Iterative Variant Research Articles

Fg-ORKA: fast and gridless reconstruction of moving and deforming objects in multidimensional data

Abstract Identifying and tracking objects over multiple observations is a frequent task in many applications. Traffic monitoring requires the tracking of vehicles or pedestrians in video data and geophysical exploration relies on identifying seismic wave fronts from data of multiple sensors, only to mention two examples. In many cases, the object changes its shape or position within the given data from one observation to another. Vehicles can change their position and angle relative to the camera while seismic waves have different arrival times, frequencies, or intensities depending on the sensor position. This complicates the task at hand.

In a previous work, the authors presented a new algorithm to solve this problem - Object reconstruction using K-approximation (ORKA). This algorithm is hindered by two conflicting limitations: the tracked movement is limited by the sampling grid while the complexity increases exponentially with the resolution. We introduce an iterative variant of the ORKA algorithm that is able to overcome this conflict. We also give a brief introduction on the original ORKA algorithm. Knowledge of the previous work is thus not required.

We give theoretical error bounds and a complexity analysis which we validate with several numerical experiments. Moreover, we discuss the influence of different parameter choices in detail. The results clearly show that the iterative approach can outperform ORKA in both accuracy and efficiency. On the example of video processing we show that the new method can be applied where the original algorithm is too time and memory intensive. Furthermore, we demonstrate on seismic exploration data that we are now able to recover much finer details on the wave front movement then before.

Maximum-Entropy Multi-Agent Dynamic Games: Forward and Inverse Solutions

In this article, we study the problem of multiple stochastic agents interacting in a dynamic game scenario with continuous state and action spaces. We define a new notion of stochastic Nash equilibrium for boundedly rational agents, which we call the entropic cost equilibrium (ECE). We show that ECE is a natural extension to multiple agents of maximum entropy optimality for a single agent. We solve both the “forward” and “inverse” problems for the multi-agent ECE game. For the forward problem, we provide a Riccati algorithm to compute closed-form ECE feedback policies for the agents, which are exact in the linear-quadratic-gaussian case. We give an iterative variant to find locally ECE feedback policies for the nonlinear case. For the inverse problem, we present an algorithm to infer the cost functions of the multiple interacting agents given noisy, boundedly rational input and state trajectory examples from agents acting in an ECE. The effectiveness of our algorithms is demonstrated in a simulated multi-agent collision avoidance scenario, and with data from the INTERACTION traffic dataset. In both cases, we show that, by taking into account the agents' game theoretic interactions using our algorithm, a more accurate model of agents' costs can be learned, compared with standard inverse optimal control methods.

Genomic Diagnosis of Rare Pediatric Disease in the United Kingdom and Ireland

BackgroundPediatric disorders include a range of highly penetrant, genetically heterogeneous conditions amenable to genomewide diagnostic approaches. Finding a molecular diagnosis is challenging but can have profound lifelong benefits.MethodsWe conducted a large-scale sequencing study involving more than 13,500 families with probands with severe, probably monogenic, difficult-to-diagnose developmental disorders from 24 regional genetics services in the United Kingdom and Ireland. Standardized phenotypic data were collected, and exome sequencing and microarray analyses were performed to investigate novel genetic causes. We developed an iterative variant analysis pipeline and reported candidate variants to clinical teams for validation and diagnostic interpretation to inform communication with families. Multiple regression analyses were performed to evaluate factors affecting the probability of diagnosis.ResultsA total of 13,449 probands were included in the analyses. On average, we reported 1.0 candidate variant per parent–offspring trio and 2.5 variants per singleton proband. Using clinical and computational approaches to variant classification, we made a diagnosis in approximately 41% of probands (5502 of 13,449). Of 3599 probands in trios who received a diagnosis by clinical assertion, approximately 76% had a pathogenic de novo variant. Another 22% of probands (2997 of 13,449) had variants of uncertain significance in genes that were strongly linked to monogenic developmental disorders. Recruitment in a parent–offspring trio had the largest effect on the probability of diagnosis (odds ratio, 4.70; 95% confidence interval [CI], 4.16 to 5.31). Probands were less likely to receive a diagnosis if they were born extremely prematurely (i.e., 22 to 27 weeks’ gestation; odds ratio, 0.39; 95% CI, 0.22 to 0.68), had in utero exposure to antiepileptic medications (odds ratio, 0.44; 95% CI, 0.29 to 0.67), had mothers with diabetes (odds ratio, 0.52; 95% CI, 0.41 to 0.67), or were of African ancestry (odds ratio, 0.51; 95% CI, 0.31 to 0.78).ConclusionsAmong probands with severe, probably monogenic, difficult-to-diagnose developmental disorders, multimodal analysis of genomewide data had good diagnostic power, even after previous attempts at diagnosis. (Funded by the Health Innovation Challenge Fund and Wellcome Sanger Institute.)

