Profile Configuration Reference

This page provides a complete reference for all options available in YAML profile files. Profiles control configuration for analysis, design, and simulation runs, including plotting options and reporting settings.

Profile Structure

A profile YAML file contains four main sections:

reporting_options: Report generation settings
rfad_plot_options: Reliability-based Failure Assessment Diagram settings
lsf_plot_options: Limit State Function plot settings
reliability_options: Reliability analysis, SORM, Monte Carlo, Importance Sampling, and optimization settings

Reporting Options

Options for saving analysis results and visualizations.

Option	Type	Default	Description
`save_plots_to_pdf`	bool	`true`	Whether to save all generated plots in PDF format
`save_plots_to_pickle`	bool	`true`	Whether to save figure objects in pickle format for later retrieval and editing
`save_excel_summary`	bool	`true`	Whether to save the numerical results summary to an Excel file

Example:

reporting_options:
  save_plots_to_pdf: true
  save_plots_to_pickle: true
  save_excel_summary: true

RFAD Plot Options

Options for Reliability-based Failure Assessment Diagram (RFAD) visualization.

Option	Type	Default	Range/Values	Description
`n_x_points`	int	`30`	[5, 60]	Number of grid points along the first variable axis
`n_y_points`	int	`29`	[5, 60]	Number of grid points along the second variable axis
`plot_beta`	bool	`true`	-	Whether to plot the safety index (reliability index beta) contours
`plot_alphas`	bool	`true`	-	Whether to plot alpha values (normalized sensitivity factors) for each variable
`plot_base_point`	bool	`true`	-	Whether to plot the base point (mean of input variables) on the diagram
`with_labels`	bool	`true`	-	Whether to add text labels to the base point on the diagram
`ignore_axis_funcs`	bool	`false`	-	Whether to ignore axis transformation functions and plot in original variable space
`view`	str or tuple	`"auto"`	`"auto"`, `"default"`, `"XY"`, `"XZ"`, `"YZ"`, `"-XY"`, `"-XZ"`, `"-YZ"` (case-insensitive) or tuple of 3 floats (elevation, azimuth, roll) in degrees	View orientation for 3D perspective
`cmap`	str or list	`"plasma"`	Valid matplotlib colormap name or list of shape (n, 4) with RGBA values in [0, 1] where 1 ≤ n ≤ 256	Colormap specification
`type`	str	`"surface"`	`"contour"`, `"surface"`	Plot visualization type

Example:

rfad_plot_options:
  n_x_points: 30
  n_y_points: 29
  plot_beta: true
  plot_alphas: true
  plot_base_point: true
  with_labels: true
  ignore_axis_funcs: false
  view: "auto"
  cmap: "plasma"
  type: "surface"

LSF Plot Options

Options for Limit State Function (LSF) 3D visualization.

Option	Type	Default	Range/Values	Description
`n_x_points`	int	`30`	[5, 60]	Number of grid points along the first variable axis
`n_y_points`	int	`29`	[5, 60]	Number of grid points along the second variable axis
`plot_base_point`	bool	`true`	-	Whether to plot the base point (mean of input variables) on the LSF surface
`plot_failure_point`	bool	`true`	-	Whether to plot the design point (Most Probable Point of Failure) on the LSF surface
`with_labels`	bool	`true`	-	Whether to add text labels to the base and failure points
`ignore_axis_funcs`	bool	`false`	-	Whether to ignore axis transformation functions and plot in original variable space
`view`	str or tuple	`"auto"`	`"auto"`, `"default"`, `"XY"`, `"XZ"`, `"YZ"`, `"-XY"`, `"-XZ"`, `"-YZ"` (case-insensitive) or tuple of 3 floats (elevation, azimuth, roll) in degrees	View orientation for 3D perspective
`cmap`	str or list	`"plasma"`	Valid matplotlib colormap name or list of shape (n, 4) with RGBA values in [0, 1] where 1 ≤ n ≤ 256	Colormap specification
`type`	str	`"surface"`	`"contour"`, `"surface"`	Plot visualization type

Example:

lsf_plot_options:
  n_x_points: 30
  n_y_points: 29
  plot_base_point: true
  plot_failure_point: true
  with_labels: true
  ignore_axis_funcs: false
  view: "auto"
  cmap: "plasma"
  type: "surface"

Reliability Options

Options for reliability calculations and related numerical settings. This section collects tolerances, algorithm choices, finite-difference settings, plotting flags, Monte Carlo controls and various checks used across FORM, SORM, inverse problems and design optimization routines.

