Model Uncertainty Research Articles

Observer-Based Fixed-Time Consensus Tracking for a Class of Nonlinear Multi-Agent Systems

In this paper, the problem of fixed-time consensus tracking for a class of nonlinear multi-agent systems (MASs) with uncertainties and external disturbances is addressed. To solve this problem, a new fixed-time consensus tracking protocol with disturbance rejection abilities is proposed that consists of a fixed-time distributed observer (FTDO), a fixed-time disturbance observer (FDO), and a nonsmooth backstepping controller with lumped disturbance compensation (NBCDC). The fixed-time stabilities are analyzed correspondingly. Firstly, an FTDO is designed to estimate a leader’s output by using the topology of communication networks for each follower. Second, an FDO is developed to observe the lumped disturbances composed of model uncertainties and external disturbances. Finally, an NBCDC is proposed for improving the closed-loop performance. The simulation results show that the proposed method is effective.

An Integrated Stochastic Optimization and Simulation Approach to SERU vs. Assembly Line Manufacturing Systems

This research compares SERU manufacturing systems to traditional assembly lines, focusing on the impact of uncertainty in task processing time on production output. The study considers worker skill levels and team identity, using a stochastic mixed integer linear programming approach to model uncertainty and optimize workforce allocation. Discrete event simulation is then integrated to evaluate performance using five key performance indicators (KPIs). Results show that SERU systems outperform traditional lines in terms of throughput when uncertainty is considered. The integrated approach provides more reliable performance data than deterministic optimization alone. The study also highlights the advantages of SERU systems when worker skill levels and team identity are factored in. This research fills a gap in the literature by proposing a stochastic optimization approach that considers uncertainty and worker skill levels, and by integrating stochastic optimization with simulation for comprehensive analysis. This approach provides valuable guidance for production managers in optimizing production systems.

Cooperative control of leader–follower ships with prescribed performance

With consideration of prescribed performance, the robust cooperative control of leader–follower ships with the existence of ocean disturbances and model uncertainties is studied. The environmental disturbances are modeled as the harmonics disturbances with unknown amplitude and frequency, which are evaluated using an adaptive disturbance observer(ADO). Meanwhile, the model uncertainties is approximated utilizing the neural network, and the prescribed performance method is employed so that the tracking errors can be limited to the predefined set. Then the anti-disturbance cooperative control strategy is presented such that the system states are uniformly ultimately bounded, in addition, the collaborative motion among the leader–follower formation ships are achieved. Eventually, comparative simulations are employed to validate the cooperative control method.

Physically based probabilistic prediction of regional rainfall-induced shallow landslides: from initiation to runout analysis

ABSTRACT In this study, a physically based method is proposed to estimate the exceedance probability of the intensity measure of the regional rainfall-induced shallow landslides. This method consists of a digital elevation model, an initiation model, a runout model and a probabilistic analysis model. In the suggested method, a study area is discretised into a grid of cells, and the stability of each cell can be evaluated through the initiation model. Then, the runout behaviour of the unstable cells can be simulated by the runout model. Finally, the exceedance probability of the intensity measures of each cell can be estimated through Monte Carlo simulation considering the uncertainties in the initiation model and runout model. The proposed method is applied to analyse the rainfall-induced landslides in a study area in the southwest of China, which can provide a reasonably accurate prediction of the impact zones of the landslides. The suggested method provides a useful tool to probabilistically predict the impacted area of the rainfall-induced landslides at a regional scale.

Quantification and validation of uncertainties in subsoil models

AbstractIn infrastructure planning and construction, modeling the subsoil and its associated uncertainty is a fundamental task of geotechnical engineers. However, probabilistic methods and tools for quantifying and displaying the uncertainty of the subsoil models are rarely used in practice where deterministic interpolation dominates. In digital planning using Building Information Modeling (BIM), the probabilistic approach supports creating a discipline model in which the uncertainties of the spatial layer structure are statistically quantified to evaluate the georisks in the design and execution of civil constructions. This article presents a case study using a combination of Sequential Gaussian Simulation (SGSIM) and Sequential Indicator Simulation (SISIM) to account for uncertainties in soil layer geometry. In a case study at the Munich Town Hall, a geostatistical approach is applied and validated based on 70 bore logs, whereby the probabilities for the occurrence of a particular layer are spatially quantified. The case study illustrates the methodology‘s great potential and benefits compared to the conventional deterministic approach based on interpolation procedures.

