Stochastic Sensitivity Analysis: Or What Happened to my Tornado Plot?

This study focuses on fatigue reliability in steel bridges, a critical concern due to increasing traffic loads. Employing the S-N curve method, a Stochastic Sensitivity Analysis (SSA) is conducted to assess the impact of input parameters. Miner’s rule and fracture mechanics are compared for fatigue assessment, considering uncertainties through stochastic sensitivity analysis. Material-related factors and the equivalent stress range are identified as pivotal contributors to fatigue reliability. The study emphasizes the importance of understanding influential parameters for improved design and predictive insights in structural behavior.

The International Commission on Radiological Protection (ICRP) has developed the reference Human Respiratory Tract Model (HRTM), detailed in ICRP Publications 66 and 130, to estimate the deposition and clearance of inhaled radionuclides. These models utilize reference anatomical and physiological parameters for particle deposition (PD). Biokinetic models further estimate retention and excretion of internalized particulates, aiding the derivation of inhalation dose coefficients (DC). This study aimed to assess variability in deterministic131I biokinetic and dosimetry models through stochastic analysis using the updated HRTM from ICRP Publication 130. The complexities of the ICRP PD model were reconstructed into a new, independent computational model. Comparison with reference data for total PD fractions for reference worker, solely a nose breather, covering activity median aerodynamic diameters from 0.3μm to 20μm, showed a 1.04% relative and 0.7% absolute difference, demonstrating good agreement with ICRP deposition fractions. The deterministic DC module was reconstructed in Python and expanded for stochastic analysis, systematically expanding deposition components from HRTM and assigning probability distribution functions to uncertain parameters. These were integrated into an in-house stochastic radiological exposure dose calculator, utilizing latin hypercube sampling. A case of an occupational radionuclide intake was explored, in which biodistribution and committed effective DC (CEDC) were computed for131I type F, considering a lognormal particle size distribution with a median of 5μm. Results showed the published ICRP reference CEDC marginally exceeds the 75th percentile of observed samples, with log-gamma distribution as the best-fit probability distribution. A Random Forest regression model with SHapley Additive exPlanations was employed for sensitivity analysis to predict feature importance. The analysis identified the HRTM particle transport rates scaling factor, followed by the aerodynamic deposition efficiency in the alveolar interstitial region as the most impactful parameters. This study offers a unique stochastic approach on inhaled particulate metabolism, enhancing radiation consequence management, medical countermeasures, and dose reconstruction for epidemiological studies.

SummaryIn this study, a post optimization technique for a correction of inaccurate optimum obtained using first‐order reliability method (FORM) is proposed for accurate reliability‐based design optimization (RBDO). In the proposed method, RBDO using FORM is first performed, and then the proposed second‐order reliability method (SORM) is performed at the optimum obtained using FORM for more accurate reliability assessment and its sensitivity analysis. In the proposed SORM, the Hessian of a performance function is approximated by reusing derivatives information accumulated during previous RBDO iterations using FORM, indicating that additional functional evaluations are not required in the proposed SORM. The proposed SORM calculates a probability of failure and its first‐order and second‐order stochastic sensitivity by applying the importance sampling to a complete second‐order Taylor series of the performance function. The proposed post optimization constructs a second‐order Taylor expansion of the probability of failure using results of the proposed SORM. Because the constructed Taylor expansion is based on the reliability method more accurate than FORM, the corrected optimum using this Taylor expansion can satisfy the target reliability more accurately. In this way, the proposed method simultaneously achieves both efficiency of FORM and accuracy of SORM. Copyright © 2015 John Wiley & Sons, Ltd.

In the stochastic sensitivity analysis, a large number of simulation models lead to low computational e‐ciency. With the dimension increasing in assigned problems, the accurate is di‐cult to achieve by popular regression methodologies. Without considering the correlations of parameters, inaccurate sensitivity coe‐cients would be calculated by analyzing the efiect of parametric variables on structures, moreover, the existing methods only calculate the local gradient as sensitivity. According to these problems, approximate model and global sensitivity method are employed for design sensitivity analysis of structures. The approximate model is constructed by the hybrid neural network which possesses signiflcant learning capacity and generalization capability with a small amount of information. The improved chaotic particle swarm is applied to optimize the neural network so as to improve the computational e‐ciency and accuracy. The proposed sensitivity analysis method values the global response of the outputs by varying all the input parameters at a time with the correlations of parameters. Uniform design and Latin hypercube sampling are used to sample points. Numerical analysis show that the proposed method can successfully measure the actual sensitivity.

