178 research outputs found

    An adaptive multi-fidelity optimization framework based on co-Kriging surrogate models and stochastic sampling with application to coastal aquifer management

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    Surrogate modelling has been used successfully to alleviate the computational burden that results from high-fidelity numerical models of seawater intrusion in simulation-optimization routines. Nevertheless, little attention has been given to multi-fidelity modelling methods to address cases where only limited runs with computationally expensive seawater intrusion models are considered affordable imposing a limiting factor for single-fidelity surrogate-based optimization as well. In this work, a new adaptive multi-fidelity optimization framework is proposed based on co-Kriging surrogate models considering two model fidelities of seawater intrusion. The methodology is tailored to the needs of solving pumping optimization problems with computationally expensive constraint functions and utilizes only small high-fidelity training datasets. Results from both hypothetical and real-world optimization problems demonstrate the efficiency and practicality of the proposed framework to provide a steep improvement of the objective function while it outperforms a comprehensive single-fidelity surrogate-based optimization method. The method can also be used to locate optimal solutions in the region of the global optimum when larger high-fidelity training datasets are available

    A Computational Framework for Efficient Reliability Analysis of Complex Networks

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    With the growing scale and complexity of modern infrastructure networks comes the challenge of developing efficient and dependable methods for analysing their reliability. Special attention must be given to potential network interdependencies as disregarding these can lead to catastrophic failures. Furthermore, it is of paramount importance to properly treat all uncertainties. The survival signature is a recent development built to effectively analyse complex networks that far exceeds standard techniques in several important areas. Its most distinguishing feature is the complete separation of system structure from probabilistic information. Because of this, it is possible to take into account a variety of component failure phenomena such as dependencies, common causes of failure, and imprecise probabilities without reevaluating the network structure. This cumulative dissertation presents several key improvements to the survival signature ecosystem focused on the structural evaluation of the system as well as the modelling of component failures. A new method is presented in which (inter)-dependencies between components and networks are modelled using vine copulas. Furthermore, aleatory and epistemic uncertainties are included by applying probability boxes and imprecise copulas. By leveraging the large number of available copula families it is possible to account for varying dependent effects. The graph-based design of vine copulas synergizes well with the typical descriptions of network topologies. The proposed method is tested on a challenging scenario using the IEEE reliability test system, demonstrating its usefulness and emphasizing the ability to represent complicated scenarios with a range of dependent failure modes. The numerical effort required to analytically compute the survival signature is prohibitive for large complex systems. This work presents two methods for the approximation of the survival signature. In the first approach system configurations of low interest are excluded using percolation theory, while the remaining parts of the signature are estimated by Monte Carlo simulation. The method is able to accurately approximate the survival signature with very small errors while drastically reducing computational demand. Several simple test systems, as well as two real-world situations, are used to show the accuracy and performance. However, with increasing network size and complexity this technique also reaches its limits. A second method is presented where the numerical demand is further reduced. Here, instead of approximating the whole survival signature only a few strategically selected values are computed using Monte Carlo simulation and used to build a surrogate model based on normalized radial basis functions. The uncertainty resulting from the approximation of the data points is then propagated through an interval predictor model which estimates bounds for the remaining survival signature values. This imprecise model provides bounds on the survival signature and therefore the network reliability. Because a few data points are sufficient to build the interval predictor model it allows for even larger systems to be analysed. With the rising complexity of not just the system but also the individual components themselves comes the need for the components to be modelled as subsystems in a system-of-systems approach. A study is presented, where a previously developed framework for resilience decision-making is adapted to multidimensional scenarios in which the subsystems are represented as survival signatures. The survival signature of the subsystems can be computed ahead of the resilience analysis due to the inherent separation of structural information. This enables efficient analysis in which the failure rates of subsystems for various resilience-enhancing endowments are calculated directly from the survival function without reevaluating the system structure. In addition to the advancements in the field of survival signature, this work also presents a new framework for uncertainty quantification developed as a package in the Julia programming language called UncertaintyQuantification.jl. Julia is a modern high-level dynamic programming language that is ideal for applications such as data analysis and scientific computing. UncertaintyQuantification.jl was built from the ground up to be generalised and versatile while remaining simple to use. The framework is in constant development and its goal is to become a toolbox encompassing state-of-the-art algorithms from all fields of uncertainty quantification and to serve as a valuable tool for both research and industry. UncertaintyQuantification.jl currently includes simulation-based reliability analysis utilising a wide range of sampling schemes, local and global sensitivity analysis, and surrogate modelling methodologies

