Prediction of Uncertainty Estimation and Confidence Calibration Using Fully Convolutional Neural Network

Convolution neural networks(CNNs)have proven to be effective clinical imagingmethods.This study highlighted some of the key issues within these systems.It is difficult to train these systems in a limited clinical image databases,and many publications present strategies including such learning algorithm.Furthermore,these patterns are known formaking a highly reliable prognosis.In addition,normalization of volume and losses of dice have been used effectively to accelerate and stabilize the training.Furthermore,these systems are improperly regulated,resulting in more confident ratings for correct and incorrect classification,which are inaccurate and difficult to understand.This study examines the risk assessment of Fully Convolutional Neural Networks(FCNNs)for clinical image segmentation.Essential contributions have been made to this planned work:1)dice loss and cross-entropy loss are compared on the basis of segment quality and uncertain assessment of FCNNs;2)proposal for a group model for assurance measurement of full convolutional neural networks trained with dice loss and group normalization;And 3)the ability of the measured FCNs to evaluate the segment quality of the structures and to identify test examples outside the distribution.To evaluate the study’s contributions,it conducted a series of tests in three clinical image division applications such as heart,brain and prostate.The findings of the study provide significant insights into the predictive ambiguity assessment and a practical strategies for outside-distribution identification and reliable measurement in the clinical image segmentation.The approaches presented in this research significantly enhance the reliability and accuracy rating of CNNbased clinical imaging methods.

Optimal Parameter and Uncertainty Estimation of a Land Surface Model: Sensitivity to Parameter Ranges and Model Complexities

Most previous land-surface model calibration studies have defined globalranges for their parameters to search for optimal parameter sets. Little work has been conducted tostudy the impacts of realistic versus global ranges as well as model complexities on the calibrationand uncertainty estimates. The primary purpose of this paper is to investigate these impacts byemploying Bayesian Stochastic Inversion (BSI) to the Chameleon Surface Model (CHASM). The CHASM wasdesigned to explore the general aspects of land-surface energy balance representation within acommon modeling framework that can be run from a simple energy balance formulation to a complexmosaic type structure. The BSI is an uncertainty estimation technique based on Bayes theorem,importance sampling, and very fast simulated annealing. The model forcing data and surface flux datawere collected at seven sites representing a wide range of climate and vegetation conditions. Foreach site, four experiments were performed with simple and complex CHASM formulations as well asrealistic and global parameter ranges. Twenty eight experiments were conducted and 50 000 parametersets were used for each run. The results show that the use of global and realistic ranges givessimilar simulations for both modes for most sites, but the global ranges tend to produce someunreasonable optimal parameter values. Comparison of simple and complex modes shows that the simplemode has more parameters with unreasonable optimal values. Use of parameter ranges and modelcomplexities have significant impacts on frequency distribution of parameters, marginal posteriorprobability density functions, and estimates of uncertainty of simulated sensible and latent heatfluxes. Comparison between model complexity and parameter ranges shows that the former has moresignificant impacts on parameter and uncertainty estimations.

A SCR method for uncertainty estimation in geodesy non-linear error propagation: Comparisons and applications

We review three derivative-free methods developed for uncertainty estimation of non-linear error propagation, namely, MC(Monte Carlo), SUT(scaled unscented transformation), and SI(sterling interpolation). In order to avoid preset parameters like as these three methods need, we introduce a new method to uncertainty estimation for the first time, namely, SCR(spherical cubature rule), which is no need for setting parameters. By theoretical derivation, we prove that the precision of uncertainty obtained by SCR can reach second-order. We conduct four synthetic experiments, for the first two experiments, the results obtained by SCR are consistent with the other three methods with optimal setting parameters, but SCR is easier to operate than other three methods, which verifies the superiority of SCR in calculating the uncertainty. For the third experiment, real-time calculation is required, so the MC is hardly feasible. For the forth experiment, the SCR is applied to the inversion of seismic fault parameter which is a common problem in geophysics, and we study the sensitivity of surface displacements to fault parameters with errors. Our results show that the uncertainty of the surface displacements is the magnitude of ±10 mm when the fault length contains a variance of 0.01 km^(2).