Combining Sparse Approximate Factorizations with Mixed-precision Iterative Refinement

The standard LU factorization-based solution process for linear systems can be enhanced in speed or accuracy by employing mixed-precision iterative refinement. Most recent work has focused on dense systems. We investigate the potential of mixed-precision iterative refinement to enhance methods for sparse systems based on approximate sparse factorizations. In doing so, we first develop a new error analysis for LU- and GMRES-based iterative refinement under a general model of LU factorization that accounts for the approximation methods typically used by modern sparse solvers, such as low-rank approximations or relaxed pivoting strategies. We then provide a detailed performance analysis of both the execution time and memory consumption of different algorithms, based on a selected set of iterative refinement variants and approximate sparse factorizations. Our performance study uses the multifrontal solver MUMPS, which can exploit block low-rank factorization and static pivoting. We evaluate the performance of the algorithms on large, sparse problems coming from a variety of real-life and industrial applications showing that mixed-precision iterative refinement combined with approximate sparse factorization can lead to considerable reductions of both the time and memory consumption.

A new alternative for matrix balancing under conflicting information

Balancing input–output tables using iterative proportional fitting techniques can be prevented due to conflicting information. What is to be done in such cases? Literature suggests a wide variety of alternative methods. Within iterative proportional fitting techniques, modifying the constraint set to circumvent conflicting information problems has been suggested as a promising avenue. Following this approach, we identify some opportunities for improvement not yet been addressed. As a result of this research, we present an iterative proportional fitting variant. Our algorithm uses information contained in the matrix to be balanced for dynamically modifying our constraint set. We ensure economically meaningful solutions, avoiding unsought sign flips. We also respect all macroeconomic aggregates. To illustrate our findings, we provide an empirical example based on the supply-use tables for the region of Galicia (Northwest Spain). Results suggest that our methodological proposal can yield estimates almost as accurate as other alternatives while avoiding undesired outcomes.

Using the (Iterative) Ensemble Kalman Smoother to Estimate the Time Correlation in Model Error

Numerical weather prediction systems contain model errors related to missing and simplified physical processes, and limited model resolution. While it has been widely recognized that these model errors need to be included in the data assimilation formulation, providing prior estimates of their spatio-temporal characteristics is a hard problem. We follow a systematic path to estimate parameters in the model error formulation, specifically related to time-correlated model errors. This problem is more difficult than the standard parameter estimation problem because the model error parameters are only visible through the random model error realisations. By concentrating on linear and nonlinear low-dimensional systems, we are able to highlight the many aspects of this problem, using state augmentation in an ensemble Kalman smoother (EnKS) and its iterative variant (IEnKS). It is not possible to estimate the model error parameters in one assimilation window because enough information has to be gathered to see the parameters through the random errors, even when every time step is observed. If only one parameter is estimated in a linear one-dimensional system the EnKS works well, but when we try to estimate two parameters the method fails. An IEnKS is able to find the correct parameter values for the linear system. For the highly nonlinear logistic map the IEnKS can get stuck in local minima, but with careful tuning of the step length in the iterations and careful transformation of the solution space the correct parameter values can be found. The main conclusion is that estimating model error parameters –even in low-dimensional systems– is a difficult problem, but via careful reformulation of the problem practical solutions can be found.

