Uncertainty quantification and statistical model validation for an offshore jacket structure panel given limited test data and simulation model

Due to inherent variability (i.e., aleatory uncertainty) in material properties, loading conditions, manufacturing processes, etc., simulation output responses should follow certain distributions, which are the outcome of input distribution models and simulation models. Thus, uncertainty quantification (UQ) using simulation-based methods is accurate only if we have (1) accurate input distribution models and (2) an accurate simulation model. However, in practical engineering applications, only limited numbers of input test data are available for modeling input distributions. Moreover, the simulation model could be biased due to assumptions and idealizations in the modeling process. Thus, the simulation model needs to be validated to correctly predict the output response of the physical system. The statistical validation of the simulation model would require large numbers of physical test data, which is extremely expensive. This study presents a computational method to obtain a target output distribution, which is a good approximation of the true output distribution given limited test data and a biased model. Using Bayesian analysis, possible candidates of output distribution are obtained, and a target output distribution is selected at the posterior median. The target output distribution is used to measure the bias of the simulation models and the surrogate models for UQ and statistical model validation. Furthermore, the cumulative distribution function of the simulation model prediction error is presented to provide (1) the median of model prediction error and (2) model confidence at a user-specified error level. To demonstrate the proposed statistical model validation method, a simulation model of an offshore jacket structure panel is generated using ANSYS. This example has eight uncertain input parameters (six of them are geometrical parameters and two of them are material properties). For input distributions of geometrical parameters, the standard deviation of manufacturing tolerances is used, and three material tests are carried out to obtain input distributions of two material properties. The output response of interest is a reaction force. The simulation model is validated using three sets of material test data and experimental test data to determine model confidence on output prediction and the validity of the simulation model. The result of statistical model validation shows how much bias the simulation model has and how much confidence engineers can have in the model prediction at a user-specified error level.

AKDE:

Adaptive KDE

AM:

Addictively manufactured

ASTM:

American Society for Testing and Material

CAE:

Computer-aided engineering

CDF:

Cumulative distribution function

DKG:

Dynamic kriging

FEA:

Finite element analysis

f _x :

Input PDF

h(y^e; h₀):

Local bandwidth in AKDE

h ₀ :

Global fixed bandwidth for modeling output distribution

K :

Kernel

KDE:

Kernel density estimation

M :

Number of MCS samples

MAE:

Mean absolute error

MAP:

Maximum a posteriori probability

MCMC:

Markov chain Monte Carlo

MCS:

Monte Carlo simulation

MLE:

Maximum likelihood estimation

MSE:

Mean squared error

nx, ny :

Number of input and output test data

UTM:

Universal testing machine

UQ:

Uncertainty quantification

PDF:

Probability density function

P(h₀):

Prior distribution of bandwidth

P(h₀|y^e):

Posterior distribution of bandwidth given output data

STD:

Standard deviation

\( {\mathbf{y}}_i^e,{\mathbf{y}}^e \) :

i^th output data and output data vector

x ^e :

Input data vector

\( \hat{\boldsymbol{\uptheta}} \) :

Input distribution parameter vector

This research was supported by a grant from Endowment Project of “Study on the Core Technology of Structural Design, Engineering and Test for Establishment of Structural Evaluation System for Offshore Structure” funded by Korea Research Institute of Ships and Ocean engineering (PES3250). The authors wish to acknowledge the technical and financial support of a joint project between the University of Iowa and the Korea Research Institute of Ships and Ocean Engineering (KRISO), as well as technical support from RAMDO Solutions, LLC.

Authors and Affiliations

1. Department of Mechanical Engineering, College of Engineering, The University of Iowa, Iowa, IA, 52242, USA

   Min-Yeong Moon & K.K. Choi

2. Korea Research Institute of Ships & Ocean Engineering, Daejeon, 34103, Republic of Korea

   Hyun-Seok Kim, Kangsu Lee & Byoungjae Park

Corresponding author

Correspondence to K.K. Choi.

Conflict of interest

The authors declare that they have no conflict of interest.

Replication of results

As the model cannot be published due to confidential issue of the funded project, detail explanation about how the simulation model for the offshore structure panel can be modeled using ANSYS is given in Section 2. Detail algorithm of sampling-based Bayesian analysis used to obtain target output distribution is given in the reference Moon et al. (2019b). Algorithm to obtain approximated input distribution given limited number of data (Fig. 5) is presented as below.

1. Step 1:

   Obtain sample mean and standard deviation of input data for each of input random variables for which limited number of data is provided. If paired data is correlated, sample Kendall’s tau is evaluated.

2. Step 2:

   Transform sample mean and standard deviation into two distribution parameters for each of six candidates of marginal input distribution (Normal, Lognormal, Weibull, Gumbel, Extreme1, and Extreme II) (Table 4).

3. Step 3:

   Evaluate likelihood value for each of six candidate distributions and select one that provides maximum likelihood value.

Responsible Editor: Erdem Acar

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