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As the power source of the engine, the Fuel Pump(FP) plays a vital role in the safe operation of the aircraft. Due to the complexity of the working mechanism of Aviation Fuel Pumps (AFP) and the strong correlation between the components, the assessment model cannot reflect the health state of the FPs better, while the initial parameters in the assessment model will affect the assessment effect of the model. Therefore, this paper proposes a health status assessment model that can fully integrate monitoring data. To improve the accuracy of the model parameters, the Random Forest algorithm is used to give the feature weights to make up for the limitation of relying on expert knowledge, and the model parameters are optimized by the Covariance Matrix Adaptive Evolutionary Strategy algorithm, which achieves an accurate assessment of the state. Finally, the AFP test bed was built and the AFP was tested. Compared with other methods, the accuracy of the proposed method in this question reaches 96%, which is greatly superior to other methods and verifies the effectiveness of the proposed method. It also provides an outlook on future research directions for health state assessment. [ABSTRACT FROM AUTHOR]

A novel approach is proposed in this paper to reconstruct the far‐field radiation pattern from the phaseless electric field of an antenna scanned on a single near‐field sphere. It adopts the dipole equivalence approach to project the near‐field electric field into a spherically distributed array of electric dipoles. A term representing the error from the linearly correlated portion in the least‐square problem associated with the dipole equivalence, namely the linear correlation error, is introduced. It is demonstrated that by iterative search to minimize the linear correlation error using the covariance matrix adaptation evolution strategy, near‐field phase distributions can be found efficiently from the magnitude‐only near‐field, and the far‐field radiation pattern can be computed. Two representative case studies are given here to validate the proposed method. Results demonstrate good agreements between computations and simulations. [ABSTRACT FROM AUTHOR]

Estimating correlations among demographic parameters is an important method in population ecology. A recent paper by Deane et al. (Ecology and Evolution 13:e9847, 2023) attempted to explore the effects of different priors for covariance matrices on inference when using mark‐recovery data. Unfortunately, Deane et al. (2023) made a mistake when parameterizing some of their models. Rather than exploring the effects of different priors, they examined the effects of the use of incorrect equations on inference. In this manuscript, we clearly describe the mistake in Deane et al. (2023). We then demonstrate the use of an alternative and appropriate method and reach different conclusions regarding the effects of priors on inference. Consistent with other recent literature, informative inverse Wishart priors can lead to flawed inference, while vague priors on covariance matrix components have little impact when sample sizes are adequate. [ABSTRACT FROM AUTHOR]

In this paper, the Star-Transformer model is improved to obtain more accurate direction of arrivals (DOA) estimation of underwater sonar uniform linear array (ULA) under low signal-to-noise ratio (SNR) conditions. The ideal real covariance matrix is divided into three channels: real part channel, imaginary part channel, and phase channel to obtain more input features. In training, the real covariance matrix is used under different SNRs. In testing, the covariance matrix of samples in the real environment is used as input. The on-grid form is used to estimate the DOA of multiple signal sources, which is modelled as a multilabel classification problem. The results show that the model can be effective and can still have a good DOA estimation performance under the conditions of trained and untrained SNRs, different snapshots, signal power mismatch, different separation angles, signal correlation, and so on. It shows that the model has excellent robustness. [ABSTRACT FROM AUTHOR]

This paper deals with finite‐horizon minimum‐variance and covariance steering problems subject to constraints. The goal of the minimum variance problem is to steer the state mean of an uncertain system to a prescribed vector while minimizing the trace of its terminal state covariance whereas the goal in the covariance steering problem is to steer the covariance matrix of the terminal state to a prescribed positive definite matrix. The paper proposes a solution approach that relies on a stochastic version of the affine disturbance feedback control parametrization. In this control policy parametrization, the control input at each stage is expressed as an affine function of the history of disturbances that have acted upon the system. It is shown that this particular parametrization reduces the stochastic optimal control problems considered in this paper into tractable convex programs or difference of convex functions programs with essentially the same decision variables. In addition, the paper proposes a variation of this control parametrization that relies on truncated histories of past disturbances, which allows for sub‐optimal controllers to be designed that strike a balance between performance and computational cost. The suboptimality of the truncated policies is formally analyzed and closed form expressions are provided for the performance loss due to the use of the truncation scheme. Finally, the paper concludes with a comparative analysis of the truncated versions of the proposed policy parametrization and other standard policy parametrizations through numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, a novel direction‐of‐arrival (DOA) estimation method is proposed for linear arrays on the basis of residual neural network (ResNet). The real parts, imaginary parts, and phase entries of the spatial covariance matrix from the on‐grid angles are used as the input of ResNet for training, and the angular directions formulated as a multilabel classification task are predicted using the sample covariance matrix from the off‐grid angles during the testing phase. ResNet demonstrates robustness in the scenarios on a fixed number of signals and a mixed number of signals. Simulation results show that ResNet can achieve significant performance in DOA estimation compared to multiple signal classification, estimation of signal parameters via rotation invariance techniques, convolutional neural network (CNN), and deep complex‐valued CNN in low signal‐to‐noise ratio. [ABSTRACT FROM AUTHOR]

Summary: Microbiome data typically lie in a high‐dimensional simplex. One of the key questions in metagenomic analysis is to exploit the covariance structure for this kind of data. In this paper, a framework called approximate‐estimate‐threshold (AET) is developed for the robust basis covariance estimation for high‐dimensional microbiome data. To be specific, we first construct a proxy matrix Γ$$ \boldsymbol{\Gamma} $$, which is almost indistinguishable from the real basis covariance matrix ∑$$ \boldsymbol{\Sigma} $$. Then, any estimator Γ^$$ \hat{\boldsymbol{\Gamma}} $$ satisfying some conditions can be used to estimate Γ$$ \boldsymbol{\Gamma} $$. Finally, we impose a thresholding step on Γ^$$ \hat{\boldsymbol{\Gamma}} $$ to obtain the final estimator ∑^$$ \hat{\boldsymbol{\Sigma}} $$. In particular, this paper applies a Huber‐type estimator Γ^$$ \hat{\boldsymbol{\Gamma}} $$, and achieves robustness by only requiring the boundedness of 2+ϵ$$ \epsilon $$ moments for some ϵ∈(0,2]$$ \epsilon \in \left(0,2\right] $$. We derive the convergence rate of ∑^$$ \hat{\boldsymbol{\Sigma}} $$ under the spectral norm, and provide theoretical guarantees on support recovery. Extensive simulations and a real example are used to illustrate the empirical performance of our method. [ABSTRACT FROM AUTHOR]

