# Presentation: 336176

- Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company,for the United States Department of Energy under contract DE-AC04-94AL85000.

***Validation Challenge Problem:***
***Structural Dynamics***

**John Red-Horse**
**Thomas L. Paez**
**Uncertainty Quantification and Validation Department**
**Sandia National Laboratories**

## Our Take on Workshop Motivation and Goal

- Validation may be thought of as a process for assessing confidence in a computational prediction
- Association with physical scenarios too early in the learning process inhibits deep understanding of what is driving discrepancy
- Goal: Validation remains poorly understood; we seek to begin the process of discovery using analytical virtual experiments as validation objects

## Workshop Objectives

- Assessment of state-of-the-art in validation science from a variety of technical fields and contributors
- Synergize various communities involved in validation-related endeavors

## Structural Dynamics-Driver Application

- Provide a structural dynamics workshop problem with many problem elements common to real applications
- Driver Application: Shock response of substructural element to transient random pressure load
- Our “truth model”:
- Regulatory requirement:

## Problem Elements

- Decision Context
- Requirements
- Type:
- Qualify System
- Resource Allocation
- Available Data
- Ensemble of Data
- Subsystem/Component level
- Not fully relevant to application
- Accreditation Test-Representative of application

## Additional Elements To Consider

- Criteria selection (Quantities of Interest)
- Metric(s)
- Presence of uncertainty: Characterize, Model, Analyze
- Variability (irreducible, inherent)
- Some parameters as random variables (RVs)
- Ignorance (reducible)
- Virtual systems: Nonlinear mechanics; Known probability distributions
- Models for the virtual systems: Linear-only mechanics; Information on RVs only gained via samples

## Part 1 – Subsystem Calibration

- System to be calibrated: Subcomponent of a larger system

- 20 realizations of the stochastic structure
- Each structure is tested with stationary, band-limited random vibration – base is fixed
- Each structure realization is tested at three excitation levels
- Excitation is applied to
- All measurements, for both the inputs and outputs, are assumed to be perfect

## Part 1 – Subsystem Calibration

- Experimental modal analysis performed on each structure – Mode frequencies, dampings, and shapes estimates provided to analysts
- Notes:
- This information can be used to make prediction of linear response. Analysts can use this information or perform own modal analysis.
- Code to estimate frequency response function will be provided on request.
- Recall: Virtual (tested) system is nonlinear; the modal model is linear, entirely described with the modal parameters

## Part 1 – Subsystem Calibration

- Deterministic or stochastic modal model to be developed. Model parameters must be “traditional,” i.e., not level or frequency dependent.
- Response accelerations measured (computed) and provided to analysts
- Excitation forces measured and provided to analysts

## Example - One structure, Force Loc x2,Resp Loc x1, Medium Level Input 

## Example - 3 Nominally Identical Structures,Force Loc x2, Resp Loc x2, Medium Level Input

## Typical Acceleration FRF from Calibration Tests

## Example - Force Between Fixed Base andMeasurement at, Resp Loc x1, Medium Level Input

## Part 1 – Subsystem Calibration

- Force between fixed base and external mass measured and provided to analysts

## Part 1 – Subsystem Validation

- System to be Validated: Subcomponent of the larger system

- 20 realizations of the stochastic structure
- Each structure is tested with classical shock excitation – base is fixed
- Each input signal contains three shock pulses
- Each structure realization is tested at three “levels”
- Each input at each level is a haversine with random amplitude and duration
- Source probability distributions of amplitude and duration are preestablished

## Part 1 – Subsystem Validation

- Each structure realization is tested three times at each level
- Three response accelerations measured (computed) and provided to analysts
- Excitation forces measured and provided to analysts

## Example – One structure, Force Loc x3,Resp Loc x1, 3 Medium Level Inputs 

## Example – 3 Nominally Identical Structures,Force Loc x3, Resp Loc x2, Medium Level Inputs

## Example – 10 Nominally Identical Structures,FRFs, Force Loc x3, Resp Loc x1, Medium Level Inputs

## Example – One Structure, Force Loc x3,Resp Loc x3, Three Levels of Input

## Part 1 – Subsystem validation

- Accuracy assessment/calibration – Judge the accuracy of the calibrated modal model for prediction of response of the system subjected to shock input.
- Criteria (quantity of interest)
- Metrics
- Effects of uncertainty
- Other...

## Part 1 – Subsystem Validation

- Force between fixed base and external mass measured and provided to analysts

## Example – Force Between Fixed Base andMeasurement at, Resp Loc x1, Medium Level Input

## Part 2 - Fully Relevant System

- Local shock load applied to system relevant to qualification system

## Part 2 - Fully Relevant System

- Shock excitation similar to that in validation shock tests
- Measure (compute) responses at many DOF
- Provide to analysts
- Given system motion at x12 compute response using modal model
- Assess accuracy/validate modal model
- Criteria ....

## Example – Excitation and responseat several points on structure plus x1 on subsystem 

## Additional thoughts:

- There is no correct or incorrect answer; objective is to examine validation approaches given simplified, although realistic constraints
- Variability
- Ignorance
- Effects of available test data can be examined
- Effects of number of function evaluations in analysis method/approach also of interest