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Statistical model improvement consists of model calibration, validation, and refinement techniques. It aims to increase the accuracy of computational models. Although engineers in industrial fields are expanding the use of computational models in the process of product development, many field engineers still hesitate to perform statistical model improvement due to its practical aspects. Therefore, this paper describes research aimed at addressing three practical issues that hinder statistical model improvement in industrial fields: (1) lack of experimental data for quantifying uncertainties of true responses, (2) numerical input variables for propagating uncertainties of the computational model, and (3) model form uncertainties in the computational model. Issues 1 and 2 deal with difficulties in uncertainty quantification of experimental and computational responses. Issue 3 focuses on model form uncertainties, which are due to the excessive simplification of computational modeling; simplification is employed to reduce the calculation cost. Furthermore, the paper outlines solutions to address these three issues, specifically: (1) kernel density estimation with estimated bounded data, (2–1) variance-based variable screening, (2–2) surrogate modeling, and (3) a model refinement approach. By examining the computational model of an automobile steering column, these techniques are shown to demonstrate efficient statistical model improvement. This case study shows that the suggested approaches can actively reduce the burden in statistical model improvement and increase the accuracy of computational modeling, thereby encouraging its use in industry. [ABSTRACT FROM AUTHOR]

The use of parametric and nonparametric statistical modeling methods differs depending on data sufficiency. For sufficient data, the parametric statistical modeling method is preferred owing to its high convergence to the population distribution. Conversely, for insufficient data, the nonparametric method is preferred owing to its high flexibility and conservative modeling of the given data. However, it is difficult for users to select either a parametric or nonparametric modeling method because the adequacy of using one of these methods depends on how well the given data represent the population model, which is unknown to users. For insufficient data or limited prior information on random variables, the interval approach, which uses interval information of data or random variables, can be used. However, it is still difficult to be used in uncertainty analysis and design, owing to imprecise probabilities. In this study, to overcome this problem, an integrated statistical modeling (ISM) method, which combines the parametric, nonparametric, and interval approaches, is proposed. The ISM method uses the two-sample Kolmogorov–Smirnov (K–S) test to determine whether to use either the parametric or nonparametric method according to data sufficiency. The sequential statistical modeling (SSM) and kernel density estimation with estimated bounded data (KDE-ebd) are used as the parametric and nonparametric methods combined with the interval approach, respectively. To verify the modeling accuracy, conservativeness, and convergence of the proposed method, it is compared with the original SSM and KDE-ebd according to various sample sizes and distribution types in simulation tests. Through an engineering and reliability analysis example, it is shown that the proposed ISM method has the highest accuracy and reliability in the statistical modeling, regardless of data sufficiency. The ISM method is applicable to real engineering data and is conservative in the reliability analysis for insufficient data, unlike the SSM, and converges to an exact probability of failure more rapidly than KDE-ebd as data increase. [ABSTRACT FROM AUTHOR]

The uncertainties of input variables are quantified as probabilistic distribution functions using parametric or nonparametric statistical modeling methods for reliability analysis or reliability-based design optimization. However, parametric statistical modeling methods such as the goodness-of-fit test and the model selection method are inaccurate when the number of data is very small or the input variables do not have parametric distributions. To deal with this problem, kernel density estimation with bounded data (KDE-bd) and KDE with estimated bounded data (KDE-ebd), which randomly generates bounded data within given input variable intervals for given data and applies them to generate density functions, are proposed in this study. Since the KDE-bd and KDE-ebd use input variable intervals, they attain better convergence to the population distribution than the original KDE does, especially for a small number of given data. The KDE-bd can even deal with a problem that has one data with input variable bounds. To verify the proposed method, statistical simulation tests were carried out for various numbers of data using multiple distribution types and then the KDE-bd and KDE-ebd were compared with the KDE. The results showed the KDE-bd and KDE-ebd to be more accurate than the original KDE, especially when the number of data is less than 10. It is also more robust than the original KDE regardless of the quality of given data, and is therefore more useful even if there is insufficient data for input variables. [ABSTRACT FROM AUTHOR]

To accurately analyze behavior of mechanical system, accurate statistical modeling of input variables is necessary by identifying probabilistic distributions of input variables. These distributions are generally determined by applying goodness-of-fit (GOF) tests or model selection methods to the given data on the input variables. However, GOF tests only accept or reject the hypothesis that a candidate distribution is appropriate to represent the given data. The model selection methods determine the best-fit distribution for the given data among various candidate distributions but do not provide any information about the adequacy of using the identified distribution to represent the given data. Therefore, in this paper, a sequential statistical modeling (SSM) method is proposed. The SSM method uses a GOF test to select appropriate candidate distributions from among all possible distributions and then identifies the best-fit distribution from among the selected candidate distributions using a model selection method. The adequacy of the identified best-fit distribution is verified by using an area metric that measures the intersection area between the probability density function (PDF) of the best-fit distribution and the data distribution. This metric can be used to analyze the similarities between the PDFs of the candidate distributions. In statistical simulation tests, it was observed that the SSM method identified correct distributions more accurately and conservatively than the GOF tests or model selection methods alone. [ABSTRACT FROM AUTHOR]