Lecture 1 Introduction. Essentially all models are wrong, but some are useful, George E.P. Box, Industrial Statistician

Size: px

Start display at page:

Download "Lecture 1 Introduction. Essentially all models are wrong, but some are useful, George E.P. Box, Industrial Statistician"

Conrad Hunt
5 years ago
Views:

1 Lecture 1 Introduction Essentially all models are wrong, but some are useful, George E.P. Box, Industrial Statistician

2 Lecture 1 Introduction What is validation, verification and uncertainty quantification? Why do we care? Motivation: Etrema Products, Inc., SolidDrive

Terfenol-D Transducer Schematic of Terfenol-D transducer in the SolidDrive Terfenol-D rod can be modeled as a rod with elastic and damped boundary conditions.

3 Terfenol-D Transducer Schematic of Terfenol-D transducer in the SolidDrive Terfenol-D rod can be modeled as a rod with elastic and damped boundary conditions. For uniform input fields, spring equation with nonlinear inputs provides good approximation of rod dynamics. What is nonlinear and hysteretic behavior of f(h,u)?

4 Magnetomechanical Material Behavior Material depends on both magnetic fields and stresses Consider application of periodic field followed by application of positive and negative stresses. Data from Pitman, Note: the source and conditions under which data was collected are crucial in the context of validation, verification and uncertainty quantification!!!

5 Development 1 Experimental Data 2 Question: Which model is better??

6 Original data: (Craik and Wood 1970) Development Representation of data used for 1: Jiles 1995 Representation of data used for 2: (Smith and Dapino 2006) Questions: 1. Are scales accurate? 2. Is data accurate? 3. What is source of loss in upper loop?

7 Development 1 Experimental Data Notes: 2 1. Numerical implementation of 1 is inaccurate (verification) 2. Neither model is true representation of physical device (validation)

8 ing Issues Validation Reality Computer Simulation Analysis Qualification Conceptual Programming Computer Verification

9 Verification Process Conceptual Computational Computational Solution Verification Test `Correct Answer Analytic solutions Highly resolved numerical solutions Benchmark solutions Verification: The process of determining that a model implementation accurately represents the developer s conceptual description of the model and the solution to the model. Note: Verification deals with mathematics

10 Validation Process Real World Conceptual Computational Computational Solution Validation Process `Correct Answer Provided by Experimental Data Benchmark cases System analysis Statistical analysis Validation: The process of determining the degree to which a model is an accurate representation of the real world from the perspective of the intended model users. Note: Validation deals with physics and statistics Reference: Oberkampf, Trucano and Hirsch 2004

11 Validation Metrics Experiment Response Experiment Response Experiment `Viewgraph Norm Input Deterministic Input Experimental Uncertainty Response Experiment Response Experiment Input Input Numerical Error Nondeterministic Computation

12 Validation Metrics: Example Metric 1: Data

13 Metric 2: Validation Metrics: Example

14 Difficulties with Using Existing Experimental Data for Validation 1. Incomplete documentation of experimental conditions Boundary and initial conditions Material properties Geometry of the system 2. Limited documentation of measurement errors Lack of experimental uncertainty estimates Note: It is critical that modelers, numerical analysts, and experimentalists work together Reference: Oberkampf, Trucano and Hirsch 2004

15 Background of Validation and Verification Validation and verification began to be formalized during the ASCI (Accelerated Strategic Computing Initiative) Program to replace physical nuclear testing by computer experiments. A large body of validation and verification research has been performed at Sandia National Lab.

Statistical Validation of Scientific Models

Statistical Validation of Scientific Models "When I use a word," Humpty Dumpty said, in a rather scornful tone, "it means just what I choose it to mean - neither more nor less, Through the Looking Glass,