This paper explores testing the equality of two covariance matrices under high‐dimensional settings. Existing test statistics are usually constructed based on the squared Frobenius norm or the elementwise maximum norm. However, the former may experience power loss when handling sparse alternatives, while the latter may have a poor performance against dense alternatives. In this paper, with a novel framework, we introduce a double verification test statistic designed to be powerful against both dense and sparse alternatives. Additionally, we propose an adaptive weight test statistic to enhance power. Furthermore, we present an analysis of the asymptotic size and power of the proposed test. Simulation results demonstrate the satisfactory performance of our proposed method. [ABSTRACT FROM AUTHOR]

In the real‐world environment, the path planning method of tracked robot is widely studied when driving on uneven terrain. How to solve the problem that the traditional path planning algorithm cannot adapt to uneven terrain because of the constraints of obstacle avoidance and path length is a challenge for tracked robots. In this paper, a stability‐based path planning framework for tracked robot is proposed to reduce the risk of rollover when the tracked robot passes through uneven terrain. First, a virtual plane method is proposed to estimate the attitude of tracked robot. Second, on this basis, a dynamic high‐stability path evaluation algorithm for tracked robot based on force angle stability margin (FASM) is proposed, which transforms the stability‐based path planning problem into a hypergraph problem. Moreover, considering that the optimization problem is strongly nonlinear and nonconvex, a hybrid algorithm of covariance matrix adaptive evolution strategy (CMAES) and Levenberg–Marquardt (LM) is designed under the framework of generalized graph optimization (G2O) to improve the solution efficiency. Finally, simulation and experiments show that the stability‐based path planning framework can effectively plan the high‐quality path, and the maximum stability of the tracked robot is 0.9156 when the robot crosses uneven terrain using optimal path 2. [ABSTRACT FROM AUTHOR]

The conventional joint transmit and receive beamforming algorithms maximise the output signal‐to‐interference‐plus‐noise ratio (SINR) by designing the weight coefficients simultaneously at the transmitter and receiver. However, their performance degrades significantly when the model mismatch exists. In this paper, the robust version of the joint transmit and receive beamforming method is considered in the context of the bistatic radar system. In particular, both the transmit array and the receive array suffer model mismatch. The designed beamformer aims to maximise its output SINR subjected to a robustness constraint by simultaneously designing the transmit beamforming vector and the receive beamforming vector. Two types of robustness constraints, namely the worst‐case constraint and the probability constraint, are considered in this paper. The proposed formulations are non‐convex, and the sub‐optimal solutions are obtained by a sequential optimization approach. In addition, a novel method to estimate the interference‐plus‐noise covariance matrices at the transmitter and receiver is proposed, which makes the proposed robust joint beamforming algorithms adapt to the variation of the surrounding environment. Numerical simulations verify the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

This paper proposes a novel variational Bayesian (VB) adaptive Kalman filter with mismatched process noise covariance matrix (PNCM). Firstly, this paper explains the reason why the predicted error covariance matrix (PECM) is chosen for variational inference. Secondly, compared with the earlier VB adaptive Kalman filter (VB‐AKF‐Q), the proposed filter calculate the dynamic model of the PECM with its historical estimation information. Therefore, the proposed filter can overcome the influence of mismatched PNCM on the initial value setting of PECM in the VB‐AKF‐Q. Finally, we use the evidence lower bound for the proposed filter and give the convergence criterion on this basis. Some examples with a target tracking simulation are carried out to demonstrate the superiority of the proposed filter. [ABSTRACT FROM AUTHOR]

Peak electron density data derived from GOLD measurements during 2018–2022 are used to analyze the magnitudes and correlations of ionospheric diurnal variability at low latitudes. The correlation distance describes the correlations between spatial locations and is defined in this paper as the angular separation at which the correlation coefficient decreases from 1 to 0.7. Variations in correlation distance with local time, season, magnetic latitude, solar activity, and geomagnetic activity are discussed in this study. The average value of the zonal correlation distance is approximately 8.55° and 3.56° for the meridional direction at low geomagnetic latitudes (magnetic latitudes <30°). The statistical results indicate that both zonal and meridional correlation distances vary little with local time premidnight, while they show pronounced seasonal and latitudinal variations. Both zonal and meridional correlation distances increase with increasing solar activity and decrease with enhancing geomagnetic activity. The EIA strength and gradient mainly modulate the distributions of correlation distances related to magnetic latitude, season, and solar flux level. An empirical model is constructed to describe the temporal and spatial variations in the correlation distance at low latitudes. The study of correlation distances would contribute to a better understanding of ionospheric variability and improvements in data assimilation. Plain Language Summary: The correlation distance is an important parameter in determining the background covariance matrix in data assimilations, which helps to transfer information from observations to the model‐driven background. The study of correlation distances can not only promote a better understanding of ionospheric variability but also improve ionospheric forecasts. More than 1,400 days of GOLD Nmax (peak electron density) data are applied for the statistical analysis of the correlation distance. In general, the correlation distance presents pronounced seasonal and latitudinal variations, varies little with local time premidnight, increases with increasing solar activity, and decreases with enhancing geomagnetic activity. The morphology of the EIA has a direct control on the correlation distance. The EIA strength and gradient mainly modulate the distributions of correlation distances related to magnetic latitude, season, and solar flux level. An empirical model is constructed, and it can effectively describe the temporal and spatial variations in the correlation distance at low latitudes. The results of correlation distances could further improve the accuracy of data assimilation. Key Points: EIA structures directly control the variation of correlation distancesHorizontal correlation distances increase with solar activity and vary with seasonAn empirical model is constructed to describe the variation in correlation distances with LT, mlat, season, solar and geomagnetic activities [ABSTRACT FROM AUTHOR]

The reasonable power quality assessment model of microgrid is significant to the planning and management for a microgrid. In the power quality assessment, how to extract and integrate the implicative information in different evaluation indicators, to realize the comprehensive power quality assessment, are needs to be further studied. To solve the above problems, a microgrid power quality assessment model based on multivariate Gaussian distribution and local sensitivity analysis is proposed in this paper. Firstly, the probability density function is used to integrate the individual assessment indicators, and the correlation between the assessment indicators is reflected by the covariance matrix, and then the above characteristics of evaluation indicators are quantized to be as the indicator weights by using the local sensitivity. Comparing with the traditional power quality assessment method, the proposed evaluation model is more suitable for microgrid. Finally, an example is developed to verify that the overall situation of microgrid power quality can be reasonably reflected by the proposed evaluation model. [ABSTRACT FROM AUTHOR]

