper observes that compression does not always reduce packet delay in a WSN as commonly perceived, whereas its effect is jointly determined by the network configuration and hardware configuration, and designs an adaptive algorithm to make online decisions such that compression is only performed when it can benefit the overall performance.
Abstract: Compression, as a popular technique to reduce data size by exploiting data redundancy, can be used in delay sensitive wireless sensor networks (WSNs) to reduce end-to-end packet delay as it can reduce packet transmission time and contention on the wireless channel. However, the limited computing resources at sensor nodes make the processing time of compression a nontrivial factor in the total delay a packet experiences and must be carefully examined when adopting compression. In this paper, we first study the effect of compression on data gathering in WSNs under a practical compression algorithm. We observe that compression does not always reduce packet delay in a WSN as commonly perceived, whereas its effect is jointly determined by the network configuration and hardware configuration. Based on this observation, we then design an adaptive algorithm to make online decisions such that compression is only performed when it can benefit the overall performance. We implement the algorithm in a completely distributed manner that utilizes only local information of individual sensor nodes. Our extensive experimental results show that the algorithm demonstrates good adaptiveness to network dynamics and maximizes compression benefit.

Proceedings ArticleDOI
31 Dec 2012
TL;DR: The paper demonstrates that the adaptive algorithm can get the lower call blocking rates and handover failure rates because of its high-efficiency in load balancing and also shows with the small appropriate power, it can get better system performances.
Abstract: Mobility Load balance(MLB) is an key technology belonging to self-organization networks(SONs) in Long Term Evolution (LTE) system. In the paper, a high-efficient algorithm is proposed to balance the uneven load between neighboring cells in LTE system. The algorithm adjusts the cell-specific offset between neighboring cells(OCN) adaptively depending on the load difference between neighboring cells. If the load difference exceeds the presetting threshold, then the algorithm will be triggered and adjust the OCN by adding or subtracting an adaptive step-size. Also, a power function is proposed to characterize the adaptive step-size and the step-size will be larger as the load difference between neighboring cells increases. This feature of the power function makes the MLB algorithm more efficient to fit the largely uneven load between neighboring cells. Furthermore, a simulation platform with 7 cell is set to evaluate the algorithm with different power of the function. It demonstrates that the adaptive algorithm can get the lower call blocking rates and handover failure rates because of its high-efficiency in load balancing. It also shows with the small appropriate power, we can get better system performances.

Journal ArticleDOI
TL;DR: An automatic adaptive algorithm based on nested sparse grids has been developed to evaluate multidimensional integrals of the Non-Intrusive Spectral Projection method, and the spectral form of the solution is explicitly identified from the constructed quadrature scheme.
Abstract: The Non-Intrusive Spectral Projection (NISP) method is widely used for uncertainty quantification in stochastic models. The determination of the expansion of the solution on the polynomial chaos requires the computation of multidimensional integrals. An automatic adaptive algorithm based on nested sparse grids has been developed to evaluate those integrals. The adapted algorithm takes into account the weight of each random variable with respect to the output of the model. To achieve that it constructs anisotropic sparse grid of the mean, leading to a reduction of the number of numerical simulations. Furthermore, the spectral form of the solution is explicitly identified from the constructed quadrature scheme. Numerical results obtained on an industrial application in NDT demonstrate the efficiency of the proposed method.