Robust design of sliding mode control for airship trajectory tracking with uncertainty and disturbance estimation

The robotic airship can provide a promising aerostatic platform for many potential applications.These applications require a precise autonomous trajectory tracking control for airship.Airship has a nonlinear and uncertain dynamics.It is prone to wind disturbances that offer a challenge for a trajectory tracking control design.This paper addresses the airship trajectory tracking problem having time varying reference path.A lumped parameter estimation approach under model uncertainties and wind disturbances is opted against distributed parameters.It uses extended Kalman filter(EKF)for uncertainty and disturbance estimation.The estimated parameters are used by sliding mode controller(SMC)for ultimate control of airship trajectory tracking.This comprehensive algorithm,EKF based SMC(ESMC),is used as a robust solution to track airship trajectory.The proposed estimator provides the estimates of wind disturbances as well as model uncertainty due to the mass matrix variations and aerodynamic model inaccuracies.The stability and convergence of the proposed method are investigated using the Lyapunov stability analysis.The simulation results show that the proposed method efficiently tracks the desired trajectory.The method solves the stability,convergence,and chattering problem of SMC under model uncertainties and wind disturbances.

Uncertainty and disturbance estimator-based model predictive control for wet flue gas desulphurization system

Wet flue gas desulphurization technology is widely used in the industrial process for its capability of efficient pollution removal.The desulphurization control system,however,is subjected to complex reaction mechanisms and severe disturbances,which make for it difficult to achieve certain practically relevant control goals including emission and economic performances as well as system robustness.To address these challenges,a new robust control scheme based on uncertainty and disturbance estimator(UDE)and model predictive control(MPC)is proposed in this paper.The UDE is used to estimate and dynamically compensate acting disturbances,whereas MPC is deployed for optimal feedback regulation of the resultant dynamics.By viewing the system nonlinearities and unknown dynamics as disturbances,the proposed control framework allows to locally treat the considered nonlinear plant as a linear one.The obtained simulation results confirm that the utilization of UDE makes the tracking error negligibly small,even in the presence of unmodeled dynamics.In the conducted comparison study,the introduced control scheme outperforms both the standard MPC and PID(proportional-integral-derivative)control strategies in terms of transient performance and robustness.Furthermore,the results reveal that a lowpass-filter time constant has a significant effect on the robustness and the convergence range of the tracking error.

DISTRIBUTED MONITORING SYSTEM RELIABILITY ESTIMATION WITH CONSIDERATION OF STATISTICAL UNCERTAINTY

Taking into account the whole system structure and the component reliability estimation uncertainty, a system reliability estimation method based on probability and statistical theory for distributed monitoring systems is presented. The variance and confidence intervals of the system reliability estimation are obtained by expressing system reliability as a linear sum of products of higher order moments of component reliability estimates when the number of component or system survivals obeys binomial distribution. The eigenfunction of binomial distribution is used to determine the moments of component reliability estimates, and a symbolic matrix which can facilitate the search of explicit system reliability estimates is proposed. Furthermore, a case of application is used to illustrate the procedure, and with the help of this example, various issues such as the applicability of this estimation model, and measures to improve system reliability of monitoring systems are discussed.

Adaptive recurrent neural network for uncertainties estimation in feedback control system

In this paper,a recurrent neural network(RNN)is used to estimate uncertainties and implement feedback control for nonlinear dynamic systems.The neural network approximates the uncertainties related to unmodeled dynamics,parametric variations,and external disturbances.The RNN has a single hidden layer and uses the tracking error and the output as feedback to estimate the disturbance.The RNN weights are online adapted,and the adaptation laws are developed from the stability analysis of the controlled system with the RNN estimation.The used activation function,at the hidden layer,has an expression that simplifies the adaptation laws from the stability analysis.It is found that the adaptive RNN enhances the tracking performance of the feedback controller at the transient and steady state responses.The proposed RNN based feedback control is applied to a DC–DC converter for current regulation.Simulation and experimental results are provided to show its effectiveness.Compared to the feedforward neural network and the conventional feedback control,the RNN based feedback control provides good tracking performance.

Mapping aboveground biomass and its prediction uncertainty using LiDAR and field data, accounting for tree-level allometric and LiDAR model errors

