Vibration in turbine blades must be prevented

Slides:

Advertisements

Similar presentations

Ordinary Least-Squares

Advertisements

1 Non-Linear and Smooth Regression Non-linear parametric models: There is a known functional form y=  x,  derived from known theory or from previous.

General Linear Model Introduction to ANOVA.

CmpE 104 SOFTWARE STATISTICAL TOOLS & METHODS MEASURING & ESTIMATING SOFTWARE SIZE AND RESOURCE & SCHEDULE ESTIMATING.

Probabilistic Analysis using FEA A. Petrella. What is Probabilistic Analysis ‣ All input parameters have some uncertainty ‣ What is the uncertainty in.

Simple Regression. Major Questions Given an economic model involving a relationship between two economic variables, how do we go about specifying the.

Training Manual Aug Probabilistic Design: Bringing FEA closer to REALITY! 2.5 Probabilistic Design Exploring randomness and scatter.

Simple Linear Regression

LECTURE 3 Introduction to Linear Regression and Correlation Analysis

Presenter: Dan SnyderDate: 10/5/2010Overhead sheet 1 File: /home/u9/engr/snyded/pub_html/EP/alternative_project.odp Assessing Sensitivity of Vibratory.

Curve-Fitting Regression

Surface Variation and Mating Surface Rotational Error in Assemblies Taylor Anderson UGS June 15, 2001.

L Berkley Davis Copyright 2009 MER301: Engineering Reliability Lecture 14 1 MER301: Engineering Reliability LECTURE 14: Chapter 7: Design of Engineering.

Tolerance Analysis of Flexible Assemblies Michael Tonks.

Finite Element Modeling with COMSOL Ernesto Gutierrez-Miravete Rensselaer at Hartford Presented at CINVESTAV-Queretaro December 2010.

Simple Linear Regression Analysis

1 1 Slide Simple Linear Regression Chapter 14 BA 303 – Spring 2011.

1 Efficient Re-Analysis Methodology for Probabilistic Vibration of Large-Scale Structures Efstratios Nikolaidis, Zissimos Mourelatos April 14, 2008.

Review for Exam 2 (Ch.6,7,8,12) Ch. 6 Sampling Distribution

(a.k.a: The statistical bare minimum I should take along from STAT 101)

Knowledge Extraction from Aerodynamic Design Data and its Application to 3D Turbine Blade Geometries Lars Graening

Stats for Engineers Lecture 9. Summary From Last Time Confidence Intervals for the mean t-tables Q Student t-distribution.

1 1 Slide © 2008 Thomson South-Western. All Rights Reserved Chapter 15 Multiple Regression n Multiple Regression Model n Least Squares Method n Multiple.

Statistics 11 Correlations Definitions: A correlation is measure of association between two quantitative variables with respect to a single individual.

Basic Probability (Chapter 2, W.J.Decoursey, 2003) Objectives: -Define probability and its relationship to relative frequency of an event. -Learn the basic.

Gu Yuxian Wang Weinan Beijing National Day School.

Curve-Fitting Regression

Regression. Population Covariance and Correlation.

1 Chapter 12 Simple Linear Regression. 2 Chapter Outline  Simple Linear Regression Model  Least Squares Method  Coefficient of Determination  Model.

1 Multiple Regression A single numerical response variable, Y. Multiple numerical explanatory variables, X 1, X 2,…, X k.

Regression. Types of Linear Regression Model Ordinary Least Square Model (OLS) –Minimize the residuals about the regression linear –Most commonly used.

Statistical test for Non continuous variables. Dr L.M.M. Nunn.

Chapter 23 Process Capability. Objectives Define, select, and calculate process capability. Define, select, and calculate process performance.

Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 13-1 Introduction to Regression Analysis Regression analysis is used.

5-1 ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved. May 28, 2009 Inventory # Chapter 5 Six Sigma.

Exam Review Day 6 Chapters 2 and 3 Statistics of One Variable and Statistics of Two Variable.

