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Kernel methods for center manifold approximation and a weak data-based version of the Center Manifold Theorem

PHYSICA D-NONLINEAR PHENOMENA 2021年 427卷 133007-133007页

作者： Haasdonk, B. Hamzi, B. Santin, G. Wittwar, D. Univ Stuttgart Inst Appl Anal & Numer Simulat Stuttgart Germany Imperial Coll London Dept Math London England Bruno Kessler Fdn Digital Soc Ctr Trento Italy

For dynamical systems with a non hyperbolic equilibrium, it is possible to significantly simplify the study of stability by means of the center manifold theory. This theory allows to isolate the complicated asymptotic behavior of the system close to the equilibrium point and to obtain meaningful predictions of its behavior by analyzing a reduced order system on the so-called center manifold. Since the center manifold is usually not known, good approximation methods are important as the center manifold theorem states that the stability properties of the origin of the reduced order system are the same as those of the origin of the full order system. In this work, we establish a data-based version of the center manifold theorem that works by considering an approximation in place of an exact manifold. Also the error between the approximated and the original reduced dynamics is quantified. We then use an apposite data-based kernel method to construct a suitable approximation of the manifold close to the equilibrium, which is compatible with our general error theory. The data are collected by repeated numerical simulation of the full system by means of a high-accuracy solver, which generates sets of discrete trajectories that are then used as a training set. The method is tested on different examples which show promising performance and good accuracy. (C) 2021 Elsevier B.V. All rights reserved.

关键词： Center manifold Kernel methods data-based modeling

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modeling of a hinged-raft wave energy converter via deep operator learning and wave tank experiments

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APPLIED ENERGY 2023年 341卷

作者： Zhang, Jincheng Zhao, Xiaowei Greaves, Deborah Jin, Siya Univ Warwick Sch Engn Intelligent Control & Smart Energy ICSE Res Grp Coventry England Univ Plymouth Sch Engn Comp & Math Plymouth England

Model identification for a hinged-raft wave energy converter (WEC) is investigated in this paper, based on wave tank experiments and deep operator learning. Different from previous works which all formulated this issue as a function approximation task, this work, for the first time, formulates it as an operator approximation task (which learns the mapping from a function space to another function space). As such, a continuous-time WEC model is identified from data, greatly expanding the horizon of data-based WEC modeling because previous works were limited to discrete-time model identification. The error accumulation for multi-step predictions in the discrete-time formulation is thus also addressed. The model is developed by first carrying out a set of wave tank experiments to generate the training data, and then the deep operator learning model, i.e. the DeepONet, is constructed and trained based on the experimental data. The validation study shows that the model captures the WEC dynamics accurately. A new set of experimental runs are further carried out and the results show that after training, the model can be used as a digital wave tank, an alternative to the expensive numerical and physical wave tanks, for accurate and real-time simulations of the WEC dynamics.

关键词： data-based modeling Deep learning DeepONet Wave energy converter Wave tank experiment

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A framework for data-based turbulent combustion closure: A priori validation

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COMBUSTION AND FLAME 2019年 206卷 490-505页

作者： Ranade, Rishikesh Echekki, Tarek North Carolina State Univ Dept Mech & Aerosp Engn Raleigh NC 27695 USA

Experimental multi-scalar measurements in laboratory flames have provided important databases for the validation of turbulent combustion closure models. In this work, we present a framework for data-based closure in turbulent combustion and establish an a priori validation of this framework. The approach is based on the construction of joint probability density functions (PDFs) and conditional statistics using experimental data based on the parameterization of the composition space using principal component analysis (PCA). The PCA on the data identifies key parameters, principal components (PCs), on which joint scalar PDFs and conditional scalar means can be constructed. To enable a generic implementation for the construction of joint scalar PDFs, we use the multi-dimensional kernel density estimation (KDE) approach. An a priori validation of the PCA-KDE approach is carried out using the Sandia piloted jet turbulent flames D, E and F. The analysis of the results suggests that a few PCs are adequate to reproduce the statistics, resulting in a low-dimensional representation of the joint scalars PDFs and the scalars' conditional means. A reconstruction of the scalars' means and RMS statistics are in agreement of the corresponding statistics extracted directly from the experimental data. We also propose one strategy to recover missing species and construct conditional means for the reaction rates based on a variation of the pairwise-mixing stirred reactor (PMSR) model. The model is demonstrated using numerical simulations based on the one-dimensional turbulence (ODT) model for the same flames. (C) 2019 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