FORM and Inverse FORM Settings

These settings apply to both FORM and Inverse FORM.

Optimization algorithm

Reliafy CLI does not use the traditional Hasofer-Lind Rackwitz-Fiessler (HL-RF) algorithm found in many reliability textbooks and commercial tools. Instead, FORM and Inverse FORM rely on scipy.optimize.minimize as the optimizer, using the method parameter set to "trust-constr" for smooth limit-state functions and "COBYQA" for non-smooth ones. This provides access to the full scipy minimizer feature set, including variable bounds and general constraints, which the classical HL-RF cannot handle.

Option	Type	Default	Range	Description
`form_xtol`	float	`0.0001`	[1e-8, 1e-2]	Tolerance for FORM termination (variable changes)
`form_gtol`	float	`0.0001`	[1e-8, 1e-2]	Tolerance for FORM termination (Lagrangian gradient norm changes)
`form_maxiter`	int	`1000`	[1, ∞)	Maximum iterations for FORM
`form_random_start`	bool	`false`	-	Use a random starting point for FORM
`form_seed`	int or null	`null`	-	Random seed for FORM/Inverse FORM random starts

Design Optimization Settings

Option	Type	Default	Range	Description
`design_xtol`	float	`0.001`	[1e-8, 1e-2]	Tolerance for design optimization termination (variable changes)
`design_gtol`	float	`0.001`	[1e-8, 1e-2]	Tolerance for design optimization termination (Lagrangian gradient norm changes)
`design_maxiter`	int	`1000`	[1, ∞)	Maximum iterations for design optimization
`design_random_start`	bool	`false`	-	Use a random starting point for design optimization
`design_seed`	int or null	`null`	-	Random seed for design optimization random starts

General Reliability Settings

Option	Type	Default	Values	Description
`alpha_direction`	str	`"outward"`	`"outward"`, `"inward"`	Direction convention for the alpha vector
`use_nearest_correlation`	bool	`false`	-	Controls fallback behavior when Cholesky decomposition of the correlation matrix fails. If `false`, the run stops with an error. If `true`, Reliafy attempts to replace the matrix with a nearest positive semidefinite (PSD) correlation matrix using the method in Higham and Strabić (2011).
`qn_epsilon`	float	`1e-8`	[1e-8, 1e-2]	Tolerance used by the quasi-Newton SR1 (Symmetric Rank 1) update when `sor_fit_method` is set to `SR1`

SORM Settings

Option	Type	Default	Values	Description
`sor_method`	str	`"SOSPA_H"`	`"Breitung"`, `"Tvedt3T"`, `"TvedtSI"`, `"TvedtDI"`, `"Hohenbichler"`, `"Koyluoglu"`, `"ZhaoEmpirical"`, `"SOSPA_L"`, `"SOSPA_H"`, `"IFFT"`	SORM method to use
`sor_approximation`	str	`"Paraboloid"`	`"Paraboloid"`, `"Taylor2"`	SORM approximation type
`sor_fit_method`	str or null	`null`	`"FiniteDiff"`, `"ZhaoPF"`, `"Kiureghian"`, `"SR1"`, `"AnalyticAll"`, `null` (auto)	Method for SORM limit state function fitting
`sor_fit_delta_factor`	float	`1.0`	[0.1, 10.0]	Factor used to scale the method-recommended delta when numerically estimating SORM fit parameters for ZhaoPF and Kiureghian methods
`sor_fdm`	str	`"forward"`	`"central"`, `"forward"`, `"backward"`	Finite-difference method for gradient and Hessian (used when `sor_fit_method` is `FiniteDiff`)
`sor_fdm_hess_form`	str	`"full"`	`"full"`, `"diagonal"`	Hessian form for finite-difference approximation (used when `sor_fit_method` is `FiniteDiff`)
`force_curvatures`	bool	`false`	-	Force curvature computations even if not strictly required by selected SORM options