Characterisation and calibration of multiversal methods

AbstractMultiverse Analysis is a heuristic for robust multiple models estimation where data fit many connected specifications of the same abstract model, instead of a singular or a small selection of specifications. Differently from the canonical application of multimodels, in Multiverse Analysis the probabilities of the specifications to be included in the analysis are never assumed independent of each other. Grounded in this consideration, this study provides a compact statistical characterisation of the process of elicitation of the specifications in Multiverse Analysis and conceptually adjacent methods, connecting previous insights from meta-analytical Statistics, model averaging, Network Theory, Information Theory, and Causal Inference. The calibration of the multiversal estimates is treated with references to the adoption of Bayesian Model Averaging vs. alternatives. In the applications, it is checked the theory that Bayesian Model Averaging reduces both error and uncertainty for well-specified multiversal models but amplifies errors when a collider variable is included in the multiversal model. In well-specified models, alternatives do not perform better than Uniform weighting of the estimates, so the adoption of a gold standard remains ambiguous. Normative implications for misinterpretation of Multiverse Analysis and future directions of research are discussed.

Abstract 4119874: Cost Effectiveness Analysis of Surgical Strategies Versus Medical Management for Rheumatic Heart Disease in Rwanda

Background: One third of the Rheumatic Heart Disease (RHD) burden is in sub-Saharan Africa. Without valve surgery, 17% of patients die. However, surgery is often deemed too expensive in this region despite the lack of cost-effectiveness analyses to support this assumption. Aim: Assess the cost-effectiveness of surgical strategies for RHD performed in Rwanda. Methods: We built a Markov model to simulate the progression of patients through different health states. We compared mechanical valve replacement, bioprosthetic valve replacement, and valve repair to medical management for patients with severe RHD. Probabilities of transitioning into different health states were derived from regional published studies. Micro-costing data was obtained from the cardiac surgery program to calculate total costs for each health state. Health effects were measured in quality-adjusted life years (QALYs) from the 2019 Global Burden of Disease Study. Sensitivity analysis was performed to account for model uncertainty. We used a willingness-to-pay threshold of three times the GDP per capita of Rwanda (USD$769). Results: All surgical strategies extended life expectancy compared to medical management, which only offered 5.05 QALYs. Mechanical valve replacement surgery was cost-effective with 11.31 QALYs for a lifetime cost of USD$10,721. The incremental cost effectiveness ratio compared to medical management was USD$1,596/QALY, which is below the willingness to pay threshold. Decreasing the initial cost of surgery and probability of long term stroke increased cost-effectiveness. Although bioprosthetic valve replacement and repair provided 6.43 and 5.70 additional QALYs compared to medical management, they had higher lifetime costs than mechanical valve replacement ($19,789.21, $22,477.27). As a result, they were not cost-effective. In the sensitivity analysis, they became cost effective if valve degeneration rates were 11% in 2 years from a baseline of 26% for repair, and 8% in 2 years from baseline of 14% for bioprosthetic valves. Conclusion: This study challenges the prevailing assumption that surgery is not cost-effective in Sub-Saharan Africa. Mechanical valve replacement surgery was most cost-effective. Watchful waiting with medical management is inexpensive but carries an average life expectancy of 5 years. Identifying cost-saving opportunities for mechanical valve replacement surgery and enhancing anticoagulation monitoring can make it even more economically favorable.

