Distribution-free stochastic simulation methodology for model updating under hybrid uncertainties

In the real world, a significant challenge faced in the safe operation and maintenance of infrastructures is the lack of available information or data. This results in a large degree of uncertainty and the requirement for robust and efficient uncertainty quantification (UQ) tools in order to derive the most realistic estimates of the behavior of structures. While the probabilistic approach has long been utilized as an essential tool for the quantitative mathematical representation of uncertainty, a common criticism is that the approach often involves insubstantiated subjective assumptions because of the scarcity or imprecision of available information. To avoid the inclusion of subjectivity, the concepts of imprecise probabilities have been developed, and the distributional probability-box (p-box) has gained the most attention among various types of imprecise probability models since it can straightforwardly provide a clear separation between aleatory and epistemic uncertainty. This thesis concerns the realistic consideration and numerically efficient calibraiton and propagation of aleatory and epistemic uncertainties (hybrid uncertainties) based on the distributional p-box. The recent developments including the Bhattacharyya distance-based approximate Bayesian computation (ABC) and non-intrusive imprecise stochastic simulation (NISS) methods have strengthened the subjective assumption-free approach for uncertainty calibration and propagation. However, these methods based on the distributional p-box stand on the availability of the prior knowledge determining a specific distribution family for the p-box. The target of this thesis is hence to develop a distribution-free approach for the calibraiton and propagation of hybrid uncertainties, strengthening the subjective assumption-free UQ approach. To achieve the above target, this thesis presents five main developments to improve the Bhattacharyya distance-based ABC and NISS frameworks. The first development is on improving the scope of application and efficiency of the Bhattacharyya distance-based ABC. The dimension reduction procedure is proposed to evaluate the Bhattacharyya distance when the system under investigation is described by time-domain sequences. Moreover, the efficient Bayesian inference method within the Bayesian updating with structural reliability methods (BUS) framework is developed by combining BUS with the adaptive Kriging-based reliability method, namely AK-MCMC. The second development of the distribution-free stochastic model updating framework is based on the combined application of the staircase density functions and the Bhattacharyya distance. The staircase density functions can approximate a wide range of distributions arbitrarily close; hence the development achieved to perform the Bhattacharyya distance-based ABC without limiting hypotheses on the distribution families of the parameters having to be updated. The aforementioned two developments are then integrated in the third development to provide a solution to the latest edition (2019) of the NASA UQ challenge problem. The model updating tasks under very challenging condition, where prior information of aleatory parameters are extremely limited other than a common boundary, are successfully addressed based on the above distribution-free stochastic model updating framework. Moreover, the NISS approach that simplifies the high-dimensional optimization to a set of one-dimensional searching by a first-order high-dimensional model representation (HDMR) decomposition with respect to each design parameter is developed to efficiently solve the reliability-based design optimization tasks. This challenge, at the same time, elucidates the limitations of the current developments, hence the fourth development aims at addressing the limitation that the staircase density functions are designed for univariate random variables and cannot acount for the parameter dependencies. In order to calibrate the joint distribution of correlated parameters, the distribution-free stochastic model updating framework is extended by characterizing the aleatory parameters using the Gaussian copula functions having marginal distributions as the staircase density functions. This further strengthens the assumption-free approach for uncertainty calibration in which no prior information of the parameter dependencies is required. Finally, the fifth development of the distribution-free uncertainty propagation framework is based on another application of the staircase density functions to the NISS class of methods, and it is applied for efficiently solving the reliability analysis subproblem of the NASA UQ challenge 2019. The above five developments have successfully strengthened the assumption-free approach for both uncertainty calibration and propagation thanks to the nature of the staircase density functions approximating arbitrary distributions. The efficiency and effectiveness of those developments are sufficiently demonstrated upon the real-world applications including the NASA UQ challenge 2019

Hierarchical Bayesian Inversion for Quantification of Mixed Aleatory and Epistemic Uncertainties in Model Parameters

The 20th working conference of the IFIP Working Group 7.5 on Reliability and Optimization of Structural Systems (IFIP 2022) will be held at Kyoto University, Kyoto, Japan, September 19-20, 2022.Uncertainties in the model parameters need to be properly characterized for the reliable and economic performance assesment of structures using a numerical model. Since not all parameters are trivial to measure directly, inverse uncertainty quantification (UQ) techniques, which infer the non-determinism in the model parameters by the measurments of the structural responses, are often necessary. Among such techniques, the class of Bayesian methods has been widely accepted as a coherent probabilistic approach to handle uncertainties in the inverse UQ. However, the main drawback of the conventional Bayesian methods is that they cannot quantify the inherent variability in the model parameters which causes the random failure of the structure. To fill this gap, the hierarchical Bayesian methods have gained increasing attention, in which a proability distribution is assigned to the model parameters to characterize their variability while its hyperparameters are treated as epistemic uncertainty and updated through Bayesian scheme. The first author and his co-workers have recently developed the hierarchical Bayesian approach using the staircase density function (SDF). This approach can consider the lack-of-knowledge on the distribution formats as epistemic uncertainty and infer the true-but-unknown distribution by updating the hyperparameters of SDF. This paper amis to illustrate its fundamental ideas and demonstrate its applicability to the estimation of a broad range of distributions through simple numerical test examples

