Modeling a production scale milk drying process: parameter estimation, uncertainty and sensitivity analysis

Identifying key sources of uncertainty in the modelling of greenhouse gas emissions from wastewater treatment

This paper focuses on the application of the variance-based global sensitivity analysis for a topological derivative method in order to solve a stochastic nonlinear time-dependent magnetoquasi-static interface problem. To illustrate the approach a permanent magnet (PM) synchronous machine has been considered. Our key objective is to provide a robust design of the rotor poles and of the tooth base in a stator for the reduction of the torque ripple and electromagnetic losses, while taking material uncertainties into account. Input variations of material parameters are modeled using the polynomial chaos expansion technique, which is incorporated into the stochastic collocation method in order to provide a response surface model. Additionally, we can benefit from the variance-based sensitivity analysis. This allows us to reduce the dimensionality of the stochastic optimization problems, described by the random-dependent cost functional. Finally, to validate our approach, we provide the 2-D simulations and analysis, which confirm the usefulness of the proposed method and yield a novel topology of a PM synchronous machine.

Modeling green recycled aggregate concrete using machine learning and variance-based sensitivity analysis

Variance-based sensitivity analysis is a well established tool for evaluating the contribution of the uncertainties in the inputs to the uncertainty in the output of a general mathematical model. While the literature on this subject is quite extensive, it has not found widespread use in metrological applications. In this article we present a succinct review of the fundamentals of sensitivity analysis, in a form that should be useful to most people familiarized with the Guide to the Expression of Uncertainty in Measurement (GUM). Through two examples, it is shown that in linear measurement models, no new knowledge is gained by using sensitivity analysis that is not already available after the terms in the so-called ‘law of propagation of uncertainties’ have been computed. However, if the model behaves non-linearly in the neighbourhood of the best estimates of the input quantities—and if these quantities are assumed to be statistically independent—sensitivity analysis is definitely advantageous for gaining insight into how they can be ranked according to their importance in establishing the uncertainty of the measurand.

A review of sensitivity analysis methods in building energy analysis

Sensitivity analyses of exposure or risk models can help identify the most significant factors to aid in risk management or to prioritize additional research to reduce uncertainty in the estimates. However, sensitivity analysis is challenged by non-linearity, interactions between inputs, and multiple days or time scales. Selected sensitivity analysis methods are evaluated with respect to their applicability to human exposure models with such features using a testbed. The testbed is a simplified version of a US Environmental Protection Agency's Stochastic Human Exposure and Dose Simulation (SHEDS) model. The methods evaluated include the Pearson and Spearman correlation, sample and rank regression, analysis of variance, Fourier amplitude sensitivity test (FAST), and Sobol's method. The first five methods are known as "sampling-based" techniques, wheras the latter two methods are known as "variance-based" techniques. The main objective of the test cases was to identify the main and total contributions of individual inputs to the output variance. Sobol's method and FAST directly quantified these measures of sensitivity. Results show that sensitivity of an input typically changed when evaluated under different time scales (e.g., daily versus monthly). All methods provided similar insights regarding less important inputs; however, Sobol's method and FAST provided more robust insights with respect to sensitivity of important inputs compared to the sampling-based techniques. Thus, the sampling-based methods can be used in a screening step to identify unimportant inputs, followed by application of more computationally intensive refined methods to a smaller set of inputs. The implications of time variation in sensitivity results for risk management are briefly discussed.

Relationship between Weather and Sociodemographic Indicators and COVID-19 Infection in Iraq

PurposeThis paper aims to measure the sensitivity of the structure’s deformation numerical model (NM) related to the various types of the design parameters, which is a suitable method for parameter selection to increase the time of model-updating.Design/methodology/approachIn this research, a variance-based sensitivity analysis (VBSA) approach is proposed to measure the sensitivity of NM of structures. In this way, the contribution of measurements of the structure (such as design parameter values and geometry) on the output of NM is studied using first-order and total-order sensitivity indices developed by Sobol’. In this way the generated data set of parameters by considering different distributions such as Gaussian or uniform distribution and different order as input along with, the resulted deformation variables of NM as output has been submitted to the Sobol’ indices estimation procedure. To the verification of VBSA results, a gradient-based sensitivity analysis (SA), which is developed as a global SA method has been developed to measure the global sensitivity of NM then implemented over the NM’s results of a tunnel.FindingsRegarding the estimated indices, it has been concluded that the derived deformation functions from the tunnel’s NM usually are non-additive. Also, some parameters have been determined as most effective on the deformation functions, which can be selected for model-updating to avoid a time-consuming process, so those may better to be considered in the group of updating parameters. In this procedure for SA of the model, also some interactions between the selected parameters with other parameters, which are beneficial to be considered in the model-updating procedure, have been detected. In this study, some parameters approximately (27 per cent of the total) with no effect over the all objective functions have been determined to be excluded from the parameter candidates for model-updating. Also, the resulted indices of implemented VBSA were approved during validation by the gradient-based indices.Practical implicationsThe introduced method has been implemented for a circular lined tunnel’s NM, which has been created by Fast Lagrangian Analysis of Continua software.Originality/valueThis paper plans to apply a statistical method, which is global on the results of the NM of a soil structure by a complex system for parameter selection to avoid the time-consuming model-updating process.

