Semiparametric Estimation and Selection for Nonstationary Spatial Covariance Functions

We propose a method for estimating nonstationary spatial covariance functions by representing a spatial process as a linear combination of some local basis functions with uncorrelated random coefficients and some stationary processes, based on spatial data sampled in space with repeated measurements. By incorporating a large collection of local basis functions with various scales at various locations and stationary processes with various degrees of smoothness, the model is flexible enough to represent a wide variety of nonstationary spatial features. The covariance estimation and model selection are formulated as a regression problem with the sample covariances as the response and the covariances corresponding to the local basis functions and the stationary processes as the predictors. A constrained least squares approach is applied to select appropriate basis functions and stationary processes as well as estimate parameters simultaneously. In addition, a constrained generalized least squares approach is proposed to further account for the dependencies among the response variables. A simulation experiment shows that our method performs well in both covariance function estimation and spatial prediction. The methodology is applied to a U.S. precipitation dataset for illustration. Supplemental materials relating to the application are available online.     

Indoor positioning system based on BLE location fingerprinting with classification approach

Position estimation is an important technique for location-based services. Many services and applications, such as navigation assistance, surveillance of patients and social networking, have been developed based on users’ position. Although the GPS plays an important role in positioning systems, its signal strength is extremely weak inside buildings. Thus, other sensing devices are necessary to improve the accuracy of indoor localisation. In the past decade, researchers have developed a series of indoor positioning technologies based on the received signal strength (RSS) of WiFi, ZigBee or Bluetooth devices under the infrastructure of wireless sensor network for location estimation. We can compute the distance of the devices by measuring their RSS, but the correctness of the result is unsatisfactory because the radio signal interference is a considerable issue and the indoor radio propagation is too complicated to model. Using the location fingerprint to estimate a target position is a feasible strategy because the location fingerprint records the characteristics of the signals and the signal strength is related to the space relation. This type of algorithm estimates the location of a target by matching online measurements with the closest a-priori location fingerprints. The matching or classification algorithm is a key issue in the correctness of location fingerprinting. In this paper, we propose an effective location fingerprinting algorithm based on the general and weighted k-nearest neighbour algorithms to estimate the position of the target node. The grid points are trained with an interval of 2 m, and the estimated position error is about 1.8 m. Thus, the proposed method is low computation consumption, and with an acceptable accuracy.     

A degradation path-dependent approach for remaining useful life estimation with an exact and closed-form solution

Remaining useful life (RUL) estimation is regarded as one of the most central components in prognostics and health management (PHM). Accurate RUL estimation can enable failure prevention in a more controllable manner in that effective maintenance can be executed in appropriate time to correct impending faults. In this paper we consider the problem of estimating the RUL from observed degradation data for a general system. A degradation path-dependent approach for RUL estimation is presented through the combination of Bayesian updating and expectation maximization (EM) algorithm. The use of both Bayesian updating and EM algorithm to update the model parameters and RUL distribution at the time obtaining a newly observed data is a novel contribution of this paper, which makes the estimated RUL depend on the observed degradation data history. As two specific cases, a linear degradation model and an exponential-based degradation model are considered to illustrate the implementation of our presented approach. A major contribution under these two special cases is that our approach can obtain an exact and closed-form RUL distribution respectively, and the moment of the obtained RUL distribution from our presented approach exists. This contrasts sharply with the approximated results obtained in the literature for the same cases. To our knowledge, the RUL estimation approach presented in this paper for the two special cases is the only one that can provide an exact and closed-form RUL distribution utilizing the monitoring history. Finally, numerical examples for RUL estimation and a practical case study for condition-based replacement decision making with comparison to a previously reported approach are provided to substantiate the superiority of the proposed model.     

On the Use of Augmented Lagrangians in the Solution of Generalized Semi-Infinite Min-Max Problems

We present an approach for the solution of a class of generalized semi-infinite optimization problems. Our approach uses augmented Lagrangians to transform generalized semi-infinite min-max problems into ordinary semi-infinite min-max problems, with the same set of local and global solutions as well as the same stationary points. Once the transformation is effected, the generalized semi-infinite min-max problems can be solved using any available semi-infinite optimization algorithm. We illustrate our approach with two numerical examples, one of which deals with structural design subject to reliability constraints.     

