Optimization or Bayesian strategy? Performance of the Bhattacharyya distance in different algorithms of stochastic model updating

The Bhattacharyya distance has been developed as a comprehensive uncertainty quantification metric by capturing multiple uncertainty sources from both numerical predictions and experimental measurements. This work pursues a further investigation of the performance of the Bhattacharyya distance in different methodologies for stochastic model updating, and thus to prove the universality of the Bhattacharyya distance in various currently popular updating procedures. The first procedure is the Bayesian model updating where the Bhattacharyya distance is utilized to define an approximate likelihood function and the transitional Markov chain Monte Carlo algorithm is employed to obtain the posterior distribution of the parameters. In the second updating procedure, the Bhattacharyya distance is utilized to construct the objective function of an optimization problem. The objective function is defined as the Bhattacharyya distance between the samples of numerical prediction and the samples of the target data. The comparison study is performed on a four degrees-of-freedom mass-spring system. A challenging task is raised in this example by assigning different distributions to the parameters with imprecise distribution coefficients. This requires the stochastic updating procedure to calibrate not the parameters themselves, but their distribution properties. The second example employs the GARTEUR SM-AG19 benchmark structure to demonstrate the feasibility of the Bhattacharyya distance in the presence of practical experiment uncertainty raising from measuring techniques, equipment, and subjective randomness. The results demonstrate the Bhattacharyya distance as a comprehensive and universal uncertainty quantification metric in stochastic model updating

A Generalized Bayesian Approach to Model Calibration

In model development, model calibration and validation play complementary roles toward learning reliable models. In this article, we expand the Bayesian Validation Metric framework to a general calibration and validation framework by inverting the validation mathematics into a generalized Bayesian method for model calibration and regression. We perform Bayesian regression based on a user's definition of model-data agreement. This allows for model selection on any type of data distribution, unlike Bayesian and standard regression techniques, that "fail" in some cases. We show that our tool is capable of representing and combining least squares, likelihood-based, and Bayesian calibration techniques in a single framework while being able to generalize aspects of these methods. This tool also offers new insights into the interpretation of the predictive envelopes (also known as confidence bands) while giving the analyst more control over these envelopes. We demonstrate the validity of our method by providing three numerical examples to calibrate different models, including a model for energy dissipation in lap joints under impact loading. By calibrating models with respect to the validation metrics one desires a model to ultimately pass, reliability and safety metrics may be integrated into and automatically adopted by the model in the calibration phase

Exploration based design methodology using the theory of constraints in extending plastics manufacturing for novel high performing fabrics

2022 Summer.Includes bibliographical references.The world of textiles is comprised of several materials. From the conventional, such as cotton and silk, to the contemporary, such as polyester and nylon, textiles have changed over time. Nonwovens, a category of material frequently referred to as the "third-generation" of textiles, have emerged as one of the most exciting breakthroughs in the textile industry during the past few years. Nonwovens, which are frequently confused with fibers, yarns, and fabrics, have evolved as a new category of versatile material with medicinal and industrial applications. An issue associated with the use of lightweight nonwovens is their single-use, in which a fabric weight category can be employed for only one product. The number of products per weight class that can be utilized in businesses that utilize the materials is limited. Therefore, companies utilizing these textiles in their operations must engage with plastic producers to plan, implement, and develop a single weight class for a single product. This procedure is time-consuming and generates plastic waste because of unfinished fabrics. By creating a multipurpose nonwoven fabric, organizations will be able to improve their operations by saving time and energy, improving profits, decreasing plastic waste, and enabling process innovation. To use a fabric with the same weight and similar physical properties in a different product, a different fabric is manufactured for that process, despite the similarity in weight and physical properties between the fabric used in the previous process and the fabric needed for the new process. Due to this limitation, the concept of redesigning nonwoven materials for different applications was conceived. Air Permeability, a barrier to airflow, is a significant component in the inability to support numerous uses. When a fabric's desired attribute is not satisfied, the fabric's air permeability can be optimized by utilizing a variety of process approaches to attain the appropriate performance qualities. This permits the use of a single fabric in a variety of items. Due to the fabric's weight and volume, the usage of nonwoven in aviation and public works has expanded drastically. Thermal insulation is one of the most prevalent applications of nonwoven materials in the aviation industry. Nonwoven fabrics are also utilized as dynamic biofilters for filtration in public works, with an aerobic layer that aids in the recovery of alkalinity in the filtration systems used in these facilities. The two significant outcomes of this research are (1) Improvement of the airflow barrier, also known as air permeability (AP), which enables the use of a single weight class to make several goods as opposed to a single weight class for a single product, and the addition of a thermal barrier to the fabric. Permeability enhancements in nonwovens enhance the fabric's sound absorption, filtration, and heat absorption. (2) The capacity to recycle undesired nonwoven fabrics following production, as opposed to disposing of the plastic components in landfills. Nonwovens are semi-crystalline polypropylene plastics that are not easily biodegradable due to the strong chemical bond between the polypropylene polymers. Because polypropylenes, which are plastics, are not biodegradable, unused nonwoven fabrics are landfilled. It was through the process of prototyping that a subsystem alteration was made that enabled the development of nonwoven fabric with better air permeability. Design as Exploration concepts are used to accomplish this. Reicofil I, II, III, and IV are the four nonwoven production systems used in this research to develop the novel fabric. In addition, this study has handled another issue by reusing and recycling unwanted fabrics to reduce the amount of plastic waste in landfills. An extrusion method that recycles rejected and waste fabrics were the result of these approaches. The innovative method used in developing the new nonwoven fabric is being explored for use in the production of plastic films to improve the quality of goods made with polyethylene plastic polymers

