Interval Parameters Research Articles

An adaptive interval many-objective evolutionary algorithm with information entropy dominance

Interval many-objective optimization problems (IMaOPs) involve more than three conflicting objectives with interval parameters. Various real-world applications under uncertainty can be modeled as IMaOPs to solve, so effectively handling IMaOPs is crucial for solving practical problems. This paper proposes an adaptive interval many-objective evolutionary algorithm with information entropy dominance (IMEA-IED) to tackle IMaOPs. Firstly, an interval dominance method based on information entropy is proposed to adaptively compare intervals. This method constructs convergence entropy and uncertainty entropy related to interval features and innovatively introduces the idea of using global information to regulate the direction of local interval comparison. Corresponding interval confidence levels are designed for different directions. Additionally, a novel niche strategy is designed through interval population partitioning. This strategy introduces a crowding distance increment for improved subpopulation comparison and employs an updated reference vector method to adjust the search regions for empty subpopulations. The IMEA-IED is compared with seven interval optimization algorithms on 60 interval test problems and a practical application. Empirical results affirm the superior performance of our proposed algorithm in tackling IMaOPs.

Ultrafast antiferromagnetic switching of Mn2Au with laser-induced optical torques

Ultrafast manipulation of the Néel vector in metallic antiferromagnets most commonly occurs by generation of spin-orbit (SOT) or spin-transfer (STT) torques. Here, we predict another possibility for antiferromagnetic domain switching by using novel laser optical torques (LOTs). We present results of atomistic spin dynamics simulations from the application of LOTs for all-optical switching of the Néel vector in the antiferromagnet Mn2Au. The driving mechanism takes advantage of the sizeable exchange enhancement, characteristic of antiferromagnetic dynamics, allowing for picosecond 90 and 180-degree precessional toggle switching of the Néel vector with laser fluences on the order of mJ/cm2. A special symmetry of these novel torques greatly minimises the over-shooting effect common to precessional spin switching by SOT and STT methods. We demonstrate the opportunity for LOTs to produce deterministic, non-toggle switching of single antiferromagnetic domains. Lastly, we show that even with sizeable ultrafast heating by laser in metallic systems, there exist a large interval of laser parameters where the LOT-assisted toggle and preferential switchings in magnetic grains have probabilities close to one. The proposed protocol could be used on its own for all-optical control of antiferromagnets for computing or memory storage, or in combination with other switching methods to lower energy barriers and/or to prevent over-shooting of the Néel vector.

Calculation of continuous reference intervals for biological parameters exhibiting strong age‐dependent level changes: Its application to glycosaminoglycans and sialic acid in urine

AbstractGlycosaminoglycan (GAG) and sialic acid (total and free) assays are used as first‐line screening tests for the diagnosis of mucopolysaccharidoses and glycoproteinoses, respectively. There is a pronounced age‐dependent variation in the urinary concentrations of these metabolites in the normal population, and the stratification of the reference values into discrete age ranges may lead to an undesirably high number of false‐positive or false‐negative results. The aim of this study was to design a method for calculating continuous reference intervals as a function of age and its application to the analysis of GAGs and sialic acid (total, free, and conjugated) in urine. In the postpubertal period, concentrations of urinary GAGs and sialic acid have reached a plateau, so a traditional calculation of the reference range in this specific age group was considered appropriate. In the prepubertal period, a nonlinear regression performed with the Excel add‐in Solver was used to fit the logarithmized concentrations of the controls to a curve that represents the mean values as a function of age. A uniform distribution of the residuals was obtained, which allowed the calculation of the reference intervals by adding the values of their 2.5 and 97.5 percentiles to the independent variable of the regression curve to calculate the upper and lower reference curves. The main advantages of the developed method are (1) a reduction in the number of control samples needed to obtain adequate reference intervals and (2) an improvement in the reliability of diagnostic screening by reducing the uncertainty generated by the gaps in the traditional age‐stratified method.

The Dunning‒Kruger effect in resident predicted and actual performance on the American Board of Emergency Medicine in-training examination.

