Statistical Uncertainty Analysis Research Articles

Modeling of scour hole characteristics under turbulent wall jets using machine learning

The novelty of the present study is to investigate the parameters that depict the scour hole characteristics caused by turbulent wall jets and develop new mathematical relationships for them. Four significant parameters i.e., depth of scouring, location of scour depth, height of the dune and location of dune crest are identified to represent a complete phenomenon of scour hole formation. From the gamma test, densimetric Froude number, apron length, tailwater level, and median sediment size are found to be the key parameters that affect these four dependent parameters. Utilizing the previous data sets, Multi Regression Analysis (linear and non-linear) has been performed to establish the relationships between the dependent parameters and influencing independent parameters. Further, artificial neural network-particle swarm optimisation (ANN-PSO) and gene expression programming (GEP) based models are developed using the available data. In addition, results obtained from these models are compared with proposed regression equations and the best models are identified employing statistical performance parameters. The performance of the ANN-PSO model (RMSE = 1.512, R2 = 0.605), (RMSE = 6.644, R2 = 0.681), (RMSE = 6.386, R2 = 0.727) and (RMSE = 1.754, R2 = 0.636) for predicting four significant parameters are more satisfactory than that of regression and other soft computing techniques. Overall, by analysing all the statistical parameters, uncertainty analysis and reliability index, ANN-PSO model shows good accuracy and predicts well as compared to other presented models.

Discharge estimation in compound channels with converging and diverging floodplains using an optimised Gradient Boosting Algorithm

ABSTRACT River discharge estimation is vital for effective flood management and infrastructure planning. River systems consist of a main channel and floodplains, collectively forming a compound channel, posing challenges in discharge calculation, particularly when floodplains converge or diverge. In the present study, ML algorithms such as XGBoost, CatBoost, and LightGBM were developed to predict discharge in a compound channel. PSO algorithm is applied for optimization of hyperparameters of gradient boosting models, denoted as PSO-XGBoost, PSO-LightGBM, and PSO-CatBoost. ML model discharge predictions were validated with existing empirical models and feature importance was explored using SHAP and sensitivity analysis. Results show that all three gradient-boosting algorithms effectively predict discharge in compound channels and are further enhanced by application of PSO algorithm. The R2 values for XGBoost, PSO-XGBoost, CatBoost, and PSO-CatBoost exceed 0.95, whereas they are above 0.85 for LightBoost and PSO-LightBoost. PSO-CatBoost performance is better than other models based on findings of statistical performance parameters, uncertainty analysis, reliability index, and resilience index for prediction of discharge in a compound channel with converging and diverging flood plains. The findings of this study validate the suitability of the proposed models especially optimized with PSO is recommended for predicting discharge in a compound channel.

Impact of DNI Forecast Quality on Performance Prediction for a Commercial Scale Solar Tower

Concerning current efforts to improve operational efficiency and to lower overall costs of concentrating solar power (CSP) plants with prediction-based algorithms, this study investigates the quality and uncertainty of nowcasting data regarding the implications for process predictions. DNI (direct normal irradiation) maps from an all-sky imager-based nowcasting system are applied to a dynamic prediction model coupled with ray tracing. The results underline the need for high-resolution DNI maps in order to predict net yield and receiver outlet temperature realistically. Furthermore, based on a statistical uncertainty analysis, a correlation is developed, which allows for predicting the uncertainty of the net power prediction based on the corresponding DNI forecast uncertainty. However, the study reveals significant prediction errors and the demand for further improvement in the accuracy at which local shadings are forecasted.

A Novel Statistical Analysis Algorithm for Angular Sampling for Measurement of the TRP of Spurious Emissions

The total radiated power (TRP) has been stipulated as the spurious emission limit for a mmWave terminal. Angular sampling is crucial for ensuring the accuracy of the measurement of the TRP of spurious emissions while improving measurement efficiency. In this study, we investigate the sampling requirements for different TRP measurement methods. A novel algorithm based on the statistical analysis of the measurement uncertainty caused by the sampling step is proposed. Specifically, the HPBW of the entire machine radiation pattern is considered instead of that of a simple antenna array. This study was conducted in strict compliance with regulatory requirements to ensure that the statistical algorithm was more closely aligned with practical testing. Based on this, the maximum sampling steps allowed by different terminal models while maintaining measurement accuracy were analyzed. The simulation results demonstrate that negligible measurement uncertainty was produced when the sampling step of the full spherical grid method was less than 6∘. However, for the two-cut and the three-cut methods, a maximum of 2 dB of measurement uncertainty should be considered. These findings are valuable inputs for the ongoing work on electromagnetic compatibility testing and standardization.