Summary This paper presents computationally optimized 2‐element and 4‐element Multiple‐Input, Multiple‐Output (MIMO) antennas for WLAN/Wi‐Fi, 5G, and UWB applications. The antenna configuration is constructed with the orthogonal placement of sawtooth‐shaped circular monopole radiating elements. The Particle Swarm Optimization (PSO) and Covariance Matrix Adaptation Evolution Strategy (CMA‐ES) optimization techniques are employed to achieve the best performance and size of the proposed antenna. Among these optimization techniques, CMA‐ES is identified as the better approach. The final optimized geometry of the 2‐element and 4‐element MIMO antennas is 49.40 mm × 24.22 mm and 49.44 mm × 45 mm, respectively. Both optimized antennas are fabricated and experimentally verified. The fractional bandwidth of the antenna is more than 110.3%, and more than −20 dB isolation is attained without employing any decoupling method. The Envelop Correlation Coefficient (ECC), Directivity Gain (DG), Total Active Reflection Coefficient (TARC), and Channel Capacity Limit (CCL) are 0.0001, 9.99, < −15 dB, and 0.1 bits/s/Hz, respectively. The proposed antenna is a good candidate for numerous current wireless applications due to its size and performance. [ABSTRACT FROM AUTHOR]

This paper proposes an adaptive fractional‐order unscented particle filter (AFOUPF) with the initial value compensation (IVC) to enhance the estimation accuracy of the state of charge (SOC) for lithium‐ion batteries (LIBs). First, to correctly reflect the dynamic properties of LIBs, a fractional‐order system (FOS) with a constant phase component is constructed. Second, to discretize the FOS equation of LIBs, the Grünwald–Letnikov difference, Caputo derivative and Rieman–Liouville difference are employed to establish the corresponding difference equation. Third, a map function is applied to keep the order and SOC of the FOS within an appropriate interval. Further, an approach of IVC is provided for the AFOUPF to increase the accuracy of SOC estimation, taking into account that the accuracy of SOC estimation is impacted if the order of the FOS is relatively small in (0, 1). By utilizing the augmented vector approach, the simultaneous estimations of order, parameters, initial value, and SOC are resolved. Besides, an iterative approach that accommodates the noise covariance matrices is proposed to improve the estimation accuracy. The AFOUPF conducts an unscented transform and resampling on each particle, resulting in a high SOC estimation accuracy in complicated situations. Finally, the availability of AFOUPF is tested by several experiments. [ABSTRACT FROM AUTHOR]

The Multiple Comparison Procedures with Modeling Techniques (MCP‐Mod) framework has been recently approved by the U.S. Food, Administration, and European Medicines Agency as fit‐for‐purpose for phase II studies. Nonetheless, this approach relies on the asymptotic properties of Maximum Likelihood (ML) estimators, which might not be reasonable for small sample sizes. In this paper, we derived improved ML estimators and correction for their covariance matrices in the censored Weibull regression model based on the corrective and preventive approaches. We performed two simulation studies to evaluate ML and improved ML estimators with their covariance matrices in (i) a regression framework (ii) the Multiple Comparison Procedures with Modeling Techniques framework. We have shown that improved ML estimators are less biased than ML estimators yielding Wald‐type statistics that controls type I error without loss of power in both frameworks. Therefore, we recommend the use of improved ML estimators in the MCP‐Mod approach to control type I error at nominal value for sample sizes ranging from 5 to 25 subjects per dose. [ABSTRACT FROM AUTHOR]

In the paper we derive new types of multivariate exponentially weighted moving average (EWMA) control charts which are based on the Euclidean distance and on the distance defined by using the inverse of the diagonal matrix consisting of the variances. The design of the proposed control schemes does not involve the computation of the inverse covariance matrix and, thus, it can be used in the high‐dimensional setting. The distributional properties of the control statistics are obtained and are used in the determination of the new control procedures. Within an extensive simulation study, the new approaches are compared with the multivariate EWMA control charts which are based on the Mahalanobis distance. [ABSTRACT FROM AUTHOR]

Gaussian processes provide probabilistic surrogates for various applications including classification, uncertainty quantification, and optimization. Using a gradient‐enhanced covariance matrix can be beneficial since it provides a more accurate surrogate relative to its gradient‐free counterpart. An acute problem for Gaussian processes, particularly those that use gradients, is the ill‐conditioning of their covariance matrices. Several methods have been developed to address this problem for gradient‐enhanced Gaussian processes but they have various drawbacks such as limiting the data that can be used, imposing a minimum distance between evaluation points in the parameter space, or constraining the hyperparameters. In this paper a diagonal preconditioner is applied to the covariance matrix along with a modest nugget to ensure that the condition number of the covariance matrix is bounded, while avoiding the drawbacks listed above. The method can be applied with any twice‐differentiable kernel and when there are noisy function and gradient evaluations. Optimization results for a gradient‐enhanced Bayesian optimizer with the Gaussian kernel are compared with the use of the preconditioning method, a baseline method that constrains the hyperparameters, and a rescaling method that increases the distance between evaluation points. The Bayesian optimizer with the preconditioning method converges the optimality, that is, the ℓ2$$ {\ell}_2 $$ norm of the gradient, an additional 5 to 9 orders of magnitude relative to when the baseline method is used and it does so in fewer iterations than with the rescaling method. The preconditioning method is available in the open source Python library GpGradPy, which can be found at https://github.com/marchildon/gpgradpy/tree/paper_precon. [ABSTRACT FROM AUTHOR]