컴퓨터 모델 내 오류 원인 식별을 위한 최적화 기반 모델 개선 기법 연구

학위논문(박사) -- 서울대학교대학원 : 공과대학 기계항공공학부, 2021.8. 윤병동.컴퓨터 이용 공학 기술의 활용도가 증가함에 따라, 각 공학분야에서는 보다 정확한 예측 능력을 가진 컴퓨터 모델을 필요로 하게 되었다. 많은 연구결과를 통해, 신뢰도 높은 계산모델을 얻기 위한 공학기술들이 개발되었다. 최적화 기반 모델 향상 기술은 계산모델 예측도 향상을 위한 공학기술 중 하나로, 모델 보정, 모델 검증, 그리고 모델 개선 과정을 포함하고 있다. 모델 보정은 계산 모델 내 미지변수의 값을 역으로 추정하는 기술이다. 모델 검증은 예측 성능의 정확도를 판단한다. 계산모델 내 미지 오류 원인이 존재하면 모델 개선을 통해 미지 원인을 탐색하는 작업을 수행한다. 최적화 기반 모델향상기술 내 세가지 세부 기술들은 모델 관련 사전 정보의 양에 따라 유기적으로, 혹은 개별적으로도 수행이 가능하다. 모델 향상 기술이 계산모델 내 영향을 주는 다양한 오류원인을 고려하여 수행되고 있으나, 최적화 기반 모델 향상기술은 여전히 계산모델의 정확도를 증가시키는데 한계점을 지니고 있다. 시험 데이터 및 계산 모델 내 다양한 오류 소스들이 결합되어 있어, 최적화 기반 모델 향상 기술은 이 오류원인들을 구분하고 각 오류원인들에 대해 적합한 솔루션을 제공하기에 부적합하다. 따라서, 이러한 문제점을 해결하고자 본 박사학위논문에서는 (1) 파라미터 추정 오류 감소를 위한 시험 설계 기법, (2) 모델 보정 시 모델링 및 시험 오류의 양을 정량화 하기 위한 비율 편향도 정량화 기법 (3) 2종 오류에 강건한 통계기반 검증 척도 비교 연구를 제안하고자 한다. 첫 번째 연구에서는 파라미터 추정 오류를 최소화하기 위한 시험 설계법 개발을 목표로 한다. 여기서 결정된 시험설계안은 모델 보정 시 사용될 시험 데이터 취득을 위한 시험 설계를 뜻한다. 계산모델 내 발생하는 모델링 오류, 그리고 시험데이터 취득 시 발생하는 계측오류 등은 모델 보정에서 정확한 파라미터 값의 추정을 방해한다. 파라미터 추정 오류를 포함한 계산모델은 주어진 시험데이터를 잘 모사하는 것처럼 보이지만, 파라미터를 과도하게 편향된 값으로 추정하여 모델링 오류를 보완한 결과이다. 이 경우, 모델 검증 시 모델이 유효하다고 판단될 수 있지만 실제로는 파라미터 추정오류와 모델링 오류를 동시에 갖고 있으므로 다양한 설계조건에서 유효하지 않은 모델이다. 따라서, 본 연구에서는 파라미터 추정오류와 모델링 오류를 구분하여 정확한 모델 검증을 유도하고자 한다. 파라미터 추정오류와 모델링 오류는 그 정도를 각각 정량화 하는 것이 불가능하므로, 파라미터 추정오류를 가장 최소화 할 수 있는 시험데이터의 종류와 취득위치를 선정할 수 있는 시험설계법을 고안하였다. 이를 위해, (1) 파라미터 추정오류를 수식적으로 유도하였고, (2) 유도된 식 내에서 사용자가 제어할 수 있는 일부항을 최소화 하도록 하였다. 제안된 시험설계법은 파라미터 추정오류와 모델링 오류를 구분하고, 모델 검증 시 유효 및 불유효의 원인이 모델링오류가 될 수 있도록 한다. 두 번째 연구에서는 파라미터 추정오류를 개선하기 위해 모델 보정 시 모델링 오류에 의한 성능 저하량을 정량화 할 수 있는 비율 편향 보정 기법을 제안한다. 첫 번째 연구에서 제안한 시험설계법은 별도의 추가 시험 데이터 없이 파라미터 추정 오류와 모델링 오류를 구분해 낼 수 있는 최선의 방법론 이지만, 모델링 오류 및 시험 오류의 영향이 큰 경우 파라미터 추정오류를 획기적으로 개선하는데 한계가 있다. 오류의 영향도가 큰 모델은 추정 파라미터의 값이 엔지니어가 가진 경험, 혹은 물리 기반 정보에 위배되는 지점으로 수렴할 수 있다. 따라서, 본 연구에서는 관측데이터 외 미지 모델 변수의 물리적 정보를 활용하여 모델링 오류 및 관측오류에 의한 성능저하도의 양을 정량화 하고자 한다. 연구에서 제안된 ‘비율편향’ 은 오류에 의한 성능저하도를 성능값의 일정한 비율로 가정하여, 모델 보정 시 최적화 알고리즘 내에서 미지모델변수와 함께 최적 값이 추정되는 항이다. 비율편향 항과 미지모델 변수가 사전의 물리적 정보에 위배되지 않는 범위 내에서 추정될 수 있도록 미지모델 변수의 범위 정보를 최적화 알고리즘의 제한조건으로 활용한다. 비율편향 보정기법은 미지모델변수의 추정값이 모델링 오류에 의한 성능저하를 보완하기 위해 과도하게 편향된 값으로 최적화 되는 현상을 바로잡을 수 있다. 세 번째 연구에서는 모델 검증 시 발생할 수 있는 결정 오류를 개선하기 위해 통계적 검증 척도의 선택 기준을 제시하고자 한다. 모델 검증은 주로 통계기반 방법인 가설검증을 활용하여 모델의 유효 및 불유효를 결정한다. 가설검증은 제 1종 오류 및 제 2종 오류의 발생 가능성을 갖고 있다. 제 2종 오류는 불유효한 모델을 유효하다고 판단하는 오류로써 실제 산업분야에 치명적인 사고를 유발할 수 있다. 본 연구에서는 제 2종 오류를 가장 적게 발생 시킬 수 있는 통계적 검증 척도를 분석하기 위해 다음과 같은 조건에서의 검증 정확도 비교 연구를 수행한다. 1) 관측 및 예측 성능의 분산이 같고 평균값의 차이로 인해 예측 성능이 불유효 한 경우, 2) 관측 및 예측성능의 평균보다 분산값의 차이로 인해 예측 성능이 불유효 한 경우. 비교연구는 모델 파라미터의 분산 정도를 4가지로 세분화 하고 관측 데이터 개수에 의한 정확도 차이를 비교하고자 관측 데이터를 3개에서 30개까지 증가시켰다. 