Structural Reliability

1. Front Matter

   Pages I-XIV

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2. A Discussion on Structural Reliability Methods

   • Jorge E. Hurtado

   Pages 1-43

3. Fundamental Concepts of Statistical Learning

   • Jorge E. Hurtado

   Pages 45-79

4. Dimension Reduction and Data Compression

   • Jorge E. Hurtado

   Pages 81-105

5. Classification Methods I — Neural Networks

   • Jorge E. Hurtado

   Pages 107-143

6. Classification Methods II — Support Vector Machines

   • Jorge E. Hurtado

   Pages 145-190

7. Regression Methods

   • Jorge E. Hurtado

   Pages 191-218

8. Classification Approaches to Reliability Indexation

   • Jorge E. Hurtado

   Pages 219-240

9. Back Matter

   Pages 241-257

   PDF

The last decades have witnessed the development of methods for solving struc­ tural reliability problems, which emerged from the efforts of numerous re­ searchers all over the world. For the specific and most common problem of determining the probability of failure of a structural system in which the limit state function g( x) = 0 is only implicitly known, the proposed methods can be grouped into two main categories: • Methods based on the Taylor expansion of the performance function g(x) about the most likely failure point (the design point), which is determined in the solution process. These methods are known as FORM and SORM (First- and Second Order Reliability Methods, respectively). • Monte Carlo methods, which require repeated calls of the numerical (nor­ mally finite element) solver of the structural model using a random real­ ization of the basic variable set x each time. In the first category of methods only SORM can be considered of a wide applicability. However, it requires the knowledge of the first and second deriva­ tives of the performance function, whose calculation in several dimensions either implies a high computational effort when faced with finite difference techniques or special programs when using perturbation techniques, which nevertheless require the use of large matrices in their computations. In or­ der to simplify this task, use has been proposed of techniques that can be regarded as variants of the Response Surface Method.

• Chaos
• Regression
• Stab
• Transformation
• Vibration
• Wavelet
• algorithms
• classification
• complexity
• linear optimization
• mechanical engineering
• simulation
• stability
• structural analysis
• structure

From the reviews:

"The methods presented and exemplified in the book are what in the statistical world would be called nonlinear and nonparametric regression or pattern recognition techniques … . The book is written from an algorithmic perspective … . the book is a valuable overview of problems and techniques used in structural safety analysis." (Georg Lindgren, Mathematical Reviews, Issue 2006 h)

• Civil Engineering, Universidad Nacional de Colombia, Manizales, Colombia

  Jorge E. Hurtado

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