Background: The increasing availability of remotely sensed data has recently challenged the traditional way of performing forest inventories, and induced an interest in model-based inference. Like traditional design-based inference, model-based inference allows for regional estimates of totals and means, but in addition for wall-to-wall mapping of forest characteristics. Recently Light Detection and Ranging(LiDAR)-based maps of forest attributes have been developed in many countries and been well received by users due to their accurate spatial representation of forest resources. However, the correspondence between such mapping and model-based inference is seldom appreciated. In this study we applied hierarchical model-based inference to produce aboveground biomass maps as well as maps of the corresponding prediction uncertainties with the same spatial resolution. Further, an estimator of mean biomass at regional level, and its uncertainty, was developed to demonstrate how mapping and regional level assessment can be combined within the framework of model-based inference.Results: Through a new version of hierarchical model-based estimation, allowing models to be nonlinear, we accounted for uncertainties in both the individual tree-level biomass models and the models linking plot level biomass predictions with LiDAR metrics. In a 5005 km2 large study area in south-central Sweden the predicted aboveground biomass at the level of 18 m×18 m map units was found to range between 9 and 447 Mg·ha^-1. The corresponding root mean square errors ranged between 10 and 162 Mg·ha^-1. For the entire study region, the mean aboveground biomass was 55 Mg·ha^-1 and the corresponding relative root mean square error 8%. At this level 75%of the mean square error was due to the uncertainty associated with tree-level models.Conclusions: Through the proposed method it is possible to link mapping and estimation within the framework of model-based inference. Uncertainties in both tree-level biomass models and models linking plot level biomass with LiDAR data are accounted for, both for the uncertainty maps and the overall estimates. The development of hierarchical model-based inference to handle nonlinear models was an important prerequisite for the study.

Back-Stepping Control for Flexible Air-Breathing Hypersonic Vehicles Based on Uncertainty and Disturbance Estimator

A theoretical framework of nonlinear flight control for a flexible air-breathing hypersonic vehicle(FAHV)is proposed in this paper.In order to suppress the system uncertainty and external disturbance,an uncertainty and disturbance estimator(UDE)based back-stepping control strategy is designed for a dynamic state-feedback controller to provide stable velocity and altitude tracking.Firstly,the longitudinal dynamics of FAHV is simplified into a closure loop form with lumped uncertainty and disturbance.Then the UDE is applied to estimate the lumped uncertainty and disturbance for the purpose of control input compensation.While a nonlinear tracking differentiator is introduced to solve the problem of“explosion of term”in the back-stepping control.The stability of the UDE-based control strategy is proved by using Lyapunov stability theorem.Finally,simulation results are presented to demonstrate the capacity of the proposed control strategy.

The K Method for Estimating Earthquake Activity Parameters and Effect of the Boundary Uncertainty of the Source Region:Discussion on the Seismic Zoning Method

Two aspects of a new method,which can be used for seismic zoning,are introduced in this paper.On the one hand,the approach to estimate b value and annual activity rate proposed by Kijko and Sellevoll needs to use the earthquake catalogue.The existing earthquake catalogue contains both historical and recent instrumental data sets and it is inadequate to use only one part.Combining the large number of historical events with recent complete records and taking the magnitude uncertainty into account,Kijko’s method gives the maximum likelihood estimation of b value and annual activity rate,which might be more realistic.On the other hand,this method considers the source zone boundary uncertainty in seismic hazard analysis,which means the earthquake activity rate across a boundary of a source zone changes smoothly instead of abruptly and avoids too large a gradient in the calculated results.

Influence of the environmental noise on determining the period of a torsion pendulum

The environmental noise can restrict the accuracy of period estimation since the torsion pendulum is sensitive to weak forces. Two typical models for the environmental noise are proposed to make an evaluation. Generally, the stationary environmental noise is modeled as a white noise, and contributes to the period uncertainty as a function of the initial amplitude, the quality factor, the variance of noise and the time length. As to a sudden sharp disturbance acting on the pendulum, a narrow impulse model is constructed. It results in a sharp jump in the phase difference, which can be excluded with the 3σ criterion for a correction. An experimental data analysis for the measurement of the gravitational constant G with the time-of-swing method shows that the period uncertainty due to the environmental noise is about one and a half times the fundamental thermal noise limit. Though this result is dependent on the ambient environment, the analysis is instructive to improve the measurement accuracy of experiments.

Assessment of soil total phosphorus storage in a complex topography along China's southeast coast based on multiple mapping scales