关键词： data-based modeling Joint probability density function Principal component analysis Kernel density estimation

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A framework for data-based turbulent combustion closure: A posteriori validation

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COMBUSTION AND FLAME 2019年 210卷 279-291页

作者： Ranade, Rishikesh Echekki, Tarek North Carolina State Univ Dept Mech & Aerosp Engn 911 Oval DrCampus Box 7910Engn Bldg 3Room 3252 Raleigh NC 27695 USA

In this work, we demonstrate a framework for developing closure models in turbulent combustion using experimental multi-scalar measurements. The framework is based on the construction of conditional means and joint scalar PDFs from experimental data based on the parameterization of the composition space using principal component analysis (PCA). The resulting principal components (PCs) act as both conditioning variables and transported variables. Their chemical source terms are constructed starting from instantaneous temperature and species measurements using a variant of the pairwise mixing stirred reactor (PMSR) approach. A multi-dimensional kernel density estimation (KDE) approach is used to construct the joint PDFs in PC space. Convolutions of these joint PDFs with conditional means are used to determine the unconditional means for the closure terms: the mean PCs chemical source terms and the density. These means are parameterized in terms of the mean PCs using artificial neural networks (ANN). The framework is demonstrated a posteriori using the data from the Sandia piloted turbulent jet flames D, E and F by performing RANS calculations. The radial profiles of mean and RMS of temperature and measured species mass fractions agree well with the experimental means for these flames. (C) 2019 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

关键词： data-based modeling Joint probability density function Principal component analysis Artificial neural networks

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A data-Driven Reduced-Order Model for Estimating the Stimulated Reservoir Volume (SRV)

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ENERGIES 2022年第15期15卷 5582页

作者： Rezaei, Ali Aminzadeh, Fred Natl Energy Technol Lab Pittsburgh PA 15236 USA FACT Inc Santa Barbara CA 93130 USA Schlumberger Houston TX 77042 USA

The main goal of hydraulic fracturing stimulation in unconventional and tight reservoirs is to maximize hydrocarbon production by creating an efficient stimulated reservoir volume (SRV) around the horizontal wells. To zreach this goal, a physics-based model is typically used to design and optimize the hydraulic fracturing process before executing the job. However, two critical issues make this approach insufficient for achieving the mentioned goal. First, the physics-based models are based on several simplified assumptions and do not correctly represent the physics of unconventional reservoirs;hence, they often fail to match the observed SRVs in the field. Second, the success of the executed stimulation job is evaluated after it is completed in the field, leaving no room to modify some parameters such as proppant concentration in the middle of the job. To this end, this paper proposes data-driven and global sensitivity approaches to address these two issues. It introduces a novel workflow for estimating SRV in near real-time using some hydraulic fracturing parameters that can be inferred before or during the stimulation process. It also utilizes a robust global sensitivity framework known as the Sobol Method to rank the input parameters and create a reduced-order (mathematically simple) model for near real-time estimation of SRV (referred to as DSRV). The proposed framework in this paper has two main advantages and novelties. First, it is based on a pure data-based approach, with no simplified assumptions due to the use of a simulator for generating the training and test dataset, which is often the case in similar studies. Second, it treats SRV generation as a rock mechanics problem (rather than a reservoir engineering problem with fixed fracture lengths), accounting for changes in hydraulic fracture topology and SRV changes with time. A dataset from the Marcellus Shale Energy and Environment Laboratory (MSEEL) project is used. The model's input parameters include s

关键词： stimulated reservoir volume (SRV) hydraulic fracturing machine learning reduced order model (ROM) data-based modeling

