How to perform global sensitivity analysis of a catchment-scale, distributed pesticide transfer model? Application to the PESHMELBA model

Pesticide transfers in agricultural catchments are responsible for diffuse but major risks to water quality. Spatialized pesticide transfer models are useful tools to assess the impact of the structure of the landscape on water quality. Before considering using these tools in operational contexts, quantifying their uncertainties is a preliminary necessary step. In this study, we explored how global sensitivity analysis can be applied to the recent PESHMELBA pesticide transfer model to quantify uncertainties on transfer simulations. We set up a virtual catchment based on a real one and we compared different approaches for sensitivity analysis that could handle the specificities of the model: high number of input parameters, limited size of sample due to computational cost and spatialized output. We compared Sobol' indices obtained from Polynomial Chaos Expansion, HSIC dependence measures and feature importance measures obtained from Random Forest surrogate model. Results showed the consistency of the different methods and they highlighted the relevance of Sobol' indices to capture interactions between parameters. Sensitivity indices were first computed for each landscape element (site sensitivity indices). Second, we proposed to aggregate them at the hillslope and the catchment scale in order to get a summary of the model sensitivity and a valuable insight into the model hydrodynamical behaviour. The methodology proposed in this paper may be extended to other modular and distributed hydrological models as there has been a growing interest in these methods in recent years.

Annual Cost and Loss Minimization in a Radial Distribution Network by Capacitor Allocation Using PSO

Increasing power demand from passive distribution networks has led to deteriorated voltage profiles and increased line flows. This has increased the annual operations and installation costs due to unavoidable reinforcement equipment. This work proposes the reduction in annual costs by optimal placement of capacitors used to alleviate power loss in radial distribution networks (RDNs). The optimization objective function is formulated for the reduction in operation costs by (i) reducing the active and reactive power losses, and (ii) the cost and installation of capacitors, necessary to provide the reactive power support and maintain the voltage profile. Initially, the network buses are ranked according to two loss sensitivity indices (LSIs), i.e., active loss sensitivity with respect to node voltage (LSI1) and reactive power injection (LSI2). The sorted bus list is then fed to the particle swarm optimization (PSO) for solving the objective function. The efficacy of the proposed work is tested on different IEEE standard networks (34 and 85 nodes) for different use cases and load conditions. In use case 1, the values finalized by the algorithm are selected without considering their market availability, whereas in use case 2, market-available capacitor sizes close to the optimal solution are selected. Furthermore, the static and seasonal load profiles are considered. The results are compared with recent methods and have shown significant improvement in terms of annual cost, losses and line flows reduction, and voltage profile.

Investigation of determinism-related issues in the Sobol′ low-discrepancy sequence for producing sound global sensitivity analysis indices

