General Sensitivity Analysis Research Articles

Sensitivity analysis for matched observational studies with continuous exposures and binary outcomes

Summary Matching is one of the most widely used study designs for adjusting for measured confounders in observational studies. However, unmeasured confounding may exist and cannot be removed by matching. Therefore, a sensitivity analysis is typically needed to assess a causal conclusion’s sensitivity to unmeasured confounding. Sensitivity analysis frameworks for binary exposures have been well-established for various matching designs and are commonly used in various studies. However, unlike the binary exposure case, there still lacks valid and general sensitivity analysis methods for continuous exposures, except in some special cases such as pair matching. To fill this gap in the binary outcome case, we develop a sensitivity analysis framework for general matching designs with continuous exposures and binary outcomes. First, we use probabilistic lattice theory to show our sensitivity analysis approach is finite-population- exact under Fisher’s sharp null. Second, we prove a novel design sensitivity formula as a powerful tool for asymptotically evaluating the performance of our sensitivity analysis approach. Third, to allow effect heterogeneity with binary outcomes, we introduce a framework for conducting asymptotically exact inference and sensitivity analysis on generalized attributable effects with binary outcomes via mixed- integer programming. Fourth, for the continuous outcomes case, we show that conducting an asymptotically exact sensitivity analysis in matched observational studies when both the exposures and outcomes are continuous is generally NP-hard, except in some special cases such as pair matching. As a real data application, we apply our new methods to study the effect of early-life lead exposure on juvenile delinquency. An implementation of the methods in this work is available in the R package doseSens.

Data poisoning attacks on traffic state estimation and prediction

Data has become ubiquitous nowadays in transportation, including vehicular data and infrastructure-generated data. The growing reliance on data poses potential cybersecurity issues to transportation systems, among which the so-called “data poisoning” attacks by adversaries are becoming increasingly critical. Such attacks aim to compromise a system’s performance by adding systematic and malicious noises, perturbations, or deviations to the dataset used by the system. Formal investigations of data poisoning attacks are essential for understanding the attacks and developing effective defense methods. This study develops a general data poisoning attack model for traffic state estimation and prediction (TSEP) that is a basic application in transportation. We first formulate data poisoning attacks as a general sensitivity analysis of parameterized optimization problems over parameter changes (i.e., data perturbations) and study the Lipschitz continuity property of the solution with the presence of general (equality and inequality) constraints. Then, we develop attack models that fit a broader spectrum of learning applications (such as TSEP) by extending existing models that only focus on learning problems with no or equality constraints (widely used in the cybersecurity field). Since the solution of such general problems is often continuous but not differentiable with data changes, we apply the generalized implicit function theorem to compute the semi-derivatives that express how the TSEP solution responds to data perturbations. The semi-derivatives enable us to evaluate TSEP models’ vulnerability (at each data point) and solve the proposed attack model. We demonstrate the generality and effectiveness of the proposed method on two TSEP models using mobile sensing data.

Error propagation and attribution in simulation-based capital models

AbstractCalculation of loss scenarios is a fundamental requirement of simulation-based capital models and these are commonly approximated. Within a life insurance setting, a loss scenario may involve an asset-liability optimization. When cashflows and asset values are dependent on only a small number of risk factor components, low-dimensional approximations may be used as inputs into the optimization and resulting in loss approximation. By considering these loss approximations as perturbations of linear optimization problems, approximation errors in loss scenarios can be bounded to first order and attributed to specific proxies. This attribution creates a mechanism for approximation improvements and for the eventual elimination of approximation errors in capital estimates through targeted exact computation. The results are demonstrated through a stylized worked example and corresponding numerical study. Advances in error analysis of proxy models enhance confidence in capital estimates. Beyond error analysis, the presented methods can be applied to general sensitivity analysis and the calculation of risk.

Causal moderated mediation analysis: Methods and software.

Research questions regarding how, for whom, and where a treatment achieves its effect on an outcome have become increasingly valued in substantive research. Such questions can be answered by causal moderated mediation analysis, which assesses the heterogeneity of the mediation mechanism underlying the treatment effect across individual and contextual characteristics. Various moderated mediation analysis methods have been developed under the traditional path analysis/structural equation modeling framework. One challenge is that the definitions of moderated mediation effects depend on statistical models of the mediator and the outcome, and no solutions have been provided when either the mediator or the outcome is binary, or when the mediator or outcome model is nonlinear. In addition, it remains unclear to empirical researchers how to make causal arguments of moderated mediation effects due to a lack of clarifications of the underlying assumptions and methods for assessing the sensitivity to violations of the assumptions. This article overcomes the limitations by developing general definition, identification, estimation, and sensitivity analysis for causal moderated mediation effects under the potential outcomes framework. We also developed a user-friendly R package moderate.mediation ( https://cran.r-project.org/web/packages/moderate.mediation/index.html ) that allows applied researchers to easily implement the proposed methods and visualize the initial analysis results and sensitivity analysis results. We illustrated the application of the proposed methods and the package implementation with a re-analysis of the National Evaluation of Welfare-to-Work Strategies (NEWWS) Riverside data.

