Uncertainty Propagation Using Probabilistic Affine Forms and Concentration of Measure Inequalities

Bouissou, Olivier; Goubault, Éric; Putot, Sylvie; Chakarov, Aleksandar; Sankaranarayanan, Sriram

doi:10.1007/978-3-662-49674-9_13

Cited by 27 publications

(48 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The second class of problems is related to finding bounds over the expected values. In [3] the authors consider bounds also over higher-order moments for a specific class of probabilistic programs with probabilistic affine assignments. This approach can handle also nonlinear terms using interval arithmetics and fresh variables, at the price to produce very conservative bounds.…”

Section: Programmentioning

confidence: 99%

Automatic Generation of Moment-Based Invariants for Prob-Solvable Loops

Bartocci

Kovács

Stankovič

2019

Automated Technology for Verification and Analysis

View full text Add to dashboard Cite

One of the main challenges in the analysis of probabilistic programs is to compute invariant properties that summarise loop behaviours. Automation of invariant generation is still at its infancy and most of the times targets only expected values of the program variables, which is insufficient to recover the full probabilistic program behaviour. We present a method to automatically generate moment-based invariants of a subclass of probabilistic programs, called Prob-solvable loops, with polynomial assignments over random variables and parametrised distributions. We combine methods from symbolic summation and statistics to derive invariants as valid properties over higher-order moments, such as expected values or variances, of program variables. We successfully evaluated our work on several examples where full automation for computing higher-order moments and invariants over program variables was not yet possible.

show abstract

Section: Programmentioning

confidence: 99%

Automatic Generation of Moment-Based Invariants for Prob-Solvable Loops

Bartocci

Kovács

Stankovič

2019

Automated Technology for Verification and Analysis

View full text Add to dashboard Cite

show abstract

“…To resolve issues of such AA approaches with too wide solution ranges, typically manifested in the low probabilities around maximum and minimum interval values, modern trends in AA-applications combine probabilistic and AA approaches, e.g. [20] and [21], where noise symbols are represented in the form of P-boxes (i.e. generic probabilistic functions) and classified into independent group and group with unknown dependencies based on the estimated or assumed probability distributions of interval values.…”

Section: Introductionmentioning

confidence: 99%

Handling uncertainties with affine arithmetic and probabilistic OPF for increased utilisation of overhead transmission lines

Fang

Zou

Coletta

et al. 2019

Electric Power Systems Research

View full text Add to dashboard Cite

Large-scale integration of variable and unpredictable renewable-based generation systems poses significant challenges to the secure and reliable operation of transmission networks. Application of dynamic thermal rating (DTR) allows for a higher utilisation of transmission lines and effectively avoids high-cost upgrading and/or reinforcing of transmission system infrastructure. In order to efficiently handle ranges of uncertainties introduced by the variations of both wind energy sources and system loads, this paper introduces a novel optimization model, which combines affine arithmetic (AA) and probabilistic optimal power flow (P-OPF) for DTR-based analysis of transmission networks. The proposed method allows for the improved analysis of underlying uncertainties on the supply, transmission and demand sides, which are expressed in the form of probability distributions (e.g. for wind speeds, wind directions, wind power generation and demand variations) and related interval values. The paper presents a combined AA-P-OPF method, which can provide important information to transmission system operators for evaluating the trade-off between security and costs at a planning stage, as well as for selecting optimal controls at operational stage. The AA-P-OPF methodology is illustrated for a day-ahead planning, using a case study of a real transmission network and a medium size test distribution network.. .

show abstract

“…• Anaesthesia delivery system benchmark : this benchmark is based on an automated anaesthesia delivery problem, with a human (an anaesthesiologist) in the loop [21,5]. The model is described in the form of a discrete-time stochastic hybrid system [1] that depends both the current state of the model and a history of the past input actions by the anaesthesiologist.…”

Section: Specific Modelling Features We Briefly List the Key Featuresmentioning

confidence: 99%

“…This section proposes a benchmark problem for stochastic verification techniques. Past benchmarks and work exist for automated anaesthesia delivery systems [21,5]. We consider the problem of providing probabilistic guarantees of safety for the automated anaesthesia delivery problem with a human (anaesthesiologist) in the loop.…”

Section: Anaesthesia Delivery System Benchmarkmentioning

confidence: 99%

ARCH-COMP18 Category Report: Stochastic Modelling

Abate

Blom

Cauchi

et al.

EPiC Series in Computing

View full text Add to dashboard Cite

This report presents the results of a friendly competition for formal verification and policy synthesis of stochastic models. The friendly competition took place as part of the workshop Applied Verification for Continuous and Hybrid Systems (ARCH) in 2018. In this first edition, we present five benchmarks with different levels of complexities and stochastic flavours. We make use of six different tools and frameworks (in alphabetical order): Barrier Certificates, FAUST2, FIRM-GDTL, Modest, SDCPN modelling & MC simulation and SReachTools; and attempt to solve instances of the five different benchmark problems. Through these benchmarks, we capture a snapshot on the current state-of the art tools and frameworks within the stochastic modelling domain. We also present the challenges encountered within this domain and highlight future plans which will push forward the development of more tools and methodologies for performing formal verification and optimal policy synthesis of stochastic processes.

show abstract

Uncertainty Propagation Using Probabilistic Affine Forms and Concentration of Measure Inequalities

Cited by 27 publications

References 34 publications

Automatic Generation of Moment-Based Invariants for Prob-Solvable Loops

Automatic Generation of Moment-Based Invariants for Prob-Solvable Loops

Handling uncertainties with affine arithmetic and probabilistic OPF for increased utilisation of overhead transmission lines

ARCH-COMP18 Category Report: Stochastic Modelling

Contact Info

Product

Resources

About