SORM References

Use these references as starting points for method details and derivation nuances. Keep in mind that explanations on this page are intentionally brief and implementation-focused.

sor_method

"Breitung": Breitung, K. (1984). "Asymptotic approximations for multinormal integrals." J. Eng. Mech., ASCE, 110(3), 357–366. →
"Tvedt3T", "TvedtSI", "TvedtDI": Although not the original reference, Der Kiureghian, A., Lin, H.-Z., and Hwang, S.-J. (1987) provides a thorough description of these methods in Appendix I — "Second-order reliability approximations." J. Eng. Mech., ASCE, 113(8), 1208–1225. →
"Hohenbichler": Hohenbichler, M., and Rackwitz, R. (1988). "Improvement of second-order reliability estimates by importance sampling." J. Eng. Mech., ASCE, 114(12), 2195–2199. →
"Koyluoglu": Köylüoğlu, H. U., and Nielsen, S. R. K. (1994). "New approximations for SORM integrals." Structural Safety, 13(4), 235–246. →
"ZhaoEmpirical": Zhao, Y.-G., and Ono, T. (1999a). "New approximations for SORM: Part 1." J. Eng. Mech., ASCE, 125(1), 79–85. →
"SOSPA_L", "SOSPA_H":
- Hu, Z., and Du, X. (2018). "Saddlepoint approximation reliability method for quadratic functions in normal variables." Structural Safety, 71, 24–32. →
- Du, X., and Sudjianto, A. (2004). "A saddlepoint approximation method for uncertainty analysis." Proc. ASME IDETC/CIE 2004, Paper DETC2004-57269, pp. 445–452. →
- Additional SOSPA reference
"IFFT":
- Zhao, Y.-G., and Ono, T. (1999b). "New approximations for SORM: Part 2." J. Eng. Mech., ASCE, 125(1), 86–93. →
- Tvedt, L. (1990). "Distribution of quadratic forms in normal space—application to structural reliability." J. Eng. Mech., ASCE, 116(6), 1183–1197. →
- Der Kiureghian, A., Lin, H.-Z., and Hwang, S.-J. (1987). "Second-order reliability approximations." J. Eng. Mech., ASCE, 113(8), 1208–1225. →

sor_approximation

Paraboloid: Local quadratic fit of the failure surface at the design point, using principal curvatures.
Taylor2: Second-order Taylor expansion of the limit-state function at the design point.
Reference: Tvedt, L. (1990). "Distribution of quadratic forms in normal space-application to structural reliability." J. Eng. Mech., ASCE, 116(6), 1183-1197. →

sor_fit_method

FiniteDiff: numerical differentiation tooling — numdifftools
SR1: quasi-Newton symmetric rank-one update — Wikipedia: Symmetric rank-one
Kiureghian: point-fitting procedure following Der Kiureghian, A. (2022). Structural and System Reliability. Cambridge University Press.
ZhaoPF: point-fitting procedure — Zhao and Ono (1999a) above.
AnalyticAll: uses user-provided analytic gradient and Hessian from the problem definition.
null (auto): Reliafy selects the most appropriate fit strategy based on available problem information.

sor_fit_delta_factor

Applies to ZhaoPF and Kiureghian fit methods as a scaling factor on the method-recommended point-fitting step size. Keep default unless Reliafy diagnostics suggest adjustment.