    Machine learning algorithms for efficient process optimisation of variable geometries at the example of fabric forming

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    FĂŒr einen optimalen Betrieb erfordern moderne Produktionssysteme eine sorgfĂ€ltige Einstellung der eingesetzten Fertigungsprozesse. Physikbasierte Simulationen können die Prozessoptimierung wirksam unterstĂŒtzen, jedoch sind deren Rechenzeiten oft eine erhebliche HĂŒrde. Eine Möglichkeit, Rechenzeit einzusparen sind surrogate-gestĂŒtzte Optimierungsverfahren (SBO1). Surrogates sind recheneffiziente, datengetriebene Ersatzmodelle, die den Optimierer im Suchraum leiten. Sie verbessern in der Regel die Konvergenz, erweisen sich aber bei verĂ€nderlichen Optimierungsaufgaben, etwa hĂ€ufigen Bauteilanpassungen nach Kundenwunsch, als unhandlich. Um auch solche variablen Optimierungsaufgaben effizient zu lösen, untersucht die vorliegende Arbeit, wie jĂŒngste Fortschritte im Maschinenlernen (ML) – im Speziellen bei neuronalen Netzen – bestehende SBO-Techniken ergĂ€nzen können. Dabei werden drei Hauptaspekte betrachtet: erstens, ihr Potential als klassisches Surrogate fĂŒr SBO, zweitens, ihre Eignung zur effiziente Bewertung der Herstellbarkeit neuer BauteilentwĂŒrfe und drittens, ihre Möglichkeiten zur effizienten Prozessoptimierung fĂŒr variable Bauteilgeometrien. Diese Fragestellungen sind grundsĂ€tzlich technologieĂŒbergreifend anwendbar und werden in dieser Arbeit am Beispiel der Textilumformung untersucht. Der erste Teil dieser Arbeit (Kapitel 3) diskutiert die Eignung tiefer neuronaler Netze als Surrogates fĂŒr SBO. Hierzu werden verschiedene Netzarchitekturen untersucht und mehrere Möglichkeiten verglichen, sie in ein SBO-Framework einzubinden. Die Ergebnisse weisen ihre Eignung fĂŒr SBO nach: FĂŒr eine feste Beispielgeometrie minimieren alle Varianten erfolgreich und schneller als ein Referenzalgorithmus (genetischer Algorithmus) die Zielfunktion. Um die Herstellbarkeit variabler Bauteilgeometrien zu bewerten, untersucht Kapitel 4 anschließend, wie Geometrieinformationen in ein Prozess-Surrogate eingebracht werden können. Hierzu werden zwei ML-AnsĂ€tze verglichen, ein merkmals- und ein rasterbasierter Ansatz. Der merkmalsbasierte Ansatz scannt ein Bauteil nach einzelnen, prozessrelevanten Geometriemerkmalen, der rasterbasierte Ansatz hingegen interpretiert die Geometrie als Ganzes. Beide AnsĂ€tze können das Prozessverhalten grundsĂ€tzlich erlernen, allerdings erweist sich der rasterbasierte Ansatz als einfacher ĂŒbertragbar auf neue Geometrievarianten. Die Ergebnisse zeigen zudem, dass hauptsĂ€chlich die Vielfalt und weniger die Menge der Trainingsdaten diese Übertragbarkeit bestimmt. Abschließend verbindet Kapitel 5 die Surrogate-Techniken fĂŒr flexible Geometrien mit variablen Prozessparametern, um eine effiziente Prozessoptimierung fĂŒr variable Bauteile zu erreichen. Hierzu interagiert ein ML-Algorithmus in einer Simulationsumgebung mit generischen Geometriebeispielen und lernt, welche Geometrie, welche Umformparameter erfordert. Nach dem Training ist der Algorithmus in der Lage, auch fĂŒr nicht-generische Bauteilgeometrien brauchbare Empfehlungen auszugeben. Weiter zeigt sich, dass die Empfehlungen mit Ă€hnlicher Geschwindigkeit wie die klassische SBO zum tatsĂ€chlichen Prozessoptimum konvergieren, jedoch kein bauteilspezifisches A-priori-Sampling nötig ist. Einmal trainiert, ist der entwickelte Ansatz damit effizienter. Insgesamt zeigt diese Arbeit, wie ML-Techniken gegenwĂ€rtige SBOMethoden erweitern und so die Prozess- und Produktoptimierung zu frĂŒhen Entwicklungszeitpunkten effizient unterstĂŒtzen können. Die Ergebnisse der Untersuchungen mĂŒnden in Folgefragen zur Weiterentwicklung der Methoden, etwa die Integration physikalischer Bilanzgleichungen, um die Modellprognosen physikalisch konsistenter zu machen

