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Parametric statistics

About: Parametric statistics is a research topic. Over the lifetime, 39200 publications have been published within this topic receiving 765761 citations.


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Journal ArticleDOI
TL;DR: The use of set-membership methods in fault diagnosis (FD) and fault tolerant control (FTC) using a deterministic unknown-but-bounded description of noise and parametric uncertainty (interval models).
Abstract: This paper reviews the use of set-membership methods in fault diagnosis (FD) and fault tolerant control (FTC). Setmembership methods use a deterministic unknown-but-bounded description of noise and parametric uncertainty (interval models). These methods aims at checking the consistency between observed and predicted behaviour by using simple sets to approximate the exact set of possible behaviour (in the parameter or the state space). When an inconsistency is detected between the measured and predicted behaviours obtained using a faultless system model, a fault can be indicated. Otherwise, nothing can be stated. The same principle can be used to identify interval models for fault detection and to develop methods for fault tolerance evaluation. Finally, some real applications will be used to illustrate the usefulness and performance of set-membership methods for FD and FTC.

157 citations

Journal ArticleDOI
TL;DR: In this paper, the adaptive Neyman test is used to check the bias vector of residuals from parametric fits against large nonparametric alternatives, and the power of the proposed tests is comparable to the F-test statistic even in situations where the F test is known to be suitable and can be far more powerful than the F -test statistic in other situations.
Abstract: Several new tests are proposed for examining the adequacy of a family of parametric models against large nonparametric alternatives. These tests formally check if the bias vector of residuals from parametric fits is negligible by using the adaptive Neyman test and other methods. The testing procedures formalize the traditional model diagnostic tools based on residual plots. We examine the rates of contiguous alternatives that can be detected consistently by the adaptive Neyman test. Applications of the procedures to the partially linear models are thoroughly discussed. Our simulation studies show that the new testing procedures are indeed powerful and omnibus. The power of the proposed tests is comparable to the F-test statistic even in the situations where the F test is known to be suitable and can be far more powerful than the F-test statistic in other situations. An application to testing linear models versus additive models is also discussed.

157 citations

Journal ArticleDOI
TL;DR: In this paper, a Lyapunov-based control strategy is proposed for simultaneous multiple-axis tracking control of piezo-flexural stages, and a robust adaptive controller is derived with its stability guaranteed through the LyAPunov criterion, which is shown that a parallelogram type zone of attraction can be explicitly formed for the closed-loop system to which the error phase trajectory converges.
Abstract: Precision control of multiple-axis piezo-flexural stages used in a variety of scanning probe microscopy systems suffers not only from hysteresis nonlinearity, but also from parametric uncertainties and the cross-coupled motions of their axes. Motivated by these shortfalls, a Lyapunov-based control strategy is proposed in this article for simultaneous multiple-axis tracking control of piezo-flexural stages. A double-axis stage is considered for system analysis and controller validation. Hysteresis and coupling nonlinearities are studied through a number of experiments, and it is demonstrated that the widely used proportional-integral (PI) controller lacks accuracy in high-frequency tracking. Adopting the variable structure control method, a robust adaptive controller is then derived with its stability guaranteed through the Lyapunov criterion. It is shown that a parallelogram-type zone of attraction can be explicitly formed for the closed-loop system to which the error phase trajectory converges. Practical implementation of the controller demonstrates effective double-axis tracking control of the stage in the presence of hysteresis and coupling nonlinearities and despite parametric uncertainties for low-and high-frequency trajectories. Moreover, good agreements are achieved between the experiments and theoretical developments.

157 citations

Proceedings ArticleDOI
13 May 1990
TL;DR: A kinematic modeling convention for robot manipulators is proposed which has complete and parametrically continuous (CPC) properties and makes the CPC model particularly useful for robot calibration.
Abstract: A kinematic modeling convention for robot manipulators is proposed. The kinematic model is named for its completeness and parametric continuity (CPC) properties. Parametric continuity of the CPC model is achieved by adopting a singularity-free line representation consisting of four line parameters. Completeness is achieved through adding two link parameters to allow arbitrary placement of link coordinate frames. The transformations from the world frame to the base frame and from the last link frame to the tool frame can be modeled with the same modeling convention used for internal link transformations. Since all the redundant parameters in the CPC model can be systematically eliminated, a linearized robot error model can be constructed in which all error parameters are independent and span the entire geometric error space. The focus is on model construction, mappings between the CPC model and the Denavit-Hartenberg model, the study of the model properties, and its application to robot kinematic calibration. >

157 citations

Journal ArticleDOI
TL;DR: This paper investigates a Gaussian process-based Bayesian MRAC architecture (GP-MRAC), which leverages the power and flexibility of GP Bayesian nonparametric models of uncertainty and enables MRAC to handle a broader set of uncertainties, including those that are defined as distributions over functions.
Abstract: Most current model reference adaptive control (MRAC) methods rely on parametric adaptive elements, in which the number of parameters of the adaptive element are fixed a priori, often through expert judgment. An example of such an adaptive element is radial basis function networks (RBFNs), with RBF centers preallocated based on the expected operating domain. If the system operates outside of the expected operating domain, this adaptive element can become noneffective in capturing and canceling the uncertainty, thus rendering the adaptive controller only semiglobal in nature. This paper investigates a Gaussian process-based Bayesian MRAC architecture (GP-MRAC), which leverages the power and flexibility of GP Bayesian nonparametric models of uncertainty. The GP-MRAC does not require the centers to be preallocated, can inherently handle measurement noise, and enables MRAC to handle a broader set of uncertainties, including those that are defined as distributions over functions. We use stochastic stability arguments to show that GP-MRAC guarantees good closed-loop performance with no prior domain knowledge of the uncertainty. Online implementable GP inference methods are compared in numerical simulations against RBFN-MRAC with preallocated centers and are shown to provide better tracking and improved long-term learning.

156 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20252
20242
20233,966
20227,822
20211,968
20202,033