Summary: Many optimal sensor placement (OSP) techniques have been developed basing on known external loads. However, it is often difficult to obtain excitation measurements. Therefore, the development of OSP under unknown inputs (OSP‐UI) is desirable. In this paper, based on modal Kalman filter (MKF), an OSP‐UI approach (MKF‐OSP‐UI) is proposed for optimally determining the number and locations of multitype sensors with the aim of minimizing the reconstructed responses errors. An MKF‐based approach previously developed by the authors is first employed for estimating multiscale structural responses and unknown loads. Then, an error covariance matrix is defined as a measure of the differences between the reconstructed responses and the corresponding actual ones. By using the covariance matrix of measurement noise for normalization, the ill‐conditioning problem caused by data fusion of multiscale responses is avoided. The sensors that have few contributions to the reconstructed responses are removed from the candidate set during iteration procedure. The sensor placement is finally determined when the estimation errors are below the preset level. Numerical results show that the sensor configuration determined by the proposed approach has a better performance on the joint estimation of multiscale responses and unknown inputs, as compared with that determined by experience. [ABSTRACT FROM AUTHOR]

This paper addresses the challenge of testing the hypothesis of what the authors call a nested block circular‐compound symmetric (NBCCS) covariance structure for the population covariance matrix. This is a covariance structure which has an outer block compound symmetric structure, where the diagonal blocks are themselves block circular matrices, while the off‐diagonal blocks are formed by all equal matrices. The NBCCS null hypothesis is decomposed into sub‐hypotheses, allowing this way for a simpler way to obtain a likelihood ratio test and its associated statistic. The exact moments of this statistic are derived, and its distribution is carefully examined. Given the complicated nature of this distribution, highly precise near‐exact distributions were developed. Numerical studies are conducted to assess the proximity between these near‐exact distributions and the exact distribution, highlighting the performance of these approximations, even in the case of very small sample sizes. Furthermore, three datasets, on bone mineral content, metabolic rates of glucose, and soil moisture are used to exemplify the practical application of the methodology derived in this study. [ABSTRACT FROM AUTHOR]

Summary: Structural damage identification is a major task in structural health monitoring. Machine learning and deep learning algorithms have been widely applied in the research of structural damage identification. Supervised algorithms require expert labeling, making it difficult to implement in engineering applications. Unsupervised structural damage identification algorithms are generally divided into two parts: damage‐sensitive factor extraction and damage determination. Existing algorithms all perform these two steps separately. This paper proposes a damage identification method combining covariance matrix and improved deep embedding clustering network (IDEC). IDEC can perform damage‐sensitive factor extraction and damage determination operations at the same time. The covariance matrix that introduces delay information contains rich damage features, and the combination of the two has been proven to effectively mine the damage‐sensitive feature space. After network hyperparameter optimization via Bayesian optimization, the proposed method is applied to the damage identification and quantification using real bridge acceleration response data under vehicle load. The results show that this method can identify structural damage with an accuracy of up to 97% with better performance than existing technologies, and it also has great performance in identifying small damages. The proposed method is expected to increase the damage identification accuracy if applied in engineering practice. [ABSTRACT FROM AUTHOR]

This paper is concerned with deriving a new test on a covariance matrix which is based on its nonlinear shrinkage estimator. The distribution of the test statistic is deduced under the null hypothesis in the large‐dimensional setting, that is, when p/n→c∈(0,+∞)$$ p/n\to c\in \left(0,+\infty \right) $$ with p$$ p $$ variables and n$$ n $$ samples both tending to infinity. The theoretical results are illustrated by means of an extensive simulation study where the new nonlinear shrinkage‐based test is compared with existing approaches, in particular with the commonly used corrected likelihood ratio test, the corrected John test, and the test based on the linear shrinkage approach. It is demonstrated that the new nonlinear shrinkage test possesses better power properties under heteroscedastic alternative. [ABSTRACT FROM AUTHOR]

This paper analyzes several covariance matrix U‐tests, which are constructed by modifying the classical John‐Nagao and Ledoit‐Wolf tests, under the elliptically distributed data structure. We study the limiting distributions of these location‐invariant test statistics as the data dimension p$$ p $$ may go to infinity in an arbitrary way as the sample size n$$ n $$ does. We find that they tend to have unsatisfactory size performances for general elliptical population. This is mainly because such population often possesses high‐order correlations among their coordinates. Taking such kind of dependency into consideration, we propose necessary corrections for these tests to cope with elliptically high‐dimensional data. For computational efficiency, alternative forms of the new test statistics are also provided. We derive the universal (n,p)$$ \left(n,p\right) $$ asymptotic null distributions of the proposed test statistics under elliptical distributions and beyond. The powers of the proposed tests are further investigated. The accuracy of the tests is demonstrated by simulations and an empirical study. [ABSTRACT FROM AUTHOR]

Covariance estimation for multiple groups is a key feature for drawing inference from a heterogeneous population. One should seek to share information about common features in the dependence structures across the various groups. In this paper, we introduce a novel approach for estimating the covariance matrices for multiple groups using a hierarchical latent factor model that shrinks the factor loadings across groups toward a global value. Using a sparse spike and slab model on these loading coefficients allows for a sparse formulation of our model. Parameter estimation is accomplished through a Markov chain Monte Carlo scheme, and a model selection approach is used to select the number of factors to use. We validate our model through extensive simulation studies. Finally, we apply our methodology to the NICHD Consecutive Pregnancies Study to estimate the correlations between birth weights and gestational ages of three consecutive birth within four different subgroups (underweight, normal, overweight, and obese) of women. [ABSTRACT FROM AUTHOR]

In geoscience and other fields, researchers use models as a simplified representation of reality. The models include processes that often rely on uncertain parameters that reduce model performance in reflecting real‐world processes. The problem is commonly addressed by adapting parameter values to reach a good match between model simulations and corresponding observations. Different optimization tools have been successfully applied to address this task of model calibration. However, seeking one best value for every single model parameter might not always be optimal. For example, if model equations integrate over multiple real‐world processes which cannot be fully resolved, it might be preferable to consider associated model parameters as random parameters. In this paper, a random parameter is drawn from a wide probability distribution for every singe model simulation. We developed an optimization approach that allows us to declare certain parameters random while optimizing those that are assumed to take fixed values. We designed a corresponding variant of the well known Covariance Matrix Adaption Evolution Strategy (CMA‐ES). The new algorithm was applied to a global biogeochemical circulation model to quantify the impact of zooplankton mortality on the underlying biogeochemistry. Compared to the deterministic CMA‐ES, our new method converges to a solution that better suits the credible range of the corresponding random parameter with less computational effort. Plain Language Summary: In geoscience and other fields, researchers use models as a simplified representation of reality. The models include processes that often rely on uncertain parameters that reduce model performance in reflecting real‐world processes. The problem is commonly addressed by adapting parameter values to reach a good match between model simulations and corresponding observations. However, seeking one best value for every single model parameter might not always be optimal. For example, if model equations integrate over multiple real‐world processes it might be preferable to consider associated model parameters as random parameters that are drawn from a wide probability distribution for every single model simulation. To explore this further, we modified a popular variant of the Covariance Matrix Adaption Evolution Strategy (CMA‐ES) in order to tune the other parameters. The new algorithm was applied to a global biogeochemical circulation model to quantify the impact of zooplankton mortality on the underlying biogeochemistry. Compared to the deterministic CMA‐ES our new method converges to a solution that better suits the credible range of the corresponding random parameter. Key Points: Model calibration is an important task in the view of parametric uncertaintiesWe allow specific uncertain model parameters to be random while optimizing other model parameters, providing an efficient tool for the taskWe apply it to a global biogeochemical circulation model to quantify the impact of zooplankton mortality on the underlying biogeochemistry [ABSTRACT FROM AUTHOR]