A model for measuring multi‐concern assurance of critical infrastructure control systems

AbstractDigital transformation of engineering practice, paradigms, processes, and workforce engender agreement uncertainty among professionals, particularly in the critical industry control system field. Control systems are susceptible to cyber‐mediated changes that can uniquely affect the control of the physical world from data‐centric information systems. Change to the system can be introduced by any proposed or forced alteration that affects the acceptability, suitability, feasibility, or resiliency to perform its intended mission, either positively or negatively. The potential impact of the cybersecurity threat on control systems is difficult to quantify. Agreement among professionals about decision authority and Command and Control (C2) over this threat is even more challenging to quantify. Understanding what cybersecurity entails still needs to be widely understood by the critical infrastructure control system workforce, and the control system assets are not widely understood by the Information Technology (IT) workforce. This research introduces a model and methodology for measuring multi‐concern assurance through the statistical uncertainty analysis of Likert semantic differential scales. The model addresses agreement in priority, the lack of which means there might be competing aims, competing spending, and competing focus on different aspects of the cybersecurity governance or policy as examples. The outcome identifies where different types of professionals do not agree about cybersecurity readiness and best practices for critical infrastructure control systems.

Empowering tomorrow, controlling today: A multi-criteria assessment of distribution grid tariff designs

The energy transition is in full development with an ever-growing omnipresence of low voltage grid-connected distributed energy resources which cause congestion in the low voltage (LV) distribution grid. Two plausible solutions to network congestion issues are increased grid control (flexibility) or capacity power reinforcements. Electricity distribution tariffs are a promising intersection of these solutions as pricing structures that match consumer patterns can influence demand and grid investments can be recovered by cost-causal pricing.Designing electricity grid tariffs is complex due to its multi-disciplinary character. As previous research has addressed the singular aspects of distribution tariff structures, it is necessary to assess the performance of tariff designs from a multitude of perspectives. For the aforesaid reason, the goal of this paper is to investigate which distribution grid tariffs perform better by drawing upon a complete and coherent set of stakeholder-relevant criteria on all multi-disciplinary objectives of distribution tariff structures and assessing those structures with systematic decision theory. Results based on a systematic literature review, a TOPSIS multi-criteria decision assessment and statistical uncertainty analyses show that tariff performance significantly increases for capacity real-time pricing tariffs, capacity-based rates with Paris-Metro pricing and capacity peak load contribution charges.

Analysis of Statistical Uncertainty of Optical Frequency Measurement Due to Measurement Dead Time of Hydrogen Maser

Analysis of Statistical Uncertainty of Optical Frequency Measurement Due to Measurement Dead Time of Hydrogen Maser

Development, verification and application of the uncertainty analysis platform CUSA

Modeling and simulation technology has gradually become an important approach to describe objective physical phenomena and carry out further research and design. However, uncertainty in the basic input of the modeling and simulation process there naturally exists, which will inevitably propagate to the simulation results. Due to the wide applicability and easy implementation, statistical sampling-based Sensitivity and Uncertainty (SU) analysis has become the mainstream option for uncertainty propagation and quantification analysis in the modeling and simulation process. This paper first establishes a statistical sampling-based framework and gives theories and implemented methods involved in our framework in detail. Based on these theories and methods, a user-friendly and functional SU analysis platform called CUSA with a Human Machine Interface (HMI) has been developed. The verification results of the main function and basic theory prove the correctness and stability of CUSA. Finally, this paper summarizes CUSA's representative applications in previous studies and conduct the uncertainty analysis of total neutron physics calculation for a mini-core using CUSA.