The Multiple Snow Data Assimilation System (MuSA v1.0)

Abstract. Accurate knowledge of the seasonal snow distribution is vital in several domains including ecology, water resources management, and tourism. Current spaceborne sensors provide a useful but incomplete description of the snowpack. Many studies suggest that the assimilation of remotely sensed products in physically based snowpack models is a promising path forward to estimate the spatial distribution of snow water equivalent (SWE). However, to date there is no standalone, open-source, community-driven project dedicated to snow data assimilation, which makes it difficult to compare existing algorithms and fragments development efforts. Here we introduce a new data assimilation toolbox, the Multiple Snow Data Assimilation System (MuSA), to help fill this gap. MuSA was developed to fuse remotely sensed information that is available at different timescales with the energy and mass balance Flexible Snow Model (FSM2). MuSA was designed to be user-friendly and scalable. It enables assimilation of different state variables such as the snow depth, SWE, snow surface temperature, binary or fractional snow-covered area, and snow albedo and could be easily upgraded to assimilate other variables such as liquid water content or snow density in the future. MuSA allows the joint assimilation of an arbitrary number of these variables, through the generation of an ensemble of FSM2 simulations. The characteristics of the ensemble (i.e., the number of particles and their prior covariance) may be controlled by the user, and it is generated by perturbing the meteorological forcing of FSM2. The observational variables may be assimilated using different algorithms including particle filters and smoothers as well as ensemble Kalman filters and smoothers along with their iterative variants. We demonstrate the wide capabilities of MuSA through two snow data assimilation experiments. First, 5 m resolution snow depth maps derived from drone surveys are assimilated in a distributed fashion in the Izas catchment (central Pyrenees). Furthermore, we conducted a joint-assimilation experiment, fusing MODIS land surface temperature and fractional snow-covered area with FSM2 in a single-cell experiment. In light of these experiments, we discuss the pros and cons of the assimilation algorithms, including their computational cost.

Revealing nanostructures in brain tissue via protein decrowding by iterative expansion microscopy.

Many crowded biomolecular structures in cells and tissues are inaccessible to labelling antibodies. To understand how proteins within these structures are arranged with nanoscale precision therefore requires that these structures be decrowded before labelling. Here we show that an iterative variant of expansion microscopy (the permeation of cells and tissues by a swellable hydrogel followed by isotropic hydrogel expansion, to allow for enhanced imaging resolution with ordinary microscopes) enables the imaging of nanostructures in expanded yet otherwise intact tissues at a resolution of about 20 nm. The method, which we named 'expansion revealing' and validated with DNA-probe-based super-resolution microscopy, involves gel-anchoring reagents and the embedding, expansion and re-embedding of the sample in homogeneous swellable hydrogels. Expansion revealing enabled us to use confocal microscopy to image the alignment of pre-synaptic calcium channels with post-synaptic scaffolding proteins in intact brain circuits, and to uncover periodic amyloid nanoclusters containing ion-channel proteins in brain tissue from a mouse model of Alzheimer's disease. Expansion revealing will enable the further discovery of previously unseen nanostructures within cells and tissues.

О некорректных задачах, экстремалях функционала Тихонова и регуляризованных принципах Лагранжа

The problem of finding a normal solution to an operator equation of the first kind on a pair of Hilbert spaces is classical in the theory of ill-posed problems. In accordance with the theory of regularization, its solutions are approximated by the extremals of the Tikhonov functional. From the point of view of the theory of problems for constrained extremum, the problem of minimizing a functional, equal to the square of the norm of an element, with an operator equality constraint (that is, given by an operator with an infinite-dimensional image) is equivalent to the classical ill-posed problem. The paper discusses the possibility of regularizing the Lagrange principle (LP) in the specified constrained extremum problem. This regularization is a transformation of the LP that turns it into a universal tool of stable solving illposed problems in terms of generalized minimizing sequences (GMS) and preserves its “general structural arrangement” based on the constructions of the classical Lagrange function. The transformed LP “contains” the classical analogue as its limiting variant when the numbers of the GMS elements tend to infinity. Both non-iterative and iterative variants of the regularization of the LP are discussed. Each of them leads to stable generation of the GMS in the original constrained extremum problem from the extremals of the regular Lagrange functional taken at the values of the dual variable generated by the corresponding procedure for the regularization of the dual problem. In conclusion, the article discusses the relationship between the extremals of the Tikhonov and Lagrange functionals in the considered classical ill-posed problem.

