Linking big models to big data: efficient ecosystem model calibration through Bayesian model emulation

Data-model integration plays a critical role in assessing and improving our capacity to predict ecosystem dynamics. Similarly, the ability to attach quantitative statements of uncertainty around model forecasts is crucial for model assessment and interpretation and for setting field research priorities. Bayesian methods provide a rigorous data assimilation framework for these applications, especially for problems with multiple data constraints. However, the Markov chain Monte Carlo (MCMC) techniques underlying most Bayesian calibration can be prohibitive for computationally demanding models and large datasets. We employ an alternative method, Bayesian model emulation of sufficient statistics, that can approximate the full joint posterior density, is more amenable to parallelization, and provides an estimate of parameter sensitivity. Analysis involved informative priors constructed from a meta-analysis of the primary literature and specification of both model and data uncertainties, and it introduced novel approaches to autocorrelation corrections on multiple data streams and emulating the sufficient statistics surface. We report the integration of this method within an ecological workflow management software, Predictive Ecosystem Analyzer (PEcAn), and its application and validation with two process-based terrestrial ecosystem models: SIPNET and ED2. In a test against a synthetic dataset, the emulator was able to retrieve the true parameter values. A comparison of the emulator approach to standard brute-force MCMC involving multiple data constraints showed that the emulator method was able to constrain the faster and simpler SIPNET model's parameters with comparable performance to the brute-force approach but reduced computation time by more than 2 orders of magnitude. The emulator was then applied to calibration of the ED2 model, whose complexity precludes standard (brute-force) Bayesian data assimilation techniques. Both models are constrained after assimilation of the observational data with the emulator method, reducing the uncertainty around their predictions. Performance metrics showed increased agreement between model predictions and data. Our study furthers efforts toward reducing model uncertainties, showing that the emulator method makes it possible to efficiently calibrate complex models.</p

Markov chain Monte Carlo with Gaussian processes for fast parameter estimation and uncertainty quantification in a 1D fluid‐dynamics model of the pulmonary circulation

The past few decades have witnessed an explosive synergy between physics and the life sciences. In particular, physical modelling in medicine and physiology is a topical research area. The present work focuses on parameter inference and uncertainty quantification in a 1D fluid‐dynamics model for quantitative physiology: the pulmonary blood circulation. The practical challenge is the estimation of the patient‐specific biophysical model parameters, which cannot be measured directly. In principle this can be achieved based on a comparison between measured and predicted data. However, predicting data requires solving a system of partial differential equations (PDEs), which usually have no closed‐form solution, and repeated numerical integrations as part of an adaptive estimation procedure are computationally expensive. In the present article, we demonstrate how fast parameter estimation combined with sound uncertainty quantification can be achieved by a combination of statistical emulation and Markov chain Monte Carlo (MCMC) sampling. We compare a range of state‐of‐the‐art MCMC algorithms and emulation strategies, and assess their performance in terms of their accuracy and computational efficiency. The long‐term goal is to develop a method for reliable disease prognostication in real time, and our work is an important step towards an automatic clinical decision support system