A real time algorithm for the location search of discontinuous conductivities with one measurement

We consider an inverse problem for finding the anomaly of discontinuous electrical conductivity by one current‐voltage observation. We develop a real time algorithm for determining the location of the anomaly. This new idea is based on the observation of the pattern of a simple weighted combination of the input current and the output voltage. Combined with the size estimation result, this algorithm gives a good initial guess for Newton‐type schemes. We give the rigorous proof for the location search algorithm. Both the mathematical analysis and its numerical implementation indicate our location search algorithm is very fast, stable and efficient. © 2001 John Wiley & Sons, Inc.     

The Finite Element Method for Computing the Stationary Distribution of an SRBM in a Hypercube with Applications to Finite Buffer Queueing Networks

This paper proposes an algorithm, referred to as BNAfm (Brownian network analyzer with finite element method), for computing the stationary distribution of a semimartingale reflecting Brownian motion (SRBM) in a hypercube. The SRBM serves as an approximate model of queueing networks with finite buffers. Our BNAfm algorithm is based on the finite element method and an extension of a generic algorithm developed by Dai and Harrison [14]. It uses piecewise polynomials to form an approximate subspace of an infinite-dimensional functional space. The BNAfm algorithm is shown to produce good estimates for stationary probabilities, in addition to stationary moments. This is in contrast to the BNAsm algorithm (Brownian network analyzer with spectral method) of Dai and Harrison [14], which uses global polynomials to form the approximate subspace and which sometimes fails to produce meaningful estimates of these stationary probabilities. Extensive computational experiences from our implementation are reported, which may be useful for future numerical research on SRBMs. A three-station tandem network with finite buffers is presented to illustrate the effectiveness of the Brownian approximation model and our BNAfm algorithm.     

Iterated Stochastic Processes: Simulation and Relationship with High Order Partial Differential Equations

In this paper, we consider the composition of two independent processes: one process corresponds to position and the other one to time. Such processes will be called iterated processes. We first propose an algorithm based on the Euler scheme to simulate the trajectories of the corresponding iterated processes on a fixed time interval. This algorithm is natural and can be implemented easily. We show that it converges almost surely, uniformly in time, with a rate of convergence of order 1/4 and propose an estimation of the error. We then extend the well known Feynman-Kac formula which gives a probabilistic representation of partial differential equations (PDEs), to its higher order version using iterated processes. In particular we consider general position processes which are not necessarily Markovian or are indexed by the real line but real valued. We also weaken some assumptions from previous works. We show that intertwining diffusions are related to transformations of high order PDEs. Combining our numerical scheme with the Feynman-Kac formula, we simulate functionals of the trajectories and solutions to fourth order PDEs that are naturally associated to a general class of iterated processes.     

Poisson source localization on the plane: change-point case

We present a detection problem where several spatially distributed sensors observe Poisson signals emitted from a single radioactive source of unknown position. The measurements at each sensor are modeled by independent inhomogeneous Poisson processes. A method based on Bayesian change-point estimation is proposed to identify the location of the source’s coordinates. The asymptotic behavior of the Bayesian estimator is studied. In particular, the consistency and the asymptotic efficiency of the estimator are analyzed. The limit distribution and the convergence of the moments are also described. The similar statistical model could be used in GPS localization problems.

     

The QNET method for two-moment analysis of open queueing networks

Consider an open network of single-server stations, each with a first-in-first-out discipline. The network may be populated by various customer types, each with its own routing and service requirements. Routing may be either deterministic or stochastic, and the interarrival and service time distributions may be arbitrary. In this paper a general method for steady-state performance analysis is described and illustrated. This analytical method, called QNET, uses both first and second moment information, and it is motivated by heavy traffic theory. However, our numerical examples show that QNET compares favorably with W. Whitt's Queueing Network Analyzer (QNA) and with other approximation schemes, even under conditions of light or moderate loading. In the QNET method one first replaces the original queueing network by what we call an approximating Brownian system model, and then one computes the stationary distribution of the Brownian model. The second step amounts to solving a certain highly structured partial differential equation problem; a promising general approach to the numerical solution of that PDE problem is described by Harrison and Dai [8] in a companion paper. Thus far the numerical solution technique has been implemented only for two-station networks, and it is clear that the computational burden will grow rapidly as the number of stations increases. Thus we also describe and investigate a cruder approach to two-moment network analysis, called ΠNET, which is based on a product form approximation, or decomposition approximation, to the stationary distribution of the Brownian system model. In very broad terms, ΠNET is comparable to QNA in its level of sophistication, whereas QNET captures more subtle system interactions. In our numerical examples the performance of ΠNET and QNA is similar; the performance of QNET is generally better, sometimes much better.     