Based on the fractional‐order model (FOM), this paper proposes an adaptive fractional‐order cubature Kalman filter (AFCKF) method for state of charge (SOC) estimation of a lithium‐ion battery (LIB). Firstly, a FOM with two constant phase elements is built, which can accurately represent the dynamic features of a LIB with a higher accuracy. Secondly, the adaptive estimations of the coefficients in the measurement equation are achieved by a linear Kalman filter algorithm, which avoids the calculation of the relationship between the open‐circuit voltage and SOC. Thirdly, an augmented state equation including the SOC, the fractional‐orders and parameters in the FOM is investigated by introducing the augmented vector method, and the state information is estimated online via the AFCKF algorithm. The algorithm requires a little computational burden while ensuring the estimation accuracy and is well adapted to complex working conditions. Besides, this study fully considers the impact of noises on the estimation effect. To better overcome the disturbances caused by unknown noises and further improve the precision and stability of the algorithm, an adaptive estimation method of the noise covariance matrices is achieved. Finally, the experimental findings are given to reveal that the proposed method can be effectively used to different working conditions and the estimation accuracy is better than the adaptive integer‐order cubature Kalman filter. [ABSTRACT FROM AUTHOR]

This paper investigates the simultaneous state and noise covariance estimation for linear systems with inaccurate noise statistics. An enhanced adaptive Kalman filtering (EAKF) based on dynamic recursive nominal covariance estimation (DNRCE) and modified variational Bayesian (VB) inference is presented. The EAKF realizes the concurrently estimation of state and noise covariance matrices by introducing a nominal parameter in the traditional recursive covariance estimation and designing a new adaptive forgotten factor for the dynamic model of the estimated information propagation. The simulation of a target tracking example shows that, compared with the existing filters, the proposed filter has good adaptive performance for inaccurate and time‐varying noise covariance matrices. [ABSTRACT FROM AUTHOR]

Researchers have recently shown an increased interest in estimating the direction‐of‐arrival (DOA) of wideband noncircular sources, but existing studies have been restricted to subspace‐based methods. An off‐grid sparse recovery‐based algorithm is proposed in this paper to improve the accuracy of existing algorithms in low signal‐to‐noise ratio situations. The covariance and pseudo covariance matrices can be jointly represented subject to block sparsity constraints by taking advantage of the joint sparsity between signal components and bias. Furthermore, the estimation problem is transformed into a single measurement vector problem utilizing the focused operation, resulting in a significant reduction in computational complexity. The proposed algorithm's error threshold and the Cramer–Rao bound for wideband noncircular DOA estimation are deduced in detail. The proposed algorithm's effectiveness and feasibility are demonstrated by simulation results. [ABSTRACT FROM AUTHOR]

Variance‐based analysis has emerged as method of choice for quantifying the sensitivity of the output, y, of a scalar‐valued square‐integrable function, f ∈ L2(χ $\boldsymbol{\upchi }$), to its d ≥ 1 input variables, x = {x1, ..., xd}, with support x∈χ⊆Rd $\mathbf{x}\in \boldsymbol{\upchi }\subseteq {\mathbb{R}}^{d}$. The prototype of this approach, Sobol's method is a generalization of the analysis of variance (ANOVA) to d > 2 independent input variables and decomposes y, as sum of elementary functions of zeroth‐, first‐, second‐, up to dth‐order. This independence assumption is mathematically convenient but may not be borne out of the causal or correlational relationships between the x's. This paper is concerned with variance‐based sensitivity analysis (SA) for correlated input variables, for example, multivariate dependencies in a posterior parameter distribution. We use high‐dimensional model representation (HDMR) of Li et al. (2010, https://doi.org/10.1021/jp9096919), Li and Rabitz (2012, https://doi.org/10.1007/s10910-011-9898-0) and replace Sobol's elementary functions with so‐called component functions with unknown expansion coefficients to disentangle the structural, correlative and total contribution of input factors. We contrast the default HDMR methodology with cubic B‐splines and sequential coefficient estimation against its successor, HDMRext of Li and Rabitz (2012, https://doi.org/10.1007/s10910-011-9898-0), which uses polynomial component functions with an extended orthonormalized basis. Benchmark experiments confirm that HDMR and HDMRext parse out the structural and correlative contributions of input factors to the model output and infer an optimal experimental design with parameter correlation. Our last study applies HDMRext to probabilistic SA of a watershed model. The multivariate posterior parameter distribution supports model emulation and yields sensitivity indices that pertain to measured discharge data. Key Points: We use high‐dimensional model representation for variance‐based sensitivity analysis with dependent input variablesWe use this method to disentangle the parameters' structural and correlative contributions across the posterior distributionCorrelation can profoundly affect input variable importance, optimal experimental design and physical underpinning of sensitivity indices [ABSTRACT FROM AUTHOR]