복잡한 공학 시스템에 대한 오경보를 고려한 리질리언스 해석 및 설계 방법론 연구

학위논문 (박사)-- 서울대학교 대학원 : 공과대학 기계항공공학부, 2018. 2. 윤병동.it estimates a healthy engineered to be faulty, resulting unnecessary system shutdown, inspection, and – in the case of incorrect inspection – unnecessary system repair or replacement. Although false alarms make a system unavailable with capital loss, it has not been considered in resilience engineering. To cope with false alarm problems, this research is elaborated to advance the resilience engineering considering false alarms. Specifically, this consists of three research thrusts: 1) resilience analysis considering false alarms, 2) resilience-driven system design considering false alarms (RDSD-FA), and 3) resilience-driven system design considering time-dependent false alarms (RDSD-TFA). In the first research thrust, a resilience measure is newly formulated considering false alarms. This enables the evaluation of resilience decrease due to false alarms, resulting in accurate analysis of system resilience. Based upon the new resilience measure, RDSD-FA is proposed in the second research thrust. This aims at designing a resilient system to satisfy a target resilience level while minimizing life-cycle cost. This is composed of three hierarchical tasks: resilience allocation problem, reliability-based design optimization (RBDO), and PHM design. The third research thrust presents RDSD-TFA that considers time-dependent variability of an engineered system. This makes one to estimate life-cycle cost in an accurate and rigorous manner, and to design an engineered system more precisely while minimizing its life-cycle cost. The framework of RDSD-TFA consists of four tasks: system analysis, PHM analysis, life-cycle simulation, and design optimization. Through theoretical analysis and case studies, the significance of false alarms in engineering resilience and the effectiveness of the proposed ideas are demonstrated.공학 시스템은 생애주기에 걸쳐 다양한 불확실성에 노출되며, 이로 인해 목표 성능을 충족시키지 못할 경우 사회적, 경계적, 인적 소실을 야기하게 된다. 이에 대한 해결 방안 중 하나로 리질리언스 주도 설계 기술 (resilience-driven system design이하 RDSD)이 개발되었다. RDSD는 건전성 예측 및 관리 기술 (prognostics & health management이하 PHM)을 설계에 도입함으로써 비용 효율적인 고장 예방을 가능케 하였다. 하지만, RDSD는 PHM의 고장 오경보 현상을 고려하지 않는 한계점을 갖는다. 고장 오경보는 건전한 시스템을 고장이라 추정하는 현상으로, 불필요한 시스템 정지 및 검사 비용을 야기하여, PHM과 RDSD의 기술적 효용성을 떨어트리게 된다. 따라서, RDSD의 기술적 약진과 실적용을 도모하기 위해서는 고장 오경보 현상을 해결해야 한다. 본 논문에서는 고장 오경보의 고려를 통해 리질리언스 해석 및 설계 방법론을 개선하고자 하며, 이를 위해 세 가지 연구 주제를 제안한다. 첫 번째 주제는 오경보를 고려한 리질리언스 분석으로, 공학 시스템의 리질리언스 시나리오 분석에 기반해 리질리언스 지수를 새롭게 정식화 한다. 이 지수는 고장 오경보로 인한 리질리언스의 저하를 분석함으로써, 정확한 리질리언스 추정을 가능케 한다. 두 번째 주제는 고장 오경보를 고려한 리질리언스 주도 설계 방법론이다. 이는 3단계의 계층적 요소로 구성된다. 먼저 목표 리질리언스 지수를 만족하면서 생애주기비용을 최소화하기 위해, 목표 신뢰도와 목표 오경보 및 유실경보율을 최적화한다. 이후 신뢰성 기반 최적 설계 (reliability-based design optimization)를 통해 목표 신뢰도를 확보하고, PHM 설계를 통해 할당된 목표 오경보 및 유실경보율을 충족시킨다. 세 번째 주제는 시변(時變) 오경보를 고려한 리질리언스 주도 설계 방법론이다. 기존의 설계 방법론들은 시스템의 건전성 상태를 시불변(時不變)하다 간주하였으나, 실제 시스템은 운행에 따라 점진적으로 건전성이 저하된다. 본 연구에서는 시변성을 분석하기 위해 시변 오경보율 및 유실경보율에 대한 개념을 새롭게 제안하였으며, 생애주기 시뮬레이션을 통한 총 유지보수 비용 분석 방법론을 개발하였다. 이를 통해 생애주기비용을 보다 엄밀하고 정확하게 추정할 수 있게 되었으며, 이를 최소화하는 방향으로 시스템과 PHM의 설계를 최적화였다. 본 연구에서 제안한 방법론들은 이론적 분석과 사례 연구를 통해 그 효용성을 입증하였다.Most engineered systems are designed with a passive and fixed design capacity and, therefore, may become unreliable in the presence of adverse events. In order to handle this issue, the resilience-driven system design (RDSD) has been proposed to make engineered systems adaptively reliable by incorporating the prognostics and health management (PHM) method. PHM tracks the health degradation of an engineered system, and provides health state information supporting decisions on condition-based maintenance. Meanwhile, one of the issues awaiting solution in the field of PHM, as well as in RDSD, is to address false alarms. A false alarm is an erroneous report on the health state of an engineered systemChapter 1. Introduction 1 1.1 Motivation 1 1.2 Research Scope and Overview 3 1.3 Dissertation Layout 6 Chapter 2. Literature Review 7 2.1 Resilience Engineering (Analysis and Design) 7 2.1.1 Resilience Analysis for Mechanical Systems 8 2.1.2 Resilience-Driven System Design (RDSD) for Mechanical Systems 15 2.2 False and Missed Alarms in Prognostics and Health Management 27 2.2.1 Definition of False and Missed Alarms 27 2.2.2 Quantification of False and Missed Alarms 32 2.3 Summary and Discussion 35 Chapter 3. Resilience Analysis Considering False Alarms 37 3.1 Resilience Measure Considering False Alarms 37 3.2 Case Studies 42 3.2.1 Numerical ample 42 3.2.2 Electro-Hydrtatic Actuator (EHA) 44 3.3 Summary and Discussion 53 Chapter 4. Resilience-Driven System Design Considering False Alarms (RDSD-FA) 55 4.1 Overview of RDSD-FA Framework 55 4.2 Resilience Allocation Problem Considering False Alarms 56 4.3 Prognostics and Health Management (PHM) Design Considering False Alarms 60 4.4 Case study: Electro-Hydrostatic Actuator (EHA) 61 4.4.1 Step 1: Resilience Allocation Considering False Alarms 61 4.4.2 Step 2: Reliability-Based Design Optimization 64 4.4.3 Step 3: PHM Design Considering False Alarms 68 4.4.4 Comparison of Design Results from RDSD and RDSD-FA 73 4.5 Summary and Discussion 75 Chapter 5. Resilience-Driven System Design Considering Time-Dependent False Alarms (RDSD-TFA) 77 5.1 Time-Dependent False and Missed Alarms in PHM 79 5.2 Resilience-Driven System Design Considering Time-Dependent False Alarms (RDSD-TFA) 83 5.2.1 Overview of RDSD-TFA Framework 83 5.2.2 Task 1: System Analysis 86 5.2.3 Task 2: PHM Analysis 89 5.2.4 Task 3: Life-Cycle Simulation 91 5.2.5 Task 4: Design Optimization 97 5.3 Case studies 98 5.3.1 Numerical Example of Life-Cycle Simulation 98 5.3.2 Electro-Hydrostatic Actuator (EHA) 107 5.4 Summary and Discussion 123 Chapter 6. Conclusions 126 6.1 Summary and Contributions 126 6.2 Suggestions for Future Research 129 References 132 Appendix 154 Abstract(Korean) 157Docto

