Reliability Analysis Methods for Structural Engineering

Calculate the failure probability of civil engineering problems with Level I up to Level III Methods. References: Spaethe (1991, ISBN:3-211-82348-4) "Die Sicherheit tragender Baukonstruktionen", Au and Beck (2001) "Estimation of small failure probabilities in high dimensions by subset simulation." , Breitung (1989) "Asymptotic approximations for probability integrals." .

TesiproV

The goal of TesiproV is to provide a flexible framework for probabilistic reliability analysis of structural systems. It implements several state-of-the-art algorithms (FORM, SORM, MVFOSM and Monte-Carlo methods) and supports parametric studies through reference classes such as SYS_PROB, SYS_PARAM, and SYS_LSF.

Class structure

TesiproV is built around reference classes for modelling probabilistic systems, limit-state functions, basic variables, and reliability methods.

classDiagram
    direction TB

    class SYS_PROB {
        +sys_input
        +sys_type
        +probMachines
        +beta_single
        +beta_sys
        +runMachines()
        +calculateSystemProbability()
        +printResults()
    }

    class SYS_PARAM {
        +beta_params
        +res_params
        +runMachines()
    }

    class SYS_LSF {
        +name
        +expr
        +func
        +vars
        +check()
        +getLSF()
    }

    class PARAM_LSF

    class PROB_BASEVAR {
        +Id
        +Name
        +DistributionType
        +Mean
        +Sd
        +prepare()
        +getlDistr()
    }

    class PROB_DETVAR {
        +Value
    }

    class PARAM_BASEVAR {
        +ParamValues
        +ParamType
        +nextParam()
    }

    class PARAM_DETVAR {
        +ParamValues
        +nextParam()
    }

    class PROB_MACHINE {
        +name
        +fCall
        +options
    }

    class PROB_QUALCON {
        +ConformityType
        +ConformityParam
        +NSim
        +DefectLimitLower
        +DefectLimitUpper
        +var
        +getOC()
        +plot()
    }

    SYS_PROB <|-- SYS_PARAM
    SYS_LSF <|-- PARAM_LSF

    PROB_BASEVAR <|-- PROB_DETVAR
    PROB_BASEVAR <|-- PARAM_BASEVAR
    PROB_BASEVAR <|-- PARAM_DETVAR

    SYS_PROB "1" *-- "0..*" SYS_LSF : sys_input
    SYS_PROB "1" *-- "0..*" PROB_MACHINE : probMachines
    SYS_LSF "1" *-- "0..*" PROB_BASEVAR : vars
    PROB_QUALCON "1" o-- "1" PROB_BASEVAR : var

Architecture

TesiproV separates the probabilistic model from the numerical solution algorithms.

The probabilistic model is represented by reference classes:

• SYS_PROB represents a reliability system and combines one or more limit-state functions with one or more analysis methods.
• SYS_LSF defines a limit-state function and its associated basic variables.
• PROB_BASEVAR represents a probabilistic basic variable including its distribution model and parameters.
• PROB_MACHINE stores the configuration of an analysis method.
• SYS_PARAM extends SYS_PROB to perform parametric studies.
• PROB_QUALCON describes a quality-control sampling plan for a basic variable and computes its OC curve. PROB_BASEVAR$updateBasevar() uses it to derive the distribution of the variable after acceptance.

The numerical reliability algorithms are implemented as functions. This includes FORM, SORM, MVFOSM, crude Monte Carlo simulation, importance sampling, and subset simulation.

This separation allows the algorithms to be used both through a SYS_PROB object and directly as standalone functions where appropriate.

Note: The reliability algorithms are intentionally implemented as functions rather than reference classes. This keeps the public API simple and allows direct use of individual methods independently from the system-model classes.

Typical analysis workflow

flowchart LR
    A["Define basic variables<br/>PROB_BASEVAR"] --> B["Define limit-state function<br/>SYS_LSF"]
    B --> C["Configure analysis method<br/>PROB_MACHINE"]
    C --> D["Build reliability system<br/>SYS_PROB"]

    D --> E["Run component analyses<br/>$runMachines()"]
    E --> F["Results<br/>beta_single / res_single"]

    D --> G["Optional system analysis<br/>$calculateSystemProbability()"]
    G --> H["System results<br/>beta_sys / res_sys"]

Installation

The stable release of TesiproV is available on CRAN:

install.packages("TesiproV")

The development version can be installed from the GitLab server of TU Dortmund University:

# install.packages("remotes")
remotes::install_gitlab("ls-massivbau/tesiprov", host = "gitlab.tu-dortmund.de")

Repository: https://gitlab.tu-dortmund.de/ls-massivbau/tesiprov. If you need any permissions, please contact the project authors (see below).

Parallel computing configuration

The Monte Carlo methods MC_CRUDE() and MC_IS() can evaluate the limit-state function in parallel. Without the argument backend they run sequentially on every system. TesiproV never changes the global future plan.

• backend = "future": the chunks are evaluated under the active future plan, which also determines the number of workers. Set the plan yourself:

  future::plan(future::multisession, workers = 4) # Windows
  future::plan(future::multicore, workers = 4)    # Linux / macOS
  

• backend = "parallel": use_threads sets the number of workers (mclapply() on Linux / macOS, a PSOCK cluster on Windows).

All random numbers are generated in the master process. With a fixed seed the result does not depend on the number of workers.

Worker processes (backend multisession or PSOCK) load the installed version of TesiproV. Install the package before running parallel analyses. Loading the source with devtools::load_all() is not sufficient for the workers.