Improved Estimation and Uncertainty Quantification Using Monte Carlo-Based Optimization Algorithms

In this article, we present a novel method to obtain both improved estimates and reliable stopping rules for stochastic optimization algorithms such as the Monte Carlo EM (MCEM) algorithm. By characterizing a stationary point, θ*, of the algorithm as the solution to a fixed point equation, we provide a parameter estimation procedure by solving for the fixed point of the update mapping. We investigate various ways to model the update mapping, including the use of a local linear (regression) smoother. This simple approach allows increased stability in estimating the value of θ* as well as providing a natural quantification of the estimation uncertainty. These uncertainty measures can then also be used to construct convergence criteria that reflect the inherent randomness in the algorithm. We establish convergence properties of our modified estimator. In contrast to existing literature, our convergence results do not require the Monte Carlo sample size to go to infinity. Simulation studies are provided to illustrate the improved stability and reliability of our estimator.     

A posteriori error estimation for a defect correction method applied to conduction convection problems

We present a posteriori error estimate for a defect correction method for approximating solutions of the stationary conduction convection problems in two dimension. The defect correction method is aiming at small viscosity ν. A reliable a posteriori error estimation is derived for the defect correction method. Finally, two numerical examples validate our theoretical results. The first example is a problem with known solution and the second example is a physical model of square cavity stationary flow. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2013     

Numerical valuation of discrete double barrier options

In the present paper we explore the problem for pricing discrete barrier options utilizing the Black-Scholes model for the random movement of the asset price. We postulate the problem as a path integral calculation by choosing approach that is similar to the quadrature method. Thus, the problem is reduced to the estimation of a multi-dimensional integral whose dimension corresponds to the number of the monitoring dates.We propose a fast and accurate numerical algorithm for its valuation. Our results for pricing discretely monitored one and double barrier options are in agreement with those obtained by other numerical and analytical methods in Finance and literature. A desired level of accuracy is very fast achieved for values of the underlying asset close to the strike price or the barriers.The method has a simple computer implementation and it permits observing the entire life of the option.     

Numerical Calculation of the Stationary Distribution of the Main Multiserver Retrial Queue

We are concerned with the main multiserver retrial queue of M/M/c type with exponential repeated attempts. It is known that an analytical solution of this queueing model is difficult and does not lead to numerical implementation. Based on appropriate understanding of the physical behavior, an efficient and numerically stable algorithm for computing the stationary distribution of the system state is developed. Numerical calculations are done to compare our approach with the existing approximations.     

Transit passenger origin-destination estimation in congested transit networks with elastic line frequencies

This paper deals with the transit passenger origin-destination (O-D) estimation problem by using updated passenger counts in congested transit networks and outdated prior O-D matrix. A bilevel programming approach is extended for the transit passenger O-D updating problem where the upper-level problem seeks to minimize the sum of error measurements in passenger counts and O-D matrices, while the lower level is the stochastic user equilibrium assignment problem for congested transit networks. The transit assignment framework is based on a frequency-adaptive transit network model in this paper, which can help determine transit line frequencies and the network flow pattern simultaneously in congested transit networks. A heuristic solution algorithm is adapted for solving the transit passenger O-D estimation problem. Finally, a numerical example is used to illustrate the applications of the proposed model and solution algorithm. The work described in this paper was mainly supported by two research grants from the Research Grants Council of the Hong Kong Special Administrative Region (Project No. PolyU 5143/03E and PolyU 5040/02E).     