    Uncertainty analysis of structural output with closed-form expression based on surrogate model

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    Uncertainty analysis (UA) is the process that quantitatively identifies and characterizes the output uncertainty and has a crucial implication in engineering applications. The research of efficient estimation of structural output moments in probability space plays an important part in the UA and has great engineering significance. Given this point, a new UA method based on the Kriging surrogate model related to closed-form expressions for the perception of the estimation of mean and variance is proposed in this paper. The new proposed method is proven effective because of its direct reflection on the prediction uncertainty of the output moments of metamodel to quantify the accuracy level. The estimation can be completed by directly using the redefined closed-form expressions of the model's output mean and variance to avoid excess post-processing computational costs and errors. Furthermore, a novel framework of adaptive Kriging estimating mean (AKEM) is demonstrated for more efficiently reducing uncertainty in the estimation of output moment. In the adaptive strategy of AKEM, a new learning function based on the closed-form expression is proposed. Based on the closed-form expression which modifies the computational error caused by the metamodeling uncertainty, the proposed learning function enables the updating of metamodel to reduce prediction uncertainty efficiently and realize the decrease in computational costs. Several applications are introduced to prove the effectiveness and efficiency of the AKEM compared with a universal adaptive Kriging method. Through the good performance of AKEM, its potential in engineering applications can be spotted

    Practical metamodel-assisted multi-objective design optimization for improved sustainability and buildability of wind turbine foundations

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    [EN] In this work, we study the potential of using kriging metamodelling to perform multi-objective structural design optimization using finite element analysis software and design standards while keeping the computational efforts low. A method is proposed, which includes sustainability and buildability objectives, and it is applied to a case study of reinforced concrete foundations for wind turbines based on data from a large Swedish wind farm project. Sensitivity analyses are conducted to investigate the influence of the penalty factor applied to unfeasible solutions and the size of the initial sample generated by Latin hypercube sampling. A multi-objective optimization is then performed to obtain the optimum designs for different weight combinations for the four objectives considered. Results show that the kriging-obtained designs from samples of 20 designs outperform the best designs in the samples of 1000 designs. The optimum designs obtained by the proposed method have a sustainability impact 8Âż15% lower than the designs developed by traditional methods.Open access funding provided by Chalmers University of Technology. This work was fnancially supported by Sweden's Innovation Agency (Grant Number: 2017-03312), the Swedish Transport Administration (Grant Number: BBT-2017- 037), the Swedish Wind Power Technology Centre (SWPTC), NCC, and Grant PID2020-117056RB-I00 funded by MCIN/AEI/ 10.13039/501100011033 and by ERDF A way of making Europe.Mathern, A.; PenadĂ©s-PlĂ , V.; Armesto Barros, J.; Yepes, V. (2022). Practical metamodel-assisted multi-objective design optimization for improved sustainability and buildability of wind turbine foundations. Structural and Multidisciplinary Optimization. 65(46):1-16. https://doi.org/10.1007/s00158-021-03154-0S1166546Boscardin JT, Yepes V, Kripka M (2019) Optimization of reinforced concrete building frames with automated grouping of columns. 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    Sensitivity analysis of agent-based models: a new protocol

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    Agent-based models (ABMs) are increasingly used in the management sciences. Though useful, ABMs are often critiqued: it is hard to discern why they produce the results they do and whether other assumptions would yield similar results. To help researchers address such critiques, we propose a systematic approach to conducting sensitivity analyses of ABMs. Our approach deals with a feature that can complicate sensitivity analyses: most ABMs include important non-parametric elements, while most sensitivity analysis methods are designed for parametric elements only. The approach moves from charting out the elements of an ABM through identifying the goal of the sensitivity analysis to specifying a method for the analysis. We focus on four common goals of sensitivity analysis: determining whether results are robust, which elements have the greatest impact on outcomes, how elements interact to shape outcomes, and which direction outcomes move when elements change. For the first three goals, we suggest a combination of randomized finite change indices calculation through a factorial design. For direction of change, we propose a modification of individual conditional expectation (ICE) plots to account for the stochastic nature of the ABM response. We illustrate our approach using the Garbage Can Model, a classic ABM that examines how organizations make decisions