Prediction of the resilient modulus of compacted subgrade soils using ensemble machine learning methods

The accurate estimation of resilient modulus (MR) of compacted subgrade soil is imperative for the safe and sustainable design of flexible pavement systems. The aim of this study is to explore the potential of ensemble machine learning techniques for predicting the MR of pavement subgrade soil. For this, 2813 data points from twelve compacted subgrade soils were collected which consists of the following inputs parameters: dry unit weight, weighted plasticity index, deviator stress, confining stress, number of freeze–thaw cycles, and moisture content. Four commonly used machine learning (ML) methods, namely, gradient boosting regression (GBR), decision tree regression (DTR), K nearest neighbour regression (KNR), and random forest regression (RFR) were developed and implemented for forecasting the MR value. Thereafter, several ensemble ML techniques including voting ensemble (VO-ENSM), voting ensemble with RF as a meta-model (VO-ENSM (RF)), stacking ensemble (ST-ENSM) and bagging ensemble (BG-ENSM) were utilised to amalgamate the outputs from the developed standalone ML models. Additionally, a multiple linear regression model was also developed as a baseline. The predictive veracity, reliability and trustworthiness of the developed ensemble models were corroborated using rigorous statistical testing, ranking technique, and uncertainty analysis. The results as obtained have shown that the BG-ENSM outperformed its counterparts in predicting the MR of subgrade soil. Hence, it can be a part of portfolio of predicting tools utilised by the practitioners in evaluating the strength of the pavement subgrade soil. Finally, the sensitivity analysis was performed to assess the strength of input variables on the MR.

The Issue of Evaluating the Effectiveness of Miniature Safety Fuses as Anti-Damage Systems

The objective of this article was to determine, in practice, whether the break time tw of safety fuses can impact the security level provided by electronic security systems (ESSs) that utilize the aforementioned elements as their components. This was the purpose of the conducted destructive testing aimed at estimating the break times for a certain random number of glass tube, miniature 5 × 20 (mm) fuse links with rapid operating characteristics, without a quenching medium and with a rated overcurrent intensity of 0.5 (A) by the selected manufacturers. For this purpose, a dedicated measuring attachment that enables forcing the flow of overcurrents with selected intensities in the range of 1.5 ÷ 11.5 (A) through the studied fuse links has been developed. The obtained results showed that the ratio of the break times between the best and the worst products in the entire tested range of overcurrents ranges from 5.41 (for 3.5 (A)) to 7.80 (at an overcurrent of 9.5 (A)). Statistical analysis of the measurement uncertainties proved that the obtained results of the break time do not depend on the applied research methodology or measuring equipment but are almost exclusively the result of the manufacturing spread of the tested components. Interestingly, the economic analysis did not bring clear conclusions. In this case, the products with the worst break time tw turned out to be almost three times cheaper than the best fuse-links. What is more, the collective packaging of the product that turned out to be the best was cheaper than the next one in the list by almost USD 2.00.

Evaluation of Height, Area, and Capacity of Concrete Elevated Water Reservoirs in a Tertiary Institution in Benin City, Nigeria

The objective of this work is to determine the height, area, and capacity of two concrete elevated water reservoirs in a Tertiary Institution in Benin City, Nigeria, to serve as reference to existing controls for future monitoring exercise. The two water reservoir involved in reality are of different shapes and sizes. The elevated heights, areas, and capacities of reservoir one and two suspended above their legs are: (8.106m, 362.778m2, 2940.680m3, and 7.485m, 320.400m2, 296.132m3), respectively. The total heights of the reservoir one and two above ground level (AGL) are approximately 22m and 18m. Statistical analysis of uncertainty in height measurement showed, 0.0153 for reservoir one and 0.0412 for reservoir two. The provision of the necessary information by the REM method about the elevated water reservoirs showed its efficacy. This method is recommended for use in the measurement of inaccessible structure/feature. The type of data and information such as provided in this work are required for institutional water board documentation, water use planning, and archival purpose.