Optimizing logistic regression coefficients for discrimination and calibration using estimation of distribution algorithms

Logistic regression is a simple and efficient supervised learning algorithm for estimating the probability of an outcome or class variable. In spite of its simplicity, logistic regression has shown very good performance in a range of fields. It is widely accepted in a range of fields because its results are easy to interpret. Fitting the logistic regression model usually involves using the principle of maximum likelihood. The Newton–Raphson algorithm is the most common numerical approach for obtaining the coefficients maximizing the likelihood of the data. This work presents a novel approach for fitting the logistic regression model based on estimation of distribution algorithms (EDAs), a tool for evolutionary computation. EDAs are suitable not only for maximizing the likelihood, but also for maximizing the area under the receiver operating characteristic curve (AUC). Thus, we tackle the logistic regression problem from a double perspective: likelihood-based to calibrate the model and AUC-based to discriminate between the different classes. Under these two objectives of calibration and discrimination, the Pareto front can be obtained in our EDA framework. These fronts are compared with those yielded by a multiobjective EDA recently introduced in the literature.      

A traffic shaping model for optimizing network operations

The management of technology in multi-service computer networks, such as university networks, has become a challenge with the explosive growth of entertainment oriented peer-to-peer (P2P) traffic. Traffic shaping is one of the tools used to manage bandwidth to improve system performance by allocating bandwidth between P2P and non-peer-to-peer (NP2P) traffic. We present a model for traffic shaping and bandwidth management that considers the trade-offs from allocating different amounts of bandwidths for different application categories and use data from a university network. The current policy allocates varying bandwidths over the day to P2P and NP2P traffic to reflect the importance of not letting entertainment based traffic choke the network during the day time at the expense of the more important traffic, such as Web traffic. We highlight the difficulties in obtaining data in the form required for analysis, and the need to estimate demand for allocations not covered by current policy. We present a goal programming model for this estimation task. We also model the traffic shaping problem as a Markov decision process and develop an algorithm for determining the optimal bandwidth allocation to maximize the utility of all users. Finally we use a numerical example to illustrate our approach.     

A hybrid optimization approach for automated parameter estimation problems

We present a hybrid optimization approach for solving automated parameter estimation models. The hybrid approach is based on the coupling of the Simultaneous Perturbation Stochastic Approximation (SPSA) [1] and a Newton-Krylov Interior-Point method (NKIP) [2] via a surrogate model. The global method SPSA performs a stochastic search to find target regions with low function values. Next, we generate a surrogate model based on the points of regions on which the local method NKIP algorithm is applied for finding an optimal solution. We illustrate the behavior of the hybrid optimization algorithm on one testcase. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Bayesian source detection and parameter estimation of a plume model based on sensor network measurements

We consider a network of sensors that measure the intensities of a complex plume composed of multiple absorption–diffusion source components. We address the problem of estimating the plume parameters, including the spatial and temporal source origins and the parameters of the diffusion model for each source, based on a sequence of sensor measurements. The approach not only leads to multiple‐source detection, but also the characterization and prediction of the combined plume in space and time. The parameter estimation is formulated as a Bayesian inference problem, and the solution is obtained using a Markov chain Monte Carlo algorithm. The approach is applied to a simulation study, which shows that an accurate parameter estimation is achievable. Copyright © 2010 John Wiley & Sons, Ltd.     

Optimal Battery Aging: An Adaptive Weights Dynamic Programming Algorithm

We present an algorithm to handle the optimization over a long horizon of an electric microgrid including a battery energy storage system. While the battery is an important and costly component of the microgrid, its aging process is often not taken into account by the energy management system, mostly because of modeling and computing challenges. We address the computing aspect by a new approach combining dynamic programming, decomposition and relaxation techniques. We illustrate this adaptive weight’ method with numerical simulations for a toy microgrid model. Compared to a straightforward resolution by dynamic programming, our algorithm decreases the computing time by more than one order of magnitude, can be parallelized, and allows for online implementations. We believe that this approach can be used for other applications presenting fast and slow variables.     

Nonmonotone projected gradient methods based on barrier and Euclidean distances

We consider nonmonotone projected gradient methods based on non-Euclidean distances, which play the role of barrier for a given constraint set. Our basic scheme uses the resulting projection-like maps that produces interior trajectories, and combines it with the recent nonmonotone line search technique originally proposed for unconstrained problems by Zhang and Hager. The combination of these two ideas leads to produce a nonmonotone scheme for constrained nonconvex problems, which is proven to converge to a stationary point. Some variants of this algorithm that incorporate spectral steplength are also studied and compared with classical nonmonotone schemes based on the usual Euclidean projection. To validate our approach, we report on numerical results solving bound constrained problems from the CUTEr library collection.