The Dunning-Kruger effect (DKE) is a cognitive bias wherein individuals who are unskilled overestimate their abilities, while those who are skilled tend to underestimate their capabilities. The purpose of this investigation is to determine if the DKE exists among American Board of Emergency Medicine (ABEM) in-training examination (ITE) participants. This is a prospective, cross-sectional survey of residents in Accreditation Council for Graduate Medical Education (ACGME)-accredited emergency medicine (EM) residency programs. All residents who took the 2022 ABEM ITE were eligible for inclusion. Residents from international programs, residents in combined training programs, and those who did not complete the voluntary post-ITE survey were excluded. Half of the residents taking the ITE were asked to predict their self-assessment of performance (percent correct), and the other half were asked to predict their performance relative to peers at the same level of training (quintile estimate). Pearson's correlation (r) was used for parametric interval data comparisons and a Spearman's coefficient (ρ) was determined for quintile-to-quintile comparisons. A total of 7568 of 8918 (84.9%) residents completed their assigned survey question. A total of 3694 residents completed self-assessment (mean predicted percentage correct 67.4% and actual 74.6%), with a strong positive correlation (Pearson's r 0.58, p<0.001). There was also a strong positive correlation (Spearman's ρ 0.53, p<0.001) for the 3874 residents who predicted their performance compared to peers. Of these, 8.5% of residents in the first (lowest) quintile and 15.7% of residents in the fifth (highest) quintile correctly predicted their performance compared to peers. EM residents demonstrated accurate self-assessment of their performance on the ABEM ITE; however, the DKE was present when comparing their self-assessments to their peers. Lower-performing residents tended to overestimate their performance, with the most significant DKE observed among the lowest-performing residents. The highest-performing residents tended to underestimate their relative performance.

A support vector regression-based interval power flow prediction method for distribution networks with DGs integration

In distribution networks with distributed generators (DGs), power generation and load demand exhibit increased randomness and volatility, and the line parameters also suffer more frequent fluctuations, which may result in significant state shifts. Existing model-driven methods face challenges in efficiently solving uncertain power flow, especially as the size of the system increases, making it difficult to meet the demand for rapid power flow analysis. To address these issues, this paper proposes an SVR-based interval power flow (IPF) prediction method for distribution networks with DGs integration. The method utilizes intervals to describe system uncertainty and employs Support Vector Regression (SVR) for model training. The input feature vector consists of the intervals of active power generation, load demand, and line parameters, while the output feature vector represents the intervals of voltage or line transmission power. Ultimately, the SVR-based IPF prediction model is established, capturing the linear mapping relationship between input data and output IPF variables. Simulation results demonstrate that the proposed method exhibits high prediction accuracy, strong adaptability, and optimal computation efficiency, meeting the requirements for rapid and real-time power flow analysis while considering the uncertainty in distribution networks with DGs integration.

Prediction of Biochar Adsorption of Uranium in Wastewater and Inversion of Key Influencing Parameters Based on Ensemble Learning.

With the rapid development of industrialization, the problem of heavy metal wastewater treatment has become increasingly serious, posing a serious threat to the environment and human health. Biochar shows great potential for application in the field of wastewater treatment; however, biochars prepared from different biomass sources and experimental conditions have different physicochemical properties, resulting in differences in their adsorption capacity for uranium, which limits their wide application in wastewater treatment. Therefore, there is an urgent need to deeply explore and optimize the key parameter settings of biochar to significantly improve its adsorption capacity. This paper combines the nonlinear mapping capability of SCN and the ensemble learning advantage of the Adaboost algorithm based on existing experimental data on wastewater treatment. The accuracy of the model is evaluated by metrics such as coefficient of determination (R2) and error rate. It was found that the Adaboost-SCN model showed significant advantages in terms of prediction accuracy, precision, model stability and generalization ability compared to the SCN model alone. In order to further improve the performance of the model, this paper combined Adaboost-SCN with maximum information coefficient (MIC), random forest (RF) and energy valley optimizer (EVO) feature selection methods to construct three models, namely, MIC-Adaboost-SCN, RF-Adaboost-SCN and EVO-Adaboost-SCN. The results show that the prediction model with added feature selection is significantly better than the Adaboost-SCN model without feature selection in each evaluation index, and EVO has the most significant effect on feature selection. Finally, the correlation between biochar adsorption properties and production parameters was discussed through the inversion study of key parameters, and optimal parameter intervals were proposed to improve the adsorption properties. Providing strong support for the wide application of biochar in the field of wastewater treatment helps to solve the urgent environmental problem of heavy metal wastewater treatment.

