% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/SORM.R
\name{SORM}
\alias{SORM}
\title{Second-Order Reliability Method (SORM)}
\usage{
SORM(lsf, lDistr, debug.level = 0)
}
\arguments{
\item{lsf}{objective function with limit state function in form of
\code{function(x) \{ x[1] + x[2] + ... \}}.}

\item{lDistr}{list ob distribiutions regarding the distribution object of TesiproV}

\item{debug.level}{If 0 no additional info if 2 high output during calculation}
}
\value{
SORM returns an object containing the following elements:
\itemize{
  \item \code{beta}: Hasofer-Lind reliability index.
  \item \code{pf}: Estimated probability of failure.
  \item \code{u_points}: Design point(s) in the standard normal space (\eqn{u}-space).
  \item \code{dy}: Gradient(s) of the limit-state function at the design point.
}
}
\description{
Second-Order Reliability Method (SORM) for the approximation
of failure probabilities in structural reliability analysis.

The SORM extends the First-Order Reliability Method (FORM)
by incorporating second-order information of the limit-state function
at the design point. By accounting for local curvature effects,
SORM generally provides more accurate failure probability estimates
for nonlinear limit-state functions.

The method evaluates the principal curvatures of the limit-state surface
in standard normal space and applies an asymptotic correction
to the FORM probability of failure.
}
\references{
Breitung, K. (1989).
Asymptotic approximations for probability integrals.
\emph{Probabilistic Engineering Mechanics}, 4(4), 187-190.

Cai, G. Q., & Elishakoff, I. (1994).
Refined second-order reliability analysis.
\emph{Structural Safety}, 14(4), 267-276.

Hohenbichler, M., Gollwitzer, S., Kruse, W., & Rackwitz, R. (1987).
New light on first- and second-order reliability methods.
\emph{Structural Safety}, 4, 267-284.

Tvedt, L. (1990).
Distribution of quadratic forms in normal space -
Applications to structural reliability.
\emph{Journal of Engineering Mechanics}, 116(6), 1183-1197.

Marelli, S., & Sudret, B. (2014).
UQLab: A framework for uncertainty quantification in Matlab.
In \emph{Proceedings of the 2nd International Conference on
Vulnerability, Risk Analysis and Management (ICVRAM2014)},
Liverpool, United Kingdom, 2554-2563.

Lacaze, S., & Missoum, S. (2015).
CODES: A toolbox for computational design (Version 1.0).
Retrieved from \url{http://www.codes.arizona.edu/toolbox/}

Wu, X. Z. (2017).
Implementing statistical fitting and reliability analysis
for geotechnical engineering problems in R.
\emph{Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards},
11(2), 173-188.
}
\author{
(C) 2021-2026 K. Nille-Hauf, T. Feiri, M. Ricker, T. Lux -- Hochschule Biberach (until 2022),
TU Dortmund University - Chair of Structural Concrete (since 2023)
}