Random Variables (1) A random variable (also known as a stochastic variable), x, is a quantity such as strength, size, or weight, that depends upon a.

Introduction to Biostatistics and Bioinformatics Regression and Correlation.

Chapter 4 Summary Scatter diagrams of data pairs (x, y) are useful in helping us determine visually if there is any relation between x and y values and,

CARE / ELAN / EUROTeV Feedback Loop on a large scale quadrupole prototype Laurent Brunetti* Jacques Lottin**

Chapter 8: Simple Linear Regression Yang Zhenlin.

Probabilistic Design Systems (PDS) Chapter Seven.

Advanced Statistical Methods: Continuous Variables REVIEW Dr. Irina Tomescu-Dubrow.

Statistical methods for real estate data prof. RNDr. Beáta Stehlíková, CSc

The general linear model and Statistical Parametric Mapping I: Introduction to the GLM Alexa Morcom and Stefan Kiebel, Rik Henson, Andrew Holmes & J-B.

Statistics 350 Lecture 2. Today Last Day: Section Today: Section 1.6 Homework #1: Chapter 1 Problems (page 33-38): 2, 5, 6, 7, 22, 26, 33, 34,

Multiple Regression Reference: Chapter 18 of Statistics for Management and Economics, 7 th Edition, Gerald Keller. 1.

Data Analysis Student Text :Chapter 7. Data Analysis MM2D1. Using sample data, students will make informal inferences about population means and standard.

Statistics and probability Dr. Khaled Ismael Almghari Phone No:

A Primer on Running Deterministic Experiments

The simple linear regression model and parameter estimation

Chapter 14 Introduction to Multiple Regression

Chapter 4 Basic Estimation Techniques

Statistical Process Control

Project COMP10: Designing for Blade Aeromechanical Integrity

Linear Inequalities in Two Variables

CH 5: Multivariate Methods

FEA Introduction.

Chapter 3: TWO-VARIABLE REGRESSION MODEL: The problem of Estimation

Probability and Statistics for Computer Scientists Second Edition, By: Michael Baron Section 11.1: Least squares estimation CIS Computational.

1) A residual: a) is the amount of variation explained by the LSRL of y on x b) is how much an observed y-value differs from a predicted y-value c) predicts.

Regression Analysis PhD Course.

Statistical Methods For Engineers

Linear Regression.

Chapter 14 Inference for Regression

Optimized Vibration Mitigation in Design of Satellite Payload Support

When You See (This), You Think (That)

Realistic multiphysics analysis

Verification of probabilistic forecasts: comparing proper scoring rules Thordis L. Thorarinsdottir and Nina Schuhen

Presentation transcript:

Assessing Sensitivity of Vibratory Mode Frequencies to Variation in Geometric Parameters Vibration in turbine blades must be prevented Modal analysis can with FEA can determine frequencies Variation in geometric parameters affects frequency

Develop Parametric Blade Model Create “flexible” turbine blade defined by numerical parameters. Using Unigraphics (CAD software) Blade can be altered from normal conditions by changing geometric parameters

Sample Design Space Whole set of parameters forms a “design space” Define normalized parameters with specified Upper limit Lower limit Zero mean Sample design space using Latin Hypercube Sampling For N variables, create N combinations of variables Orthogonal Sample Space Each set of parameters represents a potential configuration of a real blade

Analyze Potential Blade Configurations Analyze all configurations of real blades using ANSYS Modal Analysis Boundary conditions similar to engine operation Find first 5 mode frequencies Automate using iSight Develop Predictive Regression Function Linear / Non-linear Least Squares Minimization

Summary This project will simulate random variation in turbine blades The effect of geometry variation on frequency will be quantified A predictive model will be created to predict frequency based on geometric parameters.

Discussion How many parameters will be required to create a realistic and flexible model? How many configurations should be analyzed to create dense enough variable space? What type of regression function should be used? Linear / non-linear?