Practical and Optimal Likelihood Intervals and Regions for Weibull and Gumbel Distributions

Profile likelihood intervals with good coverage probabilities and convenient simple expressions are presented to estimate separately and efficiently each of the parameters and quantiles of Weibull and Gumbel distributions, widely used in reliability and environmental applications. For the first time, likelihood-confidence intervals for these distributions, that were previously unavailable, can now be easily and quickly calculated with the provided R code for sample sizes n ≥ 10 . For simultaneous estimation of both parameters, likelihood-confidence regions are also provided. The proposal takes advantage of the transformation relationship between the Weibull and Gumbel distributions, of the fact that this latter distribution belongs to the Location and Scale family of distributions, and of likelihood symmetrizing parametrizations, all leading to simpler inferences about the parameters. The plot of the relative profile likelihood of a quantile of interest and its corresponding profile likelihood intervals provide decision makers with useful information in many practical applications, particularly when comparing two treatments. The proposed intervals for the Weibull shape parameter facilitate testing if an exponential distribution is reasonable for the data. The proposed methods are illustrated with practical examples.

Experiments and Theory on Droplet Ignition with Spark Discharges

ABSTRACT Ignition experiments were performed with individual n-decane droplets, initially, about 1 mm in diameter, which were suspended in quartz fibers and subjected to electrical discharges (sparks) of controlled power and duration. Experiments were performed with glow and arc discharges in air at 1 atm and approximately 300 K . Theory is developed to predict the probability of ignition of a fuel droplet as a function of time when it is exposed to an ignition spark. The theory considers the effect of random spark-to-spark fluctuations in the heat flux into the liquid on the time for the droplet surface temperature to be high enough to enable ignition. A Bayesian analysis is also performed to evaluate confidence intervals for parameters related to droplet ignition. Reasonable agreement between theory and experiment is demonstrated, suggesting that spark-to-spark fluctuations of the heat flux into a droplet may lead to a sigmoidal variation of the probability of ignition with respect to time.

INFERENCE IN MILDLY EXPLOSIVE AUTOREGRESSIONS UNDER UNCONDITIONAL HETEROSKEDASTICITY

Mildly explosive autoregressions have been extensively employed in recent theoretical and applied econometric work to model the phenomenon of asset market bubbles. An important issue in this context concerns the construction of confidence intervals for the autoregressive parameter that represents the degree of explosiveness. Existing studies rely on intervals that are justified only under conditional homoskedasticity/heteroskedasticity. This paper studies the problem of constructing asymptotically valid confidence intervals in a mildly explosive autoregression where the innovations are allowed to be unconditionally heteroskedastic. The assumed variance process is general and can accommodate both deterministic and stochastic volatility specifications commonly adopted in the literature. Within this framework, we show that the standard heteroskedasticity- and autocorrelation-consistent estimate of the long-run variance converges in distribution to a nonstandard random variable that depends on nuisance parameters. Notwithstanding this result, the corresponding t-statistic is shown to still possess a standard normal limit distribution. To improve the quality of inference in small samples, we propose a dependent wild bootstrap-t procedure and establish its asymptotic validity under relatively weak conditions. Monte Carlo simulations demonstrate that our recommended approach performs favorably in finite samples relative to existing methods across a wide range of volatility specifications. Applications to international stock price indices and U.S. house prices illustrate the relevance of the advocated method in practice.

Interval riccati equation-based and non-probabilistic dynamic reliability-constrained multi-objective optimal vibration control with multi-source uncertainties

