Model Error Estimation Research Articles

The mechanisms and prediction of non-structural carbohydrates accretion and depletion after mechanical wounding in slash pine (Pinus elliottii) using near-infrared reflectance spectroscopy

BackgroundThe allocation of non-structural carbohydrates (NSCs) plays a critical role in the physiology and metabolism of tree growth and survival defense. However, little is known about the allocation of NSC after continuous mechanical wounding of pine by resin tapping during tree growth.ResultsHere, we examine the NSC allocation in plant tissues after 3 year lasting resin tapping, and also investigate the use of near-infrared reflectance (NIR) spectroscopy to quantify the NSC, starch and free sugar (e.g., sucrose, glucose, and fructose) concentrations in different plant tissues of slash pine. Spectral measurements on pine needle, branch, trunk phloem, and root were obtained before starch and free sugar concentrations were measured in the laboratory. The variation of NSC, starch and free sugars in different plant tissues after resin tapping was analyzed. Partial least squares regression was applied to calibrate prediction models, models were simulated 100 times for model performance and error estimation. More NSC, starch and free sugars were stored in winter than summer both in tapped and control trees. The position of resin tapping significantly influenced the NSCs allocation in plant tissues: more NSCs were transformed into free sugars for defensive resin synthesis close to the tapping wound rather than induced distal systemic responses. Models for predicting NSC and free sugars of plant tissues showed promising results for the whole tree for fructose (R2CV = 0.72), glucose (R2CV = 0.67), NSCs (R2CV = 0.66) and starch (R2CV = 0.58) estimates based on NIR models. Models for individual plant tissues also showed reasonable predictive ability: the best model for NSCs and starch prediction was found in root. The significance multivariate correlation algorithm for variable selection significantly reduced the number of variables. Important variables were identified, including features at 1021–1290 nm, 1480, 1748, 1941, 2020, 2123 and 2355 nm, which are highly related to NSC, starch, fructose, glucose and sucrose.ConclusionsNIR spectroscopy provided a rapid and cost-effective method to monitor NSC, starch and free sugar concentrations after continuous resin tapping. It can be used for studying the trade-off between growth and production of defensive metabolites.

Estimating rainfall–runoff modeling using the rainfall prognostic model-based artificial framework with a well-ordered selective genetic algorithm

Abstract Rainfall–runoff modeling is one of the most well-known applications of hydrology. The goal of rainfall–runoff modeling is to simulate the peak river flow caused by an actual or hypothetical rainfall force. In existing methods, the rainfall–runoff relationships are quantified to predict the daily streamflow of each catchment from its landscape attributes to measure the daily rainfall. However, the structural model error, infiltration rate, and the steep slopes of the hill affect the prediction process. To tackle these issues, this paper proposed a novel rainfall prognostic model-based artificial framework, which predicts day-to-day rainfall to prevent environmental disasters. The day-to-day predictions minimize the risks to life and property and also manage the agricultural farms in a better way because the possibility of rainfall has been estimated earlier. Furthermore, the posterior fire-breathing network is utilized to estimate model errors in the computational runoff by using time-dependent and random noise to the model's internal storage to solve the uncertainty problem. Since the model errors are estimated, there are limits to the infiltration rate and thus a prophetic multilayer network is utilized which relies on the soil runoff levels. Moreover, the network measures the dynamics of soil moisture to regulate the infiltration rate according to the rural or urban section. Moreover, to measure the surface water from the steep slopes, the system offered a well-ordered selective genetic algorithm to calculate the velocity of runoff in different bend areas to overcome the numerical problem. Thus, the model results showed that the work effectively predicts the rainfall from the investigation of model errors, infiltration rates, and velocity to achieve a better prediction range in the rainfall.

