COST E5 5 W orkshop Graz University of Technology May, 1 4 -1 5 , 2 0 0 7 Reliability Assessm ent of Structures Michael Havbro Faber Sw iss Federal I nstitute of Technology ETH Zurich, Sw itzerland Sw iss Federal Institute of Technology
Contents of Presentation • An introduction – what is the role of risk and reliability in engineering? • Refreshing you memory on probability and statistics • (the very) Basics of modern reliability theory • Reliability based calibration of design codes • The JCSS approach to risk assessment of engineered facilities • On the issues of risk acceptance – how safe is safe enough? Sw iss Federal Institute of Technology
Engineering Decision Making for Society? Is what we are doing of any relevance for society? Sw iss Federal Institute of Technology
Engineering Decision Making for Society? • Examples of what we help to develop Golden Gate Bridge - USA Øresund bridge - Denmark Sw iss Federal Institute of Technology
Engineering Decision Making for Society? • Examples of what we help to develop Big Dig Boston/USA Sw iss Federal Institute of Technology
Engineering Decision Making for Society? • Examples of what we help to develop Hoover Dam - USA Sw iss Federal Institute of Technology
Engineering Decision Making for Society? • Examples of what we help to develop Hong Kong Island - China Sw iss Federal Institute of Technology
Engineering Decision Making for Society? • Helping to control risks due to Natural Hazards Tornados and strong winds Sw iss Federal Institute of Technology
Engineering Decision Making for Society? • Helping to control risks due to Natural Hazards Earthquakes Sw iss Federal Institute of Technology
Engineering Decision Making for Society? • Helping to control risks due to degradation Corrosion Fatigue Sw iss Federal Institute of Technology
Engineering Decision Making for Society? • Helping to control risks due to accidents Fires Explosions Sw iss Federal Institute of Technology
Engineering Decision Making for Society? • Helping to control risks due to malevolence Bombs Airplane impacts Sw iss Federal Institute of Technology
Engineering Decision Making for Society? • Helping to reduce consequences of “unfulfilled assumptions” Extreme loads/deterioration Design/execution errors Bad Reichenhalle Siemens Arena Sw iss Federal Institute of Technology
Definition of Risk Risk is a characteristic of an activity relating to all possible events n E which may follow as a result of the activity The risk contribution R Ei from the event E i is defined through the product between the Event probability P Ei and the Consequences of the event C Ei The Risk associated with a given activity R A may then be written as n n E E ∑ ∑ = = ⋅ R R P C A E E E i i i = = i 1 i 1 Sw iss Federal Institute of Technology
Decision Problems in Engineering Uncertainties must be considered in the decision making throughout all phases of the life of an engineering facility Planning and Planning and Planning and Investigations and Investigations and Investigations and feasibility study feasibility study feasibility study tests tests tests Uncertainties Uncertainties Uncertainties Uncertainties Design Design Design Idea & Idea & Idea & Traffic volume Traffic volume Concept Concept Concept • Safety of personnel • Safety of personnel • Safety of personnel Loads Loads Manufacturing Manufacturing Manufacturing Resistances Resistances • Safety of environment • Safety of environment • Safety of environment (material, soil,..) (material, soil,..) • Economical feasibility • Economical feasibility • Economical feasibility Degradation processes Degradation processes Execution Execution Execution Service life Service life Manufacturing costs Manufacturing costs Decommissioning Decommissioning Decommissioning Operation & Operation & Operation & maintenance maintenance maintenance Execution costs Decommissioning Decommissioning costs costs Sw iss Federal Institute of Technology
Sources of Risks in Engineering Any activity carries a risk potential It is important that this potential is fully understood Only when the risk potential is fully understood can rational decisions be identified and implemented Sw iss Federal Institute of Technology
Overview of Probability Theory The probability theory provides • What are we aiming for ? the basis for the consistent treatment of uncertainties Data Model estimation in decision making ! Probabilistic model Consequences of events Probabilities of events We need to be able to Risks quantify the probability of events and to update these based on new Decision Making ! information Sw iss Federal Institute of Technology
Interpretation of Probability States of nature of which we have interest such as: - a bridge failing due to excessive traffic loads - a water reservoir being over-filled - an electricity distribution system „falling out“ - a project being delayed are in the following denoted „events“ we are generally interested in quantifying the probability that such events take place within a given „time frame“ Sw iss Federal Institute of Technology
Interpretation of Probability • There are in principle three different interpretations of probability N - Frequentistic = → ∞ A P ( A ) lim for n exp n exp n - Classical = P ( A ) A n tot - Bayesian = P ( A ) degree of belief that A will occur Sw iss Federal Institute of Technology
Conditional Probability and Bayes‘s Rule as there is = = P A ( E ) P A E P E ( ) ( ) P E A P A ( ) ( ) I i i i i we have Likelihood Prior P A E P E ( ) ( ) P A E P E ( ) ( ) = = i i i i P E A ( ) i n P A ( ) ∑ P A E P E ( ) ( ) i i = i 1 Posterior Bayes Rule Reverend Thomas Bayes (1702-1764) Sw iss Federal Institute of Technology
Uncertainties in Engineering Problems Different types of uncertainties influence decision making • Inherent natural variability – aleatory uncertainty - result of throwing dices - variations in material properties - variations of wind loads - variations in rain fall • Model uncertainty – epistemic uncertainty - lack of knowledge (future developments) - inadequate/imprecise models (simplistic physical modelling) • Statistical uncertainties – epistemic uncertainty - sparse information/small number of data Sw iss Federal Institute of Technology
Uncertainties in Engineering Problems • Consider as an example a dike structure - the design (height) of the dike will be determining the frequency of floods - if exact models are available for the prediction of future water levels and our knowledge about the input parameters is perfect then we can calculate the frequency of floods (per year) - a deterministic world ! - even if the world would be deterministic – we would not have perfect information about it – so we might as well consider the world as random Sw iss Federal Institute of Technology
Uncertainties in Engineering Problems In principle the so-called inherent physical uncertainty (aleatory – Type I) is the uncertainty caused by the fact that the world is random, however, another pragmatic viewpoint is to define this type of uncertainty as any uncertainty which cannot be reduced by means of collection of additional information the uncertainty which can be reduced is then the model and statistical uncertainties (epistemic – Type II) Sw iss Federal Institute of Technology
Uncertainties in Engineering Problems Observed annual Observed annual Model for annual Model for annual Aleatory Aleatory extreme water levels extreme water levels extremes extremes Uncertainty Uncertainty Epistemic Epistemic Uncertainty Uncertainty Regression model to Regression model to predict future extremes predict future extremes Predicted future Predicted future extreme water level extreme water level Sw iss Federal Institute of Technology
Uncertainties in Engineering Problems The relative contribution of aleatory and epistemic uncertainty to the prediction of future water levels is thus influenced directly by the applied models refining a model might reduce the epistemic uncertainty – but in general also changes the contribution of aleatory uncertainty the uncertainty structure of a problem can thus be said to be scale dependent ! Sw iss Federal Institute of Technology
Uncertainties in Engineering Problems Prediction Prediction Observation Observation Knowledge Knowledge Future Future 100% 100% Time Time Past Past Present Present The uncertainty structure changes also as function of time – is thus time dependent ! Sw iss Federal Institute of Technology
Random Variables • Probability distribution and density functions A random variable is denoted with capital letters : X A realization of a random variable is denoted with small letters : x We distinguish between - continuous random variables : can take any value in a given range - discrete random variables : can take only discrete values Sw iss Federal Institute of Technology
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