Description Usage Arguments Details Value References Examples
Use modified ABC-MCMC algorithm to obtain posterior samples of θ = (μ_a, σ_a, μ_b, σ_b, μ_c, σ_c, μ_n, σ_n, μ_σ0 , σ_σ0), given ramp and constant load failure time data.
1 |
n |
number of posterior samples |
numBurning |
number of burn-in iterations |
numThining |
number of thining iterations |
inputD |
bandwidth δ for ABC approximation |
dataNames |
a vector of strings of the names of the datasets, which must be in the format "ID_(τ_c)_(t_c)Y" (see Details and Example) |
verbose |
displays information messages to console if TRUE |
The generated posterior samples are the parameters associated with (a, b, c, n, η), which are the random effects in the Canadian Model for load duration,
d/dt α(t) = [(a * τ_s) * (τ(t) / τ_s - σ_0)_+]^b + [(c * τ_s) * (τ(t) / τ_s - σ_0)_+]^n * α(t),
where
- a|μ_a, σ_a ~ Log-Normal(μ_a, σ_a);
- b|μ_b, σ_b ~ Log-Normal(μ_b, σ_b);
- c|μ_c, σ_c ~ Log-Normal(μ_c, σ_c);
- n|μ_n, σ_n ~ Log-Normal(μ_n, σ_n);
- η|μ_σ0, σ_σ0 ~ Log-Normal(μ_σ0, σ_σ0) and set σ_0 = η / (1 + η).
* (x)_+ = max(x, 0).
* σ_0 serves as the stress ratio threshold in that damage starts to accumulate only when τ(t)/τ_s > σ_0.
* When sample pieces are subject to the load profile
τ(t) = kt if t <= T_0
τ(t) = τ_c if t > T_0
where τ_c is the selected constant-load level under the ramp-loading rate k, and T_0 is the time required for the load to reach τ_c under the ramp-loading rate k.
* The constant load level is assumed to be reached at the ramp-loading rate (k). The ramp-loading rate is 388,440 psi/hour.
* The constant load test ends at time t_c (in years).
* To achieve a ramp-load test, set τ_c to Inf
.
Returns a matrix of posterior samples where each row is one θ, and if verbose is TRUE, prints the acceptance rate.
Foschi, R. O., Folz, B., and Yao, F. (1989), Reliability-Based Design of Wood Structures (Vol. 34), Vancouver, BC: Department of Civil Engineering, University of British Columbia.
Wong, S. W., & Zidek, J. V. (2018). Dimensional and statistical foundations for accumulated damage models. Wood science and technology, 52(1), 45-65.
Yang, C. H., Zidek, J. V., & Wong, S. W. (2019). Bayesian analysis of accumulated damage models in lumber reliability. Technometrics, 61(2), 233-245.
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