THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

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Linear And Nonlinear Programming

This book equips the reader to understand every important aspect of the dynamics of rotating machines. Will the vibration be large? What influences machine stability? How can the vibration be reduced? Which sorts of rotor vibration are the worst? The book develops this understanding initially using extremely simple models for each phenomenon, in which (at most) four equations capture the behavior. More detailed models are then developed based on finite element analysis, to enable the accurate simulation of the relevant phenomena for real machines. Analysis software (in MATLAB) is associated with this book, and novices to rotordynamics can expect to make good predictions of critical speeds and rotating mode shapes within days. The book is structured more as a learning guide than as a reference tome and provides readers with more than 100 worked examples and more than 100 problems and solutions.

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Dynamics of rotating machines

Problem Given the number of times in which an unknown event has happened and failed: Required the chance that the probability of its happening in a single trial lies somewhere between any two degrees of probability that can be named. SECTION 1 Definition 1. Several events are inconsistent, when if one of them happens, none of the rest can. 2. Two events are contrary when one, or other of them must; and both together cannot happen. 3. An event is said to fail, when it cannot happen; or, which comes to the same thing, when its contrary has happened. 4. An event is said to be determined when it has either happened or failed. 5. The probability of any event is the ratio between the value at which an expectation depending on the happening of the event ought to be computed, and the value of the thing expected upon it’s 2 happening.

An essay towards solving a problem in the doctrine of chances. [Facsimil]

Linear models and synchronous response are generally adequate to describe and analyze rotors supported by hydrodynamic bearings. Hence, stiffness and damping coefficients can provide a good model for a wide range of situations. However, in some cases, this approach does not suffice to describe the dynamic behavior of the rotor-bearing system. Moreover, unstable motion occurs due to precessional orbits in the rotor-bearing system. This instability is called “oil whirl” or “oil whip”. The oil whirl phenomenon occurs when the journal bearings are lightly loaded and the shaft is whirling at a frequency close to one-half of rotor angular speed. When the angular speed of the rotor reaches approximately twice the natural frequency (first critical speed), the oil whip phenomenon occurs and remains even if the rotor angular speed increases. Its frequency and vibration mode correspond to the first critical speed. The main purpose of this paper is to validate a complete nonlinear solution to simulate the fluid-induced instability during run-up and run-down. A flexible rotor with a central disk under unbalanced excitation is modeled. A nonlinear hydrodynamic model is considered for short bearing and laminar flow. The effects of unbalance, journal-bearing parameters and rotor arrangement (vertical or horizontal) on the instability threshold are verified. The model simulations are compared with measurements at a real vertical power plant and a horizontal test rig.

Whirl and whip instabilities in rotor-bearing system considering a nonlinear force model

This paper presents an availability optimization problem of an engineering system assembled in a series configuration which has the redundancy of units and teams of maintenance as optimization parameters. The objective is to reach the maximum value of availability, considering installation and maintenance costs, weight, volume and available maintenance teams as constraints. The optimization method uses a genetic algorithm (GA), which is based on biological concepts of species evolution. It is a robust method, because it does not converge to a local optimum. It does not need the use of differential calculus, facilitating the computational implementation. The final results are significantly indicative about the fitting of the GA parameters and the application of the methodology to solve engineering design problems involving systems availability.

Availability optimization with genetic algorithm

The conventional slider-connecting rod–crank mechanism is widely applied in mechanical systems. The use of hydrodynamic bearings in the mechanism joints is of particular interest in reducing friction, mainly in special conditions of lubrication such as the connecting rod–slider joint. This bearing belongs to a class of bearings with alternating rotational motion. This paper proposes a mathematical model for this particular problem, considering the dynamics of the slider-connecting rod–crank system interacting with the lubrication phenomenon in bearings with alternating motion. Two models were used to analyze the dynamics of the system. The first model (by Eksergian Equation of Motion) represents the system when the connecting rod end is in contact with the bearing surface, assuming, in this condition, the same behavior as that of rigid bearings (without clearance). The second model (by Lagrange Method) represents the system when the connecting rod end is in the hydrodynamic lubrication mode in the slider bore clearance. In this condition, the slider moves in relation to the connecting rod, presenting a problem of multi-degrees-of-freedom. The mathematic model of hydrodynamic lubrication was introduced to obtain more realistic results of the system's dynamic behavior.

Katia Lucchesi Cavalca

Papers

Whirl and whip instabilities in rotor-bearing system considering a nonlinear force model

Availability optimization with genetic algorithm

Analysis of the dynamics of a slider–crank mechanism with hydrodynamic lubrication in the connecting rod–slider joint clearance

Formulation of five degrees of freedom ball bearing model accounting for the nonlinear stiffness and damping of elastohydrodynamic point contacts

An investigation on the influence of the supporting structure on the dynamics of the rotor system