그 결과, 성능 간 평균의 차이를 잘 정량화 하는 검증척도 및 성능 간 분산의 차이를 잘 정량화 하는 검증척도를 제안할 수 있었다. 제안된 검증척도의 평균지향 및 분산지향 특성을 증명하고자, 평균지향 척도의 극한값을 유도하여 분산값의 증가 시 척도의 값이 최대값에 도달하지 않아 검증 오류가 발생할 수 있음을 확인하였다.The increased use of computer-aided engineering (CAE) in recent years requires a more accurate prediction capability in computational models. Therefore, extensive studies have considered engineering strategies to achieve highly credible computational models. Optimization-based model improvement (OBMI), which includes model calibration, validation, and refinement, is one crucial technique that has emerged to enhance the prediction ability of computational models. Model calibration is the process of estimating unknown input parameters in a computational model. Model validation presents a judgement of the accuracy of a predicted response. If it is possible for a computational model to have model form uncertainties, model refinement explores unrecognized error sources of a computational model. OBMI can adopt these three processes individually or sequentially, according to the trustworthiness of the prior knowledge of the computational modeling. Although OBMI process improvements have emerged to try to consider the major sources of errors, OBMI can still suffer from a failure to improve a computational model. Since numerous error sources in an experimental and computational model are intertwined with each other, OBMI has difficulty identifying the error sources required to enable accurate prediction ability of the computational model. Thus, eventually, OBMI may fail to propose an appropriate solution. To cope with this challenge, this doctoral dissertation research addresses three essential issues: 1) Research Thrust 1 – a new experimental design approach for model calibration to reduce parameter estimation errors; 2) Research Thrust 2) – a device bias quantification method for considering model form errors with bound information; and, Research Thrust 3) – comparison of statistical validation metrics to consider type II errors in model validation. Research Thrust 1: A variety of sources of errors in observation and prediction can interrupt the model improvement process. These error sources degrade the parameter estimation accuracy of the model calibration. When a computational model turns out to be invalid because of these error sources, the OBMC process performs model refinement. However, since model validation cannot distinguish between parameter estimation errors and modeling errors, it is difficult for the existing method to efficiently refine the computational model. Thus, this study aims to develop a model improvement process that identifies the leading cause of invalidity of a prediction. In this work, an experimental design