Sensitivity study of thermal response test using resistively heated methods under various setups

Thermal response tests employing resistively heated methods (TRT-RH) have shown advanced performance in evaluating ground properties, while the effect of various TRT-RH setups is still vague in practice. This study examines the effect of different TRT-RH setups based on numerically generated data and field data. As a result, the various setups alter the heat transfer and change the test time required to meet the ideal linear heat source (ILHS) assumption. Time thresholds that indicate TRT-RH are positively related to eccentric distance, negatively related to borehole radius, and positively related to grout thermal conductivity difference. The distance-based general sensitivity analysis result shows that the radius of the borehole or trench, which separates the heat source and the ground, has intensive sensitivity to the test effectivity. This study presents the standard setup strategy for TRT-RH to measure the thermal and hydraulic properties based on the ILHS assumption.

Thunderstorm gust response factor: General tendencies and sensitivity analysis

This paper aims to provide a sensitivity analysis of the thunderstorm gust response factor. The study is based on the extension of the gust response factor technique to the assessment of the maximum dynamic response of structures to thunderstorm outflows, starting from an evolutionary spectral model of the thunderstorm wind speed. The thunderstorm evolutionary spectral model depends on the modulating function of the slowly-varying mean speed, which is a function of two parameters, i.e. the background mean wind speed and the duration of the intense phase of the outflow. Starting from 129 full-scale thunderstorm records, the parameters of three different analytical models of the modulating function are extracted and a statistical analysis is carried out defining their range of variation. The dependence of the gust response factor on the analytical expression of the modulating function is studied as well as its sensitivity to the parameters of the function. Results show that the dependence of the gust response factor on the analytical expression of the modulating function is negligible, while it is very sensitive to the variation of the background wind and duration of the intense phase, especially for flexible and lowly-damped systems.

Scattering attenuation of transient SH-wave by an orthotropic gaussian-shaped sedimentary basin

• Scattering attenuation of transient SH -wave. • Orthotropic Gaussian-shaped sedimentary basin. • Time-domain boundary element method. • Illustrating the responses in time and frequency domains. • Isotropy-factor, wave angle, and geometrical effect of sedimentary basin. The surface motion of an orthotropic Gaussian-shaped sedimentary basin embedded in a linear elastic half-space was successfully obtained under transient SH -wave propagation. In the use of the time-domain boundary element approach, a simple model was developed only by discretizing the interface. To achieve better convergence of the response, an attenuation rule was implemented with the assistance of the reduction exponential function applied in the boundary integral equations. After a brief overview of the method, the heterogonous sub-structured basin model was created and decomposed into two parts to satisfy the modified continuity conditions based on the normal direction at the interface node position. Then, the coupled matrices were temporarily solved at each time-step to obtain the boundary values. The developed computer code was tested by solving a validation example. Finally, to illustrate the valley surface response in the time/frequency-domain, a general sensitivity analysis was performed by considering the parameters of frequency, shape-ratio, isotropy-factor, and wave angle in the form of snapshots, seismograms, and amplification patterns. The results showed that the effect of orthotropic anisotropy was very efficient on the ground response and different seismic patterns on the surface of sedimentary basins were extracted by changes in the quantity of this parameter.

Assessment of RELAP5/MOD3.2 for simulating density wave oscillation with a two-phase natural circulation test facility

The slight boiling mode (SBM) of the nuclear heating reactor (NHR) designed to operating under two-phase natural circulation with low vapor quality and PWR-type reactor design is rigorously constrained by the flow instability and the extent of saturated boiling in the core. The objective of this study is to evaluate the applicability of the RELAP5 code to simulate flow instability in natural circulation systems and then to quantitatively estimate the operating parameters space of the SBM. Based on a well-scaled facility of NHR200, a RELAP5 model is developed. After a general assessment, sensitivity analysis and frequency spectrum analysis of flow resistance coefficients, numerical method, and drift velocity are further conducted for better understanding the deviations existing in simulations. It can be found that the nature of density wave oscillation (DWO) can be revealed by the RELAP5 code from the reasonable agreements between the simulation results and experimental data. Furthermore, a reasonable calibration of the drift velocity can greatly improve the accuracy of both static parameters and oscillating characteristic frequency. Ultimately, quantitative calculation of the operating parameter space is achieved with the RELAP5 code assisted by the dimensionless number Nsub/Npch. This work paves the way for studying the start-up and operating characteristics of SBM.