A Control Method for Path Following of AUVs Considering Multiple Factors Under Ocean Currents

To improve the path-following performance of autonomous underwater vehicles (AUVs) under ocean currents, a control method based on line-of-sight with fuzzy controller (FLOS) guidance and the fuzzy sliding mode controller (FSMC) is proposed. This method considers multiple factors affecting guidance and adaptively determines the optimal heading angle through the fuzzy controller to enhance guidance capability. Additionally, a novel FSMC based on Lyapunov stability theory is designed to suppress the influence of model uncertainty and external disturbances on the control system. Simulations and experiments of the proposed control method demonstrate that it can maintain precise tracking under disturbances, improving path-following performance metrics by more than 15%.

Adaptive Two-Degree-of-Freedom Robust Gain-Scheduling Control Strategy

This study introduces a novel tracking control strategy tailored to aeroengines, which are highly nonlinear and characterized by significant uncertainty. The proposed method entails a robust extended Kalman filter (REKF) enhanced by a forgetting factor for improved performance. An accompanying augmented, mixed onboard adaptive model based on the REKF precisely estimates and manages engine performance degradation. This advanced model effectively counters the degradation term in the perturbation block of the engine’s uncertain model. Using this strategic approach, a robust gain-scheduling controller was constructed and was found to outperform its predecessors, marking a notable advancement in control system design. Controlling twin rotor multi-input, multi-output (MIMO) systems is a highly complex process due to model uncertainties and unpredictable external disturbances. To address these challenges, we constructed an adaptive two-degree-of-freedom robust gain-scheduling controller (ATDF-RGSC) using a mixed sensitivity approach. Rigorous performance analysis confirms that this controller offers enhanced robustness, faster tracking, and more precise disturbance attenuation compared to other methods. These advanced control strategies successfully manage uncertainties and disturbances, improving performance metrics in both simulated and experimental scenarios. The proposed method may significantly enhance the safety and reliability of aeroengines and MIMO systems in practical applications.

Predictive Model and Optimization of Micromixers Geometry using Gaussian Process with Uncertainty Quantification and Genetic Algorithm

Abstract Microfluidic devices are gaining attention for their small size and ability to handle tiny fluid volumes. Mixing fluids efficiently at this scale, known as micromixing, is crucial. This article builds upon previous research by introducing a novel optimization approach in microfluidics, combining Computational Fluid Dynamics (CFD) with Machine Learning (ML) techniques. Our research focuses on enhancing global optimization techniques while minimizing computational costs. It draws inspiration from a Y-type micromixer, initially featuring cylindrical grooves on the main channel's surface and internal obstructions. Simulations, conducted using OpenFOAM software, evaluate the impact of circular obstructions on mixing percentage and pressure drop, considering variations in obstruction diameter and offset. A Gaussian Process (GP) was utilized to model the data, providing model uncertainty. This study optimizes geometries by using genetic algorithm (GA) based on the reduced order model provided by GP. Results align with previous research, showing that medium-sized obstructions (137 mm diameter, 10 mm offset) near the channel wall are optimal. This approach not only provides efficient microfluidic optimization with uncertainty quantification but also highlights the effectiveness of combining CFD and ML techniques in achieving desired outcomes.

Flow-dependent observation errors for greenhouse gas inversions in an ensemble Kalman smoother

Abstract. Atmospheric inverse modeling is the process of estimating emissions from atmospheric observations by minimizing a cost function, which includes a term describing the difference between simulated and observed concentrations. The minimization of this difference is typically limited by uncertainties in the atmospheric transport model rather than by uncertainties in the observations. In this study, we showcase how a temporally varying, flow-dependent atmospheric transport uncertainty can enhance the accuracy of emission estimation through idealized experiments using an ensemble Kalman smoother system. We use the estimation of European CH4 emissions from the in situ measurement network as an example, but we also demonstrate the additional benefits for trace gases with more localized sources, such as SF6. The uncertainty in flow-dependent transport is determined using meteorological ensemble simulations that are perturbed by physics and driven at the boundaries by an analysis ensemble from a global meteorology and a CH4 simulation. The impact of direct representation of temporally varying transport uncertainties in atmospheric inversions is then investigated in an observation system simulation experiment framework in various setups and for different flux signals. We show that the uncertainty in the transport model varies significantly in space and time and that it is generally highest during nighttime. We apply inversions using only afternoon observations, as is common practice, but also explore the option of assimilating hourly data irrespective of the hour of day using a filter based on transport uncertainty and taking into account the temporal covariances. Our findings indicate that incorporating flow-dependent uncertainties in inversion techniques leads to more accurate estimates of GHG emissions. Differences between estimated and true emissions could be reduced more effectively by 9 % to 82 %, with generally larger improvements for the SF6 inversion problem and for the more challenging setup with small flux signals.

