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Title: A new approach to stochastic reduced order modeling

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Resource Type:
Journal Article: Publisher's Accepted Manuscript
Journal Name:
Computers and Chemical Engineering
Additional Journal Information:
Journal Volume: 93; Journal Issue: C; Related Information: CHORUS Timestamp: 2017-10-04 21:21:58; Journal ID: ISSN 0098-1354
Country of Publication:
United Kingdom

Citation Formats

Sen, Kinnar, and Diwekar, Urmila. A new approach to stochastic reduced order modeling. United Kingdom: N. p., 2016. Web. doi:10.1016/j.compchemeng.2016.06.010.
Sen, Kinnar, & Diwekar, Urmila. A new approach to stochastic reduced order modeling. United Kingdom. doi:10.1016/j.compchemeng.2016.06.010.
Sen, Kinnar, and Diwekar, Urmila. Sat . "A new approach to stochastic reduced order modeling". United Kingdom. doi:10.1016/j.compchemeng.2016.06.010.
title = {A new approach to stochastic reduced order modeling},
author = {Sen, Kinnar and Diwekar, Urmila},
abstractNote = {},
doi = {10.1016/j.compchemeng.2016.06.010},
journal = {Computers and Chemical Engineering},
number = C,
volume = 93,
place = {United Kingdom},
year = {Sat Oct 01 00:00:00 EDT 2016},
month = {Sat Oct 01 00:00:00 EDT 2016}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1016/j.compchemeng.2016.06.010

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  • The stochastic collocation (SC) and stochastic Galerkin (SG) methods are two well-established and successful approaches for solving general stochastic problems. A recently developed method based on stochastic reduced order models (SROMs) can also be used. Herein we provide a comparison of the three methods for some numerical examples; our evaluation only holds for the examples considered in the paper. The purpose of the comparisons is not to criticize the SC or SG methods, which have proven very useful for a broad range of applications, nor is it to provide overall ratings of these methods as compared to the SROM method.more » Furthermore, our objectives are to present the SROM method as an alternative approach to solving stochastic problems and provide information on the computational effort required by the implementation of each method, while simultaneously assessing their performance for a collection of specific problems.« less
  • The present paper reports on a numerical scheme for compressing in parametric form small signal electromechanical responses of multimachine power systems, originating from transient stability programs (TSP) or actual field testing. The result is achieved by using a multi-input multi-output (MIMO) minimal realization algorithm based on singular value decomposition (SVD), which can explicitly take into account the critical impact of the input interactions. The resulting parametric model is a reduced order representation of the underlying complex system, yet it is optimal (in the least-squares sense). Besides compact storage of damping information, the balanced state-space realization as such retains the principalmore » components of the response signals, and could thus be useful for the tuning of static Var systems (SVS) and power system stabilizers (PSS). When it is transformed in the modal space, the model also provides insight into modal interaction mechanisms. Several examples are included for illustration purposes and other applications and improvements are also discussed.« less
  • The concept of integral manifolds is used to systematically create improved reduced order models of synchronous machines. The approach is illustrated through a detailed example of a single machine connected to an infinite bus. The example shows the advantages of the manifold approach and also clarifies several issues about reduced order models of synchronous machines. The basic objective of the method is to include the effects of more complex models without actually including the additional differential equations. This is illustrated by including the effects of stator transients and damper windings on the swing equation without including the differential equations.
  • Existing land surface models (LSMs) describe physical and biological processes that occur over a wide range of spatial and temporal scales. For example, biogeochemical and hydrological processes responsible for carbon (CO 2, CH 4) exchanges with the atmosphere range from the molecular scale (pore-scale O 2 consumption) to tens of kilometers (vegetation distribution, river networks). Additionally, many processes within LSMs are nonlinearly coupled (e.g., methane production and soil moisture dynamics), and therefore simple linear upscaling techniques can result in large prediction error. In this paper we applied a reduced-order modeling (ROM) technique known as "proper orthogonal decomposition mapping method" thatmore » reconstructs temporally resolved fine-resolution solutions based on coarse-resolution solutions. We developed four different methods and applied them to four study sites in a polygonal tundra landscape near Barrow, Alaska. Coupled surface–subsurface isothermal simulations were performed for summer months (June–September) at fine (0.25 m) and coarse (8 m) horizontal resolutions. We used simulation results from three summer seasons (1998–2000) to build ROMs of the 4-D soil moisture field for the study sites individually (single-site) and aggregated (multi-site). The results indicate that the ROM produced a significant computational speedup (> 10 3) with very small relative approximation error (< 0.1%) for 2 validation years not used in training the ROM. We also demonstrate that our approach: (1) efficiently corrects for coarse-resolution model bias and (2) can be used for polygonal tundra sites not included in the training data set with relatively good accuracy (< 1.7% relative error), thereby allowing for the possibility of applying these ROMs across a much larger landscape. By coupling the ROMs constructed at different scales together hierarchically, this method has the potential to efficiently increase the resolution of land models for coupled climate simulations to spatial scales consistent with mechanistic physical process representation.« less
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