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Self-Learning data-based Models as Basis of a Universally Applicable Energy Management System

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ENERGIES 2020年第8期13卷 2084-2084页

作者： Lachmann, Malin Maldonado, Jaime Bergmann, Wiebke Jung, Francesca Weber, Markus Bueskens, Christof Univ Bremen Ctr Ind Math Bibliothekstr 5 D-28359 Bremen Germany Univ Bremen Cognit Neuroinformat Enrique Schmidt Str 5 D-28359 Bremen Germany Steinbeis Innovat Ctr Optimizat & Control Schmalenbecker Str 33 D-28879 Grasberg Germany

In the transfer from fossil fuels to renewable energies, grid operators, companies and farms develop an increasing interest in smart energy management systems which can reduce their energy expenses. This requires sufficiently detailed models of the underlying components and forecasts of generation and consumption over future time horizons. In this work, it is investigated via a real-world case study how data-based methods based on regression and clustering can be applied to this task, such that potentially extensive effort for physical modeling can be decreased. Models and automated update mechanisms are derived from measurement data for a photovoltaic plant, a heat pump, a battery storage, and a washing machine. A smart energy system is realized in a real household to exploit the resulting models for minimizing energy expenses via optimization of self-consumption. Experimental data are presented that illustrate the models' performance in the real-world system. The study concludes that it is possible to build a smart adaptive forecast-based energy management system without expert knowledge of detailed physics of system components, but special care must be taken in several aspects of system design to avoid undesired effects which decrease the overall system performance.

关键词： data-based modeling data-driven modeling least-squares regression linear regression clustering simulated annealing nonlinear optimization self-consumption optimization energy management

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Multi-objective Optimization of Integrated Iron Ore Sintering Process Using Machine Learning and Evolutionary Algorithms

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TRANSACTIONS OF THE INDIAN INSTITUTE OF METALS 2020年第8期73卷 2033-2039页

作者： Singh, Kuldeep Vakkantham, Phanibhargava Nistala, Sri Harsha Runkana, Venkataramana Tata Consultancy Serv Ltd TCS Res Pune 411013 Maharashtra India

In the iron ore sintering process, it is desirable to maximize the productivity and quality of sinter while minimizing the fuel consumption for any given raw material (iron ore, flux and solid fuel) quality. However, given the complexity of the sintering process and the large number of manipulated variables, it is not practical for operators to identify appropriate set points for the manipulated variables to achieve these conflicting objectives. While significant amount of research is devoted to optimization of the on-strand sintering process, optimization of the integrated sintering process, viz. granulation and on-strand sintering together, has not received much attention. This is, however, necessary as the granulation process dictates the moisture content, mean size and voidage of the green mix bed, which in turn have a very strong influence on the sintering process and sinter quality. In this work, we have formulated and solved a multi-objective optimization problem to maximize both sinter productivity and quality for the integrated iron ore sintering process. Predictive models for productivity and quality parameters such as tumbler index (TI) and reduction degradation index (RDI) are built using machine learning algorithms. The optimization problem is solved using an evolutionary algorithm called non-dominated sorting genetic algorithm II (NSGA-II) to obtain a set of Pareto-optimal solutions. Optimal settings for key manipulated variables such as moisture content of green mix, fuel content, bed height and strand speed are obtained for the Pareto solutions. The optimization results are useful for identifying the operational range of the sintering process and can be used by operators for running the sinter plant optimally for a given set of raw materials.

关键词： Sintering Granulation Multi-objective optimization data-based modeling

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Analysis of the Spatiotemporal Evolution Characteristics of Travel Demand 20

Analysis of the Spatiotemporal Evolution Characteristics of ...