Structural vibration control is used to ensure the safety of structures in service and has become an active research area in the past few years. In this study, uncertainties in structural dynamics are considered to propose an interval linear quadratic regulator (LQR) method based on an interval Riccati equation. Multi-objective optimization with non-probabilistic dynamic reliability as a constraint is performed to design an optimal uncertain vibration control system. To alleviate the difficulty of quantifying the probabilistic uncertainty and accurately characterize uncertainty information for small samples, multi-source uncertainties are regarded as interval parameters. The bounds on these uncertainties are determined, and the deterministic and uncertain parts of an interval state-space equation for vibration control are then formulated using an expanded-order matrix and the interval analysis method. Next, the interval perturbation method with a matrix series is used to develop a novel solution method for the linear inhomogeneous time-invariant equation in the interval state-space equation for the vibration control system and is used to accurately predict the interval bounds of the state responses. The conventional LQR method from modern control theory is used to propose a novel optimal control method based on a novel interval Riccati equation using the Lyapunov equation and interval uncertainty propagation. The proposed interval control method can be used to estimate the uncertain bounds of the controlled gain and cost function. A non-probabilistic dynamic reliability model is established to evaluate the reliability index of the system, which can overcome the limitations of the large computational cost of determining the probabilistic reliability. The deterministic controlled cost and uncertain states are considered as two optimization objectives with the proposed reliability constraint. The resulting constrained multi-objective optimal vibration control problem is designed and solved using c-DPEA. A flowchart is presented as a clear overview of the uncertain vibration control method, and the effectiveness of the proposed method is validated using two numerical examples. Different optimal control designs are obtained using different reliability constraints for quantitatively analyzing the safety of the control system.

Environmental risk evaluation for radionuclide transport through natural barriers of nuclear waste disposal with multi-scale streamline approaches

Natural barriers, encompassing stable geological formations that serve as the final bastion against radionuclide transport, are paramount in mitigating the long-term contamination risks associated with the nuclear waste disposal. Therefore, it is important to simulate and predict the processes and spatial-temporal distributions of radionuclide transport within these barriers. However, accurately predicting radionuclide transport on the field scale is challenging due to uncertainties associated with parameter scaling. This study develops an integrated evaluation framework that combines upscaled parameters, streamline transport models, and response surface techniques to systematically assess environmental risk metrics and parameter uncertainties across different scales. Initially, upscaling methods are established to estimate the prior interval of critical transport parameters at the field scale, and streamline models are derived by considering the radionuclides transport with a variety of physicochemical mechanisms and geological characterizations in natural barriers. To assess uncertainty ranges of the risk metrics related to upscaled parameters, uncertainty quantification is performed on the ground of 5000 Monte Carlo simulations. The results indicate that the upscaled dispersivity of fractured media (αLf) has a relatively high sensitivity ranking on release dose for all nuclides, and upscaled matrix sorption coefficient (Kd) of Pu-242 strongly affects breakthrough time and release dose of Pu-242. Facilitated by robust response surface with the lowest R2 of 0.89, it is shown that the release doses of Pu-242 and Pb-210 increase under conditions of low Kd and αLf, respectively. Furthermore, statistical analysis reveals that employing limited laboratory-scale parameters results in narrower confidence intervals for risk metrics, while upscaling methods better account for the highly heterogeneous properties of large-scale field conditions. The developed risk evaluation framework provides valuable insights for utilizing upscaled parameters and modeling radionuclide transport within natural barriers under various scenarios.

Establishment of Reference Intervals for Common Renal and Liver Function Parameters in Healthy Adults in Mogadishu, Somalia: A Cross-Sectional Study.

Reference intervals (RIs) are crucial for the accurate interpretating of laboratory test results in clinical settings, serving as benchmarks for evaluating individual health status. This study investigates the influence of sex and age on common liver function tests (LFTs) and renal function tests (RFTs) in healthy adults in Mogadishu, Somalia. A community-based cross-sectional study was carried out from October 2022 to January 2023 on a randomly selected sample of 255 healthy participants from Mogadishu, Somalia. Approximately 5 mL of whole blood was collected from each participant and processed screening of hepatitis B and C, and human immunodeficiency virus, and then biochemical analyses were conducted for common liver and kidney parameters. The study found significant sex and age-related differences in the measured LFTs and RFTs parameters. For LFTs, males had higher levels of alanine aminotransferase (ALT) and aspartate aminotransferase (AST) compared to females (ALT: 11.5 vs 7.5 U/L; AST: 25.5 vs 19.1 U/L; both p < 0.001). Age-related differences were also observed, with individuals aged 30 and above had higher levels of ALT and AST compared to those aged 18-29 (ALT: 10.9 vs 8.5 U/L; AST: 24.3 U/L vs 21.0 U/L, both p < 0.001). For RFTs, males had higher levels of creatinine (0.9 vs 0.7 mg/dL), urea (23.1 vs 16.1 mg/dL), and uric acid (5.2 vs 4.2 mg/dL) than females, all with p < 0.001. The study established population specific RIs for common liver and renal function parameters and revealed significant variations across sex and age groups. These findings underscore the importance of developing and using local RIs to ensure accurate clinical interpretation and effective patient management. Further research with larger sample sizes and in diverse regions of Somalia is highly recommended.