Soil phosphorus (P) plays a vital role in both ecological and agricultural ecosystems, where total P (TP) in soil serves as a crucial indicator of soil fertility and quality. Most of the studies covered in the literature employ a single or narrow range of soil databases, which largely overlooks the impact of utilizing multiple mapping scales in estimating soil TP, especially in hilly topographies. In this study, Fujian Province, a subtropical hilly region along China’s southeast coast covered by a complex topographic environment, was taken as a case study. The influence of the mapping scale on soil TP storage (TPS)estimation was analyzed using six digital soil databases that were derived from 3 082 unique soil profiles at different mapping scales, i.e., 1:50 000 (S5),1:200 000 (S20), 1:500 000 (S50), 1:1 000 000 (S100), 1:4 000 000 (S400), and 1:10 000 000 (S1000). The regional TPS in the surface soil (0–20 cm) based on the S5, S20, S50, S100, S400, and S1000 soil maps was 20.72, 22.17, 23.06, 23.05, 22.04, and 23.48 Tg, respectively, and the corresponding TPS at0–100 cm soil depth was 80.98, 80.71, 85.00, 84.03, 82.96, and 86.72 Tg, respectively. By comparing soil TPS in the S20 to S1000 maps to that in the S5map, the relative deviations were 6.37%–13.32%for 0–20 cm and 0.33%–7.09%for 0–100 cm. Moreover, since the S20 map had the lowest relative deviation among different mapping scales as compared to S5, it could provide additional soil information and a richer soil environment than other smaller mapping scales. Our results also revealed that many uncertainties in soil TPS estimation originated from the lack of detailed soil information, i.e., representation and spatial variations among different soil types. From the time and labor perspectives, our work provides useful guidelines to identify the appropriate mapping scale for estimating regional soil TPS in areas like Fujian Province in subtropical China or other places with similar complex topographies. Moreover, it is of tremendous importance to accurately estimate soil TPS to ensure ecosystem stability and sustainable agricultural development, especially for regional decision-making and management of phosphate fertilizer application amounts.

Machine learning for recovery factor estimation of an oil reservoir:A tool for derisking at a hydrocarbon asset evaluation

Well-known oil recovery factor estimation techniques such as analogy,volumetric calculations,material balance,decline curve analysis,hydrodynamic simulations have certain limitations.Those techniques are time-consuming,and require specific data and expert knowledge.Besides,though uncertainty estimation is highly desirable for this problem,the methods above do not include this by default.In this work,we present a data-driven technique for oil recovery factor(limited to water flooding)estimation using reservoir parameters and representative statistics.We apply advanced machine learning methods to historical worldwide oilfields datasets(more than 2000 oil reservoirs).The data-driven model might be used as a general tool for rapid and completely objective estimation of the oil recovery factor.In addition,it includes the ability to work with partial input data and to estimate the prediction interval of the oil recovery factor.We perform the evaluation in terms of accuracy and prediction intervals coverage for several tree-based machine learning techniques in application to the following two cases:(1)using parameters only related to geometry,geology,transport,storage and fluid properties,(2)using an extended set of parameters including development and production data.For both cases,the model proved itself to be robust and reliable.We conclude that the proposed data-driven approach overcomes several limitations of the traditional methods and is suitable for rapid,reliable and objective estimation of oil recovery factor for hydrocarbon reservoir.

Static Frame Model Validation with Small Samples Solution Using Improved Kernel Density Estimation and Confidence Level Method

An improved method using kernel density estimation （KDE） and confidence level is presented for model validation with small samples. Decision making is a challenging problem because of input uncertainty and only small samples can be used due to the high costs of experimental measurements. However, model validation provides more confidence for decision makers when improving prediction accuracy at the same time. The confidence level method is introduced and the optimum sample variance is determined using a new method in kernel density estimation to increase the credibility of model validation. As a numerical example, the static frame model validation challenge problem presented by Sandia National Laboratories has been chosen. The optimum bandwidth is selected in kernel density estimation in order to build the probability model based on the calibration data. The model assessment is achieved using validation and accreditation experimental data respectively based on the probability model. Finally, the target structure prediction is performed using validated model, which are consistent with the results obtained by other researchers. The results demonstrate that the method using the improved confidence level and kernel density estimation is an effective approach to solve the model validation problem with small samples.

Trajectory prediction of ballistic missiles using Gaussian process error model

Ballistic Missile Trajectory Prediction(BMTP)is critical to air defense systems.Most Trajectory Prediction(TP)methods focus on the coast and reentry phases,in which the Ballistic Missile(BM)trajectories are modeled as ellipses or the state components are propagated by the dynamic integral equations on time scales.In contrast,the boost-phase TP is more challenging because there are many unknown forces acting on the BM in this phase.To tackle this difficult problem,a novel BMTP method by using Gaussian Processes(GPs)is proposed in this paper.In particular,the GP is employed to train the prediction error model of the boost-phase trajectory database,in which the error refers to the difference between the true BM state at the prediction moment and the integral extrapolation of the BM state.And the final BMTP is a combination of the dynamic equation based numerical integration and the GP-based prediction error.Since the trained GP aims to capture the relationship between the numerical integration and the unknown error,the modified BM state prediction is closer to the true one compared with the original TP.Furthermore,the GP is able to output the uncertainty information of the TP,which is of great significance for determining the warning range centered on the predicted BM state.Simulation results show that the proposed method effectively improves the BMTP accuracy during the boost phase and provides reliable uncertainty estimation boundaries.