Quantitative uncertainty estimation in biophysical models of fish larval connectivity in the Florida Keys

Abstract The impacts of seven uncertain biological parameters on simulated larval connectivity in the Florida Keys are investigated using Polynomial chaos surrogates. These parameters describe biological traits and behaviours—such as mortality, swimming abilities, and orientation—and modulate larval settlement as well as dispersal forecasts. However, these parameters are poorly constrained by observations and vary naturally between individual larvae. The present investigation characterizes these input uncertainties with probability density functions informed by previous studies of Abudefduf saxatilis. The parametric domain is sampled via ensemble calculations, then a polynomial-based surrogate is built to explicitly approximate the dependence of the model outputs on the uncertain model inputs, which enables a robust statistical analysis of uncertainties. This approach allows the computation of probabilistic dispersal kernels that are further analyzed to understand the impact of the parameter uncertainties. We find that the biological input parameters influence the connectivity differently depending on dispersal distance and release location. The global sensitivity analysis shows that the interactions between detection distance threshold, orientation ontogeny, and orientation accuracy, are the dominant contributors to the uncertainty in settlement abundance in the Florida Keys. Uncertainties in swimming speed and mortality, on the other hand, seem to contribute little to dispersal uncertainty.

Relying on machine learning methods for predicting hydrogen solubility in different alcoholic solvents

There are high demands for reliable hydrogen-alcohol phase equilibria in separation and conversion-related industrial processes. Since experimental measurements cannot be directly included in the computer-aided handling of these processes, this study utilizes various computational techniques for estimating hydrogen solubility in seven alcoholic solvents (methanol, ethanol, 1-propanol, 2-propanol, allyl alcohol, 1-butanol, and furfuryl alcohol). Ranking analysis shows that the adaptive-neuro fuzzy inference system having genfis2 (ANFIS2) is the best choice for this purpose. The model predictions are in excellent agreement with the 194 laboratory measurements (RAD = 3.32%, MSE = 6.9 × 10−4, and R2 = 0.998896). Statistical uncertainty analysis confirms that the ANFIS2 model is superior to the previously proposed equations of state and empirical correlations in the literature. Simulation results confirm that 1-butanol and furfuryl alcohol has the highest and lowest hydrogen absorption tendency, respectively. Furthermore, the ANFIS2 justifies that the solubility of hydrogen in all alcohols obeys Henry's law and decreases by decreasing temperature and pressure.

New association schemes for tri-ethylene glycol: Cubic-Plus-Association parameterization and uncertainty analysis

Transportation of natural gas extracted from subterranean reservoirs is subject to several risks introduced by the presence of water. These risks can be mitigated through subsea dehydration, the design of which requires an accurate understanding of the thermodynamics of these systems. Having previously investigated the use of mono-ethylene glycol as a dehydration agent, this research focusses on the industry workhorse: tri-ethylene glycol (TEG). The Cubic-Plus-Association (CPA) equation of state has previously provided a good description for systems of equal complexity and in this work the literature 4C and 6D association schemes, as well as four newly proposed association schemes (4F, 5F, 6F and 5C) are evaluated for the description of TEG. These association schemes, which are explained in the manuscript, represent different ways of self-association for TEG.Pure component parameters are estimated by fitting to vapor pressure, liquid density, and liquid-liquid equilibrium data, with statistical uncertainty analysis implemented to determine the confidence intervals of the parameters. Binary interaction parameters are similarly fitted to binary vapor-liquid equilibrium (VLE) data. Optimized parameters are evaluated by testing their performance in predicting binary and ternary VLE systems.Due to the strong influence of certain experimental data sets, the literature 6D parameters are shown to be unsuitable for the applications in this work. The need for consistent experimental data quantifying both vapor and liquid phases, specifically for TEG – CH4 has been highlighted. The best overall performance was obtained using the newly proposed 4F association scheme. Along with improved overall description of various VLE and LLE systems, with average absolute relative deviations generally between 2-20%, single parameter sensitivity analysis shows improved optimality for several systems also not included in the parameterization. This is indicative of a better fundamental characterization of the TEG molecule. The value of the uncertainty analysis is shown for the binary interaction parameters, where for TEG – CH4 VLE a temperature-dependent correlation is shown to be unnecessary using the optimum association schemes.