Some new results on rough interval linear programming problems and their application to scheduling and fixed-charge transportation problems

This paper focuses on linear programming problems in a rough interval environment. By introducing four linear programming problems, an attempt is being made to propose some results on optimal value of a linear programming problem with rough interval parameters. To obtain optimal solutions of a linear programming problem with rough interval data, constraints of the four proposed linear problems are applied. In this regard, firstly, the largest and the smallest feasible spaces for a linear constraint set with rough interval coefficients and parameters are introduced. Then, a rough interval for optimal value of such problems is obtained. Further, an upper approximation interval and a lower approximation interval as the optimal solutions of linear programming problems with rough interval parameters are achieved. Moreover, two solution concepts, surely and possibly solutions, are defined. Some numerical examples demonstrate the validity of the results. In particular, a scheduling problem and a fixed-charge transportation problem (FCTP) under rough interval uncertainty are investigated.

Sex- and age-based reference intervals for capillary complete blood count parameters among urban preschoolers in southeast China based on a large community population

Background and aimPediatricians commonly use the complete blood count (CBC) of capillary blood to evaluate health status, guide diagnoses, and determine treatment strategies. This study aimed to establish sex- and age-specific reference intervals (RIs) for 23 capillary CBC parameters for urban preschoolers in Fuzhou, Southeast China. Materials and methodsCapillary blood CBC data of 18,369 healthy preschoolers who underwent annual physical examinations at Fujian Maternity and Child Health Hospital between January 01, 2022, and November 31, 2023, were analyzed retrospectively. To fully validate the new RIs, the data of all apparently healthy children within the same age cohort at the same institution were comprehensively analyzed in December 2023. The new RIs were assessed by comparing them with the RIs currently used in laboratories and those obtained from different regions, sample types, or methodologies. ResultsDynamic temporal changes that differ between males and females were observed in the blood system of 3-7-year-old children in this region. The new sex- and age-specific RIs for capillary CBC parameters were feasible to guide clinical decision-making in the local region. ConclusionsOur findings demonstrated the importance of establishing sex- and age-specific RIs for each region and underscored the necessity of continuous adjustment of clinical Rls based on statistical rules and clinical responses.

Estimation and uncertainty quantification of magma interaction times using statistical emulation

The evolution of volcanic plumbing systems, which controls the style and size of eruptions, is largely determined by processes at depths that are not observable. Scientists use numerical models to simulate these processes and compare the outputs with data on erupted products to understand the plumbing system and eruption processes. However, our ability to explore the parameter space in order to match petrological and geophysical observations is limited by the computational cost required for such simulations. As an alternative, we present a statistical emulator that can reproduce the numerical results as a function of a set of input parameters. This approach can be used to invert the observed distribution of whole rock chemistry to determine the duration of interaction between magmas preceding an eruption and identify the best matching input parameters. This method intrinsically includes error propagation, thus providing reliable confidence intervals for the relevant parameters of the numerical simulations.

Damping efficiency of the fractional Duffing system and an assessment of its solution accuracy

Dynamical systems with high damping efficiency in a wide frequency band can be useful on a small scale – for harvesting energy from ambient vibrations, and on a large scale – for damping harmful vibrations of mechanical structures. In this paper we present an assessment of the quality of solutions and damping efficiency of systems with fractional order derivatives. To simulate the fractional system the fourth-order Runge–Kutta method and Grünwald–Letnikov methods are used. We propose a coefficient for assessing the quality of solutions to fractional systems by reference to the quality of the calculated energy balance. As an exemplary system we study the Duffing model with embedded additional fractional-order derivative terms. Based on this coefficient, intervals of key numerical simulation parameters are determined to ensure the appropriate quality for the calculations of energy flows and energy balance. The determined values of these parameters are then used in tests of the damping efficiency of the studied system. Our results show that by modifying the fractional terms it is possible to configure a system that exhibits a “broadband effect”, i.e. a system that is characterized by high-amplitude vibrations and, consequently, high energy efficiency in a wide range of excitation frequencies.