method is integrated with optimization-based model improvement to minimize the effect of estimation errors in model calibration. Through use of the proposed method, after calibration, the computational model mainly includes the effects of unrecognized modeling errors. Research Thrust 2: The experimental design method proposed in Research Thrust 1 has the advantage of being able to identify two error sources without additional observation. However, model calibration still suffers from parameter estimation errors, since experimental design is affected by model form errors. The parameters estimated by model calibration are often unreasonable for engineers in practical settings because they have expert-based prior knowledge about the model parameters. Among the variety of physical information available, bound information about model parameters is a suitable constraint in optimization-based model calibration (OBMC). Using prior information about parameter bounds, Research Thrust 2 devises proportionate bias calibration to quantify the amount of degradation of the predicted responses that is due to model form errors in a computational model. The bias term is estimated in the optimization-based model calibration (OBMC) algorithm with unknown parameters to enable OBMC to support accurate estimation of unknown parameters within a prior bound. This study proposes a new formulation of a bias term that depends on the output responses to resolve the gap in appropriate bias that arises due to the different dimensions of the predicted responses. Research Thrust 3: Statistical model validation (SMV) evaluates the accuracy of a computational model’s predictions. In SMV, hypothesis testing is used to determine the validity or invalidity of a prediction, based on the value of a statistical validation metric that quantifies the difference between the predicted and observed results. Errors in hypothesis testing decisions are troublesome when evaluating the accuracy of a computational model, since an invalid model might be used in practical engineering design activities and incorrect results in these settings may lead to safety issues. This research compares various statistical validation metrics to highlight those that show fewer errors in hypothesis testing. The resulting work provides a statistical validation metric that is sensitive to a discrepancy in the mean or variance of the two distributions from the predictions and observations. Statistical validation metrics examined in this study include Kullback-Leibler divergence, area metric with U-pooling, Bayes factor, likelihood, probability of separation, and the probability residual.Chapter 1 Introduction 1 1.1 Motivation 1 1.2 Research Scope and