MC_IS_system: Monte-Carlo Importance Sampling for a system of limit-state...

In TesiproV: Reliability Analysis Methods for Structural Engineering

Monte-Carlo Importance Sampling for a system of limit-state functions

Description

Monte-Carlo Importance Sampling for a system of limit-state functions

Usage

MC_IS_system(
  lsf,
  lDistr,
  cov_user = 0.05,
  n_batch,
  n_max,
  use_threads,
  sys_type,
  dataRecord = TRUE,
  beta_l,
  densityType,
  dps = NULL,
  debug.level = 0,
  streams = NULL,
  libPaths_local = .libPaths(),
  seed = NULL,
  backend = "future",
  adaptive_alpha = FALSE,
  alpha_update_rate = 0.1,
  adaptive_batch = FALSE,
  batch_control = list(),
  min_adapt_samples = 10000,
  alpha_min = 0.02,
  stability_mode = c("robust", "fast")
)

Arguments

lsf	Objective (limit state) function in form function(x) { ... }.
lDistr	List of input variable distributions created from TesiproV base variable objects.
cov_user	Target coefficient of variation for convergence criterion.
n_batch	Number of samples per batch (recommended > 1000).
n_max	Maximum total number of samples before forced stop.
use_threads	Number of threads/workers to use for parallel computation.
sys_type	Either "parallel" (default) or "serial"
dataRecord	Logical; if 'TRUE', all intermediate results are recorded and returned as data frame.
beta_l	Optional threshold for reliability index screening. Limit-state functions with \beta > beta_l may be excluded from mixture construction in system analysis.
densityType	Character; type of sampling density ("origin" keeps original input distributions).
dps	Optional vector of design points supplied by user instead of FORM result.
debug.level	Integer verbosity level: 0 = silent, 1 = info, 2 = detailed output during calculation.
streams	RNG stream object created by ['init_rng_master()'].
libPaths_local	Local library paths passed to cluster workers for package availability.
seed	Optional integer seed for reproducibility across parallel runs. If 'NULL', a random seed is used.
backend	Character; either '"parallel"' or '"future"' backend for parallelization on multiple cores.
adaptive_alpha	Logical; if TRUE, adaptive mixture weights are used (system case only).
alpha_update_rate	Damping factor \lambda \in [0,1] controlling adaptation speed of mixture weights.
adaptive_batch	Logical; if TRUE, the batch size is adapted dynamically based on the current effective sample size (ESS) and target RSE.
batch_control	List controlling adaptive batch behaviour: n_min Minimum batch size n_max Maximum batch size K_future Desired number of remaining iterations
min_adapt_samples	Integer. Minimum total number of MC samples required before adaptive mixtures are updated. The adaption mechanism is activated only after this threshold has been exceeded to ensure statistically stable estimates.
alpha_min	Numeric scalar in (0,1). Lower bound for mixture weights \alpha_i during adaptive updating. This prevents individual components of the importance sampling density from collapsing to zero and ensures numerical stability in multimodal system analyses.
stability_mode	Character string specifying the numerical stabilization strategy used for importance sampling weight accumulation. "robust" Default. Uses full log-domain accumulation of weights across Monte Carlo iterations. This improves numerical stability for high-dimensional systems and very small failure probabilities. "fast" Uses shifted exponentiation with batch-level scaling. Computationally equivalent under normal engineering conditions but may be slightly less stable in extreme rare-event scenarios. Both modes are mathematically equivalent for typical reliability problems. The "robust" mode is recommended for research applications and extreme reliability levels.

Details

The failure probability is estimated with the standard importance sampling estimator \hat{p}_f = n^{-1} \sum_i I_i w_i with w = \varphi(u) / h(u), where h is a mixture of unit-variance normal densities centred at the proposal points. I_i = 1 if g_k(x_i) < 0 for at least one component (serial) or for all components (parallel), otherwise I_i = 0. The coefficient of variation is derived from the sample variance of I w.

• Serial systems: the component design points (FORM) are the centres. If they are close and nearly parallel, a single shift at their mean is used.

• Parallel systems: the design point of the joint failure domain \max_i g_i < 0 is used as the main centre (weight 0.7). The component design points are kept as a defensive part of the mixture.

The returned ESS is the effective number of failure samples (\sum I w)^2 / \sum (I w)^2. The argument stability_mode no longer influences the result because all sums are accumulated in the log domain.

TesiproV documentation built on Oct. 28, 2026, 5:13 p.m.