Example

This is a basic example which shows how to define a limit-state function and run a FORM analysis:

library("TesiproV")
Var1 <- PROB_BASEVAR(Id = 1, Name = "X1", DistributionType = "norm", Mean = 0.25, Sd = 1) # kN/m²
Var2 <- PROB_BASEVAR(Id = 2, Name = "X2", DistributionType = "norm", Mean = 0.25, Sd = 1) # m

lsf <- SYS_LSF(vars = list(Var1, Var2), name = "UQLab 2d_hat")
lsf$func <- function(X1, X2) {
  return(20 - (X1 - X2)^2 - 8 * (X1 + X2 - 4)^3)
}

form <- PROB_MACHINE(name = "FORM Rack.-Fieß.", fCall = "FORM")

ps <- SYS_PROB(
  sys_input = list(lsf),
  probMachines = list(form)
)
ps$runMachines()

ps$beta_single
#>                     UQLab 2d_hat
#> FORM Rack.-Fieß. 3.4345652859862

Parametric study example

A simple sweep over different mean values can be performed with PARAM_BASEVAR and SYS_PARAM:

pvar <- PARAM_BASEVAR(
  Name = "E_mod",
  DistributionType = "norm",
  ParamType = "Mean",
  ParamValues = c(30e3, 35e3, 40e3),
  Sd = 3000
)

lsf_param <- SYS_LSF(vars = list(pvar), name = "ParamStudy")
lsf_param$func <- function(E_mod) {
  E_mod / 1000 - 30
}

machine_form <- PROB_MACHINE(name = "FORM", fCall = "FORM")

ps_param <- SYS_PARAM(
  sys_input = list(lsf_param),
  probMachines = list(machine_form)
)
ps_param$runMachines()
print(ps_param$beta_params)

System reliability

SYS_PROB$calculateSystemProbability(calcType, params) evaluates systems of several limit-state functions (sys_type = "serial" or "parallel"). Available methods:

A system analysis by FORM or SORM is not available. SORM and FORM only provide single results that enter the simple bounds.

Quality control and Bayesian updating

PROB_QUALCON defines a sampling plan and computes its OC curve, i.e. the acceptance probability as a function of the defect fraction. The plan is chosen with ConformityType:

• "fck_EN-206": conformity criterion of EN 206 for the compressive strength. ConformityParam = c(n) holds the sample size. The OC curve is simulated, the Monte-Carlo sample size per defect fraction is set with the field NSim (default 100000). The characteristic strength $f_{ck}$ is given as DefectLimitLower.
• "dim_k||n": attribute plan, a lot is accepted if at most c_accept of n units are defective. ConformityParam = c(n, c_accept). A unit is defective if it lies below DefectLimitLower or above DefectLimitUpper. Both limits are freely selectable.

DefectLimitLower and DefectLimitUpper only define when a unit counts as defective. The acceptance criterion is determined by the sampling plan. The OC curve can also be specified manually with theta_grid and Pa_grid.

fc <- PROB_BASEVAR(Id = 1, Name = "fc", DistributionType = "lt",
                   DistributionParameters = c(3.75, 0.105, 3, 10))

plan <- PROB_QUALCON(Name = "EN206_n15", ConformityType = "fck_EN-206",
                     ConformityParam = c(15), DefectLimitLower = 30, var = fc)
plan$getOC()
plan$plot()

fc_post <- fc$updateBasevar(plan)

The prior variable must have the distribution type "st" (Student-t) or "lt" (log-Student-t) with the hyperparameters c(m', s', n', v'). updateBasevar() returns a new PROB_BASEVAR and leaves the prior unchanged.

Recent changes

Version 1.0.0 is a consolidated release based on more than two years of use. It solves single limit-state functions as well as systems.

• New: quality control with PROB_QUALCON (plans "fck_EN-206" and "dim_k||n" with freely selectable defect limits) and Bayesian updating via PROB_BASEVAR$updateBasevar().
• Revised importance sampling for systems ("MCIS") and an overview of the available system methods (see above).
• MC_CRUDE and MC_IS never change the active future plan. Without backend they run sequentially.
• FORM with optim_type = "auto" reports a switch from SLSQP to iHLRF in the result field fallback.
• Parallel workers need the installed package, no further packages have to be installed separately.

Version 0.9.5 introduces major refactoring:

• Improved consistency between probabilistic objects (SYS_PROB, SYS_PARAM, …).
• Corrected implementation of the Gumbel distribution in $prepare().
• Enhanced error handling in $check() for limit-state functions.
• Automatic parallel plan configuration via .onLoad() with capped worker pool (default 4 cores).
• Added new distribution type: Empirical ("emp").

For a complete changelog see NEWS.md.

Further information

For more, check out the vignette! There are plenty more demonstrations and detailed explanations for each object class.

You can open it directly in R:

vignette("TesiproV-Vignette")

Contact & Citation

If you use TesiproV for research or teaching, please cite it as:

Lux T., Nille-Hauf K., Feiri T., Ricker M. (2026): TesiproV — Probabilistic Reliability Analysis Framework. TU Dortmund University.

For questions or bug reports please contact [email protected].

License

TesiproV is licensed under the MIT License.
You are free to use, modify and redistribute the software provided that the original copyright notice and license terms are retained.

© 2021-2026 Til Lux, Konstantin Nille-Hauf, Tania Feiri, Marcus Ricker — TU Dortmund University / Hochschule Biberach.