Overview 8 1.3 Dissertation Layout 13 Chapter 2 Literature Review: Optimization-based and Bayesian-based Model Improvement 14 2.1 Optimization-based Model Improvement (OBMI) 14 2.1.1 Model Calibration 15 2.1.2 Model Validation 18 2.1.3 Model Refinement 22 2.2 Bayesian-based Model Improvement with Bias Correction 25 2.3 Summary and Discussion 28 Chapter 3 Experimental Design for Identifying Error Sources Between Parameter Estimation Errors and Model Form Errors 31 3.1 Coupled Error Sources in Model Calibration 33 3.2 Optimization-based Model Improvement with Experimental Design 37 3.2.1 Derivation of Parameter Estimation Errors in Model Calibration 37 3.2.2 Identification of Error Sources by Employing Experimental Design 39 3.3 Case Studies 42 3.3.1 Analytical Case Study: Cantilever Beam Model 43 3.3.2 Engineering Case Study: Automotive Wheel Rim FEM Model 52 3.4 Summary and Discussion 64 Chapter 4 Proportionate Bias Calibration with Bound Information to Consider Unrecognized Model Form Errors 66 4.1 Limitations of Experimental Design for OBMI with the Effect of Model Form Errors 68 4.2 Proportionate Bias Calibration with Bound Information of Model Parameters 71 4.2.1 The Formulation of Proportionate Bias 71 4.2.2 Proportionate Bias Calibration with Bound Information of Unknown Model Parameters 74 4.3 Case Studies 76 4.3.1 Analytical Case Study: Cantilever Beam Model 77 4.3.2 Engineering Case Study 1: Automotive Wheel Rim FEM Model 82 4.3.3 Engineering Case Study 2: Automotive Steering Column Assembly FEM model 86 4.4 Summary and Discussion 92 Chapter 5 Comparison of Statistical Validation Metrics to Reduce Type II Errors in Model Validation 94 5.1 Brief Review of Statistical Validation Metrics 97 5.1.1 Area metric 100 5.1.2 Likelihood 100 5.1.3 Kullback-Leibler Divergence (KLD) 101 5.1.4 Bayes Factor 101 5.1.5 Probability of Separation (PoS) 102 5.1.6 Probability Residual (PR) 102 5.2 A comparison study of statistical validation metrics 103 5.2.1 Problem definition 103 5.2.2 Results of statistical model validation accuracy 108 5.3 Discussion and Demonstration 116 5.3.1 Discussion about the low accuracy of the area metric in a variance change 116 5.3.2 Discussion about the low accuracy of the Probability of Separation (PoS) in a variance change 121 5.4 Case Study 124 5.5 Summary and Discussion 132 Chapter 6 Conclusion 134 6.1 Contributions and Significance 134 6.2 Suggestions for Future Research 137 Appendix A Analytical Derivation of Probability of Separation (PoS) with Normal and Lognormal Distribution 140 A.1 Analytical Derivation of PoS Metric with a Normal Distribution 141 A.2 Analytical Derivation of PoS Metric with a Lognormal Distribution 143 References 147 국문 초록 159박