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20th COTA International Conference of Transportation Professionals (CICTP) - Advanced Transportation, Enhanced Connection

作者： Ren, Yilong Jiang, Han Liu, Runkun Wang, Fei Zhang, Le Yu, Haiyang Natl Engn Lab Comprehens Transportat Big Data App Beijing 100191 Peoples R China Beihang Univ Sch Transportat Sci & Engn Beijing 100191 Peoples R China Beijing Adv Innovat Ctr Big Data & Brain Comp Beijing 100191 Peoples R China Beihang Univ Hefei Innovat Res Inst Hefei 230013 Anhui Peoples R China

ISBN: (数字)9780784482933

ISBN: (纸本)9780784482933

Due to the great diversity and complexity of travel demand, the analysis of spatiotemporal evolution characteristics of travel demand is of significance to the planning and management of urban traffic systems. To investigate the spatiotemporal evolution characteristics of travel demand, this research obtains massive order data from Didi Platform in Haikou, including longitude and latitude of departure and destination points of order as well as time stamps. based on these data, characteristics that affect travel demand from may to october and the main factors are analyzed. A model is established to describe the relationship between travel demand and the service level of public bus in Haikou. The conclusions of this research can contribute to the planning of public transportation networks and provide effective reference to citizens' travel choices under special weather conditions.

关键词： Travel demand analysis Visualized analysis data-based modeling

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Machine learning assisted prediction of exhaust gas temperature of a heavy-duty natural gas spark ignition engine

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APPLIED ENERGY 2021年 300卷 117413-117413页

作者： Liu, Jinlong Huang, Qiao Ulishney, Christopher Dumitrescu, Cosmin E. West Virginia Univ Mech & Aerosp Engn Morgantown WV 26506 USA West Virginia Univ Chem & Biomed Engn Morgantown WV 26506 USA

Exhaust gas temperature is a key parameter for optimizing engine performance and emissions. Of particular interest is forecasting the exhaust gas temperature in a diesel engine converted to spark ignition natural gas operation, as the combustion process in this engine is significantly different from the one in a conventional engine. The goal was to assess four different machine learning algorithms namely the artificial neural network, random forest, support vector regression, and gradient boosting regression trees, with respect to a physical 1D CFD model and relative to one another, when predicting the exhaust temperature. The spark timing, equivalence ratio, and engine speed were model inputs. First, the artificial neural network predicted the exhaust temperature more accurately than the physical model, because of the complex premixed combustion phenomena inside a conventional diesel chamber. When compared relative to one another, all machine learning models predicted the exhaust gas temperature with acceptable error while also capturing its relationship with the three model inputs. The gradient boosting regression trees predicted the best, but it usually requires high quality noise-free data. The random forest had the least accuracy, but it required the least amount of calibration. The support vector regression had the smallest error, but it required the highest computational resources. The artificial neural network algorithm was the most appropriate, but it required effort in tuning its hyperparameters. Overall, the results showed that well-trained machine learning models can complement more complex physical model while also helping with optimizing the engine performance, emissions, and life.

关键词： Physics-based modeling data-based modeling Exhaust gas temperature Natural gas spark ignition engine Machine learning algorithm

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Integrating data-based modeling and nonlinear control tools for batch process control

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AICHE JOURNAL 2012年第7期58卷 2105-2119页

作者： Aumi, Siam Mhaskar, Prashant McMaster Univ Dept Chem Engn Hamilton ON L8S 4L7 Canada

A data-based multimodel approach is developed in this work for modeling batch systems in which multiple local linear models are identified using latent variable regression and combined using an appropriate weighting function that arises from fuzzy c-means clustering. The resulting model is used to generate empirical reverse-time reachability regions (RTRRs) (defined as the set of states from where the data-based model can be driven inside a desired end-point neighborhood of the system), which are subsequently incorporated in a predictive control design. Simulation results of a fed-batch reactor system under proportional-integral (PI) control and the proposed RTRR-based design demonstrate the superior performance of the RTRR-based design in both a fault-free and faulty environment. The data-based modeling methodology is then applied on a nylon-6,6 batch polymerization process to design a trajectory tracking predictive controller. Closed-loop simulation results illustrate the superior tracking performance of the proposed predictive controller over PI control. (C) 2011 American Institute of Chemical Engineers AIChE J, 2012

关键词： process control control optimization batch control data-based modeling

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