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How is the robustness of systems measured?


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Disclaimer The concepts and methods presented in this document are for illustrative purposes only, and are not intended to be exhaustive. Ontonix assumes no liability or responsibility to any person or company for direct or indirect damages resulting from the use of any information contained herein. Any reproduction or distribution of this document, in whole or in part, without the prior written consent of Ontonix is prohibited. Reverse-engineering of the concepts, methods or ideas contained in this document is strictly forbidden. The methods described in the present document are protected by US patents. OntoSpace , OntoDyn, OntoNet , OntoTest and OntoView are trademarks of Ontonix. All other trademarks are the property of their respective owners. Copyright  2011 Ontonix S.r.l. All Rights Reserved.

What is Robustness?:

What is Robustness? Input variables: Loads Material properties Dimensions Boundary conditions Initial conditions etc. Output variables: Frequencies Stresses Displacements Temperatures Energy etc. . . . . In a generic system inputs are transformed into outputs Uncertainties and scatter in the inputs will lead to uncertainties and scatter in the outputs This may lead to unexpected or unwanted behavior as well as loss of functionality

What is Robustness? A Common Misconception:

What is Robustness? A Common Misconception Often, a system is said to be robust when the scatter of its outputs is small. However, scatter of the outputs is related to quality NOT to robustness. Quality may be measured easily via standard deviation. Low scatter System is said to be robust High scatter System is said to be less robust

A Modern Look at Robustness:

A Modern Look at Robustness Robustness is the ability of a system to retain functionality in the presence of: Uncertainties in its environment Manufacturing imperfections Mishandling Extreme events Robustness is a global characteristic of a system and may be measured as the amount of non-conformity a system is able to absorb before loss of functionality.

Functionality and the Topology of Information Flow:

Functionality and the Topology of Information Flow The functionality of a system depends on a correct and stable flow of information between its components, inputs and outputs. Industrial process Pedestrian bridge

Complexity, Information and Robustness:

Complexity, Information and Robustness Upper complexity bound Current complexity Lower complexity bound Complexity is a scalar function of the topology of information flow and entropy. It measures the total amount of structured information within a given system. Each systems possess a lower and upper bound of complexity. The robustness of a system depends on how its complexity is positioned with respect to its upper and lower bound. Close to critical complexity the system is dominated by uncertainty and chaos. Performance is unpredictable. Close to the lower complexity bound the system is dominated by structure. Performance is predictable.

Complexity, Information and Robustness:

Complexity, Information and Robustness Robustness is a function of a system’s complexity bounds and its current value of complexity. Robustness is measured on a scale ranging from 0% to 100%. It measures the ability of a system’s Complexity Map to retain its topology in the presence of endogenous and exogenous disturbances. Based on the value of robustness, it is possible to issue a robustness rating , which ranges from one to five stars.

Robustness Rating:

Robustness Rating The next slide shows how a system, when exposed to increasing scatter, becomes progressively more complex, evolving from deterministic behavior to a fragile uncertainty-dominated configuration. As the scatter plots, which correspond to functional relationships between pairs of variables, become increasingly fuzzy, the rating of the systems decreases. Increasingly fuzzy scatter plots lead to weaker relationships between variables, forming ultimately a less resilient Complexity Map which, in proximity of a one-star rating, is close to collapsing.

Slide 10:

Critical Complexity Minimum Complexity Complexity = Very Low Robustness = 93% Predictability = Very High Rating Complexity = Low Robustness = 78% Predictability = High Rating Complexity = Medium Robustness = 65% Predictability = Medium Rating Complexity = High Robustness = 52% Predictability = Low Rating Complexity = Very High Robustness = 19% Predictability = Very Low Rating

Measuring Robustness Online!:

Measuring Robustness Online!

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