SUMMARYThis paper presents three new computational methods for calculating design sensitivities of statistical moments and reliability of high‐dimensional complex systems subject to random input. The first method represents a novel integration of the polynomial dimensional decomposition (PDD) of a multivariate stochastic response function and score functions. Applied to the statistical moments, the method provides mean‐square convergent analytical expressions of design sensitivities of the first two moments of a stochastic response. The second and third methods, relevant to probability distribution or reliability analysis, exploit two distinct combinations built on PDD: the PDD‐saddlepoint approximation (SPA) or PDD‐SPA method, entailing SPA and score functions; and the PDD‐Monte Carlo simulation (MCS) or PDD‐MCS method, utilizing the embedded MCS of the PDD approximation and score functions. For all three methods developed, the statistical moments or failure probabilities and their design sensitivities are both determined concurrently from a single stochastic analysis or simulation. Numerical examples, including a 100‐dimensional mathematical problem, indicate that the new methods developed provide not only theoretically convergent or accurate design sensitivities, but also computationally efficient solutions. A practical example involving robust design optimization of a three‐hole bracket illustrates the usefulness of the proposed methods. Copyright © 2014 John Wiley & Sons, Ltd.

The presence of time-varying electromagnetic fields across a neuron cell may cause changes in its electrical characteristics, most notably, in the action potential dynamics. This phenomenon is examined by simulating electrophysiology of a single cortex neuron. Magnetic flux is captured by using a polynomial approximation of a memristor embedded into Hodgkin–Huxley model, equivalent electrical circuit of a neuron cell. Bifurcation analysis is carried out for two different electrical modes associated with the nature of the external neuronal stimulus. Aiming to determine the true influence of the variability of ion channels conductivity, the stochastic sensitivity analysis is undertaken post hoc. Additionally, numerical simulations are enriched with uncertainty quantification, observing values of ion channel conductivity as random variables. The aim of the study is to computationally determine the sensitivity of the action potential dynamics with respect to changes in conductivity of each ion channel so that the future experimental procedures, most often medical treatments, may be adapted to different individuals in various environmental conditions.

Oseltamivir is effective in the treatment of influenza. Utilisation in The Netherlands is limited, but increasing. To estimate the cost effectiveness of oseltamivir treatment (vs symptom relief only) for patients with influenza-like illness (ILI) who are at increased risk for serious complications of influenza. A cost-effectiveness analysis was used, building on a previously developed model (decision tree) that was applied for evaluating influenza vaccination and pandemic preparedness plans. Three patient subgroups were assessed (elderly patients [aged > or = 65 years] without chronic disease, elderly patients with chronic disease, and chronically ill, non-elderly patients). Inputs for the model were taken from various sources including a meta-analysis. A societal perspective was adopted and costs were expressed in euro per life-year gained (year 2003 values). Life-years lost were discounted at 4% in accordance with Dutch guidelines. Deterministic and probabilistic sensitivity analyses were employed to assess the robustness of the results. For chronically ill patients with ILI, visits to the GP for oseltamivir treatment were cost saving. For non-chronically ill elderly patients, incremental cost-effectiveness was estimated at 1759 euros per life-year gained. Cost savings and favourable cost effectiveness were robust in a deterministic and stochastic sensitivity analysis. Our model-based analysis suggests that at-risk people presenting with ILI to a GP could be offered oseltamivir at favourable cost effectiveness or even cost savings in the Dutch setting compared with symptom relief with analgesics only.

BackgroundThe effectiveness of specific regimens of adjuvant therapy for gastric cancer has not been verified by large clinical trials. Recently, several large trials attempted to verify the effectiveness of adjuvant therapy. The Adjuvant Chemotherapy Trial of TS-1 for Gastric Cancer in Japan, a randomized controlled trial of adjuvant S-1 therapy for resected gastric cancer, demonstrated significant improvement in overall and relapse-free survival, compared to surgery alone. To evaluate value for money of S-1 therapy, cost-effective analysis was carried out.MethodsThe analysis was carried out from a payer’s perspective. As an economic measure, cost per quality-adjusted life-year (QALY) gained was estimated. Overall survival was estimated by the Kaplan-Meier method, up to 5-year observation. Beyond this period, it was simulated by the modified Boag model. Utility score is derived from interviews with sampled patients using a time trade-off method. Costs were estimated from trial data during observation, while in the period beyond observation they were estimated using simulation results. To explore uncertainty of the results, qualitative and stochastic sensitivity analyses were done.ResultsAdjuvant S-1 therapy gained 1.24 QALYs per patient and increased costs by $3,722 per patient for over lifetime (3% discount rate for both effect and costs). The incremental cost-effectiveness ratio (95% confidence intervals) for over lifetime was estimated to be $3,016 ($1,441, $8,840) per QALY. The sensitivity analyses showed the robustness of these results.ConclusionAdjuvant S-1 therapy for curatively resected gastric cancer is likely cost-effective. This therapy can be accepted for wide use in Japan.