A computationally efficient and robust sampling scheme can support a sensitivity analysis of models to discover their behaviour through Quasi Monte Carlo approximation. This is especially useful for complex models, as often occur in environmental domains when model runtime can be prohibitive. The Sobol' sequence is one of the most used quasi-random low-discrepancy sequences as it can explore the parameter space significantly more evenly than pseudo-random sequences. The built-in determinism of the Sobol' sequence assists in achieving this attractive property. However, the Sobol' sequence tends to deteriorate in the sense that the estimated errors are distributed inconsistently across model parameters as the dimensions of a model increase. By testing multiple Sobol' sequence implementations, it is clear that the deterministic nature of the Sobol' sequence occasionally introduces relatively large errors in sensitivity indices produced by well-known global sensitivity analysis methods, and that the errors do not diminish by averaging through multiple replications. Problematic sensitivity indices may mistakenly guide modellers to make type I and II errors in trying to identify sensitive parameters, and this will potentially impact model reduction attempts based on these sensitivity measurements. This work investigates the cause of the Sobol' sequence's determinism-related issues. References I. A. Antonov and V. M. Saleev. An economic method of computing LPτ-sequences. USSR Comput. Math. Math. Phys. 19.1 (1979), pp. 252–256. doi: 10.1016/0041-5553(79)90085-5 P. Bratley and B. L. Fox. Algorithm 659: Implementing Sobol’s quasirandom sequence generator. ACM Trans. Math. Soft. 14.1 (1988), pp. 88–100. doi: 10.1145/42288.214372 J. Feinberg and H. P. Langtangen. Chaospy: An open source tool for designing methods of uncertainty quantification. J. Comput. Sci. 11 (2015), pp. 46–57. doi: 10.1016/j.jocs.2015.08.008 on p. C90). S. Joe and F. Y. Kuo. Constructing Sobol sequences with better two-dimensional projections. SIAM J. Sci. Comput. 30.5 (2008), pp. 2635–2654. doi: 10.1137/070709359 S. Joe and F. Y. Kuo. Remark on algorithm 659: Implementing Sobol’s quasirandom sequence generator. ACM Trans. Math. Soft. 29.1 (2003), pp. 49–57. doi: 10.1145/641876.641879 W. J. Morokoff and R. E. Caflisch. Quasi-random sequences and their discrepancies. SIAM J. Sci. Comput. 15.6 (1994), pp. 1251–1279. doi: 10.1137/0915077 X. Sun, B. Croke, S. Roberts, and A. Jakeman. Comparing methods of randomizing Sobol’ sequences for improving uncertainty of metrics in variance-based global sensitivity estimation. Reliab. Eng. Sys. Safety 210 (2021), p. 107499. doi: 10.1016/j.ress.2021.107499 S. Tarantola, W. Becker, and D. Zeitz. A comparison of two sampling methods for global sensitivity analysis. Comput. Phys. Com. 183.5 (2012), pp. 1061–1072. doi: 10.1016/j.cpc.2011.12.015 S. Tezuka. Discrepancy between QMC and RQMC, II. Uniform Dist. Theory 6.1 (2011), pp. 57–64. url: https://pcwww.liv.ac.uk/~karpenk/JournalUDT/vol06/no1/5Tezuka11-1.pdf I. M. Sobol′. On the distribution of points in a cube and the approximate evaluation of integrals. USSR Comput. Math. Math. Phys. 7.4 (1967), pp. 86–112. doi: 10.1016/0041-5553(67)90144-9 I. M. Sobol′. Sensitivity estimates for nonlinear mathematical models. Math. Model. Comput. Exp 1.4 (1993), pp. 407–414.

A Global Sensitivity Analysis Framework for Hybrid Simulation with Stochastic Substructures

Hybrid simulation is an experimental method used to investigate the dynamic response of a reference prototype structure by decomposing it to physically-tested and numerically-simulated substructures. The latter substructures interact with each other in a real-time feedback loop and their coupling forms the hybrid model. In this study, we extend our previous work on metamodel-based sensitivity analysis of deterministic hybrid models to the practically more relevant case of stochastic hybrid models. The aim is to cover a more realistic situation where the physical substructure response is not deterministic, as nominally identical specimens are, in practice, never actually identical. A generalized lambda surrogate model recently developed by some of the authors is proposed to surrogate the hybrid model response, and Sobol’ sensitivity indices are computed for substructure quantity of interest response quantiles. Normally, several repetitions of every single sample of the inputs parameters would be required to replicate the response of a stochastic hybrid model. In this regard, a great advantage of the proposed framework is that the generalized lambda surrogate model does not require repeated evaluations of the same sample. The effectiveness of the proposed hybrid simulation global sensitivity analysis framework is demonstrated using an experiment.

Stability Metric Based on Sensitivity Analysis Applied to Electrical Repowering System

Stability metrics are used to quantify a system’s ability to maintain equilibrium under disturbances. We did not identify the proposition of a stability metric using sensitivity analysis within the literature. This work proposes a system stability metric and its application to an electrical repowering system. The methodology for applying the proposed metric comprises: (i) system parameters sensitivity analysis and spider diagram construction, (ii) determining the array containing the line segments inclination angles of each spider diagram curve, and (iii) stability calculation using the array mean and maximum inclination value of a line segment. After simulating the model built for the electrical repowering system and applying the methodology, we obtain results regarding the sensitivity indices and stability values of system inputs relative to their outputs, considering the original system and with reduced parameters. Using the stability study, it was possible to determine different stability categories for the system parameters, which indicates the need for different analysis levels.

