Abstract
The main objective of a smart energy system is to make control decisions that would make energy systems more efficient and more reliable. To select such decisions, the system must know the consequences of different possible decisions. Energy systems are very complex, they cannot be described by a simple formula, and the only way to reasonably accurately find such consequences is to test each decision on a simulated system. The problem is that the parameters describing the system and its environment are usually known with uncertainty, and we need to produce reliable results – i.e., results that will be true for all possible values of the corresponding parameters. In this chapter, we describe techniques for performing reliable simulations under such uncertainty.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
L. Brevault, J. Morio, M. Balesdent, Aerospace System Analysis and Optimization in Uncertainty (Springer Verlag, 2020)
M. Bruns, C.J.J. Paredis, Numerical methods for propagating imprecise uncertainty. In: Proceedings of the 2006 ASME Design Engineering Technical Conference (2006)
A.C. Calder, M.M. Hoffman, D.E. Willcox, M.P. Katz, F.D. Swesty, S. Ferson, Quantification of incertitude in black box simulation codes. J. Phys. Conf. Ser. 1031(1), 012016 (2018)
R. Callens, M.G.R. Faes, D. Moens, Local explicit interval fields for non-stationary uncertainty modelling in finite element models. Comp. Methods Appl. Mech. Eng. 379, 113735 (2021)
M. Ceberio, O. Kosheleva, V. Kreinovich, L. Longpré, Between Dog and Wolf: A Continuous Transition from Fuzzy to Probabilistic Estimates, in Proceedings of the IEEE International Conference on Fuzzy Systems FUZZ-IEEE’2019, (New Orleans, 2019), pp. 906–910
M. de Angelis, S. Ferson, E. Patelli, V. Kreinovich, Black-box propagation of failure probabilities under epistemic uncertainty, in Proceedings of the 3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering UNCECOMP’2019, ed. by M. Papadrakakis, V. Papadopoulos, G. Stefanou, (Crete, 2019), pp. 713–723
M.G.R. Faes, M. Daub, S. Marelli, E. Patelli, M. Beer, Engineering analysis with probability boxes: A review on computational methods. Struct. Saf. 93, 102092 (2021a)
M.G.R. Faes, M.A. Valdebenito, D. Moens, M. Beer, Operator norm theory as an efficient tool to propagate hybrid uncertainties and calculate imprecise probabilities. Mechanical Systems and Signal Processing 152, Paper 107482 (2021b)
S. Ferson, C.A. Joslyn, J.C. Helton, W.L. Oberkampf, K. Sentz, Summary from the epistemic uncertainty workshop: Consensus amid diversity. Reliab. Eng. Syst. Saf. 85(1–3), 355–369 (2004)
M. Fuchs, Simulation based uncertainty handling with polyhedral clouds, in Proceedings of the 4th International Workshop on Reliable Engineering Computing REC’2010, ed. by M. Beer, R.L. Muhanna, R.L. Mullen, (National University of Singapore, 2010), pp. 526–535
M. Fuchs, Simulated polyhedral clouds in robust optimisation. Int. J. Reliab. Saf. 6(1–3), 65–81 (2012)
I. Goodfellow, Y. Bengio, A. Courville, Deep Learning (MIT Press, Cambridge, MA, 2016)
L. Jaulin, M. Kiefer, O. Didrit, E. Walter, Applied Interval Analysis, with Examples in Parameter and State Estimation, Robust Control, and Robotics (Springer, London, 2001)
C.O. Johnston, A. Mazaheri, P. Gnoffo, B. Kleb, D. Bose, Radiative heating uncertainty for hyperbolic earth entry, part 1: Flight simulation modeling and uncertainty. J. Spacecr. Rocket. 50(1), 19–38 (2013)
B. Kleb, C.O. Johnston, Uncertainty analysis of air radiation for lunar return shock layers, in Proceedings of the AIAA Atmospheric Flight Mechanics Conference, (AIAA, Honolulu, 2008), pp. 2008–6388
O. Kosheleva, V. Kreinovich, Low-Complexity Zonotopes Can Enhance Uncertainty Quantification (UQ), in Proceedings of the 4th International Conference on Uncertainty Quantification in Computational Sciences and Engineering UNCECOMP’2021, (Athens, 2021a)
O. Kosheleva, V. Kreinovich, Limit theorems as blessing of dimensionality: Neural-oriented overview. Entropy 23(5), 501 (2021b)
V. Kreinovich, Application-Motivated Combinations of Fuzzy, Interval, and Probability Approaches, with Application to Geoinformatics, Bioinformatics, and Engineering, in Proceedings of the International Conference on Information Technology InTech’07, (Sydney, 2007), pp. 11–20
V. Kreinovich, Interval computations and interval-related statistical techniques: Estimating uncertainty of the results of data processing and indirect measurements, in Advanced Mathematical and Computational Tools in Metrology and Testing AMTCM’X, ed. by F. Pavese, W. Bremser, A. Chunovkina, N. Fisher, A.B. Forbes, (World Scientific, Singapore, 2015), pp. 38–49
