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Spline Models for Observational Data


Spline Models for Observational Data

Author: Grace Wahba

language: en

Publisher: SIAM

Release Date: 1990-01-01


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This book serves well as an introduction into the more theoretical aspects of the use of spline models. It develops a theory and practice for the estimation of functions from noisy data on functionals. The simplest example is the estimation of a smooth curve, given noisy observations on a finite number of its values. The estimate is a polynomial smoothing spline. By placing this smoothing problem in the setting of reproducing kernel Hilbert spaces, a theory is developed which includes univariate smoothing splines, thin plate splines in d dimensions, splines on the sphere, additive splines, and interaction splines in a single framework. A straightforward generalization allows the theory to encompass the very important area of (Tikhonov) regularization methods for ill-posed inverse problems. Convergence properties, data based smoothing parameter selection, confidence intervals, and numerical methods are established which are appropriate to a wide variety of problems which fall within this framework. Methods for including side conditions and other prior information in solving ill-posed inverse problems are included. Data which involves samples of random variables with Gaussian, Poisson, binomial, and other distributions are treated in a unified optimization context. Experimental design questions, i.e., which functionals should be observed, are studied in a general context. Extensions to distributed parameter system identification problems are made by considering implicitly defined functionals.

Data-Driven Remaining Useful Life Prognosis Techniques


Data-Driven Remaining Useful Life Prognosis Techniques

Author: Xiao-Sheng Si

language: en

Publisher: Springer

Release Date: 2017-01-20


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This book introduces data-driven remaining useful life prognosis techniques, and shows how to utilize the condition monitoring data to predict the remaining useful life of stochastic degrading systems and to schedule maintenance and logistics plans. It is also the first book that describes the basic data-driven remaining useful life prognosis theory systematically and in detail. The emphasis of the book is on the stochastic models, methods and applications employed in remaining useful life prognosis. It includes a wealth of degradation monitoring experiment data, practical prognosis methods for remaining useful life in various cases, and a series of applications incorporated into prognostic information in decision-making, such as maintenance-related decisions and ordering spare parts. It also highlights the latest advances in data-driven remaining useful life prognosis techniques, especially in the contexts of adaptive prognosis for linear stochastic degrading systems, nonlinear degradation modeling based prognosis, residual storage life prognosis, and prognostic information-based decision-making.

Fundamentals of Manipulator Calibration


Fundamentals of Manipulator Calibration

Author: Benjamin W. Mooring

language: en

Publisher: Wiley-Interscience

Release Date: 1991-03-19


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Describes the details of the calibration process step-by-step, covering systems modeling, measurement, identification, correction and performance evaluation. Calibration techniques are presented with an explanation of how they interact with each other as they are modified. Shows the reader how to determine if, in fact, a robot problem is a calibration problem and then how to analyze it.