Nonlinear Schrodinger Equation-Based Adjoint Sensitivity Analysis

A general nonlinear adjoint sensitivity analysis (ASA) approach for the time-dependent nonlinear Schrodinger equation (NLSE) is presented. The proposed algorithm estimates the sensitivities of a desired objective function with respect to all design parameters using only one extra adjoint system simulation. The approach efficiency is shown here through a numerical example.

VOID COEFFICIENT SENSITIVITY ANALYSIS FOR THE TRIGA MARK II REACTOR AT L.E.N.A. (UNIPV)

Sensitivity analysis studies the effect of a change in a given parameter to a response function of the system under investigation. In reactor physics, this usually translates into the study of how cross sections and fission spectrum modifications affect the value of the multiplication factor, the delayed neutron fraction or the void coefficient for example. Generalized Perturbation Theory provides a useful tool for the assessment of adjoint weighed functions such as keff and void coefficient sensitivities. In this work, the capability of SERPENT code to perform sensitivity calculation based on GPT is used to study the TRIGA Mark II research reactor installed at L.E.N.A. of University of Pavia. A general sensitivity analysis to the most important reactor’s cross sections has been performed in order to highlight the biggest reactivity contributions. Two numerically challenging tasks related to GPT calculation have been performed thanks to the relatively quick Monte Carlo approach allowed by this reactor: investigating the linearity of the reactivity injection caused by the flooding of the central channel, and calculating the fuel void coefficient sensitivity to the coolant density.

Third order adjoint sensitivity analysis of reaction rate responses in a multiplying nuclear system with source

Until recently, the 2nd-order sensitivities of reactor physics model responses to the nuclear data characterizing the respective model were impractical to compute exactly and exhaustively, because of the so-called “curse of dimensionality.” Hence, the effects of the 2nd-order sensitivities on the uncertainties produced in responses by the uncertain nuclear data have been routinely neglected. Recently, the author has developed a general 2nd-order adjoint sensitivity analysis methodology which overcame the “curse of dimensionality” to perform the first-ever complete computation of the exact 21,976 first-order, and 482,944,576 s-order sensitivities for a OECD/NEA reactor physics benchmark response to the uncertain nuclear data that characterize the neutron transport computational model of this benchmark. In particular, the numerical results obtained for the benchmark’s leakage response with respect to the benchmark’s group-averaged isotopic total cross sections indicated that, contrary to the widely held belief that the 2nd-order response sensitivities in reactor physics systems are negligible, the opposite turned out to be the case, i.e., many of the 2nd-order sensitivities were orders of magnitude larger than the corresponding 1st-order ones. Consequently, neglecting the 2nd-order sensitivities would cause very large non-conservative errors by under-reporting the response variance and erroneously reporting its expected value.The fact that a large number of 2nd-order response sensitivities are significantly larger than the 1st-order sensitivities has motivated the development of the general expressions presented in this work for the efficient and exact computation of the 3rd-order response sensitivities of reaction rate responses to nuclear data for subcritical reactor physics systems modeled by the neutron transport equation. The mathematical results derived in this work are currently implemented in production-oriented three-dimensional neutron transport code systems to enable the computation of 3rd-order sensitivities of reactor physics systems, commencing with the OECD/NEA benchmark mentioned above.

Impedance Modeling and Controllers Shaping Effect Analysis of PMSG Wind Turbines

Oscillation issues of permanent magnet synchronous generator (PMSG) wind turbines (WTs) have an increasingly significant impact on grid stability, especially with their increased generation capacity. However, the machine-side model (MSM), involving machine-side converter (MSC) and generator, is generally simplified as an ideal voltage source to comprising the impedance model of a PMSG-WT used for stability analysis, thus causing deficiency in describing the machine dynamics. Besides, the impedance-based method considering the PMSG-WT as a black box only describes the system from the external output characteristics; as such, the shaping effect of the internal controllers on the impedance model has not been fully studied yet. This article proposes the impedance model of PMSG-WTs consisting of generator, MSC, dc-bus and grid-side converter (GSC) for more accurate stability analysis. Furthermore, based on the general Nyquist criteria (GNC) and eigenvalue sensitivity analysis method, the shaping effect of the controllers inside GSC and MSC on the PMSG external impedance is quantitatively studied. The influence of the MSM on the system stability is investigated by comparing with the simplified model through extensive simulation studies.