Enhancing Model-Based Anticipatory Traffic Signal Control with Metamodeling and Adaptive Optimization

Traffic signal control is one effective way to alleviate traffic congestion. Anticipatory traffic signal control determines signal settings from a network planning perspective, which takes into account the influence of travelers’ route choice response and triggers better equilibrium flow patterns for better network performance. For the route choice response, it is usually predicted by a response function known as traffic assignment model. However, the response behavior can never be precisely modeled, leading to a mismatch between the modeled and real traffic flow patterns. This model-reality mismatch generally contributes to suboptimal control performance and hence brings unexpected congestion in real-life traffic operations. This study aims to address the model-reality mismatch and proposes an effective anticipatory traffic control for real operations. A metamodel is introduced that serves as a surrogate of the unknown structural model bias. Then an iterative optimizing control scheme is applied to correct the model bias by learning from observations. By integrating the model-based control design with data-driven learning techniques, the metamodeling framework is able to enhance the control performance. Moreover, the analytical model bias formulation allows theoretical investigation of the model approximation error. To further improve the control performance, a joint traffic model parameter estimation is developed, hence achieving a better model calibration jointly with the model bias correction. The proposed control method is examined on a test network. Numerical examples confirm the effectiveness of the proposed method in improving control performance despite the model-reality mismatch. Comparison results show that the proposed method outperforms the traditional model-based control method and an improvement of 14.8% in total travel time is achieved in the example network.

EEG/MEG source imaging in the absence of subject's brain MRI scan: Perspective on co‐registration and MRI selection approach

AbstractEEG/MEG source localization requires a subject's brain MRI to compute the sourcemodel and headmodel. As part of this computation, co‐registration of the digitized head information and brain MRI scan is the essential step. However, in the absence of a brain MRI scan, an approximated sourcemodel and headmodel can be computed from the subject's digitized head information and brain MRI scans from other subjects. In the present work, we compared the fiducial (FID)‐ and iterative closet point (ICP)‐based co‐registration approaches for computing an approximated sourcemodel using single and multiple available brain MRI scans. We also evaluated the two different template MRI selection strategies: one is based on objective registration error, and another on sourcemodel approximation error. The outcome suggests that averaged approximated solutions using multiple template brain MRI scans showed better performance than single‐template MRI‐based solutions. The FID‐based approach performed better than the ICP‐based approach for co‐registration of the digitized head surface and brain MRI scan. While selecting template MRIs, the selection approach based on objective registration error showed better performance than a sourcemodel approximation error‐based criterion. Cross‐dataset performance analysis showed a higher model approximation error than within‐dataset analysis. In conclusion, the FID‐based co‐registration approach and objective registration error‐based MRI selection criteria provide a simple, fast and more accurate solution to compute averaged approximated models compared with the ICP‐based approach. The demography of brain MRI scans should be similar to that of the query subject whose brain MRI scan was unavailable.

New impact diagnostics for cross‐validation of different observation types

AbstractNew cross‐validation diagnostics have been derived by further partitioning well‐established impact diagnostics. They are related to consistency relations, the most prominent of which indicates whether the first‐guess departures of a given observation type pull the model state into the direction of the verifying data (when processed with the ensemble estimated model error covariances). Alternatively, this can be regarded as cross‐validation between model error covariance estimates from the ensemble (which are used in the data assimilation system) and estimates diagnosed directly from the observations. A statistical cross‐validation tool has been developed that includes an indicator of statistical significance as well as a normalization that makes the statistical comparison largely independent from the total number of data and the closeness of their collocation. We also present a version of these diagnostics related to single‐observation experiments that exploits the same consistency relations but is easier to compute. Diagnostics computed within the Deutscher Wetterdienst's localized ensemble transform Kalman filter (LETKF) are presented for various kinds of bins. Results from well‐established in‐situ measurements are taken as a benchmark for more complex observations. Good agreement is found for radio‐occultation bending angle measurements, whereas atmospheric motion vectors are generally also beneficial but substantially less optimal than the corresponding in‐situ measurements. This is consistent with reported atmospheric motion vector height assignment problems. To illustrate its potential, a recent example is given where the method allowed identifying bias problems of a subgroup of aircraft measurements.Another diagnostic relationship compares the information content of the analysis increments with a theoretical optimum. From this, the information content of the LETKF increments is found to be considerably lower than those of the deterministic hybrid ensemble–variational system, which is consistent with the LETKF's limitation to the comparably low‐dimensional ensemble space for finding the optimal analysis.