Hydrological models are widely used for flood forecasting, and proper initialization of hydrological models is essential. Although the unscented Kalman filter (UKF) has shown promise in the context of operational forecasting, it is limited by its intrinsic instability caused by the loss of positive semidefiniteness of the covariance matrix. Effective methods for tackling this problem have not been seen in the literature. The cubature Kalman filter (CKF) is a powerful nonlinear filter for state estimation, which has received little attention in the hydrologic context. In this paper, to overcome the instability problem of the UKF, a new modified UKF (UKF‐M) is proposed by modifying the default UKF tuning strategy, and a novel nonlinear filter (CKF) is introduced to update the states of hydrological models. The methods are tested using a lumped hydrological model. The results of the stability experiment suggest that both the UKF‐M and CKF can overcome the instability problem, while the original UKF can fail due to the loss of positive semidefiniteness of the covariance matrix. The results of a reforecast experiment in an operational context show that both filters can improve the forecast performance by updating the model state based on the observed discharge, with the UKF‐M achieving better forecast performances. The UKF‐M and CKF can be used to overcome the instability problem of the original UKF and are valuable methods for improving forecast performances of hydrological models by state updating. Key Points: A new modified unscented Kalman filter is proposed to overcome the instability problem caused by the loss of positive semidefinitenessAn effective filter (cubature Kalman filter) is introduced to improve hydrological models' forecast performances by state updatingBoth filters can improve the forecast performance, with the modified unscented Kalman filter achieving better forecast performance [ABSTRACT FROM AUTHOR]

Summary: This paper considers estimation of factor‐augmented panel data regression models. One of the most popular approaches towards this end is the common correlated effects (CCE) estimator of Pesaran (Estimation and inference in large heterogeneous panels with a multifactor error structure. Econometrica, 2006, 74, 967–1012, 2006). For the pooled version of this estimator to be consistent, either the number of observables must be larger than the number of unobserved common factors, or the factor loadings must be distributed independently of each other. This is a problem in the typical application involving only a small number of regressors and/or correlated loadings. The current paper proposes a simple extension to the CCE procedure by which both requirements can be relaxed. The CCE approach is based on taking the cross‐section average of the observables as an estimator of the common factors. The idea put forth in the current paper is to consider not only the average but also other cross‐section combinations. Asymptotic properties of the resulting combination‐augmented CCE (C3E) estimator are provided and tested in small samples using both simulated and real data. [ABSTRACT FROM AUTHOR]

The conventional parameter identification process generally assumes that parameters remain constant. However, under extreme loading conditions, structures may exhibit nonlinear behavior, and parameters could demonstrate time‐variant characteristics. The unscented Kalman filter (UKF), as an efficient online recursive estimator, is widely used for identifying parameters of nonlinear systems. Nevertheless, it exhibits limitations when attempting to identify time‐variant parameters. To address this issue, this paper proposes a covariance matching technique that produces an array of adaptive UKF algorithms. Firstly, the sensitivity parameter η is defined to identify the instant when the parameter change occurs, and its threshold is calculated based on the sensitivity parameter time history curve. Secondly, an adaptive forgetting factor is introduced to simultaneously update the innovation, cross, and state covariance matrices when the kth‐step sensitive parameter surpasses the threshold. Finally, a secondary correction forgetting factor (SCFF) is employed to further re‐update the state covariance values at the identified damage locations. This creative step enhances the adaptive capability and optimizes the identification accuracy of the proposed algorithms. Both the numerical simulations and shaking table test demonstrate that the proposed adaptive algorithms can efficiently identify the time‐variant stiffness‐type parameters, and accurately capture their time‐variant characteristics. [ABSTRACT FROM AUTHOR]

The concept of complexity has become pivotal in multiple disciplines, including quantum information, where it serves as an alternative metric for gauging the chaotic evolution of a quantum state. This paper focuses on Krylov complexity, a specialized form of quantum complexity that offers an unambiguous and intrinsically meaningful assessment of the spread of a quantum state over all possible orthogonal bases. This study is situated in the context of Gaussian quantum states, which are fundamental to both Bosonic and Fermionic systems and can be fully described by a covariance matrix. While the covariance matrix is essential, it is insufficient alone for calculating Krylov complexity due to its lack of relative phase information is shown. The relative covariance matrix can provide an upper bound for Krylov complexity for Gaussian quantum states is suggested. The implications of Krylov complexity for theories proposing complexity as a candidate for holographic duality by computing Krylov complexity for the thermofield double States (TFD) and Dirac field are also explored. [ABSTRACT FROM AUTHOR]

Precision matrix (inverse covariance matrix) estimation is a rising challenge in contemporary applications while dealing with high‐dimensional data. This paper focuses on large‐scale precision matrix of the random vector that only has lower polynomial moments. We mainly investigate upper bounds of the proposed estimator under the spectral norm in terms of the probability and mean estimation respectively. It is shown that the data‐driven estimator is fully adaptive and achieves the same optimal convergence order as under Gaussian assumption on the data. Simulation studies further support our theoretical claims. [ABSTRACT FROM AUTHOR]

The joint probability distribution of different intensity measures (IMs)$({IMs})$ at different sites in one earthquake is needed to define the stochastic process regulating the exceedance (in time) of the IMs$IMs$ at the ensemble of the sites, which in turn is a funding element of the so‐called multi‐site probabilistic seismic hazard analysis (MSPSHA). The simplest model for the joint distribution of the IMs$IMs$ in one seismic event requires the mean vector and the covariance matrix of the IMs$IMs$ at all sites, conditional to the magnitude and location of the earthquake, which may need a large amount of data to be calibrated. The conditional hazard (CH) approach, originally developed for single‐site surrogate vector‐valued probabilistic seismic hazard analysis, may be a simplified option for MSPSHA, as it explicitly models only part of the covariance matrix of the IMs$IMs$ at the sites, while the rest forcefully follows the working assumptions. The presented paper compares the CH approach for MSPSHA against the benchmark in which the complete covariance matrix is modelled, using a testbed in which one‐hundred sites are considered. When the comparison metric is the probability of a given number of IM$IM$ exceedances observed at the sites in some time intervals, it is found that CH is a viable alternative to MSPSHA, although the degree of approximation is sensitive to which and how many IMs$IMs$ are considered (e.g., which spectral acceleration). When the analysis is taken all the way to the risk, considering the fragilities of a portfolio of hypothetical buildings, and taking as the metric the probability of observing a given number of structural failures in a time interval, it is found that the approximation introduced by CH with respect to the benchmark is further reduced. [ABSTRACT FROM AUTHOR]

Wireless sensor networks are vulnerable to false data injection attacks, which may mislead the state estimation. To solve this problem, this paper presents a chi‐square test‐based adaptive secure state estimation (CTASSE) algorithm for state estimation and attack detection. Taking advantage of Kalman filters, attack signal together with process noise or measurement noise are described as total white Gaussian noise with uncertain covariance matrix. The chi‐square test method is used in the adaptation of the total noise covariance and attack detection. Then, a standard adaptive unscented Kalman filter (UKF) is used for the state estimation. Finally, simulation results show that the proposed CTASSE algorithm performs better than other UKFs in state estimation and is also effective in real‐time attack detection. [ABSTRACT FROM AUTHOR]

