Stepwise regression | EPFL Graph Search

In statistics, stepwise regression is a method of fitting regression models in which the choice of predictive variables is carried out by an automatic procedure. In each step, a variable is considered for addition to or subtraction from the set of explanatory variables based on some prespecified criterion. Usually, this takes the form of a forward, backward, or combined sequence of F-tests or t-tests. The frequent practice of fitting the final selected model followed by reporting estimates and confidence intervals without adjusting them to take the model building process into account has led to calls to stop using stepwise model building altogether or to at least make sure model uncertainty is correctly reflected. Alternatives include other model selection techniques, such as adjusted R2, Akaike information criterion, Bayesian information criterion, Mallows's Cp, PRESS, or false discovery rate. Main approaches The main approaches for stepwise regression are:

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Calibration of Ultra-high-precision Robots Operating in an Unsteady Environment

Emanuele Lubrano

In recent years nanotechnology has become an enabling technology for the development and fabrication of new innovative products. The growth of micro- and nano-manufacturing lies in the ability of converting micro- and nano-fabrication techniques into mass-production industrial processes, where small-scale products can be economically manufactured in a short period of time. When dealing with nano-scale objects and industrial processes it is necessary to take into account the physics acting at this level of precision. Phenomena such as friction, heat transfer, and adhesion forces have far more dramatic effects on the deformation of the robot geometry at the nano-scale than at macro- and micro-scales, thus affecting the industrial process that the robot will perform. The development of micro- and nano-fabrication techniques thus requires a thorough understanding of the physics behind nanorobotics. Specifically, to enable sub-micrometer accuracy for ultra-high-precision robots it is necessary to acquire a complete knowledge of how all sources of inaccuracy deform the robots at nano-scale. Furthermore, a way to compensate for such effects to maintain an acceptable level of accuracy has to be found. In this thesis we fulfill these needs by proposing a new calibration procedure specifically designed for industrial nano-systems working in a thermally unstable environment, a method to evaluate and compensate for external forces acting on ultra-high-precision robots and a method to relate the calibration of several robots working together. This is done by measuring how each source of inaccuracy deforms the robot, modeling this effect and compensating it in real-time. To allow this modus operandi, we propose a new calibration procedure summarized in the following six steps: Step 0 A judicious design of the robot that takes into account the calibration problem and the pose measurement, Step 1 Study of the sources of inaccuracy linked to the robot and the industrial process that it will perform, Step 2 Measurement of several end-effector poses, Step 3 Identification of a function that describes the robot geometry and its behavior when subjected to the sources of inaccuracy identified in Step 1, Step 4 Implementation of the model found in Step 3 into the robot controller, Step 5 Validation and potential return to Step 1 or Step 0. The effectiveness of this calibration procedure is proven by testing it on three case studies, examined in order of complexity: A 1 DOF (degree(s)-of-freedom) ultra-high-precision linear axis was calibrated while thermal effects were deforming it. The 3 DOF ultra-high-precision parallel robot Agietron Micro-Nano was calibrated while thermal effects and an external force were acting on it. An ultra-high-precision 2-robot system was calibrated while thermal effects were acting on it. Thus, an exhaustive study on relating the references of the two robots was carried out. For each case we developed an appropriate ultra-high-precision measuring system used to acquire the pose of the robot end-effector. We measured the end-effector position throughout the workspace while the sources of inaccuracy were acting on the robot to map how they affect the robot geometry. We used the Stepwise Regression algorithm to identify a mathematical model able to describe the geometric features of the robot while all the sources of inaccuracy are acting on it. The model is then implemented in the robot controller and a validation of the calibration accuracy is performed. For every ultra-high-precision robot considered in this work we reached an absolute accuracy of ±100 nm. We finished the coverage of this thesis by analyzing the nano-indentation process as a calibration confirmation tool and as an industrial process. Furthermore, we describe how to use a multiple ultra-high-precision concurrent system of robots. This work was financed by the FNS (Swiss National Foundation for research).

EPFL2011

Formal Homo-Nazarov and Other Cyclization Reactions of Activated Cyclopropanes

Fides Benfatti, Filippo De Simone, Tanguy Jean Daniel Saget, Jérôme Waser

The Nazarov cyclization of divinyl ketones gives access to cyclopentenones. Replacing one of the vinyl groups by a cyclopropane leads to a formal homo-Nazarov process for the synthesis of cyclohexenones. In contrast to the Nazarov reaction, the cyclization of vinyl-cyclopropyl ketones is a stepwise process, often requiring harsh conditions. Herein, we describe two different approaches for further polarization of the three-membered ring of vinyl-cyclopropyl ketones to allow the formal homo-Nazarov reaction under mild catalytic conditions. In the first approach, the introduction of an ester group α to the carbonyl on the cyclopropane gave a more than tenfold increase in reaction rate, allowing us to extend the scope of the reaction to non-electron-rich aryl donor substituents in the β position to the carbonyl on the cyclopropane. In this case, a proof of principle for asymmetric induction could be achieved using chiral Lewis acid catalysts. In the second approach, heteroatoms, especially nitrogen, were introduced β to the carbonyl on the cyclopropane. In this case, the reaction was especially successful when the vinyl group was replaced by an indole heterocycle. With a free indole, the formal homo-Nazarov cyclization on the C3 position of indole was observed using a copper catalyst. In contrast, a new cyclization reaction on the N1 position was observed with Brønsted acid catalysts. Both reactions were applied to the synthesis of natural alkaloids. Preliminary investigations on the rationalization of the observed regioselectivity are also reported.

2011

Thermal Behavior of an Ultra High-Precision Linear Axis Operating in Industrial Environment

Reymond Clavel, Emanuele Lubrano

Thermal expansion is the major source of inaccuracy for ultra high-precision robots. In this paper we propose a strategy to model and compensate this effect. The experiment is run using a 1 DOF (degree-of-freedom) parallel robot equipped with ten temperature sensors; the displacements of the end-effector are measured using an interferometer. After a session of measurements the data collected has been processed using the stepwise regression algorithm. A model of the thermal robot behavior has been found and implemented in the robot controller. In this way it has been possible to compensate all the thermal effects, reaching an absolute accuracy of 10 nanometers.

Schönenfeld & Ziegler2008

Calibration of Ultra-high-precision Robots Operating in an Unsteady Environment

Emanuele Lubrano

EPFL2011