A map of global peatland extent created using machine learning (Peat-ML)

Abstract. Peatlands store large amounts of soil carbon and freshwater, constituting an important component of the global carbon and hydrologic cycles. Accurate information on the global extent and distribution of peatlands is presently lacking but is needed by Earth system models (ESMs) to simulate the effects of climate change on the global carbon and hydrologic balance. Here, we present Peat-ML, a spatially continuous global map of peatland fractional coverage generated using machine learning (ML) techniques suitable for use as a prescribed geophysical field in an ESM. Inputs to our statistical model follow drivers of peatland formation and include spatially distributed climate, geomorphological and soil data, and remotely sensed vegetation indices. Available maps of peatland fractional coverage for 14 relatively extensive regions were used along with mapped ecoregions of non-peatland areas to train the statistical model. In addition to qualitative comparisons to other maps in the literature, we estimated model error in two ways. The first estimate used the training data in a blocked leave-one-out cross-validation strategy designed to minimize the influence of spatial autocorrelation. That approach yielded an average r2 of 0.73 with a root-mean-square error and mean bias error of 9.11 % and −0.36 %, respectively. Our second error estimate was generated by comparing Peat-ML against a high-quality, extensively ground-truthed map generated by Ducks Unlimited Canada for the Canadian Boreal Plains region. This comparison suggests our map to be of comparable quality to mapping products generated through more traditional approaches, at least for boreal peatlands.

Disturbance observer supported fuzzy model based controller with application to bilateral teleoperation systems

This paper proposes a disturbance observer supported Takagi-Sugeno (TS) fuzzy model-based control scheme for uncertain systems. The baseline controller is a guaranteed performance fuzzy model based parallel distributed controller (PDC) which is constructed using the nominal system’s parameters. The model approximation error and parametric uncertainties are treated as a lumped disturbance and a nonlinear disturbance observer (NDOB) is introduced to counter the lumped disturbance. The applicability of the proposed scheme is demonstrated on the bilateral control of nonlinear teleoperation system in MATLAB/Simulink/QUARC environment through simulations as well as semi-real time experiments.

On the Choice of the Item Response Model for Scaling PISA Data: Model Selection Based on Information Criteria and Quantifying Model Uncertainty.

In educational large-scale assessment studies such as PISA, item response theory (IRT) models are used to summarize students’ performance on cognitive test items across countries. In this article, the impact of the choice of the IRT model on the distribution parameters of countries (i.e., mean, standard deviation, percentiles) is investigated. Eleven different IRT models are compared using information criteria. Moreover, model uncertainty is quantified by estimating model error, which can be compared with the sampling error associated with the sampling of students. The PISA 2009 dataset for the cognitive domains mathematics, reading, and science is used as an example of the choice of the IRT model. It turned out that the three-parameter logistic IRT model with residual heterogeneity and a three-parameter IRT model with a quadratic effect of the ability provided the best model fit. Furthermore, model uncertainty was relatively small compared to sampling error regarding country means in most cases but was substantial for country standard deviations and percentiles. Consequently, it can be argued that model error should be included in the statistical inference of educational large-scale assessment studies.