Sensitivity analysis of parametric uncertainties and modeling errors in computational-mechanics models by using a generalized probabilistic modeling approach

The general characteristics of deep water offshore field development are the uncertainty of geological conditions, high technology requirements and development costs, and volatility of oil and gas prices. Despite these challenges, the development of a deep water offshore field remains a strategic project for sustainable economic growth. This study will evaluate the impact of current fiscal of the three offshore field development and estimates the limits of oil and gas price, reserves, and expenses. The intention is to obtain the optimal conditions to encourage the development of new offshore fields. The approached will used a discounted cash flow modelling, followed by evaluate the profitability risk using deterministic and stochastic sensitivity analysis. Monte Carlo simulation used to take into account the uncertainty of several variables, such as oil and gas prices, operating costs, development costs, and reserves. The result shows that investment decisions for the development of new and/or extensions fields in offshore areas remain quite challenging economically, considering to the high development and operating costs, as well as fluctuating of oil and gas prices. The opportunity to obtain a positive net present value on new deep water offshore development fields is less than 41%, thus indicates that further initiative of cost efficiency and fiscal incentive is required in preparing investment planning of new deep water offshore field to compensate the high development and operational cost.

Non-intrusive polynomial chaos expansion (PCE) and stochastic collocation (SC) methods are attractive techniques for uncertainty quantification (UQ) due to their strong mathematical basis and ability to produce functional representations of stochastic variability. PCE estimates coefficients for known orthogonal polynomial basis functions based on a set of response function evaluations, using sampling, linear regression, tensor-product quadrature, or Smolyak sparse grid approaches. SC, on the other hand, forms interpolation functions for known coefficients, and requires the use of structured collocation point sets derived from tensor product or sparse grids. When tailoring the basis functions or interpolation grids to match the forms of the input uncertainties, exponential convergence rates can be achieved with both techniques for a range of probabilistic analysis problems. In addition, analytic features of the expansions can be exploited for moment estimation and stochastic sensitivity analysis. In this paper, the latest ideas for tailoring these expansion methods to numerical integration approaches will be explored, in which expansion formulations are modified to best synchronize with tensor-product quadrature and Smolyak sparse grids using linear and nonlinear growth rules. The most promising stochastic expansion approaches are then carried forward for use in new approaches for mixed aleatory-epistemic UQ, employing second-order probability approaches, and design under uncertainty, employing bilevel, sequential, and multifidelity approaches.

The inherent heavy use of computer-based numerical methods in stochastic modeling has given rise to the natural application of mathematical computer packages to queueing analyses. We present a summary of how our queueing package, QTK, was built up from the well-established TK Solver tool kit of mathematical problemsolving routines. The rule-based, interactive TK software is especially well suited for easy access from the desktop, and, with the queueing modules added, it now permits queueing analyses that include complex “what if?” exercises; comprehensive, stochastic sensitivity analyses; the natural adaptation of standard modules to problems very different than those in the package; and the establishment of cost models and their optimization.

Uncertainty propagation analysis of an N 2O emission model at the plot and landscape scale

We study the effects of noise and diffusion in an excitable slow-fast population system of the Leslie-Gower type. The phenomenon of noise-induced excitement is investigated in the zone of stable equilibria near the Andronov-Hopf bifurcation with the Canard explosion. The stochastic generation of mixed-mode oscillations is studied by numerical simulation and stochastic sensitivity analysis. Effects of the diffusion are considered for the spatially distributed variant of this slow-fast population model. The phenomenon of the diffusion-induced generation of spatial patterns-attractors in the Turing instability zone is demonstrated. The multistability and variety of transient processes of the pattern formation are discussed. This article is part of the theme issue 'Patterns in soft and biological matters'.

The capture and storage of CO2 from combustion of fossil fuels is gaining attraction as a means to deal with climate change. CO2 emissions from biomass conversion processes can also be captured. If that is done, biomass energy with CO2 capture and storage (BECS) would become a technology that removes CO2 from the atmosphere and at the same time deliver CO2-neutral energy carriers (heat, electricity or hydrogen) to society. Here we present estimates of the costs and conversion efficiency of electricity, hydrogen and heat generation from fossil fuels and biomass with CO2 capture and storage. We then insert these technology characteristics into a global energy and transportation model (GET 5.0), and calculate costs of stabilizing atmospheric CO2 concentration at 350 and 450 ppm. We find that carbon capture and storage technologies applied to fossil fuels have the potential to reduce the cost of meeting the 350 ppm stabilisation targets by 50% compared to a case where these technologies are not available and by 80% when BECS is allowed. For the 450 ppm scenario, the reduction in costs is 40 and 42%, respectively. Thus, the difference in costs between cases where BECS technologies are allowed and where they are not is marginal for the 450 ppm stabilization target. It is for very low stabilization targets that negative emissions become warranted, and this makes BECS more valuable than in cases with higher stabilization targets. Systematic and stochastic sensitivity analysis is performed. Finally, BECS opens up the possibility to remove CO2 from the atmosphere. But this option should not be seen as an argument in favour of doing nothing about the climate problem now and then switching on this technology if climate change turns out to be a significant problem. It is not likely that BECS can be initiated sufficiently rapidly at a sufficient scale to follow this path to avoiding abrupt and serious climate changes if that would happen.