Bayesian Model Updating in Time Domain with Metamodel-Based Reliability Method

In this study, a two-step approximate Bayesian computation (ABC) updating framework using dynamic response data is developed. In this framework, the Euclidian and Bhattacharyya distances are utilized as uncertainty quantification (UQ) metrics to define approximate likelihood functions in the first and second steps, respectively. A new Bayesian inference algorithm combining Bayesian updating with structural reliability methods (BUS) with the adaptive Kriging model is then proposed to effectively execute the ABC updating framework. The performance of the proposed procedure is demonstrated with a seismic-isolated bridge model updating application using simulated seismic response data. This application denotes that the Bhattacharyya distance is a powerful UQ metric with the capability to recreate wholly the distribution of target observations, and the proposed procedure can provide satisfactory results with much reduced computational demand compared with other well-known methods, such as transitional Markov chain Monte Carlo (TMCMC)

Pilot study of a basic individualized cognitive behavioral therapy program for chronic pain in Japan

Background: Chronic pain is a major health problem, and cognitive behavioral therapy (CBT) is its recommended treatment; however, efforts to develop CBT programs for chronic pain and assess their feasibility are remarkably delayed in Asia. Therefore, we conducted this pilot study to develop a basic individualized CBT for chronic pain (CBT-CP) and assessed its feasibility for use in Japan. Methods: Our study was an open-labeled before–after trial without a control group conducted cooperatively in five Japanese tertiary care hospitals. Of 24 outpatients, 15, age 20–80, who experienced chronic pain for at least three months were eligible. They underwent an eight-session CBT-CP consisting of relaxation via a breathing method and progressive muscle relaxation, behavioral modification via activity pacing, and cognitive modification via cognitive reconstruction. The EuroQol five-dimensional questionnaire five level (EQ5D-5 L) assessment as the primary outcome and quality of life (QOL), pain severity, disability, catastrophizing, self-efficacy, and depressive symptoms as secondary outcomes were measured using self-administered questionnaires at baseline, post-treatment, and 3-month follow-up. Intention-to-treat analyses were conducted. Results: Effect size for EQ5D-5 L score was medium from baseline to post-treatment (Hedge’s g = − 0.72, 90% confidence interval = − 1.38 to − 0.05) and up to the 3-month follow-up (g = − 0.60, CI = − 1.22 to 0.02). Effect sizes for mental and role/social QOL, disability, catastrophizing, self-efficacy, and depressive symptoms were medium to large, although those for pain severity and physical QOL were small. The dropout rate was acceptably low at 14%. No severe adverse events occurred. Conclusion: The findings suggest that CBT-CP warrants a randomized controlled trial in Japan

Literature survey on epidemiology and pathology of gangliocytic paraganglioma

<p>Abstract</p> <p>Background</p> <p>Although gangliocytic paraganglioma (GP) has generally been regarded as a neuroendocrine tumor, its origin remains unclear. We therefore aimed to investigate the details of this disease by carefully analyzing and extracting common features of the disease as presented in selected publications.</p> <p>Methods</p> <p>We searched for English and Japanese cases of GP using the PubMed and IgakuChuoZasshi databases on August 2010. We then extracted and sampled raw data from the selected publications and performed appropriate statistical analyses. Additionally, we evaluated the expression of hormone receptors based on our previously reported case.</p> <p>Results</p> <p>192 patients with GP were retrieved from the databases. Patient ages ranged from 15 y to 84 y (mean: 52.3 y). The gender ratio was 114:76 (male to female, 2 not reported). Maximum diameter of the tumors ranged from 5.5 mm to 100 mm (mean: 25.0 mm). The duodenum (90.1%, 173/192) was found to be the most common site of the disease. In 173 patients with duodenal GP, gastrointestinal bleeding (45.1%, 78/173) was found to be the most common symptom of the disease, followed by abdominal pain (42.8%, 74/173), and anemia (14.5%, 25/173). Rate of lymph node metastasis was 6.9% (12/173). Our statistical analysis indicated that significant differences were found for gender between GP within the submucosal layer and exceeding the submucosal layer. Furthermore, our immunohistochemical evaluation showed that both epithelioid and pancreatic islet cells showed positive reactivity for progesterone receptors.</p> <p>Conclusions</p> <p>Our literature survey revealed that there were many more cases of GP exceeding the submucosal layer than were expected. Meanwhile, our statistical analyses and immunohistochemical evaluation supported the following two hypotheses. First, vertical growth of GP might be affected by progesterone exposure. Second, the origin of GP might be pancreatic islet cells. However, it is strongly suspected that our data have been affected by publication bias and to confirm these hypotheses, further investigation is required.</p

Bayesian updating with two-step parallel Bayesian optimization and quadrature

This work proposes a Bayesian updating approach, called parallel Bayesian optimization and quadrature (PBOQ). It is rooted in Bayesian updating with structural reliability methods (BUS) and offers a coherent Bayesian approach for the BUS analysis by assuming Gaussian process priors. The first step of the method, i.e., parallel Bayesian optimization, effectively explores a constant c in BUS by a novel parallel infill sampling strategy. The second step (parallel Bayesian quadrature) then infers the posterior distribution by another parallel infill sampling strategy using subset simulation. The proposed approach enables to make the fullest use of prior knowledge and parallel computing, resulting in a substantial reduction of the computational burden of model updating. Four numerical examples with varying complexity are investigated for demonstrating the proposed method against several existing methods. The results show the potential benefits by advocating a coherent Bayesian fashion to the BUS analysis