Refraction Surface-Based Stellar Atmospheric Refraction Correction and Error Estimation for Terrestrial Star Tracker

Stellar atmospheric refraction imaging error, as the optical imaging variation of starlight before and after passing through Earth&#x2019;s atmosphere, is one of the key issues for terrestrial star trackers to obtain accurate attitude measurement results. To resolve the problem, a refraction surface-based stellar atmospheric refraction correction method is presented in this paper. Different from existing correction methods, a new atmospheric refraction feature, i.e., stellar atmospheric refraction surface, is proposed to represent the random irregular optical phenomena of starlight, and avoids the limitations of theoretical atmospheric models and empirical formulas. On the basis of the principles of &#x201C;collinear refraction surfaces&#x201D;, &#x201C;invariable refraction surface&#x201D;, the proposed model successfully realizes the accuracy atmospheric refraction correction by the sensor itself, without external atmospheric parameters. Then, by analyzing the error factors parallel and perpendicular to the atmospheric refraction surface, the atmospheric refraction correction error estimation model is established to forecast the attitude accuracy after correction. Numerical simulations and night sky experiments validate the reliability of our atmospheric refraction correction method and error estimation model. The average angular distance error of the test star tracker is reduced from <inline-formula> <tex-math notation="LaTeX">$31.1310''$ </tex-math></inline-formula> into <inline-formula> <tex-math notation="LaTeX">$1.7705''$ </tex-math></inline-formula>, which is significantly decreased by 94.31&#x0025;.

Adaptive event‐triggered H∞ state estimation of semi‐Markovian jump neural networks with randomly occurred sensor nonlinearity

AbstractThis article mainly discusses the problem for adaptive event‐triggered H state estimation of semi‐Markovian jump neural networks (s‐MJNNs) subject to random sensor nonlinearity. To reduce the communication load, adaptive event‐triggered scheme (AETS) is introduced to decide whether to transmit sampled data or not. Also, considering the possible sensor nonlinearity, a new estimation error model is established under the framework of AETS. An appropriate Lyapunov–Krasovskii functional (LKF) containing the proposed adaptive event trigger condition is constructed, and sufficient conditions are obtained to guarantee the asymptotic stability of the estimation error system. Then, through a set of feasible linear matrix inequalities (LMIs), the co‐design method of estimator and AETS is proposed. Finally, the feasibility of this paper is proved by three numerical examples.

An effective Smith predictor based fractional-order PID controller design methodology for preservation of design optimality and robust control performance in practice

In this study, an optimal and robust fractional order PID (FOPID) controller design approach is suggested for Smith predictor based FOPID (SP-FOPID) control system design. This new design approach considers continued fraction expansion (CFE) based approximate models in the optimal design task of FOPID controllers, and this approach preserves the design optimality in control applications. For this purpose, an inverse controller loop shaping design methodology is performed in order to approximate the frequency response of a Bode’s ideal loop reference model, and robust performance CFE based FOPID controller models are obtained by solving a multi-objective optimisation problem via a genetic algorithm. Thus, the suggested algorithm can deal with several controller realisation concerns in the design task of FOPID controllers and overcome real-world controller performance issues related with model approximation errors and signal saturation boundaries of electronic hardware. Illustrative design examples demonstrate that the suggested design scheme can preserve design optimality and improve practical control performance in practice.

Surface transfer coefficients estimation for heat conduction problem using the Bayesian framework

This work deals with an inverse two-dimensional nonlinear heat conduction problem to determine the top and lateral surface transfer coefficients. For this, the Bayesian framework with the Markov Chain Monte Carlo algorithm is used to determine the posterior distribution of unknown parameters. To handle the computational burden, a lumped one-dimensional model is proposed. The lumped model approximations are considered within the parameter estimation procedure thanks to the Approximation Error Model. The experiments are carried out for several configurations of chamber ventilator speed. Experimental observations are obtained through a complete measurement uncertainty propagation. By solving the inverse problem, accurate probability distributions are determined. Additional investigations are performed to demonstrate the reliability of the lumped model, in terms of accuracy and computational gains.