    A Probabilistic Machine Learning Approach for the Uncertainty Quantification of Electronic Circuits Based on Gaussian Process Regression

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    This paper introduces a probabilistic machine learning framework for the uncertainty quantification (UQ) of electronic circuits based on Gaussian process regression (GPR). As opposed to classical surrogate modeling techniques, GPR inherently provides information on the model uncertainty. The main contribution of this work is twofold. First, it describes how, in an UQ scenario, the model uncertainty can be combined with the uncertainty of the input design parameters to provide confidence bounds for the statistical estimates of the system outputs, such as moments and probability distributions. These confidence bounds allows assessing the accuracy of the predicted statistics. Second, in order to deal with dynamic multi-output systems, principal component analysis (PCA) is effectively employed to compress the time-dependent output variables into a smaller set of components, for which the training of individual GPR models becomes feasible. The uncertainty on the principal components is then propagated back to the original output variables. Several application examples, ranging from a trivial RLC circuit to real-life designs, are used to illustrate and validate the advocated approach

    Managing computational complexity through using partitioning, approximation and coordination

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    Problem: Complex systems are composed of many interdependent subsystems with a level of complexity that exceeds the ability of a single designer. One way to address this problem is to partition the complex design problem into smaller, more manageable design tasks that can be handled by multiple design teams. Partitioning-based design methods are decision support tools that provide mathematical foundations, and computational methods to create such design processes. Managing the interdependency among these subsystems is crucial and a successful design process should meet the requirements of the whole system which needs coordinating the solutions for all the partitions after all. Approach: Partitioning and coordination should be performed to break down the system into subproblems, solve them and put these solutions together to come up with the ultimate system design. These two tasks of partitioning-coordinating are computationally demanding. Most of the proposed approaches are either computationally very expensive or applicable to only a narrow class of problems. These approaches also use exact methods and eliminate the uncertainty. To manage the computational complexity and uncertainty, we approximate each subproblem after partitioning the whole system. In engineering design, one way to approximate the reality is using surrogate models (SM) to replace the functions which are computationally expensive to solve. This task also is added to the proposed computational framework. Also, to automate the whole process, creating a knowledge-based reusable template for each of these three steps is required. Therefore, in this dissertation, we first partition/decompose the complex system, then, we approximate the subproblem of each partition. Afterwards, we apply coordination methods to guide the solutions of the partitions toward the ultimate integrated system design. Validation: The partitioning-approximation-coordination design approach is validated using the validation square approach that consists of theoretical and empirical validation. Empirical validation of the design architecture is carried out using two industry-driven problems namely the a hot rod rolling problem’, ‘a dam network design problem’, ‘a crime prediction problem’ and ‘a green supply chain design problem’. Specific sub-problems are formulated within these problem domains to address various research questions identified in this dissertation. Contributions: The contributions from the dissertation are categorized into new knowledge in five research domains: ‱ Creating an approach to building an ensemble of surrogate models when the data is limited – when the data is limited, replacing computationally expensive simulations with accurate, low-dimensional, and rapid surrogates is very important but non-trivial. Therefore, a cross-validation-based ensemble modeling approach is proposed. ‱ Using temporal and spatial analysis to manage the uncertainties - when the data is time-based (for example, in meteorological data analysis) and when we are dealing with geographical data (for example, in geographical information systems data analysis), instead of feature-based data analysis time series analysis and spatial statistics are required, respectively. Therefore, when the simulations are for time and space-based data, surrogate models need to be time and space-based. In surrogate modeling, there is a gap in time and space-based models which we address in this dissertation. We created, applied and evaluated the effectiveness of these models for a dam network planning and a crime prediction problem. ‱ Removing assumptions regarding the demand distributions in green supply chain networks – in the existent literature for supply chain network design, there are always assumptions about the distribution of the demand. We remove this assumption in the partition-approximate-compose of the green supply chain design problem. ‱ Creating new knowledge by proposing a coordination approach for a partitioned and approximated network design. A green supply chain under online (pull economy) and in-person (push economy) shopping channels is designed to demonstrate the utility of the proposed approach
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