Uncertainty and Complexity ManagementHeidelberg 23 jun 2001 At SC2001 in Heidelberg, Dr. Jacek Marczyk, EASi Engineering GmbH, Alzenau, Germany, described their business which consists of about 400 engineers, providing services using stochastic modelling techiniques for solving problems within the automotive industry. His main thesis is that problems such as crashes, exhibit chaotic behaviour and therefore deterministic models are often inadequate. Using points to create functions can be dangarous because the points chosen may not be a true representation of the physics. He went on to say that Western culture prefers certainty to knowledge. The aim should be to run ensembles of the model, quantify the risks as a statistical distribution and then proceed to shift this distribution to provide the knowledge needed for re-engineering a better product, such as a car. (author: Chris Lazou).
Heidelberg - Germany, June 21-23: At the SC2001 conference, Dr. Jacek Marczyk, EASi Engineering GmbH, Alzenau, Germany, described their business which consists of about 400 engineers, providing services using stochastic modelling techiniques for solving problems within the automotive industry.
He first quoted the formulation of the complexity principle by L. Zadeh, UCLA, as follows: "When the complexity and uncertainty of an engineering system increase, our ability to predict its behaviour diminishes until a
threshold is reached beyond which accuracy and significance become almost mutually exclusive".
He went on to lament the state of HPC/CAE today. He asserted that CAE is presently, stagnant, dogmatic, totalitarian, and geocentric. It ignores uncertainty and complexity, is reductionist, automation-based, with a strong emphasis on numerics, obsessed with accuracy, optimality and detail based on bi-valued logic, and yet this determistic approach often violates the underlying physics. One has to remember that the order of the model determines the number of minima/maxima it can possess. The results are of course useless if they ignore model validity and confidence tests. This lack of new methodologies leads to a fragmentation crisis.
HPC fragments CAE because companies concentrate on just hardware, instead of developing new computing techniques or paradigms. HPC is used mostly for building larger models and running them faster. Confidence
in models is not addressed and the Complexity Principle is ignored. By doing this, hardware vendors are promoting analysis rather than simulation. They are looking at too much fine grain instead of coarseness. This ironically drastically limits the amount of business they can generate.
When one does a car crash experiment one must perform a series of tests for chaos on the crash signal.
The typical tests for chaos are: 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 which exhibit structure.
According to these tests, the measured crash signal is seen to originate from a chaotic system. Crash chaos can be described by closed-form deterministic equations since chaos does not mean random. In fact chaos is characterised by extreme sensitivity to initial conditions. Memory of initial conditions is quickly lost in chaotic
phenomena (i.e. butterfly effect). Examples of chaotic phenomena are: Tornados (weather in general), Stock market evolution, crash, impacts, etc.
Phenomena that are chaotic, are unpredictable (non-repeatable). The main reason for this is extreme sensitivity to initial conditions. Most systems in nature contain some chaos. Note that phenomena that are unpredictable, cannot be optimized. All that can be done with chaotic phenomena is to increase our understanding of their
nature, properties, patterns, structure, main features, and quantify the associated risks. Therefore, models for Risk Analysis must be realistic to be of any use.
Essentially, risk is associated with the existence of outliers: Warranty, recall, and a lawsuit is the most likely
response. Note: DOE and response surface techniques cannot capture outliers since an outlier is defined as unfortunate combinations of operating conditions and design parameters that lead to unexpected behaviour.
The task of risk and uncertainty management is to understand and remove outliers, shift the entire distribution from system fail state to system is safe region. To achieve this it invariably leads to re-engineering to improve the initial design. For example in an experiment consisting of full-car NVH analysis in which 5% of the spotwelds have been removed randomly, using 100 Monte Carlo samples, 7 outliers appear. Thus the performance is unacceptable in those 7 regions. When one looks closer the 7 outliers correspond to sudden loss of performance or quality.
Today, HPC concentrates on fast and efficient generation of massive amounts of data, but neglects model validation and confidence. One-to-one test-analysis are not validations but mere comparisons. In the most favourable conditions they lead to accidental correlation.
What is Model Validation? The gateway to realistic modeling are random fields, that is random variables which
depend on both space and time (eg. Surface of the sea). Random fields constitute the most common form of uncertainty in nature. For example in computing algorithms random fields can help to establish an upper
bound of an Finite Element mesh resolution.
Idealised geometry is often used in deterministic crash models but this frequently fails to capture realistically the problem. Including a random field (geometry), and a distribution describing geometry errors, boosts the levels
of realism of the model. In practice, realistic modeling of geometry has substantial impact on the response of crash models.
With a single test, a numerical model can be verified, but not validated. With a single test and single analysis, one can perform model comparison, but not correlation. A single test can also be used to falsify a theory. Different theories can fit the same observed data, especially if only one test is performed.
Rigorous model validation requires repeated experiments. Lots of Gflop/s and elements are not sufficient to
reduce/replace testing. Model validation requires the knowledge of the measured and computed covariance matrices. The necessary (but not sufficient) conditions for having a valid model are: Null Mahalanobis distance and matching of spectral properties of covariance matrices
Computer models, to be of any use, must be realistic and validated rather than verified. Today, HPC resources are being used in the wrong direction: They focus on accuracy, optimality, and not comprehension. Large scale models instead of realistic large scope models.
Running large deterministic models on powerful parallel computers is like using the slide-rule, in the slide-rule days, to only draw straight lines!
Chris Lazou |
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