Life cycle assessment as a decision-making tool for the design of urban solid waste pre-collection and collection/transport systems

This paper compares the environmental performance of different municipal waste pre-collection and collection/transport systems, using the life cycle assessment methodology. The scenarios compared consider conventional containerisation systems, underground containerisation and pneumatic collection/transport systems.The results show that pneumatic systems have a greater impact on climate change, acidification, particulate matter and stratospheric ozone depletion due to their significant electricity consumption and the environmental impact of pipelines manufacture. However, in relation to terrestrial eutrophication and photochemical ozone formation, underground containers exhibit a greater impact.A general sensitivity analysis was carried out, for all of the scenarios analysed, and a specific one for the pneumatic scenario. Results show that the environmental impact of pneumatic systems and underground containerization is higher than that of conventional systems. These results are completely determined by the consumption of materials (in the two cases) and energy (for pneumatic scenario). This environmental conclusion has to be taken into account for policy making in urban areas, along with other social and economic aspects.In terms of climate change, the comparison allows us to conclude that pneumatic systems have a carbon footprint 119% higher than the lowest impact scenario (side-loading containers located in drop-off-points). Among the conventional pre-collection and collection/transport scenarios, the one with the greatest carbon footprint is the one that uses underground containers; 16% higher than the scenario with side-loading containers located at drop-off-points. Among the scenarios that use conventional containers on the surface, the door-to-door scenario has the greatest impact.

A General Sensitivity Analysis Approach for Demand Response Optimizations

In this work, we build upon existing literature on the demand response (DR) market, which consists of price-taking prosumers each with various appliances, an electric utility company and a social welfare optimizing distribution system operator, to design a general sensitivity analysis approach (GSAA) that can quantitatively estimate the potential of each consumer's contribution to the social welfare when given more resource capacity, such as allowing net-selling behavior. GSAA is based on existence of an efficient competitive equilibrium, which we establish in the paper. When prosumers' utility functions are quadratic, GSAA can give closed forms characterization on social welfare improvement based on duality analysis. Furthermore, we extend GSAA to a general convex settings, i.e., utility functions with strong convexity and Lipschitz continuous gradient. Even without knowing the specific forms the utility functions, we can derive upper and lower bounds of the social welfare improvement potential of each prosumer, when extra resource is introduced. For both settings, several applications and numerical examples are provided: including extending AC comfort zone, ability of EV to discharge and net-selling behavior. The estimation results show that GSAA can be used to decide how to allocate potentially limited DR market resources in a more impactful way.

The optimal stopping problem revisited

We consider an optimal stopping time problem, related with many models found in real options problems. We present analytical solutions for a broad class of gain functions, considering quite general assumptions over the model. Also, an extensive and general sensitivity analysis is provided.

A thermostatted kinetic theory model for event-driven pedestrian dynamics

This paper is devoted to the modeling of the pedestrian dynamics by means of the thermostatted kinetic theory. Specifically the microscopic interactions among pedestrians and an external force field are modeled for simulating the evacuation of pedestrians from a metro station. The fundamentals of the stochastic game theory and the thermostatted kinetic theory are coupled for the derivation of a specific mathematical model which depicts the time evolution of the distribution of pedestrians at different exits of a metro station. The perturbation theory is employed in order to establish the stability analysis of the nonequilibrium stationary states in the case of a metro station consisting of two exits. A general sensitivity analysis on the initial conditions, the magnitude of the external force field and the number of exits is presented by means of numerical simulations which, in particular, show how the asymptotic distribution and the convergence time are affected by the presence of an external force field. The results show how, in evacuation conditions, the interaction dynamics among pedestrians can be negligible with respect to the external force. The important role of the thermostat term in allowing the reaching of the nonequilibrium stationary state is stressed out. Research perspectives are underlined at the end of paper, in particular for what concerns the derivation of frameworks that take into account the definition of local external actions and the introduction of the space and velocity dynamics.