A precision matrix is the inverse of a covariance matrix. In this paper, we study the problem of estimating the precision matrix with a known graphical structure under high-dimensional settings. We propose a simple estimator of the precision matrix based on the connection between the known graphical structure and the precision matrix. We obtain the rates of convergence of the proposed estimators and derive the asymptotic normality of the proposed estimator in the high-dimensional setting when the data dimension grows with the sample size. Numerical simulations are conducted to demonstrate the performance of the proposed method. We also show that the proposed method outperforms some existing methods that do not utilize the graphical structure information. [ABSTRACT FROM AUTHOR]

Principal components have been used in conjunction with Hotelling's T2 chart to monitor multivariate processes. It is known that prohibitively large sample sizes are needed to estimate the process parameters with enough precision to deploy the chart. We investigate whether principal components can be used to reduce the dimensionality of a process so that multivariate process control can be performed using estimated parameters. The chart based on the first k principal components, which we will refer to as the TPC,k2$T^2_{{\rm PC},k}$ chart, is investigated. Specifically, we explore three research questions in this paper: (1) can the TPC,k2$T^2_{{\rm PC},k}$ chart with estimated parameters be applied with moderate preliminary sample sizes?, (2) are there situations where the TPC,k2$T^2_{{\rm PC},k}$ charts are able to detect a shift in the mean vector quicker than the T2 charts?, and (3) is it possible to exploit assumptions about the covariance matrix, such as equal covariances, to improve the performance of the TPC,k2$T^2_{{\rm PC},k}$ chart. Using simulation, we find that for high dimensions, the TPC,k2$T^2_{{\rm PC},k}$ chart with estimated parameters can be used to detect shifts in the direction of the first principal component. Otherwise, the chart requires very large preliminary sample sizes. When it is reasonable to assume equal covariances, the number of parameters to be estimated is substantially reduced and the performance of the TPC,k2$T^2_{{\rm PC},k}$ chart is improved. [ABSTRACT FROM AUTHOR]

The present paper is the third and last part of an investigation on what determines reliability in fuel cell model identification. In continuation to the effect of experimental design (Part I) and a process method for stochastic calculation of a model's parameters (Part II), this paper concentrates on the assessment of a model validation. Four criteria are examined. The fit of the model's output to experimental data, the determinant of the covariance matrix of the parameters, the determinant of their correlation matrix, and the product of their variances. As regards the fit to the data, results show that this is mainly a function of the number of measurement points. Repetitions do not seem to improve the average of the fit significantly, but it does improve its variation. For the other three criteria, which are also mathematically linked, results show a counterbalance between them, leading to the conclusion that they cannot be optimized simultaneously. This happens especially between the determinants of the covariance and the correlation matrices. [ABSTRACT FROM AUTHOR]

There is widespread evidence of parameter instability in the literature. One way to account for this feature is through the use of time‐varying parameter (TVP) models that discount older data in favor of more recent data. This practice is often known as forgetting and can be applied in several different ways. This paper introduces and examines the performance of different (flexible) forgetting methodologies in the context of the Kalman filter. We review and develop the theoretical background and investigate the performance of each methodology in simulations as well as in two empirical forecast exercises using dynamic model averaging (DMA). Specifically, out‐of‐sample DMA forecasts of Consumer Price Index (CPI) inflation and S&P500 returns obtained using different forgetting approaches are compared. Results show that basing the amount of forgetting on the forecast error does not perform as well as avoiding instability by placing bounds on the parameter covariance matrix. [ABSTRACT FROM AUTHOR]

The aim of this paper is to develop control charts for a simultaneous monitoring of the mean vector and covariance matrix of multivariate multiple linear regression profiles in phase II, when the independence assumption of the observations within each profile is violated, and there is multivariate autoregressive moving average (MARMA)(1,1) autocorrelation structure within each profile. A transformation method is applied to eliminate the autocorrelation, and six control charts for a simultaneous monitoring of the mean vector and covariance matrix of auto‐correlated multivariate multiple linear regression profiles are proposed. Then, through simulation runs, in terms of the average run length (ARL) criterion, it is shown that the proposed methods have better performance in comparison with the competing methods in detecting shifts in the parameters of regression profiles. Finally, the application of the proposed control charts is shown using real data in a machining process. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of distributed target detection in partially homogeneous Gaussian clutter whose covariance matrix is unknown but persymmetric. It is assumed that primary data and training data share the same clutter covariance matrix structure but different power levels. The target signal is supposed to lie in a multi‐rank subspace with unknown coordinates. A persymmetric subspace detector is designed based on the generalised likelihood ratio test criteria. It is theoretically demonstrated that the proposed detector possesses constant false alarm rate property with respect to the unknown clutter covariance matrix as well as the power level. Experimental results illustrate the performance advantage of the proposed detector over the existing competitors, especially in training‐limited scenarios. [ABSTRACT FROM AUTHOR]

The state of charge (SOC) of lithium‐ion batteries is the main parameter of the battery management system. To improve the accuracy of lithium‐ion battery SOC estimation, this paper uses a double RC physical characteristic circuit network to model the polarization reaction inside the battery and realizes the full parameter identification of the model based on the double‐exponential fitting strategy. Then, using the spherical unscented transform (SUT) to realize the selection of sigma points and the calculation of weight coefficients, at the same time, the adaptive factor is introduced to correct the error covariance matrix in real time and an adaptive spherical unscented Kalman filter (AS‐UKF) algorithm. Finally, the algorithm is compared with the unscented Kalman filter (UKF) and adaptive unscented Kalman filter (AUKF) algorithms through simulation. The results show that the average error of the AS‐UKF algorithm is reduced by 0.5% and 1.18% under the Hybrid Pulse Power Characterization (HPPC) and the Beijing Bus Dynamic Street Test (BBDST) conditions. The AS‐UKF algorithm not only improves the accuracy but also is more stable. [ABSTRACT FROM AUTHOR]

