Why and Hows in Uncertainty Modelling

by Elishakoff, I.

• ISBN13: 9783211831557
• ISBN10: 321183155X
• Format: Paperback
• Copyright: 2000-04-01
• Publisher: Springer Verlag

Summary

This book presents, as a single package, three semingly contradictory and often competitive approaches to deal with ever present uncertainty in science and engineering. The book describes, as a unique view, probabilistic, fuzzy sets based and antioptimization based approaches, in order to remedy the present 'œtower ob Babel' situation, in which researchers in competing fields do not communicate.Integrative approach will attract scientists and engineers alike and provide a strong impetus towards integrative, hybrid approaches.

Table of Contents

Preface
How to Utilize the Anti-Optimization Analysis to Treat Uncertainty in Seismic Excitation?	1	(62)
A. Baratta
G. Zuccaro
Introduction	1	(2)
Basic Equations and Behaviour of the SDOF Shear-Type Frame	3	(6)
Basic Test Accelerograms	9	(4)
Optimization Process Combined with Stochastic Generation of Site-Compatible Synthetic Accelerograms	13	(18)
Convex Modelling for Treatment of Uncertainty in Seismic Action	31	(32)
What are the Random and Fuzzy Sets and How to Use them for Uncertainty Modelling in Engineering Systems?	63	(64)
A. Bernardini
Why do we need Random and Fuzzy Sets?	64	(10)
How do Random and Fuzzy Sets Work?	74	(10)
Why do we need Fuzzy Logic?	84	(11)
How to Apply Random and Fuzzy Sets in Structural Engineering?	95	(12)
How to Appy Fuzzy Logic to Approximate Reasoning?	107	(20)
What is Ellipsoidal Modelling and How to Use it for Control and State Estimation?	127	(62)
F.L. Chernousko
What is the Guaranteed Approach to Uncertainties?	128	(10)
What are the Fundamentals of the Ellipsoidal Modelling?	138	(8)
How does the Ellipsoidal Modelling Work?	146	(11)
What are the Properties of the Approximating Ellipsoids?	157	(10)
How to Use Ellipsoidal Modelling in Control?	167	(10)
How to Use Ellipsoidal Modelling in State Estimation?	177	(12)
What is Differential Stochastic Calculus?	189	(74)
M. Di Paola
What are the Basic Concepts of the Stochastic Differential Calculus?	191	(22)
How to Analyze the Non-Linear Systems under Poisson white Noise Processes?	213	(30)
How to Apply Stochastic Differential Calculus to Earthquake Engineering?	243	(20)
Are Probabilistic and Anti-Optimization Approaches Compatible?	263	(94)
I. Elishakoff
What may go Wrong with Probabilistic Methods?	265	(20)
Are Probabilistic and Antioptimization Methods Interrelated?	285	(34)
How to Combine Probabilistic and Antioptimization Methods? (with Qiang Li)	319	(22)
How to Find the Range of Eigenvalues due to Uncertain Elastic Modulus and Mass Density?	341	(16)
Dehe Duan
Zhiping Qiu
James H. Starnes, Jr.
How to Develop and Utilize Numerical Algorithms with Automatic Result Verification?	357
U. Kulisch
Introduction	358
Universal, Floating-Point Arithmetic	371
Interval Arithmetic, a Simple but Powerful Calculus to Deal with Inequalities	380
Availability of the Necessary Arithmetic in Hardware and Suitable Programming Support	388