A dual-driven linear modeling approach for multiple energy flow calculation in electricity–heat system

The multiple energy flow (MEF) model is inherently nonlinear, which challenges the fast steady-state analysis and the efficient optimization of the integrated energy system (IES). This paper presents a hybrid mechanism- and data-driven (dual-driven) modeling approach to generate accurate linear models for MEF calculation. A linear regression model for the electricity–heat system is proposed to represent the underlying linear relationship among electrical, thermal, and hydraulic variables. Partial least squares (PLS) regression is used to deal with data collinearity which may lead to over-fitting. Furthermore, a dual-driven modeling approach is proposed to realize the complementarity between mechanism- and data-driven approaches. In this approach, mechanism analysis screens critical features before data processing and provides a fundamental linear model based on physical mechanism. Data-driven regression generates linear models to replace the complicated nonlinear elements and trains an approximation error model to further improve the overall accuracy. Numerical findings on a basic and a complex electricity–heat system confirmed the dual-driven linear model’s accuracy advantage over existing linear models. Overall, this study proposes a dual-driven modeling approach that provides high-precision linear models while avoiding the intractable convergence problem in the nonlinear MEF calculation. It also reveals that linear models driven by data and mechanisms can closely fit the energy flows in the nonlinear electricity–heat system.

Fast Bayesian Tomography of a Two-Qubit Gate Set in Silicon

Benchmarking and characterising quantum states and logic gates is essential in the development of devices for quantum computing. We introduce a Bayesian approach to self-consistent process tomography, called fast Bayesian tomography (FBT), and experimentally demonstrate its performance in characterising a two-qubit gate set on a silicon-based spin qubit device. FBT is built on an adaptive self-consistent linearisation that is robust to model approximation errors. Our method offers several advantages over other self-consistent tomographic methods. Most notably, FBT can leverage prior information from randomised benchmarking (or other characterisation measurements), and can be performed in real time, providing continuously updated estimates of full process matrices while data is acquired.

Metering equipment running error estimation model based on genetic optimized LM algorithm

The current method of smart meter verification relies on manual regular sampling inspection, which is heavy in workload and poor in real-time, and can’t fully monitor all the equipments. Therefore, a remote real-time error monitoring algorithm is indispensable. We propose a smart meter error estimation model based on genetic optimized Levenberg-Marquarelt (LM) algorithm. Firstly, based on the law of conservation of energy, the relationship between smart meter error and electricity consumption is established. Then, LM algorithm is optimized based on genetic algorithm and used to estimate the operating error of electricity meter. Finally, we used the actual data of the pilot cities in a province for the experiment. The results show that the proposed method can effectively improve the accuracy of smart meter error estimation.

Remote error estimation of smart meter based on clustering and adaptive gradient descent method

At present, the main way for electric power companies to check the accuracy of electric meters is that professionals regularly bring standard electric meters to the site for verification. With the widespread application of smart meters and the development of data processing technology, remote error estimation based on the operating data of smart meters becomes possible. In this paper, an error estimation method of smart meter based on clustering and adaptive gradient descent method is proposed. Firstly, the fuzzy c-means clustering method is used to preprocess the data to classify the operating conditions of each measurement, and then the adaptive gradient descent method is used to establish the error estimation model. The simulation results show that this method has high error estimation accuracy. This method has a small amount of calculation and high reliability and is suitable for large-scale power grids.

Robust tube-based model predictive control with Koopman operators

Koopman operators are of infinite dimension and capture the characteristics of nonlinear dynamics in a lifted global linear manner. The finite data-driven approximation of Koopman operators results in a class of linear predictors, useful for formulating linear model predictive control (MPC) of nonlinear dynamical systems with reduced computational complexity. However, the robustness of the closed-loop Koopman MPC under modeling approximation errors and possible exogenous disturbances is still a crucial issue to be resolved. Aiming at the above problem, this paper presents a robust tube-based MPC solution with Koopman operators, i.e., r-KMPC, for nonlinear discrete-time dynamical systems with additive disturbances. The proposed controller is composed of a nominal MPC using a lifted Koopman model and an off-line nonlinear feedback policy. The proposed approach does not assume the convergence of the approximated Koopman operator, which allows using a Koopman model with a limited order for controller design. Fundamental properties, e.g., stabilizability, observability, of the Koopman model are derived under standard assumptions with which, the closed-loop robustness and nominal point-wise convergence are proven. Simulated examples are illustrated to verify the effectiveness of the proposed approach.