The poor out‐of‐sample performance of mean–variance portfolio model is mainly caused by estimation errors in the covariance matrix and the mean return, especially the mean return vector. Meanwhile, in financial practice, what most investors actually like is to hold a few stocks in their portfolio. The goal of this paper is to propose some new efficient mean–variance portfolio selection models by considering the following aspects: (i) use the L1‐regularization in objective function to obtain sparse portfolio; (ii) use the shrinkage method of Ledoit and Wolf, Journal of Economics Financial, 2003, 10, 603–621 to estimate the covariance matrix; (iii) use the robust optimization method to mitigate the estimation errors of the expected return. Finally, empirical analysis demonstrates that the proposed strategies have better out‐of‐sample performance. [ABSTRACT FROM AUTHOR]

Estimating the parameters of spatial models for large spatial datasets can be computationally challenging, as it involves repeated evaluation of sizable spatial covariance matrices. In this paper, we aim to develop Krylov subspace‐based methods that are computationally efficient for large spatial data. Specifically, we approximate the inverse and the log‐determinant of the spatial covariance matrix in the log‐likelihood function via conjugate gradient and stochastic Lanczos on a Krylov subspace. These methods reduce the computational complexity from O(N3) to O(N2logN) and O(NlogN) for dense and sparse matrices, respectively. Moreover, we quantify the difference between the approximated log‐likelihood function and the original log‐likelihood function and establish the consistency of parameter estimates. Simulation studies are conducted to examine the computational efficiency as well as the finite‐sample properties. For illustration, our methodology is applied to analyze a large dataset comprising LiDAR estimates of forest canopy height in western Alaska. [ABSTRACT FROM AUTHOR]

The global minimum variance portfolio (GMVP) is the starting point of the Markowitz mean‐variance efficient frontier. The estimation of the GMVP weights is therefore of much importance for financial investors. The GMVP weights depend only on the inverse covariance matrix of returns on financial risky assets, for this reason the estimated GMVP weights are subject to substantial estimation risk, especially in high‐dimensional portfolio settings. In this paper we review the recent literature on traditional sample estimators for the unconditional GMVP weights which are typically based on daily asset returns, as well as on modern realized estimators for the conditional GMVP weights based on intraday high‐frequency returns. We present various types of GMVP estimators with the corresponding stochastic results, discuss statistical tests and point on some directions for further research. Our empirical application illustrates selected properties of realized GMVP weights. This article is categorized under:Statistical and Graphical Methods of Data Analysis > Multivariate AnalysisStatistical and Graphical Methods of Data Analysis > Analysis of High Dimensional DataStatistical Models > Multivariate Models [ABSTRACT FROM AUTHOR]

Energy beamforming (EB) is a key technique to enhance the efficiency of wireless power transfer. In this paper, we study the optimal EB under per‐antenna power constraint (PAC), which is more practical than the conventional sum‐power constraint. We consider a multiantenna energy transmitter with PAC that broadcasts wireless energy to multiple energy receivers (ER)s. We consider sum‐energy maximization problem with PAC and provide the optimal solution structure for the general case. This optimal structure implies that sending one energy beam is optimal under PAC, which means that the rank of transmit covariance matrix is one similar to sum‐power constraint. We also derive closed‐form solutions for two special cases and propose two suboptimal solutions for general case, which performs very close to optimal beamforming. [ABSTRACT FROM AUTHOR]

Multivariate nonparametric control charts are highly sought‐after due to their flexibility to adapt to different distribution assumptions. However, many of the existing multivariate nonparametric control charts are only distribution‐free for certain distribution families. Although those distribution families may contain different distributions, it is still difficult to verify whether the underlying multivariate distribution from a particular application belongs to those distribution families in practice. A few existing multivariate nonparametric control charts are fully nonparametric. As shown in the literature and in our simulation studies, most of them are not efficient in detecting location shifts. In this paper, we propose a new multivariate nonparametric control chart based on the idea of projection pursuit. The proposed control chart is fully nonparametric and can be applied to any multivariate distribution as long as its covariance matrix exists. The control limit of the proposed control chart only depends on the nominal ARL0$\text{ARL}_0$, which makes its implementation much easier. Our simulation study and real data analysis show that the proposed control chart performs well across a variety of settings, and compares favorably with existing multivariate nonparametric control charts. [ABSTRACT FROM AUTHOR]

Outliers are common in longitudinal data analysis, and the multivariate contaminated normal (MCN) distribution in model‐based clustering is often used to detect outliers and provide robust parameter estimates in each subgroup. In this paper, we propose a method, the mixture of MCN (MCNM), based on the joint mean‐covariance model, specifically designed to analyze longitudinal data characterized by mild outliers. Our model can automatically detect outliers in longitudinal data and provide robust parameter estimates in each subgroup. We use iteratively expectation‐conditional maximization (ECM) algorithm and Aitken acceleration to estimate the model parameters, achieving both algorithm acceleration and stable convergence. Our proposed method simultaneously clusters the population, identifies progression patterns of the mean and covariance structures for different subgroups over time, and detects outliers. To demonstrate the effectiveness of our method, we conduct simulation studies under various cases involving different proportions and degrees of contamination. Additionally, we apply our method to real data on the number of people infected with AIDS in 49 countries or regions from 2001 to 2021. Results show that our proposed method effectively clusters the data based on various mean progression trajectories. In summary, our proposed MCNM based on the joint mean‐covariance model and MCD of covariance matrices provides a robust method for clustering longitudinal data with mild outliers. It effectively detects outliers and identifies progression patterns in different groups over time, making it valuable for various applications in longitudinal data analysis. [ABSTRACT FROM AUTHOR]

Software refactoring solutions aim at mitigating the negative effects of code and design smells on the overall software quality. Many efforts have been exerted to improve the software refactoring process. However, most of these efforts, despite their contributions, overlooked the side effects of the identified refactoring opportunities that may lead to new smells that will go unnoticed. This paper addresses the side effects of software refactoring and proposes sound solutions for handling them. Unlike current practices in software maintenance, we recommend three different approaches to handle the refactoring side effects. In the first approach, called the baseline, we opt to ignore the smells, caused by refactoring, while executing the identified refactoring decisions. In the second one, refactoring decisions are continually updated to fix all smells caused by side effects. In the last approach, only a subset of these smells is appended to the original smell sequence during the execution of the refactoring decisions. Thanks to the proposed approaches, optimal refactoring decisions are identified using a multi‐objective (MO) optimization algorithm commonly known as the MO covariance matrix adaptation evolution strategy (MO‐CMA‐ES). Experiment results corroborate our assumptions and show the superiority of the second approach over the other ones. [ABSTRACT FROM AUTHOR]