High Resolution Models using Monte Carlo

Measurement Uncertainty Research Group

Marco Wolf, ETH Zürich

Martin Müller, ETH Zürich

Dr. Matthias Rösslein, Empa St. Gallen

Prof. Walter Gander, ETH Zürich

PTB-BIPM Workshop

Impact of Information Technology in MetrologyJune 4th 2007

Outline

Introduction

Describing models with MUSE

Selected examples

Summary

Outline

Introduction

Describing models with MUSE

Selected examples

Summary

MUSE – Measurement Uncertainty Simulation and Evaluation

Software package for evaluation of measurement uncertainty

Currently developed at ETH Zürich in cooperation with Empa St. Gallen

Based on first supplement of GUM

Available from project page http://www.mu.ethz.ch for Linux/Unix Windows

Uncertainty Measurement Evaluation

Analytical Solution Only applicable in simple cases Even then it gets too complicated

22

21 XXY )1,1(~1 NX )1,0(~2 NX

Uncertainty Measurement Evaluation

Analytical Solution Only applicable in simple cases Even then it gets too complicated

GUM Uncertainty Framework Applicable in many cases Does not use all information Needs linearized model Ambiguous calculation of degrees of

freedom

22

21 XXY )1,1(~1 NX )1,0(~2 NX

Uncertainty Measurement Evaluation

Analytical Solution Only applicable in simple cases Even then it gets too complicated

GUM Uncertainty Framework Applicable in many cases Does not use all information Needs linearized model Ambiguous calculation of degrees of

freedom Monte Carlo Method

Always applicable Arbitrary accuracy Uses all information provided for input

quantities

22

21 XXY )1,1(~1 NX )1,0(~2 NX

Outline

Introduction

Describing models with MUSE

Selected examples

Summary

Modeling Measurement Equipment

Models of measurement equipment

Basic Models can be instantiated abritrary often

Using different sets of parameters

Database of Basic Models

Equivalent models allow global and direct comparison of results

Describing Measurement Procedure using Processes

Using instances of Basic Models together with other processes

Processes encapsulate their own settings for each instance or other processes

Splitting of description of devices and measurement scenario

Dependencies can be modeled by connecting processes

Definition of Calculation Parameters

Random number generator

Options for adaptive Monte Carlo

Settings for self-validation

Settings for analyzing data files

Global variables and variation settings

Equation(s) of the measurand(s)

Adaptive MC

Variation

Variables

Number of simulations

Analyzing

Validation

Random number genenerator

Combination for Measurement Scenario

Adaptive MC

Variation

Variables

Number of simulations

Analysation

Validation

Instances ofBasic Models

Process definition

Calculation Section

Outline

Introduction

Describing models with MUSE

Selected examples

Summary

Example: Gauge Block Calibration

From GUM Supplement 1, section 9.5

Shows difference of results of MC and GUM uncertainty framework

Model equation with following distributions: Normal Arc sine (U-shaped) Curvelinear trapezoidal Rectangular Student-t

Example: Gauge Block CalibrationLength L

Length Ls of the reference

standard

Difference d in lengths of gauge

block and reference standard

Average length

difference D

Random effects d1

Systematic effects d2

Difference δα in expansion coefficient

Deviation θ of

temperature

Average tempera

ture deviatio

n θ0

Effect Δ of cyclic temperat

ure variation

Thermal expansion

coefficient αs

Difference δθ in

temperatures

)(1

)](1[

s

ss dLL

21 ddDd 0

Example: Gauge Block Calibration

Example: Gauge Block Calibration

Example: Gauge Block Calibration

Method Number of simulations Mean* Standard

deviation*

Shortest 95% interval*

Shortest 99% interval*

Shortest 99.9% interval*

GUF 838 32 [746, 930]

MCM (GS1) 1.36*106 838 36 [745, 931]

MCM (MUSE) 104 838 36 [707, 959] [744, 933] [766, 908]

MCM (MUSE) 105 838 36 [718, 958] [743, 931] [768, 909]

MCM (MUSE) 106 838 36 [718, 959] [745, 931] [768, 908]

MCM (MUSE) 107 838 36 [718, 959] [745, 931] [768, 908]

MCM (MUSE) 108 838 36 [718, 958] [745, 931] [768, 908]

* in 1/nm

Example: Chemical experiment

More complex scenariousing processes

Splitting the model equation into three parts: Creating stock solution sols Creating first solution sol1 Creating second solution sol2

2,

2,

1,

1,

, Flask

Pipette

Flask

Pipette

sFlask V

V

V

V

V

puritymc

sols sol1 sol2

2,

2,

1,

1,

, Flask

Pipette

Flask

Pipette

sFlask V

V

V

V

V

puritymc

Example: Chemical experiment

2,1,, Flask

Pipette

Flask

Pipette

sFlask V

V

V

V

V

puritymc

What is the difference if we use the same pipette?

Example: Chemical experiment

Example: Chemical experiment

Example: Chemical experiment

Example: Chemical experiment

Example: Measurement series

More than one formula for measurement uncertainty

More complex evaluation of the overall measurement uncertainty in a measurement series

Simulation of different measurement scenarious and strategies for analysing

Example: Measurement series

Example: Measurement series

Example: Measurement series

Example: Measurement series

Outline

Introduction

Describing models with MUSE

Selected examples

Summary

Summary

The examples show some features of the software and that the software is capable of handling high resoluted models

MUSE is under continuous development. It is thought for advanced users who want to analyze their uncertainty budget in detail

Current work: Calibration Module to analyze results Simplification of definition of measurement series Parallel computing

Thank you!

Contact us directly or write to:

muse@inf.ethz.ch

Homepage:

www.mu.ethz.ch