IFFT Settings (for IFFT-based SORM)

Option	Type	Default	Range	Description
`ifft_std_domain`	float	`16.0`	[2, 24]	Standard deviations covered when computing IFFT of characteristic functions
`ifft_n`	int	`4096`	[2^8, 2^16], powers of 2	Number of points used in IFFT
`plot_ifft_funcs`	bool	`true`	-	Generate diagnostic plots for IFFT operations

SOSPA Settings (for SOSPA-based SORM)

Option	Type	Default	Description
`plot_sospa_funcs`	bool	`true`	Generate diagnostic plots for SOSPA characteristic functions and derivatives

Derivative Checking

These options validate user-provided derivatives against numerical finite differences.

Option	Type	Default	Values	Description
`check_lsf_diffs_wrtx`	bool	`false`	-	Validate user-provided LSF derivatives against numerical diffs w.r.t. real-space variables
`check_lsf_diffs_wrtu`	bool	`true`	-	Validate user-provided LSF derivatives against numerical diffs w.r.t. standard-normal (U-space) variables
`lsf_diffs_check_method`	str	`"forward"`	`"central"`, `"forward"`, `"backward"`, `"complex"`	Method for LSF derivative checks
`check_varscf_diffs_wrtx`	bool	`false`	-	Validate user-provided stochastic variables constraints (real-space)
`check_varscf_diffs_wrtu`	bool	`true`	-	Validate user-provided stochastic variables constraints (U-space)
`varscf_diffs_check_method`	str	`"forward"`	`"central"`, `"forward"`, `"backward"`, `"complex"`	Method for stochastic variables constraint derivative checks
`check_dof_diffs`	bool	`true`	-	Validate user-provided design objective function derivatives against numerical diffs
`dof_diffs_check_method`	str	`"forward"`	`"central"`, `"forward"`, `"backward"`, `"complex"`	Method for design objective function derivative checks
`check_dcf_diffs`	bool	`true`	-	Validate user-provided design constraint function derivatives against numerical diffs
`dcf_diffs_check_method`	str	`"forward"`	`"central"`, `"forward"`, `"backward"`, `"complex"`	Method for design constraint function derivative checks

Monte Carlo Settings

Option	Type	Default	Range	Description
`mc_n`	float or null	`null`	[1e3, 1e8] or `null` (auto)	Monte Carlo sample size (null means automatic)
`mc_max_cv`	float	`0.05`	[0.01, 1.0]	If `mc_n` is `null`, MC runs in cycles until the estimated failure-probability CV is <= `mc_max_cv`
`mc_seed`	int or null	`null`	-	Random seed for Monte Carlo simulations; set a value for repeatable results, or leave as `null` to allow small run-to-run differences
`mc_remove_oob`	bool	`true`	-	Remove out-of-bounds samples during MC simulation (bounds or constraint violations)

Importance Sampling Settings

Option	Type	Default	Values/Range	Description
`is_method`	str	`"kde"`	`"kde"`, `"mixture"`, `"mcmc"`, `"mpp_normal"`	Importance sampling proposal method
`is_kde_bandwidth`	str or float	`"scott"`	`"scott"`, `"silverman"` or positive float	Bandwidth selection method for KDE or numeric value
`is_mixture_components`	int	`6`	[1, 16]	Number of mixture components for mixture IS methods
`is_mixture_cov_type`	str	`"full"`	`"full"`, `"tied"`, `"diag"`, `"spherical"`	Covariance type for mixture IS methods
`is_fit_samples`	int	`2000`	[100, 100000]	Number of samples to collect for fitting the proposal distribution (for KDE and mixture IS)

MCMC Importance Sampling Settings

Option	Type	Default	Range	Description
`is_mcmc_chains`	int	`5`	[1, 100]	Number of parallel Metropolis chains to run during MCMC proposal fitting; a practical starting point is about 2 times the number of stochastic variables
`is_mcmc_chain_length`	int	`500`	[100, 10000]	Length of each MCMC chain during proposal fitting
`is_mcmc_thinning`	int	`3`	[1, 100]	Number of samples skipped between retained samples in each MCMC chain during proposal fitting
`is_mcmc_burnin`	int	`200`	[100, 1000]	Number of samples to discard as burn-in during MCMC proposal fitting
`is_mcmc_fit_method`	str	`"kde"`	`"kde"`, `"mixture"`	Method used to fit the MCMC proposal distribution

