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A nonparametric procedure to estimate the conditional probability that a nonstationary geostatistical process exceeds a certain threshold value is proposed. The method consists of a bootstrap algorithm that combines conditional simulation techniques with nonparametric estimations of the trend and the variability. The nonparametric local linear estimator, considering a bandwidth matrix selected by a method that takes the spatial dependence into account, is used to estimate the trend. The variability is modeled estimating the conditional variance and the variogram from corrected residuals to avoid the biasses. The proposed method allows to obtain estimates of the conditional exceedance risk in non-observed spatial locations. The performance of the approach is analyzed by simulation and illustrated with the application to a real data set of precipitations in the USA.Supplementary materials accompanying this paper appear on-line. [ABSTRACT FROM AUTHOR]

Process monitoring based on neural networks is getting more and more attention. Compared with classical neural networks, high-order neural networks have natural advantages in dealing with heteroscedastic data. However, high-order neural networks might bring the risk of overfitting, which learning both the key information from original data and noises or anomalies. Orthogonal constraints can greatly reduce correlations between extracted features, thereby reducing the overfitting risk. This paper proposes a novel fault detection method called second-order component analysis (SCA). SCA rules out the heteroscedasticity of process data by optimizing a second-order autoencoder with orthogonal constraints. In order to deal with this constrained optimization problem, a geometric conjugate gradient algorithm is adopted in this paper, which performs geometric optimization on the combination of Stiefel manifold and Euclidean manifold. Extensive experiments on the Tennessee-Eastman benchmark process show that SCA outperforms the compared state-of-the-art methods with missed detection rate (MDR) and false alarm rate (FAR). • Second-order component analysis (SCA) is proposed for fault detection. • SCA uses the structure of autoencoder and adds second-order terms to improve nonlinear mapping capabilities. • SCA adopts orthogonal constraints to reduce the overfitting problem. • SCA adopts a geometric conjugate gradient (GCG) algorithm to deal with constrained optimization problem. [ABSTRACT FROM AUTHOR]

The problem of fitting two concentric objects (circles and ellipses) to noisy data plays a vital role in many fields. In this paper, statistical methodologies are deployed by additionally assuming that the angular differences between successively measured data points are known, which is known as Berman's model. The heteroscedasticity between covariates is also assumed here, and hence, several estimators for the problem of fitting concentric circles and ellipses are developed and their statistical properties are established. Unlike concentric circles, the problem of fitting concentric ellipses turns out to be nonlinear even with Berman's assumption, and as such, iterative algorithms are implemented. Extensive numerical experiments were conducted to validate our results. • Fitting two concentric objects to noisy data plays a vital role in many fields. • The statistical properties of the three developed estimators have been established. • Numerically stable algorithm for fitting concentric ellipses has been proposed. [ABSTRACT FROM AUTHOR]

In chip multiprocessors, the thermal hot spot prediction is vital to take proactive thermal management decisions for mitigating its impact on the performance of the application. Core temperature prediction for a range of future time steps is challenging because workload changes dynamically at runtime. This article presents an adaptive multistep temperature prediction (MSTP) algorithm, which uses iterative steps to generate core temperature predictions for a range of future time steps using the initial temperature information and the application workload profile obtained offline. MSTP considers the autocorrelation of temperature and addresses the nonlinear heteroscedasticity across observations. We evaluate the proposed MSTP on a real hardware platform and compare it to the model-based approach for a wide range of parallel benchmarks. Experimental results show that the proposed algorithm achieves more than 96% prediction accuracy and minimizes the heteroscedastic residual variance. In case of thermal hot spot prediction, we show that the performance throttling problem is alleviated using a process migration mechanism with a minimal migration overhead. [ABSTRACT FROM AUTHOR]