Updating reduced-order dynamic model for flexible-joint arm to design adaptive feedback linearization control

This study deals with the construction of an enhanced dynamic model for a lever-arm with flexible-joint to design a feedback linearization controller. The uncertainties of reduced-order model with nominal parameters are compensated via a complementary term to upgrade it to the actual system. The proposed method uses data fusion of encoder/gyroscope to remove the measurement errors. Mathematical analyses are provided to show the stochastic stability of the proposed scheme. Accordingly, a fuzzy adaptive solution is presented to effectively schedule the free parameters of the algorithm. The enhanced reduced-order model is used to design a feedback linearization law for control of lever-arm position. The controller adapts itself to the actual system, and is reliable and cost-effective because of using less sensors. The simulation studies indicate a higher accuracy of the proposed system compared with the controller designed by the full-order model in the presence of parametric uncertainties and disturbances. Also, experimental results conducted on a fabricated platform demonstrate the effectiveness of the suggested system to control the arm position in different scenarios. The comparative results with prevalent controllers indicate higher accuracy with smaller control input for the proposed controller to reject the disturbances and other uncertainties.

A Finite-Time Disturbance Observer for Tracking Control of Nonlinear Systems Subject to Model Uncertainties and Disturbances

In this study, a finite-time disturbance observer (FTDOB) with a new structure is originally put forward for the motion tracking problem of a class of nonlinear systems subject to model uncertainties and exogenous disturbances. Compared to existing disturbance estimator designs in the literature, in which the estimation error only converges to the origin asymptotically under assumptions that the first and/or second derivatives are vanishing, the suggested DOB is able to estimate the disturbance exactly in finite time. Firstly, uncertainties (parametric and unstructured uncertainties), unknown dynamics, and external disturbances in system dynamics are lumped into a generalized disturbance term that is subsequently estimated by the proposed DOB. Based on this, a DOB-based backstepping controller is synthesized to ensure high-accuracy tracking performance under various working conditions. The stability analysis of not only the DOB but also the overall closed-loop system is theoretically confirmed by the Lyapunov stability theory. Finally, the advantages of the proposed FTDOB and the FTDOB-based controller over other DOBs and existing DOB-based controllers are explicitly simultaneously demonstrated by a series of numerical simulations on a second-order mechanical system and comparative experiments on an actual DC motor system.

A High Performance Nonlinear Longitudinal Controller for Fixed-Wing UAVs Based on Fuzzy-Guaranteed Cost Control

Unmanned aerial vehicles (UAVs) have garnered more attention across various industries in recent years, leading to significant development in their design and application globally. Due to the high coupling between UAV states, model uncertainties, and various disturbances, precise longitudinal control of UAVs remains a significant research challenge. Oriented for the speed and altitude control of an electrical-powered fixed-wing UAV, this paper introduces a new control strategy based on the fuzzy guaranteed cost control (F-GCC) technique, which results in a nonlinear longitudinal state feedback control law with strict stability criterion, effectively addressing the issue of state coupling. Moreover, the strategy also includes a thrust estimation model of the electrical propulsion system to significantly reduce the nonlinearity, simplifying the controller design while effectively preserving tracking control performance. Through numerical validation, the UAV longitudinal nonlinear controller designed using the F-GCC technique offers better transient response and stronger robustness than the traditional linear and ADRC controllers.