Proposing an Uncertainty Management Framework to Implement the Evidence Theory for Vehicle Crash Applications

The purpose of this work is to enable the use of the Dempster-Shafer evidence theory for uncertainty propagation on computationally expensive automotive crash simulations. This is necessary as the results of these simulations are influenced by multiple possibly uncertain aspects. To avoid negative effects, it is important to detect these factors and their consequences. The challenge when pursuing this effort is the prohibitively high computational cost of the evidence theory. To this end, we present a framework of existing methods that is specifically designed to reduce the necessary number of full model evaluations and parameters. An initial screening removes clearly irrelevant parameters to mitigate the curse of dimensionality. Next, we approximate the full-scale simulation using metamodels to accelerate output generation and thus enable the calculation of global sensitivity indices. These indicate effects of the parameters on the considered output and more profoundly sort out irrelevant parameters. After these steps, the evidence theory can be performed rapidly and feasibly due to fast-responding metamodel and reduced input dimension. It yields bounds for the cumulative distribution function of the considered quantity of interest. We apply the proposed framework to a simplified crash test dummy model. The elementary effects method is used for screening, a kriging metamodel emulates the finite element simulation, and Sobol' sensitivity indices are determined before the evidence theory is applied. The outcome of the framework provide engineers with information about the uncertainties they may face in hardware testing and that should be addressed in future vehicle design.

The Insulin Sensitivity Mcauley Index (Mcai) is Associated with 40-Year Cancer Mortality in a Cohort of Men and Women Free of Diabetes at Baseline

Background:The association between insulin resistance and cancer mortality is not fully explored. We investigated the association between several insulin sensitivity indices (ISIs) and cancer mortality in a cohort of adult men and women free of diabetes. We hypothesized that higher insulin resistance (Q1 of the Mcauley index (MCAi), calculated by fasting insulin and triglycerides, and Q4 of the Homeostatic Model Assessment (HOMA), calculated by fasting plasma glucose and insulin) will be associated with greater cancer mortality risk.Methods: A cohort of 1612 men and women free of diabetes during baseline were followed since 1979 through 2016 for cause specific mortality as part of the Israel study on Glucose Intolerance, Obesity and Hypertension (GOH). Results: Mean age at baseline was 51.5 ± 8.0 years, 804 (49.9%) were males, and 871 (54.0%) had prediabetes. Mean follow-up was 36.7±0.2 years and 47,191 person years were accrued. Cumulative incidence analysis using Cox proportional hazard model and competing risks analysis adjusted for age, sex, country of origin, BMI, blood pressure, total cholesterol, smoking and glycemic status (table 2), revealed an increased risk for cancer death, sub-distribution HR=1.4 (95% CI: 1.1-1.9, p=0.02) for individuals in the lower quartile of MCAi (Q1), denoting higher insulin resistance, compared with the upper quartiles (Q2-4). No statistically significant association was observed between the other insulin resistance surrogates and cancer death.Conclusion: The MCAi was found to independently associate with an increased risk for cancer mortality in adult men and women free of diabetes. The MCAi may be considered as a long-term prognostic biomarker in diabetes-free adults.

Metamodel-Based Slope Reliability Analysis—Case of Spatially Variable Soils Considering a Rotated Anisotropy

A rotation of the anisotropic soil fabric pattern is commonly observed in natural slopes with a tilted stratification. This study investigates the rotated anisotropy effects on slope reliability considering spatially varied soils. Karhunen–Loève expansion is used to generate the random fields of the soil shear strength properties (i.e., cohesion and friction angle). The presented probabilistic analyses are based on a meta-model combining Sparse Polynomial Chaos Expansion (SPCE) and Global Sensitivity Analysis (GSA). This method allows the number of involved random variables to be reduced and then the computational efficiency to be improved. Two kinds of deterministic models, namely a discretization kinematic approach and a finite element limit analysis, are considered. A variety of valuable results (i.e., failure probability, probability density function, statistical moments of model response, and sensitivity indices of input variables) can be effectively provided. Moreover, the influences of the rotated anisotropy, autocorrelation length, coefficient of variation and cross-correlation between the cohesion and friction angle on the probabilistic analysis results are discussed. The rotation of the anisotropic soil stratification has a significant effect on the slope stability, particularly for the cases with large values of autocorrelation length, coefficient of variation, and cross-correlation coefficient.

Global Sensitivity Analysis of Ultimate Limit States of Stainless Steel Structural Members

The article presents global Sobol sensitivity analysis of a rolled member in tension made from austenitic chromium-nickel stainless steel of type 1.4307/AISI 304 L. The statistical characteristics of yield strength and of the geometry of the rolled steel IPE cross-section are presented on the basis of published experimental research. The sensitivity analysis showed the dominant effect of the yield strength on the static resistance. The second dominant variable is the flange thickness. Higher-order sensitivity indices oriented at detecting the presence of interaction effects between input variables are very small. The characteristics of other types of sensitivity analyses oriented at quantiles or the probability of failure are discussed, especially in terms of a higher proportion of higher-order sensitivity indices. The results of Sobol sensitivity analysis of stainless steel are compared with similar results of carbon steels.