Car Crash: Are There Physical Limits To Improvement?

Transcription

1 Car Crash: Are There Physical Limits To Improvement? J. Marczyk Ph.D. CTO, Ontonix

2 CONTENTS Models are only models! Outliers, risk, optimality Does optimal mean best? Crash and chaos Complexity: the source of fragility Examples of complexity-based CAD Robustness and complexity Conclusions

3 Models Are Only Models! Assumptions: Beam is slender Costraints are perfect Material is elastic Material is homogeneous Displacements are small Loads applied far from constraints Sections remain plane Rotational inertia neglected Properties are deterministic (!) Questions: Who checks if the assumptions are respected? How much physics is lost? 10%? The E-B equation is discterized via the FEM: how much more physics is lost? Copyright 2007, Ontonix srl. All rights reserved. No part of this document may be reproduced in any form without the written consent of Ontonix srl.

4 Quantifying Model Credibility Objectives: to investigate how solver parameters settings influence the results in a CFD problem toevaluate the impact of solver-specific FLUENT numerical modeling in the presence of scatter in physical parameters adiabatic wall heated wall Copyright 2007, Ontonix srl. All rights reserved. No part of this document may be reproduced in any form without the written consent of Ontonix srl.

5 Quantifying Model Credibility Turbulence models 1 Laminar model 2 Spalart Allmaras model: Vorticity-Based Production 3 Spalart Allmaras model: Strain/Vorticity-Based Production 4 k-epsilon model: Standard 5 k-epsilon model: RNG 6 k-epsilon model: Realizable 7 k-omega model: Standard 8 k-omega model: SST 9 Reynolds stress model different solver parameters combinations! Parameter Pressure Density Momentum Turbulence Kinetic Energy Turbulence Dissipation Rate Energy Discretisation scheme 1. STANDARD 2. PRESTO! 3. Linear 4. Second order 5. Body force weighted 1. First order upwind 2. Second order upwind 3. QUICK 1. First order upwind 2. Second order upwind 3. Power law 4. QUICK 1. First order upwind 2. Second order upwind 3. Power law 4. QUICK 1. First order upwind 2. Second order upwind 3. Power law 4. QUICK 1. First order upwind 2. Second order upwind 3. Power law 4. QUICK Copyright 2007, Ontonix srl. All rights reserved. No part of this document may be reproduced in any form without the written consent of Ontonix srl.

6 Quantifying Model Credibility Results : The scatter in results due to physical parameters scatter is around 22%-25% in mean heat flux value. The scatter in results due to the various (solver-specific) modeling parameters amounts to 25%-27% in mean heat flux value! Heat Heat flux flux Copyright 2007, Ontonix srl. All rights reserved. No part of this document may be reproduced in any form without the written consent of Ontonix srl.

7 Models Are Only Models! A FEM model (fruit of numerous assumptions and discretization) is further used in: Parametric Studies Building a Response Surface (often based on DOE) here another 5-10% is lost. Optimization (!) A numerical artifact, which is fruit of a series of assumptions, and which is therefore an approximation of reality, is used to produce optimal designs. Moreover, different optimization strategies yield different results. Copyright 2007, Ontonix srl. All rights reserved. No part of this document may be reproduced in any form without the written consent of Ontonix srl.

8 The Philosophy of Optimality Does Optimal Mean Best?

9 Does Optimal Mean Best?

10 Outliers and pathological behaviour Outlier Most likely response. The best way to understand Nature is to understand her anomalies. F. Bacon

11 Launcher Failure Rate Source:

12 Outliers = Risk

13 Capturing physics, not pursuing perfection: An example (1997) Stochastic approach Deterministic approach

14 A Typical Car Crash Test Scenario (test lab) Courtesy of BMW AG.. in reality.

15 Copyright 2007, Ontonix srl. All rights reserved. No part of this document may be reproduced in any form without the written consent of Ontonix srl.

16 Bifurcations in Car Crash: HPC Discovers New Knowledge Initial design Is this really the optimum? Courtesy, BMW AG Example of bifurcation (clustering) in automotive crash (PAM-Crash, 128 samples 512 CPU Cray T3E, 1997). It has been found that the dominating variable in this case was the angle of impact, neither the properties of the structure, nor that of the materials. A tiny change in the angle of impact will change dramatically the response. Sounds like chaos Copyright 2007, Ontonix srl. All rights reserved. No part of this document may be reproduced in any form without the written consent of Ontonix srl.

17 The Physics of Crash: Some Questions Is crash deterministic or stochastic? Is crash predictable? Is crash optimizable? Does it make sense to speak of precision in crash simulations? Do we need to increase the number of elements in our crash models? What is the reasonable limit? What is the future of computer-based crash analysis? Is crash a chaotic phenomenon?... Copyright 2007, Ontonix srl. All rights reserved. No part of this document may be reproduced in any form without the written consent of Ontonix srl.

18 Example of Measured Acceleration Signal QUESTION: Is there chaos in this signal?

19 Log-linear Power Law Systems that exhibit a log-linear Power Spectrum are, potentially, chaotic.

20 Typical Tests for Chaos Hausdorff (Capacity dimension). Fractal dimension (1.8) Log-linear Power Spectrum (yes) Correlation dimension (5) Lyapunov Characteristic Exponents (+0.4) Poincare sections or Return Maps (yes, do exhibit structure) According to these tests, the measured crash signal does contain a chaotic component. The source of chaos in crash is a bifurcation-driven response (a cascade or crushings) which is very sensitive to boundary conditions. Copyright 2007, Ontonix srl. All rights reserved. No part of this document may be reproduced in any form without the written consent of Ontonix srl.

