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Various parameters including biodiesel price, capital cost, interest rate and feedstock price, may exhibit variation in the techno-economic assessments of biodiesel production within project's lifetime due to economic and technical uncertainties.

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In this paper, a surrogate‐based iterative importance sampling (IS) method is proposed to efficiently evaluate failure probability (FP) of engineering structures. The surrogate is constructed by the training points centered at the most probable failure point (MPP), which is estimated by an approximate algorithm without any additional evaluations of the real limit state function (LSF), and the IS method using the estimated MPP is further obtained; and an iterative procedure combined with the surrogate and the IS method is finally proposed to improve the accuracy of the estimated result for the FP. Three numerical examples are employed to demonstrate the accuracy of the proposed method, and further, an inside flap of an aircraft is employed to demonstrate the practical application of the proposed method in engineering problems. The results show that the reasonable estimated result of the FP within the range of 10−3‐10−5 can be evaluated by the proposed method with only hundreds of the evaluations of the real LSF.

Abstract:Techno-economic assessments (TEA) of biodiesel production may comply with various economic and technical uncertainties during the lifespan of the project, resulting in the variation of many parameters associated with biodiesel production, including price of biodiesel, feedstock price, and rate of interest. Engineers may only collect very limited information on these uncertain parameters such as their variation intervals with lower and upper bound. This paper proposes a novel non-probabilistic strategy for uncertainty analysis (UA) in the TEA of biodiesel production with interval parameters, and non-probabilistic reliability index (NPRI) is employed to measure the economically feasible extent of biodiesel production. A sensitivity analysis (SA) indicator is proposed to assess the sensitivity of NPRI with regard to an individual uncertain interval parameter. The optimization method is utilized to solve NPRI and SA. Results show that NPRI in the focused biodiesel production of interest is 0.1211, and price of biodiesel, price of feedstock, and cost of operating can considerably affect TEA of biodiesel production.

A safety instrumented system (SIS) is extensively used to prevent or reduce risk. The Probability of Failure to perform its intended functions on Demand (PFD) of a practical SIS may vary within multiple safety integrity levels (SIL) due to uncertainties relevant to input parameters. An SIS will be considered to be unsafe when its PFD is greater than a prescribed value, and unsafety probability (UP) is employed to measure the unsafety degree of the investigated SIS in this work. Redundancy architecture is commonly employed to improve the reliability of an SIS. This paper investigates the effects of multiple uncertain input parameters on the UP of an SIS with the k‐out‐of‐n redundancy arrangement. We derive the detailed formulations of the sensitivity for such effects and we also discuss the physical meaning of the proposed sensitivity. An example is employed to demonstrate the proposed sensitivity and the results show that the estimated sensitivity values will be kept to be unchanged with respect to the redundancy when the redundancy is high, whereas the results will vary with the redundancy when the redundancy is low. Meanwhile, we provide a comparison of the results for the truncated uncertain parameters and the non‐truncated uncertain parameters. The results for truncated uncertain parameters and non‐truncated uncertain parameters will approach the same values as the truncated region of the uncertain parameter reduces to zero. The results show that we can approximate the sensitivities of the truncated parameters by the ones of the non‐truncated parameters with less computation time when the truncated region is less than 10−3.

An efficient numerical simulation method for the evaluation of global sensitivity analysis with parameter uncertainty, Appl. Math. Modelling (2015), doi: http://dx.Abstract: For structural systems with both epistemic and aleatory uncertainties, an efficient numerical simulation method is proposed to evaluate the effect of epistemic uncertainty on failure probability measured by the variance based sensitivity analysis. The direct evaluation of the effect needs a "triple-loop" crude sampling procedure and is time consuming. To circumvent the difficulty associated with the direct sampling based procedure, an improved importance sampling (IS) method is first constructed, and further the improved IS based procedure is proposed for efficient evaluation of the effect of epistemic uncertainty. The core of the proposed method is to construct the same IS probability density function (PDF) for failure probability corresponding to individual realization of epistemic uncertainty. Using the proposed improved IS based method, only an IS run with a set of input-output IS samples is needed to determine the estimated values of the effects for all epistemic uncertainties. Several examples are employed to demonstrate the feasibility of the proposed method for different situations. Examples show that the proposed method can ensure a reasonable accuracy of results with less evaluations of performance function compared with the available methods.