This paper deals with the modelling and the prediction of the dynamic instabilities for a rubbing system. Two hybrid approaches are introduced for dynamic instability analysis and applied to a reduced disc brake system. The methods are based on stochastic algorithms coupled with the finite element method (FEM) using the complex eigenvalue analysis technique. By considering the input parameters as random variables, the uncertainty analysis is performed through two approaches to predict the unstable frequencies of a braking system (1) Monte-Carlo (MC) using Mersenne-Twister (MT19937) algorithm and (2) periodic sampling technique. Since the mechanism of brake squeal involves many design parameters, stochastic finite element approaches will be coupled with sensitivity algorithms, e.g. Variance-Based Sensitivity Analysis and Fourier Sensitivity Analysis Test, to analyze the contribution of each random variable on the dynamic instabilities. First, a comparison between the two stochastic algorithms is performed on standard analytical models. The objective is to validate the accuracy and to assess the numerical efficiency that FAST presents to (1) propagate the uncertainties upstream of the model and (2) to compute the partial variances of the model output. Secondly, the coupling of the previous stochastic algorithms with FEM is carried out and tested through a reduced brake system consisting of a rotating disc with two flat pads. Results show that the hybrid approach FAST-FE is more robust and computationally more efficient compared to the widely used MC-FE for these types of problems. FAST-FE solver converges, within a reasonable computing time, either to approximate the probability density function of the random variables or to compute the partial variances of the dynamic instabilities. Hence, it can be considered as an efficient numerical method for squeal instability analysis in order to reduce squeal noise of such a mechanical system.

Purpose: In particle therapy, treatment planning and evaluation are frequently based on biological models to estimate the relative biological effectiveness (RBE) or the equivalent dose in 2 Gy fractions (EQD2). In the context of the linear-quadratic model, these quantities depend on biological parameters (α, β) for ions as well as for the reference radiation and on the dose per fraction. The needed biological parameters as well as their dependency on ion species and ion energy typically are subject to large (relative) uncertainties of up to 20–40% or even more. Therefore it is necessary to estimate the resulting uncertainties in e.g. RBE or EQD2 caused by the uncertainties of the relevant input parameters. Methods: We use a variance-based sensitivity analysis (SA) approach, in which uncertainties in input parameters are modeled by random number distributions. The evaluated function is executed 10{sup 4} to 10{sup 6} times, each run with a different set of input parameters, randomly varied according to their assigned distribution. The sensitivity S is a variance-based ranking (from S = 0, no impact, to S = 1, only influential part) of the impact of input uncertainties. The SA approach is implemented for carbon ion treatment plans on 3D patient data,more » providing information about variations (and their origin) in RBE and EQD2. Results: The quantification enables 3D sensitivity maps, showing dependencies of RBE and EQD2 on different input uncertainties. The high number of runs allows displaying the interplay between different input uncertainties. The SA identifies input parameter combinations which result in extreme deviations of the result and the input parameter for which an uncertainty reduction is the most rewarding. Conclusion: The presented variance-based SA provides advantageous properties in terms of visualization and quantification of (biological) uncertainties and their impact. The method is very flexible, model independent, and enables a broad assessment of uncertainties. Supported by DFG grant WI 3745/1-1 and DFG cluster of excellence: Munich-Centre for Advanced Photonics.« less

Instrumental variable (IV) analysis has been widely used in economics, epidemiology, and other fields to estimate the causal effects of covariates on outcomes, in the presence of unobserved confounders and/or measurement errors in covariates. However, IV methods for time-to-event outcome with censored data remain underdeveloped. This paper proposes a Bayesian approach for IV analysis with censored time-to-event outcome by using a two-stage linear model. A Markov chain Monte Carlo sampling method is developed for parameter estimation for both normal and non-normal linear models with elliptically contoured error distributions. The performance of our method is examined by simulation studies. Our method largely reduces bias and greatly improves coverage probability of the estimated causal effect, compared with the method that ignores the unobserved confounders and measurement errors. We illustrate our method on the Women's Health Initiative Observational Study and the Atherosclerosis Risk in Communities Study.