V. Kreinovich, How to deal with uncertainties in computing: from probabilistic and interval uncertainty to combination of different approaches, with applications to engineering and bioinformatics, in Advances in Digital technologies. Proceedings of the Eighth International Conference on the Applications of Digital Information and Web Technologies ICADIWT’2017, ed. by J. Mizera-Pietraszko, R. Rodriguez Jorge, D. Almazo Pérez, P. Pichappan, (IOS Press, Amsterdam, Ciudad Juarez, 2017), pp. 3–15
V. Kreinovich, Global independence, possible local dependence: towards more realistic error estimates for indirect measurements, in Proceedings of the XXII International Conference on Soft Computing and Measurements SCM’2019, (St. Petersburg, 2019), pp. 4–8
V. Kreinovich, S. Ferson, A new Cauchy-based black-box technique for uncertainty in risk analysis. Reliab. Eng. Syst. Saf 85(1–3), 267–279 (2004)
V. Kreinovich, M.I. Pavlovich, Error estimate of the result of indirect measurements by using a calculational experiment. Izmeritelnaya Tekhnika 1985(3), 11–13 (in Russian); English translation: Measurement Techniques 28(3), 201–205 (1985)
V. Kreinovich, A. Lakeyev, J. Rohn, P. Kahl, Computational Complexity and Feasibility of Data Processing and Interval Computations (Kluwer, Dordrecht, 1998)
G. Mayer, Interval Analysis and Automatic Result Verification (de Gruyter, Berlin, 2017)
R.G. McClarren, Uncertainty Quantification and Predictive Computational Science: A Foundation for Physical Scientists and Engineers (Springer Verlag, 2018)
R.E. Moore, R.B. Kearfott, M.J. Cloud, Introduction to Interval Analysis (SIAM, Philadelphia, 2009)
J. Morio, M. Balesdent, D. Jacquemart, C. Vergé, A survey of rare event simulation methods for static input-output models. Simul. Model. Pract. Theory 49, 287–304 (2015)
M. Oberguggenberger, J. King, B. Schmelzer, Imprecise probability methods for sensitivity analysis in engineering, in Proceedings of the Fifth International Symposium on Imprecise Probability: Theory and Applications ISIPTA’07, ed. by G. de Cooman, J. Vejnarova, M. Zaffalon, (Prague, 2007), pp. 155–164
A. Pownuk, V. Kreinovich, Combining Interval, Probabilistic, and Other Types of Uncertainty in Engineering Applications (Springer Verlag, Cham, 2018a)
A. Pownuk, V. Kreinovich, (Hypothetical) negative probabilities can speed up uncertainty propagation algorithms, in Quantum Computing: An Environment for Intelligent Large Scale Real Application, ed. by A. E. Hassanien, M. Elhoseny, A. Farouk, J. Kacprzyk, (Springer Verlag, 2018b), pp. 251–271
A. Pownuk, J. Cerveny, J.J. Brady, Fast Algorithms for Uncertainty Propagation, and their Applications to Structural Integrity, in Proceedings of the 27th International Conference of the North American Fuzzy Information Processing Society NAFIPS’2008, (New York, 2008)
S.G. Rabinovich, Measurement Errors and Uncertainties: Theory and Practice (Springer, New York, 2005)
G. Rebner, M. Beer, E. Auer, M. Stein, Verified stochastic methods – Markov set-chains and dependency modeling of mean and standard deviation. Soft. Comput. 17, 1415–1423 (2013)
A. Rico, O. Strauss, Imprecise expectations for imprecise linear filtering. Int. J. Approx. Reason. 51(8), 933–947 (2010)
K. Semenov, A. Tselischeva, The interval method of bisection for solving the nonlinear equations with interval-valued parameters, in Proceedings of the International Scientific Conference on Telecommunications, Computing, and Control Teleccon 2019, November 18–21, 2019, ed. by N. Voinov, T. Schreck, S. Khan, (Springer Verlag, 2021), pp. 373–384
D.J. Sheskin, Handbook of Parametric and Non-Parametric Statistical Procedures (Chapman & Hall/CRC, London, 2011)
R. Trejo, V. Kreinovich, Error estimations for indirect measurements: Randomized vs. deterministic algorithms for ‘black-box’ programs, in Handbook on Randomized Computing, ed. by S. Rajasekaran, P. Pardalos, J. Reif, J. Rolim, (Kluwer, Boston/Dordrecht, 2001), pp. 673–729
Acknowledgments
This work was supported in part by the National Science Foundation grants:• 1623190 (A Model of Change for Preparing a New Generation for Professional Practice in Computer Science), and• HRD-1834620 and HRD-2034030 (CAHSI Includes).It was also supported:• by the AT&T Fellowship in Information Technology, and• by the program of the development of the Scientific-Educational Mathematical Center of Volga Federal District No. 075-02-2020-1478.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 Springer Nature Switzerland AG
About this entry
Cite this entry
Kreinovich, V., Kosheleva, O. (2023). How to Simulate If We Only Have Partial Information but We Want Reliable Results. In: Fathi, M., Zio, E., Pardalos, P.M. (eds) Handbook of Smart Energy Systems. Springer, Cham. https://doi.org/10.1007/978-3-030-97940-9_132
Download citation
DOI: https://doi.org/10.1007/978-3-030-97940-9_132
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-97939-3
Online ISBN: 978-3-030-97940-9
eBook Packages: Business and ManagementReference Module Humanities and Social SciencesReference Module Business, Economics and Social Sciences