Uncertainty and sensitivity analysis of boundary conditions during water droplet phase change regimes

This paper presents the heat and mass transfer model of a liquid droplet in the consistently changing condensation, transit and equilibrium evaporation regimes, and iterative scheme of numerical simulation of the instantaneous temperature of a semi-transparent droplet in the case of complex radiative-convective heating. The whole cycle of the phase transition regimes of medium and large water droplets flowing in the flue gas was modeled, taking into account the application of water spraying into the flue gas of a biofuel furnace. Simulation results expressed as thermal, energy and phase transformation parameters of water droplets are analyzed in the universal Fourier time scale. The factors defining the change of heat transfer regime of a water droplet are termed as the suppression of droplet slipping in flue gas flow at initial phase transformation stage, and the decrease of radiation absorption at the final stage. Particular attention is paid to the evaluation of the influence of parameters defining the interaction of complex transfer processes on the droplet's phase transformations performing the sensitivity analysis of the heat and mass transfer parameters for the “hypothetical” droplet case (the diameter and the slipping velocity in to gas did not change). It is substantiated, that the main parameters defining the sensitivity of water droplets equilibrium evaporation temperature are flue gas humidity, droplets dispersity, flue gas temperature and droplets slipping velocity.The performed statistical uncertainty and sensitivity analysis showed that the uncertainty of heat and mass transfer parameters describing the phase transformations of a water droplet until equilibrium evaporation regime is affected mostly by droplet dispersity, slipping velocity, flue gas temperature and pressure. The size of droplets and their slip velocity in the flue gas flow were identified as very important parameters for the interaction of complex heat and mass transfer processes of a sprayed water. The main uncertainties were defined at the transition from condensing to transit evaporation regime, and it was defined that with a confidence interval of at least 95 % and accepting a tolerance limit with a probability of at least 95 %, the transit evaporation regime starts at the range Fo ≈ (0.02–0.1). The droplet surface temperature, i.e. parameter determining the droplet phase transformations and its dynamics, could be assessed with a mean error of ±10 %, accepting 95 % probability with 95 % confidence level.

Model Structure Uncertainty in the Characterization and Growth of Geographic Atrophy.

PurposeTo identify the most suitable model for assessing the rate of growth of total geographic atrophy (GA) by analysis of model structure uncertainty.MethodsModel structure uncertainty refers to unexplained variability arising from the choice of mathematical model and represents an example of epistemic uncertainty. In this study, we quantified this uncertainty to help identify a model most representative of GA progression. Fundus autofluorescence (FAF) images and GA progression data (i.e., total GA area estimation at each presentation) were acquired using Spectralis HRA+OCT instrumentation and RegionFinder software. Six regression models were evaluated. Models were compared using various statistical tests, [i.e., coefficient of determination (r2), uncertainty metric (U), and test of significance for the correlation coefficient, r], as well as adherence to expected physical and clinical assumptions of GA growth.ResultsAnalysis was carried out for 81 GA-affected eyes, 531 FAF images (range: 3–17 images per eye), over median of 57 months (IQR: 42, 74), with a mean baseline lesion size of 2.62 ± 4.49 mm2 (range: 0.11–20.69 mm2). The linear model proved to be the most representative of total GA growth, with lowest average uncertainty (original scale: U = 0.025, square root scale: U = 0.014), high average r2 (original scale: 0.92, square root scale: 0.93), and applicability of the model was supported by a high correlation coefficient, r, with statistical significance (P = 0.01).ConclusionsStatistical analysis of uncertainty suggests that the linear model provides an effective and practical representation of the rate and progression of total GA growth based on data from patient presentations in clinical settings.Translational RelevanceIdentification of correct model structure to characterize rate of growth of total GA in the retina using FAF images provides an objective metric for comparing interventions and charting GA progression in clinical presentations.