21 Chaos and Predictability Phenomena that are chaotic, are unpredictable (non-repeatable). The main reason is extreme sensitivity to initial conditions. Phenomena that are unpredictable, cannot be optimized. They must be treated from a stochastic perspective. Patterns, not details! All that can be done with chaotic phenomena is to increase our understanding of their nature, properties, patterns, structure, main features, quantify the associated risks. Models for Risk Analysis must be realistic to be of any use. They must be stochastic. Copyright 2007, Ontonix srl. All rights reserved. No part of this document may be reproduced in any form without the written consent of Ontonix srl.

22 Why are the limits to improving crashworthiness? Due to physics: the physics of crash includes chaotic and random behaviour crash is essentially a non-repeatable phenomenon. Each crash is unique. Boundary conditions are never known a-priori. Due to limitations of models, which capture only part of the physics (80%?, 90?). Models are deterministic they ignore uncertainties, tolerances, scatter, etc. Copyright 2007, Ontonix srl. All rights reserved. No part of this document may be reproduced in any form without the written consent of Ontonix srl.

23 Self-randomization in MD Nastran In case the user wishes to apply defaul uncertainties to all the P, M, C and Loads, it is sufficient to specify STOCHASTICS = ALL in the CCD as illustrated below. In this case, it is no longer necessary to specify any BDD entries.

24 Application Example 5% CoV for all M-entries The model contains 244 weld points. 5% corresponds to approximately 12. Remove randomly 5% of welds

25 Complex or Complicated? A system may be complicated, but still have low complexity. A large number of parts doesn t generally imply high complexity. It does, in general, imply a complicated system. In order to measure the amount of complexity it is necessary to take uncertainty into account. Complexity implies capacity to surprise, to deliver unexpected behaviour. Copyright 2007, Ontonix srl. All rights reserved. No part of this document may be reproduced in any form without the written consent of Ontonix srl.

26 Complexity Principles Principle of Complexity: When the complexity and uncertainty of an engineering system increase, our ability to predict its behavior diminishes until a threshold is reached beyond which accuracy and significance become almost mutually exclusive. Principle of Incompatibility: High precision is incompatible with high complexity. L. Zadeh, UCLA Copyright 2007, Ontonix srl. All rights reserved. No part of this document may be reproduced in any form without the written consent of Ontonix srl.

27 Complexity x Uncertainty = Fragility When uncertainty meets high complexity, the result is fragility. Simple systems can cope better with uncertainty than highly complex systems. Highly complex systems are more exposed to the effects of uncertainty because of the countless ways in which they process information. They can fail in many ways, often due to apparently innocent causes. Uncertainty in the environment, cannot be avoided. We must learn to live with it. Hence the need to manage complexity. Since fragility is the prelude to risk, holistic risk management can be accomplished via complexity management. Copyright 2007, Ontonix srl. All rights reserved. No part of this document may be reproduced in any form without the written consent of Ontonix srl.

28 Why Complex Products Often Fail? Product Complexity x Manufacturing Uncertainty = Fragility of the Product

29 Complexity-Based CAD: Pedestrian Bridge Geometric parameters Quarter model view: Rib Spacing is the amount of holes between ribs The dimension fraction is D/T T D x The spacing factor is S/T S Height t is the flange distance t Thickness factor = x/height If the thickness factor is increased Cut depth, width and radius determine the shape of the ribs Copyright 2007, Ontonix srl. All rights reserved. No part of this document may be reproduced in any form without the written consent of Ontonix srl.

30 Complexity-Based CAD The Concept Which one is best? What is best?

31 y* Complexity-Based Design The Concept Five solutions which deliver identical performance are found. They all possess a characteristic value of complexity. The simplest is chosen. f(x) Desired performance C1 C2 C3 C4 C5 x1 x2 x3 x4 x5 x Allowable design range

32 Complexity-Based CAD Option 1 Option 2

33 Complexity-Based Design: The James Webb Space Telescope Option 1 Option 2 Option 3 Option 4 James Webb Space Telescope payload adapter. Courtesy EADS CASA Espacio.

34 Geopolitics, Failing States and Conflict Anticipation Convergence of failed states, WMD proliferation, and global terrorism destabilizes the region and the world

35 Computational Geopolitics and Conflict Anticipation: How Complex is The World Getting? Input data

36 Copyright 2007, Ontonix srl. All rights reserved. No part of this document may be reproduced in any form without the written consent of Ontonix srl.

37 ATC: Classifying Airports Using Complexity (Peak Period) Airport 1 Airport 2 Airport 3

38 Car Crash Complexity Processing Test Data with OntoSpace

39 Car Crash Complexity:

40 Conclusions There exist physical limits to improvement of car crashworthiness (uncertain boundary conditions, bifurcation-driven response with chaotic content). Further limits stem from the fact that models used to design cars for crash do not capture all the physics no model does. Moreover, models are used in a deterministic perspective, while crash is an exquisitely stochastic (non-repeatable) phenomenon. Finally, the human component will almost always do all it can to cancel out even outstanding engineering. In a similar setting, optimizing a car for crash is a futile exercise. Copyright 2007, Ontonix srl. All rights reserved. No part of this document may be reproduced in any form without the written consent of Ontonix srl.