A novel sensitivity index for analyzing the response of numerical models with interval inputs

Qi, Chenhao; Zhou, Changcong; Valdebenito, Marcos A.; Liu, Hongwei; Yue, Zhufeng

doi:10.1016/j.cma.2022.115509

Cited by 8 publications

(5 citation statements)

References 42 publications

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“…This will lead to complex derivation and lower efficiency. For the proposed model, in the interval analysis, the reliability in t ∈ (t 0 , t s ) (which can be regarded as countless discrete instants) is transformed into the time-independent problem relating to two instants (instant t MPP + y and instant t MPP − y ) through the performance function at the maximum and minimum values of the upper and lower boundaries of the interval process shown in Equation (19). Thus, the reliability of the structure can be solved more directly and conveniently.…”

Section: Discussion Of the Conventional Reliability Model And The Pro...mentioning

confidence: 99%

“…Then, the computational strategy and corresponding numerical tools for linear equations with random and interval variables are established by using perturbation theory and Taylor expansion. Chang et al 19 proposed a new sensitivity index for the numerical model containing interval variables, and established a double‐loop strategy based on global meta‐modeling and optimization to evaluate the influence of input variables on output. By extending the interval arithmetic rules, Wang et al 20 used the modified Taylor series to expand the interval variables and transformed the uncertain constraints into deterministic constraints for the given confidence level.…”

Section: Introductionmentioning

confidence: 99%

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Hybrid time‐dependent reliability analysis under a mixture of random and interval uncertainties

Zhou

Gao

et al. 2023

Numerical Meth Engineering

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A new time‐dependent reliability analysis model with a mixture of random variables and interval variables is proposed in this paper. First, samples of random variables are generated according to their probability density functions. Then, the samples are substituted into the performance function to obtain the interval processes corresponding to these samples. The reliability index of each interval process is computed to finally obtain the upper and lower bounds of failure probability. The adaptive Kriging surrogate model based on the global addition strategy is used in the calculation process to increase the computational efficiency. The accuracy of the computational strategy is demonstrated by a mathematical example and three engineering practical cases. The proposed new hybrid time‐dependent reliability model is compared to the conventional hybrid reliability model. The comparison results show that the proposed model is more convenient to implement than the conventional reliability model. It can accurately evaluate the reliability of the structure and can be applied to real‐world engineering practice thereby providing assistance and guidance for hybrid time‐dependent reliability analysis of structures.

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Section: Discussion Of the Conventional Reliability Model And The Pro...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Hybrid time‐dependent reliability analysis under a mixture of random and interval uncertainties

Zhou

Gao

et al. 2023

Numerical Meth Engineering

Self Cite

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“…The sensitivity analysis method generally uses the differential relationship of variables to indicate the sensitivity of output variables to the variations of input variables (Shang et al, 2021). According to different physical interpretations of variables, multiple sensitivity indicators are defined (Chang et al, 2022). For instance, the indicators dU i /dP j and dU i /dQ j represent the sensitivity of the voltage at node i to the variations of active and reactive power injections at node j. Voltage sensitivity indicators have been widely used in many research fields, including voltage stability analysis, voltage control, and DG allocation.…”

Section: Introductionmentioning

confidence: 99%

Complex affine arithmetic based uncertain sensitivity analysis of voltage fluctuations in active distribution networks

Quanjun,

Huazhong,

Mingming

et al. 2024

Front. Energy Res.

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The uncertainties of distribution generations (DGs) and loads lead to severe voltage fluctuations in active distribution networks (ADNs). Meanwhile, energy storage systems (ESSs) and static var compensators (SVCs) can mitigate the uncertainties of power injections by regulating the active and reactive power. Considering the variations of multiple uncertain factors, this paper proposes a complex affine arithmetic (CAA) based uncertain sensitivity analysis method of voltage fluctuations in ADNs. First, affine models of active and reactive power injections are established. The correlations of noisy symbols are used to reflect the mitigation effects of ESSs and SVCs on the uncertainties introduced by DGs and loads. Next, sensitivity indicators of voltage fluctuations are defined based on the transitivity of noisy symbols. Then, a calculation method for sensitivity indicators based on the micro-increments of coefficients is proposed. Combined with the obtained indicators, a fast sensitivity method for calculating interval values of voltages is further proposed. The modified IEEE 33-bus system is tested to validate the accuracy and efficiency of the proposed method by comparison with the continuous utilization of power flow method. Moreover, the 292-bus system is tested to validate its applicability in a large distribution system. Facts have proved that this method improves the efficiency and reliability of calculations, and in different scenarios, it can achieve fast calculation of nodes and online analysis of the voltage fluctuation range in uncertain environments, provides an effective tool for voltage quality management in active distribution networks.

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“…The belief reliability is proposed by Kang 31 to cope with uncertainties, which is defined as the chance that a system state is within a feasible domain 32 . Finally, the interval model arose from the need to deal with uncertainty and has been used in numerous applications recently 33,34 . Li 20 showed that the interval method results in more accurate and detailed estimates than the fuzzy method in some cases, and also produce consistent and meaningful result which the fuzzy method cannot obtain.…”

Section: Introductionmentioning

confidence: 99%

“…32 Finally, the interval model arose from the need to deal with uncertainty and has been used in numerous applications recently. 33,34 Li 20 showed that the interval method results in more accurate and detailed estimates than the fuzzy method in some cases, and also produce consistent and meaningful result which the fuzzy method cannot obtain. In the engineering practice, some variables are presented by interval form, such as design tolerance, assembly clearance and installation position of mechanical parts.…”

Section: Introductionmentioning

confidence: 99%

How dependent basic events with interval‐valued probabilities affect fault tree analysis

Zhou

Zhao

et al. 2022

Quality & Reliability Eng

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This paper studies the effect of the dependence state between basic events (BEs) on fault tree analysis (FTA) when the probabilities of events are characterized by interval values. The well-known Frèchent bounds are extended for modeling six different types of dependence states between BEs. Three indices, called average dependence effect (ADE), location effect (LE) and size effect (SE), are defined for evaluating the effect of the dependence states between BEs on the probability of top event (TE) and identifying influential and non-influential dependence states. Then, the proposed method is applied to fault tree (FT) examples, thereby explaining the dependence problem in FTA. To further verify the practicability of the method, FTA of the unilateral asymmetric movement failure of an aircraft flap mechanism is performed. The results show that: (i) the opposite and negative dependence contribute to the reliability of a parallel system while the perfect and positive dependence reduce it, (ii) the perfect and positive dependence contribute to the reliability of a series system while the opposite and negative dependence reduce it, and (iii) parallel systems are more reliable than series systems regardless of the dependence between BEs.

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A novel sensitivity index for analyzing the response of numerical models with interval inputs

Cited by 8 publications

References 42 publications

Hybrid time‐dependent reliability analysis under a mixture of random and interval uncertainties

Hybrid time‐dependent reliability analysis under a mixture of random and interval uncertainties

Complex affine arithmetic based uncertain sensitivity analysis of voltage fluctuations in active distribution networks

How dependent basic events with interval‐valued probabilities affect fault tree analysis

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