Rapid development of fast and flexible environmental models: the Mobius framework v1.0

Abstract. The Mobius model building system is a new open-source framework for building fast and flexible environmental models. Mobius makes it possible for researchers with limited programming experience to build performant models with potentially complicated structures. Mobius models can be easily interacted with through the MobiView graphical user interface and through the Python programming language. Mobius was initially developed to support catchment-scale hydrology and water-quality modelling but can be used to represent any system of hierarchically structured ordinary differential equations, such as population dynamics or toxicological models. Here, we demonstrate how Mobius can be used to quickly prototype several different model structures for a dissolved organic carbon catchment model and use built-in auto-calibration and statistical uncertainty analysis tools to help decide on the best model structures. Overall, we hope the modular model building platform offered by Mobius will provide a step forward for environmental modelling, providing an alternative to the “one size fits all” modelling paradigm. By making it easier to explore a broader range of model structures and parameterisations, users are encouraged to build more appropriate models, and in turn this improves process understanding and allows for more robust modelling in support of decision making.

Discerning Changes in High‐Frequency Climate Variability Using Geochemical Populations of Individual Foraminifera

AbstractIndividual foraminiferal analysis (IFA) has proven to be a useful tool in reconstructing the amplitude of high‐frequency climate signals such as the annual cycle and the El Niño‐Southern Oscillation (ENSO). However, using IFA to evaluate past changes in climate variability is complicated by many factors including geographic location, foraminiferal ecology, methods of sample processing, and the influence of multiple, superimposed high‐frequency climate signals. Robust statistical tools and rigorous uncertainty analysis are therefore required to ensure the reliability of IFA‐based interpretations of paleoclimatic change. Here, we present a new proxy system model—called the Quantile Analysis of Temperature using Individual Foraminiferal Analyses (QUANTIFA)—that combines methods for assessing IFA detection sensitivity with analytical tools for processing and interpreting IFA data to standardize and streamline reconstructions employing IFA‐Mg/Ca measurements. Model exercises with simulated and real IFA data demonstrate that the dominant signal retained by IFA populations is largely determined by the annual‐to‐interannual ratio of climate variability at a given location and depth and can be impacted by seasonal biases in foraminiferal productivity. In addition, our exercises reveal that extreme quantiles can be reliable indicators of past changes in climate variability, are often more sensitive to climate change than quantiles within the distributional interior, and can be used to distinguish changes in interannual phenomena like ENSO from seasonality. Altogether, QUANTIFA provides a useful tool for modeling IFA uncertainties and processing IFA data that can be leveraged to establish a history of past climate variability.

Statistical analysis of measurement uncertainty in total radiated power of wireless devices in reverberation chamber

Due to the explosive increase of wireless devices, efficient over-the-air testing of such devices is highly desirable. The reverberation chamber (RC) offers efficient and cost-effective means to determine performance metrics of wireless devices, such as total radiated power (TRP). In this study, the distribution of the measured TRP in an RC is analytically derived, based on which the statistics (i.e. mean, variance) of the measured TRP are derived as well. RC measurements have been performed to verify the analytically derived statistics.

New Strategies in the Code of Uncertainty and Sensitivity Analysis (CUSA) and Its Application in the Nuclear Reactor Calculation

Best-Estimation Plus Uncertainty (BEPU) analysis method can provide more information to improve the reliability of calculation results than the safety analysis with conservative assumption. And the statistical sampling-based uncertainty and sensitivity analysis methods are widely used in practical applications of the multiphysics, multiscale coupling nuclear reactor system. In this paper, a novel and efficient sampling method for inputs with normal and uniform distributions is introduced and a systematic theory for uncertainty and sensitivity analysis is established based on the classical statistical theory. Then the Code of Uncertainty and Sensitivity Analysis (CUSA) is updated based on these new strategies. For applications, the explicit and implicit effects for resonance and nonresonance isotopes are studied in depth, and a simple UO2 pin cell is considered to examine the performance of CUSA and the total uncertainty and sensitivity analysis abilities. The numerical results indicate that the implicit sensitivity analysis model and the uncertainty quantification functions developed in CUSA are correct and can be used for sensitivity and uncertainty analysis in nuclear reactor calculations. Even more important, the LHS-SVDC is recommended to propagate the uncertainties in multigroup cross sections.