Bayesian parameter estimation and uncertainty quantification in fluid-dynamics models of the pulmonary circulation system

The past few decades have witnessed an explosive synergy between physics and the life sciences. In particular, physical modelling in medicine and physiology is a topical research area. The present work focuses on the inverse problem, more specifically on the parameter inference and uncertainty quantification in a 1D fluid-dynamics model for quantitative physiology: the pulmonary blood circulation. The particular application is pulmonary hypertension, requiring an analysis of the blood pressure, whose measurement in the pulmonary system can only be obtained invasively for patients. The ultimate goal is to develop a non-invasive disease diagnostication method. This could be accomplished by combining non-invasively obtained haemodynamic data (blood flow measured with MRI) with imaging data (CT scans of the lung structure), to be used in conjunction with mathematical and statistical modelling. This will provide a decision-making support mechanism in the clinic, ultimately aiding in personalised medicine. This thesis adopts a Bayesian approach to uncertainty quantification in physiological models, allowing to assess the credibility of these models. The danger with using overly confident models is that they could produce biased predictions, ultimately leading to the wrong disease diagnosis and treatment. Inference of unknown and immeasurable parameters of several 1D fluid-dynamics models, expressed through partial differential equations, is performed with Markov Chain Monte Carlo. These parameters act as bio-indicators for the disease, e.g. vessel wall stiffness, which is high in pulmonary hypertension patients. In addition, the uncertainty in the model form and the data measurement process (jointly called model mismatch) is captured, and the model mismatch is represented with Gaussian Processes. Given that the mathematical model is not a perfect representation of the reality, and that the data measurement process is prone to errors, this introduces an extra layer of uncertainty. If unaccounted for, the result is biased and overly confident parameter estimates and model predictions. Yet another source of uncertainty modelled in this study is the variability in the vessel network geometry, connectivity and size, which is shown to introduce variability in the model predictions, and must be accounted for. The uncertainty in the model parameters, model form, data measurement process and vessel network propagates through to the model predictions, which is also quantified. Lastly, this thesis is concerned with accelerating the computational efficiency of the statistical inference procedure, aiming to make the methods suitable for use in the clinic. Statistical emulation is used in conjunction with a series of efficient Hamiltonian Monte Carlo algorithms, particularly adapted to computationally expensive models. A comparative evaluation study is carried out to identify the algorithm giving the best trade-off between accuracy and efficiency on a set of representative benchmark differential equation models

The Application of Contemporary Numerical Methods to the Modeling, Analysis, and Uncertainty Quantification of Glacier Dynamics

Warming temperatures have led to accelerating ice loss from the Greenland ice sheet, contributing to global sea level rise. Understanding the stability of the Greenland ice sheet to further warming is crucial to estimating rates of sea level rise over the next century. Estimating sea level rise is complicated by uncertainties in the physical mechanisms governing ice motion as well as uncertainties in the broader Arctic climate system of which the ice sheet is an integral part. In chapter 2, we focus on how surface melt water input to the ice sheet bed influences the rate of basal sliding, which is thought to depend on the seasonal evolution of the subglacial drainage system. Models of subglacial drainage have developed considerably in recent years. However, the recent sublglacial hydrology model intercomparison project (SHMIP), presented in Appendix A, shows that a wide gamut of models underpredict subglacial water pressure in winter when compared to borehole water pressure observations from Greenland. We investigate possible causes for this unphysical model behavior, ranging from poorly constrained model parameters to uncertainties in the physical equations for subglacial drainage. We conclude that the mismatch between modeled and observed winter water pressure can be remedied by dynamically adjusting the hydraulic conductivity parameter, which accounts for missing physics in the models describing seasonal changes in drainage system connectivity. Chapter 3 focuses on contextualizing modern climate change in the Arctic by investigating past changes in temperature and precipitation. In particular, we exploit a new chronology of ice sheet retreat in west Central Greenland, along with a novel data assimilation method based on the unscented transform (UT), to estimate changes in precipitation during the Holocene Thermal Maximum (HTM) -- a period of higher than modern temperatures that occurred some eight-thousand years ago. We demonstrate the effectiveness of the UT as a method for data assimilation and uncertainty quantification and show new evidence that the HTM was associated with greater than modern snowfall, which helped mitigate ice sheet retreat