Configuración de rutinas de capacidad de absorción

Esta disertación doctoral presenta el diseño e implementación de un producto de software (simulador por computador) de una propuesta modelo del constructo ?capacidad de absorción? (ACAP) para organizaciones. La ACAP es un constructo que describe la capacidad dinámica de las organizaciones para detectar en su entorno el conocimiento que puede serle útil, incorporarlo en sus procesos y aplicarlo para sacarle provecho. Esta investigación propone un modelo implementable en computador de ACAP que asiste a los tomadores de decisión de la organización en la configuración de esta capacidad dinámica. La propuesta del modelo se fundamenta en la consolidación conceptual de las interrelaciones de las nociones de adquisición de tecnología, difusión, adopción, adaptación, apropiación, aceptación, asimilación y compatibilidad tecnológica para derivar en innovación tecnológica que impacta interna y externamente a la organización, con la generación de ventajas competitivas, incremento en la productividad y, como novedad, impactos positivos en el desarrollo económico en donde se inscribe la organización. Las ideas básicas que conforman la implementación del modelo son: (i) la dinámica evolutiva del conocimiento organizacional y (ii) la estructura del conocimiento organizacional implementada por medio de rutinas organizacionales. A partir de la implementación de un simulador basado en agentes, la validación con usuarios expertos permite concluir que el conocimiento organizacional es esencialmente un saber-hacer que evoluciona en el tiempo y que permite la adaptación de la organización a su entorno cambiante.This doctoral dissertation introduces the design and implementation of a software product (computer simulator) implementing a proposal for a model of the ‘absorptive capacity’ (ACAP) construct for organizations. ACAP is a construct describing the dynamic capacity of organizations to identify knowledge in its environment potentially useful, assimilate it and exploit it. This research proposes a computer implementable model of ACAP to assist decision makers when configuring this dynamic capacity. The model proposed is founded in the conceptual consolidation of the interactions of the notions of technology acquisition, diffusion, adoption, adaptation, appropriation, acceptance, assimilation an compatibility to derive in technological innovation that impacts internally and externally an organization, generating competitive advantages, productivity increases and, considered as completely new, positive impacts in economic development in the context were the organization resides. Basic ideas underlying the model implementation are: (i) evolutionary dynamics of organizational knowledge and (ii) organizational knowledge implemented by means of organizational routines. Since the implementation of an agent-based simulator, expert user validation leads to infer that organizational knowledge is essentially a know-how evolving in time in order to allow adaptation of the organization to its changing environment.Doctor en IngenieríaDoctorad

Modular Bayesian uncertainty assessment for structural health monitoring

Civil infrastructure are critical elements to a society’s welfare and economic thriving. Understanding their behaviour and monitoring their serviceability are relevant challenges of Structural Health Monitoring (SHM). Despite the impressive improvement of miniaturisation, standardisation and diversity of monitoring systems, the ability to interpret data has registered a much slower progression across years. The underlying causes for such disparity are the overall complexity of the proposed challenge, and the inherent errors and lack of information associated with it. Overall, it is necessary to appropriately quantify the uncertainties which undermine the SHM concept. This thesis proposes an enhanced modular Bayesian framework (MBA) for structural identification (st-id) and measurement system design (MSD). The framework is hybrid, in the sense that it uses a physics-based model, and Gaussian processes (mrGp) which are trained against data, for uncertainty quantification. The mrGp act as emulators of the model response surface and its model discrepancy, also quantifying observation error, parametric and interpolation uncertainty. Finally, this framework has been enhanced with the Metropolis–Hastings for multiple parameters st-id. In contrast to other probabilistic frameworks, the MBA allows to estimate structural parameters (which reflect a performance of interest) consistently with their physical interpretation, while highlighting patterns of a model’s discrepancy. The MBA performance can be substantially improved by considering multiple responses which are sensitive to the structural parameters. An extension of the MBA for MSD has been validated on a reduced-scale aluminium bridge subject to thermal expansion (supported at one end with springs and instrumented with strain gauges and thermocouples). A finite element (FE) model of the structure was used to obtain a semi-optimal sensor configuration for stid. Results indicate that 1) measuring responses which are sensitive to the structural parameters and are more directly related to model discrepancy, provide the best results for st-id; 2) prior knowledge of the model discrepancy is essential to capture the latter type of responses. Subsequently, an extension of the MBA for st-id was also applied for identification of the springs stiffness, and results indicate relative errors five times less than other state of the art Bayesian/deterministic methodologies. Finally, a first application to field data was performed, to calibrate a detailed FE model of the Tamar suspension bridge using long-term monitored data. Measurements of temperature, traffic, mid-span displacement and natural frequencies of the bridge, were used to identify the bridge’s main/stay cables initial strain and friction of its bearings. Validation of results suggests that the identified parameters agree more closely with the true structural behaviour of the bridge, with an error that is several orders of magnitude smaller than other probabilistic st-id approaches. Additionally, the MBA allowed to predicted model discrepancy functions to assess the predictive ability of the Tamar bridge FE model. It was found, that the model predicts more accurately the bridge mid-span displacements than its natural frequencies, and that the adopted traffic model is less able to simulate the bridge behaviour during periods of traffic jams. Future developments of the MBA framework include its extension and application for damage detection and MSD with multiple parameter identification