Gravity data inversion for parameters assessment over geologically faulted structures—A hybrid particle swarm optimization and gravitational search algorithm technique

AbstractInterpreting gravity anomalies caused by fault formations is associated with hydrocarbon systems, mineralized areas and hazardous zones and is the main goal of this research. To achieve an effective and robust model over the geologically faulted structures from gravity anomalies, we present a nature‐inspired hybrid algorithm, which synergizes the physics of the particle swarm optimization and gravitational search algorithm with variable inertia weights. The basic principle of developed particle swarm optimization and gravitational search algorithm method is to synergistically use the exploratory strengths of gravitational search algorithm with the exploitation capacity of particle swarm optimization in order to optimize and enhance the effectiveness by both algorithms. The technique has been tested on synthetic gravity data with varying settings of noises over geologically faulted structure before being applied to field data taken from Ahiri‐Cherla and Aswaraopet master fault present in Pranhita–Godavari valley, India. The optimization process is further refined through normalized Gaussian probability density functions, confidence intervals, histograms and correlation matrices to quantify uncertainty, stability, sensitivity and resolution. When dealing with field data, the true model is never known; in these circumstances, the quality of the outcome can only be inferred from the uncertainty in the mean model. The research utilizes a 68.27% confidence intervals to identify a location where the probability density function is more dominant. This region is then used to evaluate the mean model, which is expected to be more appropriate and closer to the genuine model. Correlation matrices further provide a clear demonstration of the strong connection between layer parameters. The results suggest that particle swarm optimization and gravitational search algorithm is less affected by model parameters and yields geologically more consistent outcomes with little uncertainty in the model, aligning well with the available results. The analysed results show that the method we came up with works well and is stable when it comes to solving the two‐dimensional gravity inverse problem. Future research may involve extending the approach to three‐dimensional inversion problems, with potential improvements in computational efficiency and search accuracy for global optimization methods.

Overbounding the Model Uncertainty for Kalman Filter-Based Advanced Receiver Autonomous Integrity Monitoring in the Presence of Time Correlation by the Hybrid Evolutionary Algorithm

Overbounding the Model Uncertainty for Kalman Filter-Based Advanced Receiver Autonomous Integrity Monitoring in the Presence of Time Correlation by the Hybrid Evolutionary Algorithm

A study of the role of data and model uncertainty in active learning

Uncertainty-based active learning strategies have demonstrated significant superiority in small data research of materials domain. This study explores the effects of model uncertainty and data uncertainty separately on the performance of active learning strategies, specifically focusing on the number of iterations required to identify the optimal samples. For model uncertainty, three kinds of acquisition functions are compared, including predicted value strategy (PV), ranking of predicted value strategy (PR) and expected improvement strategy (EI). Among these, the active learning model utilizing PR requires the fewest average iterations (1.75). For data uncertainty, we evaluate the iterations of active learning by Gaussian process models that incorporate the uncertainty of the observations and noise samples that takes account into the uncertainty of the input features respectively. The results indicate that the active learning iterations of the three strategies converge to similar at the optimal weighting when the uncertainty of the observations is considered in the model (EI for 1.75, PV for 1.21 and PR for 1.18). In contrast, incorporating noise samples into the augmented dataset after the original samples would severely deteriorate the efficiency of active learning recommendations. Our findings aim to offer guidance for exploring more favorable acquisition functions and methods for active learning strategies.

Asymmetric interval numbers: A new approach to modeling uncertainty

This paper introduces Asymmetric Interval Numbers (AINs), a novel type of interval numbers that combines the straightforward identification characteristic of classical interval numbers with the advanced capability for modeling uncertainty found in fuzzy sets, all while maintaining simplicity. AINs incorporate the expected value within the interval, providing a more accurate representation of the uncertainty of the data compared to the classical interval numbers. We define basic arithmetic operations for AINs, discuss their properties, and provide proofs. Additionally, we present theorems on symmetry and asymmetry for fundamental binary and unary operations, enhancing the mathematical framework for AINs. Several illustrative examples demonstrate the practical application of AINs. Although challenges remain, such as exploring performance with different distributions and reducing overestimation, AINs present a promising advancement in interval arithmetic. This study underscores the practical and theoretical implications of AINs, paving the way for further research and application in diverse scientific and industrial contexts.

