Stability and consistency analysis of semi-Lagrangian methods for the linear problem

Author(s):  
Steven J. Fletcher
2021 ◽  
Vol 16 (3) ◽  
pp. 1273-1284
Author(s):  
Hye Ji Kim ◽  
Hosung Jung ◽  
Young Jun Ko ◽  
Eun Su Chae ◽  
Hyo Jin Kim ◽  
...  

AbstractThis paper proposes an algorithm for the cooperative operation of air conditioning facilities and the energy storage system (ESS) in railway stations to minimize electricity. Unlike traditional load patterns, load patterns of an urban railway station can peak where energy charge rates are not high. Due to this possibility, if applying the traditional peak-reduction algorithm to railway loads, energy changes can increase, resulting in higher electricity bills. Therefore, it is required to develop a new method for minimizing the sum of capacity charges and energy charges, which is a non-linear problem. To get a feasible solution for this problem, we suggest an algorithm that optimizes the facility operation through two optimizations (primary and secondary). This method is applied to the air-quality change model for operating air conditioning facilities as demand-response (DR) resources in railway stations. This algorithm makes it possible to estimate operable DR capacity every hour, rather than calculating the capacity of DR resources conservatively in advance. Finally, we perform a simulation for the application of the proposed method to the operation of DR resources and ESS together. The simulation shows that electricity bills become lowered, and the number of charging and discharging processes of ESS is also reduced.


Optik ◽  
2021 ◽  
Vol 231 ◽  
pp. 166414
Author(s):  
Liang Guo ◽  
Yang Liu ◽  
Huagui He ◽  
Hong Lin ◽  
Guangxin Qiu ◽  
...  

1993 ◽  
Vol 8 (2) ◽  
pp. 99-109
Author(s):  
Oscar Gutierrez

Current demands on prototyping emphasize increasingly complex and dynamic applications that require sophisticated social mechanism and process enablers. However, much of the emphasis placed today in systems development under prototyping focuses on the supporting technology. The imbalance between product and process perspectives under this approach is explored. A view of prototyping effectiveness is presented in terms of non-linear problem solving, adequate technical and procedural solutions, and organizational support. Implications of this view are presented on the selection of prototyping techniques and on project management concerns. Future developments in prototyping practice are explored.


2008 ◽  
Vol 10 (2) ◽  
pp. 153-162 ◽  
Author(s):  
B. G. Ruessink

When a numerical model is to be used as a practical tool, its parameters should preferably be stable and consistent, that is, possess a small uncertainty and be time-invariant. Using data and predictions of alongshore mean currents flowing on a beach as a case study, this paper illustrates how parameter stability and consistency can be assessed using Markov chain Monte Carlo. Within a single calibration run, Markov chain Monte Carlo estimates the parameter posterior probability density function, its mode being the best-fit parameter set. Parameter stability is investigated by stepwise adding new data to a calibration run, while consistency is examined by calibrating the model on different datasets of equal length. The results for the present case study indicate that various tidal cycles with strong (say, >0.5 m/s) currents are required to obtain stable parameter estimates, and that the best-fit model parameters and the underlying posterior distribution are strongly time-varying. This inconsistent parameter behavior may reflect unresolved variability of the processes represented by the parameters, or may represent compensational behavior for temporal violations in specific model assumptions.


2006 ◽  
Vol 2006 ◽  
pp. 1-14 ◽  
Author(s):  
M. C. Leseduarte ◽  
R. Quintanilla

This paper is devoted to the study of the elasticity with porous dissipation. In the context of the nonlinear problem, we prove instability and nonexistence of solutions. In the context of the linear problem, we obtain exponential growth. We also obtain uniqueness of solutions of the backward in time problem of the linear equations.


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