Error Modeling and Anomaly Detection of Smart Electricity Meter Using TSVD+L Method

Using remote data analysis to estimate smart electricity meters (SMs) and detect SMs&#x2019; anomaly, has aroused considerable discussion in power industry, because its lower cost and higher efficiency compared to traditional field calibration. However, the trouble of lacking topology and parameter of the distribution grid and the ill-posed problem in the SMs&#x2019; error estimation and anomaly detection (AD) are not well resolved in most energy conservation theorem-based SMs AD methods. This paper presents a sorted Top-N anomaly detection mechanism to generate a list of suspicious anomalous SMs. The error estimation model (EEM) only using SMs electricity consumption data is investigated. The truncated singular value decomposition regularization with L-curve optimization (TSVD+L) method is proposed to address the model&#x2019;s ill-posedness. Three data processing modes, namely one-pot mode, segmentation mode and sliding window technique (SWT), are suggested to obtain multiple calculation results for SMs error comprehensive evaluation. The top <i>N</i>% SMs in error sequence is proposed for onsite calibration instead of full inspection. The effectiveness and practicality of the proposed method are verified through both simulation case and practical distribution network application. The results show that the proposed method has higher accuracy in SMs anomaly detection, compared with the ordinary least squares (OLS) method, recursive least squares (RLS) method, and Tikhonov regularization (Tik) method.

A Remote Estimation Method of Smart Meter Errors Based on Neural Network Filter and Generalized Damping Recursive Least Square

To solve large-scale smart meter verification and periodic replacement problems, a remote estimation method based on neural network filter (NNF) and generalized damping recursive least square (GDRLS) is proposed. In this article, a smart meter error estimation model with a loss noise filter is built. A typical loss noise filter is designed with a neural network, so that the filtered loss noise meets the Gauss–Markov condition, which paves the way for the best linear unbiased estimation (BLUE). GDRLS algorithm is applied to solve the novel estimation model, which can effectively address the problem that large loss estimation errors merge small smart meter errors. Then, a complete process of the proposed method is constructed, which can estimate both the user smart meter errors, and the loss noises accurately. Finally, the effectiveness, superiority, and applicability of the proposed method are verified through simulation analysis and practical distribution network application.

Random Weighting Adaptive Estimation of Model Errors on Attitude Measurement for Rotary Steerable System

During drilling, a rotary steerable system (RSS) is affected by vibration, rotation, and other random noises. This paper presents a random weighting adaptive estimation of model errors on attitude measurement for RSS drilling tools. The algorithm is used to estimate the covariance matrix of the dynamic model errors and the state prediction vectors for RSS tools, to reduce the effect of abnormal noises of the dynamic model on the estimation of state parameters. The random weighting estimations of observation&#x2019;s systematic error and covariance matrices of observation error vectors to control the effect of observation model noises anomaly on state parameter estimation, enhance the use efficiency of the latest observation information, indirectly weaken the impact of model error on state parameter vector, and improve the accuracy of attitude calculation of RSS. Experimental results and comparison analysis demonstrate that the proposed algorithm achieves better outcomes than the Kalman filtering and Extended Kalman filtering. The maximum solution error is controlled at 0.15&#x00B0;, and the tool face angle error is less than 3&#x00B0;. It cannot only control the covariance matrix of the observation error vector and predicted residual vector, but it can also effectively resist the disturbances of kinematic model error. It also can improve the dynamic measurement accuracy of attitude parameters, and solves the problem of uncertainty in dynamic attitude measurement of rotary steerable drilling tools.