A Compositional Approach to the Simulation of Queuing Systems with Random Parameters

A general approach to modeling random service processes under conditions of disturbances and uncertainty of the initial data is substantiated. A compositional approach to constructing simulation models of queuing with parametric uncertainty based on phase-type distributions and phase functions is proposed. The calculation and comparison of the characteristics of the developed simulation models with analytical solutions were carried out to confirm their effectiveness and accuracy. The problems of uncertainty of the initial data and their impact on the modeling of service systems are highlighted. The importance of taking into account parametric uncertainty in simulation models is emphasized in order to increase their adequacy and applicability in practice. The study includes a description of a general approach to modeling random service processes with uncertainty, as well as methodological foundations for the application of phase distributions and functions in compositional modeling. Four classes of service models are considered, differing in the type of integral core and phase function, which makes it possible to implement a variety of random service processes, taking into account their characteristics and conditions of their occurrence. The analysis of a model with an exponential integral core and various types of phase functions is carried out, which demonstrates the flexibility and wide possibilities of the proposed compositional approach to the study and modeling of service systems. The results of simulation modeling are presented, confirming analytical studies and showing the applicability and effectiveness of the developed approach in the construction and analysis of models of service systems with random parameters. The practical significance of the compositional method for the design and modernization of information and computing systems at various stages of their development, taking into account the uncertainty of the initial data, is noted. The work is focused on the development of simulation methods for queuing systems and opens up new prospects for their research and optimization in conditions of uncertainty of initial parameters.

Demonstrating almost half of cotton fiber quality variation is attributed to climate change using a hybrid machine learning-enabled approach

Understanding the effects of climate change on cotton fiber quality will reduce the risks to production caused by global warming. Machine learning algorithms are effective for forecasting climate impacts on crops. However, the impact of climate change on cotton fiber quality is unclear. Hence, a hybrid machine learning-enabled approach, the Bayesian model average (BMA) method with multiple machine learning algorithms (linear regressor, SVR, RFR, GBDT, LightGBM, and XGBoost) and bootstrap resampling, was developed to explore the impact and screen the important climatic factors affecting various traits of fiber quality. On the basis of fiber quality data from 1033 test stations across Xinjiang, China, from 2016 to 2022, the explained variance for climate change in the hybrid machine learning model was as follows: 44.72 %–50.55 % for white cotton grade, 44.06 %–53.95 % for length, 51.72 %–56.81 % for micronaire, 32.70 %–49.50 % for length uniformity, and 45.66 %–53.09 % for strength in the 1000 bootstrapping samples. In addition, recursive feature elimination with cross-validation (RFECV) was used to select the optimal feature set and calculate the contribution of each feature. The variability in micronaire in the hybrid model was affected primarily by climate factors, such as the daily minimum temperature, rainfall, and wind speed, whereas the other quality traits were affected mainly by radiation-related climatic indicators. The climate during the harvest stage in October had a significant effect on cotton quality, explaining 33.0 % of the variance in white cotton grade, 32.1 % in length, and 48.3 % in fiber strength. Conversely, the climate during the boll opening and early harvest stages in September had a greater influence on micronaire and length uniformity, accounting for 21.4 % and 37.2 % of the variance, respectively. This study highlights that climate change explains nearly 50 % of the variation in fiber quality, with the influence being notably more considerable during the later stages of the cotton growth period. These findings clarify the uncertainty in the impact of climate change on cotton fiber quality considering the uncertainty of the single machine model and model errors. Equally important, this information can be valuable for farmers and growers seeking to improve fiber quality under climate change.