Fuel Evaporation in an Atmospheric Premixed Burner: Sensitivity Analysis and Spray Vaporization

Calculation of evaporation requires accurate thermophysical properties of the liquid. Such data are well-known for conventional fossil fuels. In contrast, e.g., thermal conductivity or dynamic viscosity of the fuel vapor are rarely available for modern liquid fuels. To overcome this problem, molecular models can be used. Currently, the measurement-based properties of n-heptane and diesel oil are compared with estimated values, using the state-of-the-art molecular models to derive the temperature-dependent material properties. Then their effect on droplet evaporation was evaluated. The critical parameters were liquid density, latent heat of vaporization, boiling temperature, and vapor thermal conductivity where the estimation affected the evaporation time notably. Besides a general sensitivity analysis, evaporation modeling in a practical burner ended up with similar results. By calculating droplet motion, the evaporation number, the evaporation-to-residence time ratio can be derived. An empirical cumulative distribution function is used for the spray of the analyzed burner to evaluate evaporation in the mixing tube. Evaporation number did not exceed 0.4, meaning a full evaporation prior to reaching the burner lip in all cases. As droplet inertia depends upon its size, the residence time has a minimum value due to the phenomenon of overshooting.

Sensitivity and Uncertainty Analysis of Counter-Flow Mechanical Draft Cooling Towers—I: Adjoint Sensitivity Analysis

For counter-flow mechanical draft cooling towers, the air in the fill can reach the point of saturation before leaving the fill section. The heat and mass transfer to the saturated air by evaporative cooling inside the fill are modeled with some assumptions and with over 50 parameters for boundary conditions, cooling tower geometries, heat and mass transfer correlations, water and air thermal properties, etc. Because of the parameter uncertainties and modeling assumptions, the accuracy and reliability of the cooling tower model need to be evaluated by quantifying the uncertainties associated with the model output. First, sensitivities of the model output with respect to all the model parameters need to be analyzed. Based on the cooling tower model, this work developed adjoint sensitivity models for the saturated case to compute efficiently and exactly the sensitivities of the model responses to all model parameters by applying the general adjoint sensitivity analysis methodology for nonlinear systems. The solution of the adjoint sensitivity models are independently verified. With the sensitivities known, the model parameters can be ranked in their importance for contributing to response uncertainties. The propagation of the uncertainties in the model parameters to the uncertainties in the model outputs can be evaluated. By further applying the predictive modeling for coupled multiphysics systems methodology, the cooling tower model for the saturated case can be improved by reducing the model prediction uncertainties through assimilation of experimental measurements and calibration of model parameters.

Response sensitivity analysis for plastic plane problems based on direct differentiation method

Response sensitivity analysis is of significant value to solve various inverse problems in engineering practice using gradient-based optimization algorithms. In the context of finite element (FE) method, an efficient, accurate and general sensitivity analysis approach, namely the direct differentiation method (DDM), has been developed and extended to various element and material models. However, the DDM has not been addressed for the response sensitivity of plastic plane problems (i.e., plane stress and plane strain problems), in spite of their wide applications in practice. This paper bridges this gap by extending the DDM based response sensitivity algorithm to general plastic plane problems, which is solved by taking advantage of general three dimensional (3D) constitutive models. The newly developed DDM-based sensitivity analysis algorithm is implemented in the open source finite element framework (OpenSees) and verified using two realistic application examples of plane problems, i.e., a concrete dam and a steel shear wall. The efficiency and accuracy of the DDM are verified by using the forward finite difference method.

Predictive Modeling of a Buoyancy-Operated Cooling Tower under Unsaturated Conditions: Adjoint Sensitivity Model and Optimal Best-Estimate Results with Reduced Predicted Uncertainties

Nuclear and other large-scale energy-producing plants must include systems that guarantee the safe discharge of residual heat from the industrial process into the atmosphere. This function is usually performed by one or several cooling towers. The amount of heat released by a cooling tower into the external environment can be quantified by using a numerical simulation model of the physical processes occurring in the respective tower, augmented by experimentally measured data that accounts for external conditions such as outlet air temperature, outlet water temperature, and outlet air relative humidity. The model’s responses of interest depend on many model parameters including correlations, boundary conditions, and material properties. Changes in these model parameters induce changes in the computed quantities of interest (called “model responses”), which are quantified by the sensitivities (i.e., functional derivatives) of the model responses with respect to the model parameters. These sensitivities are computed in this work by applying the general adjoint sensitivity analysis methodology (ASAM) for nonlinear systems. These sensitivities are subsequently used for: (i) Ranking the parameters in their importance to contributing to response uncertainties; (ii) Propagating the uncertainties (covariances) in these model parameters to quantify the uncertainties (covariances) in the model responses; (iii) Performing model validation and predictive modeling. The comprehensive predictive modeling methodology used in this work, which includes assimilation of experimental measurements and calibration of model parameters, is applied to the cooling tower model under unsaturated conditions. The predicted response uncertainties (standard deviations) thus obtained are smaller than both the computed and the measured standards deviations for the respective responses, even for responses where no experimental data were available.