IS References

Use these references as starting points for method details and implementation background. Keep in mind that explanations on this page are intentionally brief and implementation-focused.

is_method: "kde"

KernelDensity from scikit-learn — sklearn.neighbors.KernelDensity. Bandwidth selection follows the is_kde_bandwidth option ("scott" or "silverman" rules, or a numeric value).

is_method: "mixture"

BayesianGaussianMixture from scikit-learn — sklearn.mixture.BayesianGaussianMixture. Number of components and covariance type are controlled by is_mixture_components and is_mixture_cov_type.

is_method: "mcmc"

Xiao, S., and Nowak, W. (2022). "Reliability sensitivity analysis based on a two-stage Markov chain Monte Carlo simulation." Aerospace Science and Technology, 130, 107938. →
Cotter, S. L., Roberts, G. O., Stuart, A. M., and White, D. (2013). "MCMC methods for functions: modifying old algorithms to make them faster." Statistical Science, 28(3), 424–446. →
Roberts, G. O., and Rosenthal, J. S. (2007). "Coupling and ergodicity of adaptive Markov chain Monte Carlo algorithms." Journal of Applied Probability, 44(2), 458–475. →

is_method: "mpp_normal"

Centers the importance sampling proposal distribution on the Most Probable Point (MPP), also called the design point or failure point. The MPP is the point on the limit-state surface closest to the origin in standard normal space, found by FORM. A Gaussian proposal centered there concentrates samples near the dominant failure region. See the FORM method and the textbooks listed on the home page.

Example:

reliability_options:
  # FORM
  form_xtol: 0.0001
  form_gtol: 0.0001
  form_maxiter: 1000
  form_random_start: false
  form_seed: null

  # Design
  design_xtol: 0.001
  design_gtol: 0.001
  design_maxiter: 1000
  design_random_start: false
  design_seed: null

  # General
  alpha_direction: "outward"
  use_nearest_correlation: false
  qn_epsilon: 1e-8

  # SORM
  sor_method: "SOSPA_H"
  sor_approximation: "Paraboloid"
  sor_fit_method: null
  sor_fit_delta_factor: 1.0
  sor_fdm: "forward"
  sor_fdm_hess_form: "full"
  force_curvatures: false

  # IFFT
  ifft_std_domain: 16.0
  ifft_n: 4096
  plot_ifft_funcs: true

  # SOSPA
  plot_sospa_funcs: true

  # Derivative checking
  check_lsf_diffs_wrtx: false
  check_lsf_diffs_wrtu: true
  lsf_diffs_check_method: "forward"
  check_varscf_diffs_wrtx: false
  check_varscf_diffs_wrtu: true
  varscf_diffs_check_method: "forward"
  check_dof_diffs: true
  dof_diffs_check_method: "forward"
  check_dcf_diffs: true
  dcf_diffs_check_method: "forward"

  # Monte Carlo
  mc_n: null
  mc_max_cv: 0.05
  mc_seed: null
  mc_remove_oob: true

  # Importance Sampling
  is_method: "kde"
  is_kde_bandwidth: "scott"
  is_mixture_components: 6
  is_mixture_cov_type: "full"
  is_fit_samples: 2000
  is_mcmc_chains: 5
  is_mcmc_chain_length: 500
  is_mcmc_thinning: 3
  is_mcmc_burnin: 200
  is_mcmc_fit_method: "kde"

Notes

Enum-style fields accept either the enum member name (case-insensitive) or the enum value
Out-of-range or invalid values trigger a profile validation error
Set form_seed, design_seed, and/or mc_seed to a non-null integer for repeatable runs when random number generation is involved