Introduction. In an electrical power system, the output of the synchronous generators varies due to disturbances or sudden load changes. These variations in output severely affect power system stability and power quality. The synchronous generator is equipped with an automatic voltage regulator to maintain its terminal voltage at rated voltage. Several control techniques utilized to improve the response of the automatic voltage regulator system, however, proportional integral derivative (PID) controller is the most frequently used controller but its parameters require optimization. Novelty. In this paper, the chaotic sequence based on the logistic map is hybridized with particle swarm optimization to find the optimal parameters of the PID for the automatic voltage regulator system. The logistic map chaotic sequence-based initialization and global best selection enable the algorithm to escape from local minima stagnation and improve its convergence rate resulting in best optimal parameters. Purpose. The main objective of the proposed approach is to improve the transient response of the automatic voltage regulator system by minimizing the maximum overshoot, settling time, rise time, and peak time values of the terminal voltage, and eliminating the steady-state error. Methods. In the process of parameter tuning, the Chaotic particle swarm optimization technique was run several times through the proposed hybrid objective function, which accommodates the advantages of the two most commonly used objective functions with a minimum number of iterations, and an optimal PID gain value was found. The proposed algorithm is compared with current metaheuristic algorithms including conventional particle swarm optimization, improved kidney algorithm, and others. Results. For performance evaluation, the characteristics of the integral of time multiplied squared error and Zwe-Lee Gaing objective functions are combined. Furthermore, the time-domain analysis, frequency-domain analysis, and robustness analysis are carried out to show the better performance of the proposed algorithm. The result shows that automatic voltage regulator tuned with the chaotic particle swarm optimization based PID yield improvement in overshoot, settling time, and function value of 14.41 %, 37.91 %, 1.73 % over recently proposed IKA, and 43.55 %, 44.5 %, 16.67 % over conventional particle swarm optimization algorithms. The improvement in transient response further improves the automatic voltage regulator system stability for electrical power systems.

We investigate microphysical uncertainties in hailstorms using statistical emulation in a single model framework with the objective to disentangle the relative contributions from aerosols, microphysical parameters and environmental conditions to the uncertainty in cloud-, precipitation- and hail-related parameters.Our selected case study is the Andreas hailstorm on 28 July 2013 in the Neckar Valley and over the Swabian Jura in Southwest Germany. We perform model simulations on cloud-resolving scale with the numerical weather prediction model ICON coupled with the aerosol module ART (ICON-ART). We use a two-moment cloud microphysics scheme with a representation of ice nucleation by dust aerosols.We generated a perturbed parameter ensemble (PPE) to sample uncertainties in cloud-, precipitation- and hail related parameters. Six parameters from the categories aerosols, microphysics and environmental conditions were jointly perturbed, namely the cloud condensation nuclei (CCN) and ice nuclei (IN) concentrations, the riming efficiency of graupel and hail, the convective available potential energy (CAPE) and vertical wind shear. The defined parameter ranges are based on forecast analysis and literature. We used the maximin Latin hypercube algorithm to distribute the parameters well-spaced in the six-dimensional parameter uncertainty space. For these six parameters, an ensemble of 90 members was generated and in addition a smaller independent ensemble of 45 members serves for validation.We used the Gaussian process emulation and developed emulators for hail- and precipitation related output variables. To quantify contributions to the uncertainty in the output variables from the perturbed parameters individually as well as interactions between them, a variance-based sensitivity analysis was performed. We will present first results, which reveal the importance of the CCN concentration for controlling the number concentration of hail particles as well as the CCN concentration and environmental conditions for controlling the amount of hail and precipitation in the model. The geographical distribution of hail and precipitation shows a large variety among the ensemble members, with storm tracks shifted further to the north or south compared to the reference simulation. The path of the storm track is thereby mainly controlled by CAPE and the vertical wind shear, however, aerosol parameters seem to be important for the development of multiple storm tracks. 

Variance-based sensitivity analysis provides a quantitative measure of how uncertainty in a model input contributes to uncertainty in the model output. Such sensitivity analyses arise in a wide variety of applications and are typically computed using Monte Carlo estimation, but the many samples required for Monte Carlo to be sufficiently accurate can make these analyses intractable when the model is expensive. This work presents a multifidelity approach for estimating sensitivity indices that leverages cheaper low-fidelity models to reduce the cost of sensitivity analysis while retaining accuracy guarantees via recourse to the original, expensive model. This paper develops new multifidelity estimators for variance and for the Sobol' main and total effect sensitivity indices. We discuss strategies for dividing limited computational resources among models and specify a recommended strategy. Results are presented for the Ishigami function and a convection-diffusion-reaction model that demonstrate up to $10\times$ speedups for fixed convergence levels. For the problems tested, the multifidelity approach allows inputs to be definitively ranked in importance when Monte Carlo alone fails to do so.

Small datasets, which are common in many traditional science and engineering disciplines, present a challenge for powerful machine learning methods that are better suited for large datasets. Through the example of spontaneous colloidal sol-gel transition, we present a data-driven framework based on Gaussian Processes (GPs) for modeling and inference with limited data. GPs are well-suited for small datasets and automatically provide uncertainty quantification for model predictions. We explore GPs with two different structures (single and multi-output) to map synthesis parameters to gelation characteristics. While both GP structures quantitatively capture the relationships between the input and output variables, we favor multioutput GP, which attempts to simultaneously learn correlations between different outputs, due to its superior uncertainty calibration. To address inverse problems, we introduce a Bayesian framework that embeds a GP model into a Markov Chain Monte Carlo sampling algorithm. It enables the discovery of multiple synthesis pathways for achieving desired material properties. Therefore, this work presents a robust methodology for data-constrained modeling, with broad applicability to material design in general and the colloidal domain in particular.