Robust Control of Robotic Manipulators in the Task-Space Using an Adaptive Observer Based on Chebyshev Polynomials

In this paper,an adaptive observer for robust control of robotic manipulators is proposed.The lumped uncertainty is estimated using Chebyshev polynomials.Usually,the uncertainty upper bound is required in designing observer-controller structures.However,obtaining this bound is a challenging task.To solve this problem,many uncertainty estimation techniques have been proposed in the literature based on neuro-fuzzy systems.As an alternative,in this paper,Chebyshev polynomials have been applied to uncertainty estimation due to their simpler structure and less computational load.Based on strictly-positive-rea Lyapunov theory,the stability of the closed-loop system can be verified.The Chebyshev coefficients are tuned based on the adaptation rules obtained in the stability analysis.Also,to compensate the truncation error of the Chebyshev polynomials,a continuous robust control term is designed while in previous related works,usually a discontinuous term is used.An SCARA manipulator actuated by permanent magnet DC motors is used for computer simulations.Simulation results reveal the superiority of the designed method.

RGB Image‑ and Lidar‑Based 3D Object Detection Under Multiple Lighting Scenarios

In recent years,camera-and lidar-based 3D object detection has achieved great progress.However,the related researches mainly focus on normal illumination conditions;the performance of their 3D detection algorithms will decrease under low lighting scenarios such as in the night.This work attempts to improve the fusion strategies on 3D vehicle detection accuracy in multiple lighting conditions.First,distance and uncertainty information is incorporated to guide the“painting”of semantic information onto point cloud during the data preprocessing.Moreover,a multitask framework is designed,which incorpo-rates uncertainty learning to improve detection accuracy under low-illumination scenarios.In the validation on KITTI and Dark-KITTI benchmark,the proposed method increases the vehicle detection accuracy on the KITTI benchmark by 1.35%and the generality of the model is validated on the proposed Dark-KITTI dataset,with a gain of 0.64%for vehicle detection.

Lines cluster approaching mode control for air-breathing hypersonic vehicle under disturbances and uncertainties

This paper investigates the velocity and altitude tracking control problem for airbreathing hypersonic vehicle(AHV)in the presence of external disturbances and parameter uncertainties.A composite controller containing improved lines cluster approaching mode control(LCAMC)and nonlinear disturbance observer(NDO)is developed to guarantee the tracking errors converge to zero and enhance the robustness of control system.Meanwhile,considering the multiple uncertain parameters,a genetic algorithm(GA)based Pareto uncertainty estimation is employed to predict the parameter uncertainties of the AHV dynamics.Besides,the mathematical proofs of proposed method are analyzed by utilizing Lyapunov theory.Simulation results demonstrate the effective tracking performance,excellent disturbance estimation and uncertainty estimation ability of the composite method.

Active disturbance rejection control： Applications in aerospace

Control of uncertain dynamical systems has been an area of active research for the past several decades and to this end, various robust control approaches have been proposed in the literature. The active disturbance rejection control （ADRC） represents one prominent approach that has been widely studied and applied for designing robust controllers in diverse areas of engineering applications. In this work, a brief review of the approach and some of its applications in aerospace are discussed. The results show that the approach possesses immense potential to offer viable solution to real-life aerospace problems.

Prescribed fast tracking control for flexible air-breathing hypersonic vehicles:An event-triggered case

In this paper,a prescribed fast tracking control scheme is proposed for Flexible Airbreathing Hypersonic Vehicles(FAHV)subject to lumped disturbances and limited resources.To maintain tracking errors of velocity and altitude converge to a predefined region with a prescribed time and release the transient intense fluctuations encountered in classical Prescribed Performance Control(PPC)using a fast decaying rate,a tracking differentiator-based PPC is presented,where the reaching time and the maximum time differentiation of preselected envelopes can be regulated as a prior via fixing an acceleration factor,so that a guaranteed fast convergence speed can be realized with reduced oscillations.Besides,to avoid the excessive occupation of limited resources(energy and communication)and guarantee a remarkable tracking accuracy,switching event-triggered mechanisms are constructed for FAHV control realization,which provide a promising way to pursue a desired level of tracking performance with a low energy consumption.Subsequently,Uncertainty and Disturbance Estimators(UDE)and Sigmoid function-based Tracking Differentiators(STD)are employed to provide disturbance estimation and reference derivation with a low computational complexity.Finally,robust control laws are designed to compensate for the sampling error induced by event-triggered conditions,meanwhile Zeno phenomena can be effectively eliminated.The simulation results and comparisons validate the effectiveness of the proposed scheme.