Inference of multi‐sample stage life testing model under Weibull distribution

AbstractIn this article we consider the meta‐analysis of stage life testing experiments. We propose a method to combine the data obtained from number of independent stage life testing experiments. We have assumed that there are only two stress levels for each stage life testing experiment and lifetime of the experimental units follows Weibull distribution at each stress level. The distributions under two stress levels are connected through Khamis–Higgings model assumption. We assume that the shape parameters of Weibull distribution are same for all the samples; however, the scale parameters are different. We provide the maximum likelihood estimation and the asymptotic confidence intervals of the model parameters. We also provide the Bayesian inference of the model parameters. The Bayes estimates and the associated credible intervals are obtained using Gibbs sampling technique since the explicit forms of the Bayes estimates do not exist. We have performed an extensive simulation study to see the performances of the different estimators, and the analyses of two data sets for illustrative purpose. The results are quite satisfactory.

Optimal hydraulic PTO and linear permanent magnet generator for a floating two-buoy wave energy converter

A fully coupled fluid-structure-power take-off model is used to investigate the optimal energy capture of a floating two-buoy wave energy converter excited by regular waves and irregular waves. The system incorporates hydraulic power take-off and a linear permanent magnet generator. By considering the coupling relationship between the power take-off parameters for regular waves, a power take-off parameter interval is determined for the optimization model. Parametric optimization of the hydraulic power take-off and linear permanent magnet generator systems is proposed, based on response surface methodology in conjunction with central combination design for sensitivity analysis and optimal configuration of different parameters. The methodology efficiently predicts optimal electric efficiency while reducing the requirement for multiple boundary element simulations. It is found that a model with predicted optimal configuration of the hydraulic power take-off system can achieve 10 % more electrical efficiency than that with linear permanent magnet generator. Comparison between the energy capacities of the different systems indicates that a device with linear permanent magnet generator attains higher energy conversion efficiency within a wider power take-off bandwidth. This study provides guidance for the design and selection of efficient power take-off systems for floating two-buoy wave energy converters.

Hybrid uncertainty propagation for mechanical dynamics problems via polynomial chaos expansion and Legendre interval inclusion function

This paper investigates a non-intrusive hybrid uncertainty propagation framework in mechanical dynamic systems, utilizing polynomial chaos expansion (PCE) and Legendre inclusion function. Uncertainties with substantial knowledge and information are conceptualized as stochastic parameters and described using PCE, while Legendre polynomials are employed to represent uncertain, bounded parameters, specifically interval uncertainties. During the computation, the PCE model for each time step is developed through Galerkin projection and sparse grid numerical integration. Consequently, the statistical moments of the dynamic responses relative to the stochastic parameters are derived from the orthogonality of the PCE and transformed into functions reflecting the interval parameters. The interval bounds for these statistical moments are further determined using the Legendre inclusion function, which is obtained through optimal Latin hypercube sampling and collocation methods. Three dynamics examples, respectively, modeled by differential–algebraic equations, finite element method, and commercial software proves its applicability and superiority. Detailed assessment demonstrates that this method offers high computational efficiency and accuracy. As a non-intrusive approach, it poses no particular limitations on numerical methods for solving differential equations, making it universally applicable.

Airport time profile construction driven by flight delay prediction

Slot structure is the equilibrium result of market demand side and slot resource supply side, while slot parameters reflect the operational support capacity of the aviation system. Time parameters reflect the operational support capability of the aviation system. Time structure should not only reflect changes in market demand, but also meet the constraints of operational efficiency. Constructing a reasonable 18–24 h timetable profile for busy airports that meets normal expectations for declared capacity and seasonal scheduling is a challenge in civil aviation slot management. This study utilizes historical data on airport flights and weather conditions to establish a regression prediction model for the time structure using K-means clustering and partial least squares regression. Additionally, ensemble learning is employed to forecast flight delay levels. The findings demonstrate that random forest yields favorable results in regression and prediction tasks, allowing for the integration of upper (good weather) and lower (severse weather) limits of the time profile with delay predictions as time parameter intervals. Consequently, the flights falling within these intervals achieve an average delay level of less than 15 min which meets the expectations of normal flight.