A genetic programming learning approach to generate dispatching rules for flexible shop scheduling problems

This paper deals with a Genetic Programming (GP) approach for solving flexible shop scheduling problems. The adopted approach aims to generate priority rules in the form of an expression tree for dispatching jobs. Therefore, in a list-scheduling algorithm, the available jobs can be ranked using the tree-based priority rules generated using GP.These priority rules were tested on benchmark problem settings, such as those of Brandimarte and Lawrence, in a static and dynamic environment. The GP approaches were then applied to a special case based on the problem setting of an industrial partner. The goal of these approaches was to minimize the maximum completion time of all jobs, which is known as the makespan.To reach this goal, we considered job assignment and machine sequencing decisions simultaneously in a single-tree representation and compared this single tree with a multi-tree approach, where the terminal sets (job- and machine-related) were strictly separated. This resulted in two parallel GP populations; they were used to first decide which job to choose and then which machine it should be assigned to. Furthermore, for both tree approaches, we implemented an iterative variant that stores recorded information of past schedules to achieve further improvements. Computational experiments revealed a consistent advantage compared to the existing advanced priority rules from the literature with considerably increased performance under the presence of unrelated parallel machines and larger instances in general.

Towards Safe Human-Quadrotor Interaction: Mixed-Initiative Control via Real-Time NMPC

This article presents a novel algorithm for blending human inputs and automatic controller commands, guaranteeing safety in mixed-initiative interactions between humans and quadrotors. The algorithm is based on nonlinear model predictive control (NMPC) and involves using the state solution to assess whether safety- and/or task-related rules are met to mix control authority. The mixing is attained through the convex combination of human and actual robot costs and is driven by a continuous function that measures the rules' violation. To achieve real-time feasibility, we rely on an efficient real-time iteration (RTI) variant of a sequential quadratic programming (SQP) scheme to cast the mixed-initiative controller. We demonstrate the effectiveness of our algorithm through numerical simulations, where a second autonomous algorithm is used to emulate the behavior of pilots with different skill levels. Simulations show that our scheme provides suitable assistance to pilots, especially novices, in a workspace with obstacles while bolstering computational efficiency.

Position Paper: The Collapse Macro in Best-First Search Algorithms and an Iterative Variant of RBFS

This paper makes two pedagogical contributions. First, we describe two macrooperators for best-first search algorithms: the collapse macro where asubtree is deleted from memory and its best frontier value is stored in itsroot, and, the restore macro (the inverse of collapse) where thesubtree is restored to its previous structure. We show that many known searchalgorithms can be easily described by using these macros. The secondcontribution is an algorithm called Iterative Linear Best-first Search (ILBFS). ILBFS is equivalent to RBFS. While RBFS uses a recursive structure,ILBFS uses the regular structure of BFS with occasionally using the collapseand restore macros. ILBFS and RBFS are identical in the nodes that they visitand have identical properties. But, I believe that ILBFS is pedagogicallysimpler to describe and understand; it could at least serve as a pedagogicaltool for RBFS.

Benchmark of algorithms for multiple DNA sequence alignment across livestock species

Background: Due to the growing amount of biological data, it is often necessary to select the most optimal estimation method for DNA sequence alignment across livestock species. One of the most important benches of genomics is to modelling homology between considered DNA sequences. A multiple sequence alignment is a potent tool for molecular and evolutionary biology, and there are several programs and algorithms applicable for this purpose. The purpose of this paper was to study the most commonly used DNA alignment algorithms to select the optimal tool dedicated for short sequences.Methods: Four steps of bioinformatics pipelines were considered to benchmark the algorithms for multiple DNA sequence alignment across livestock species: 1) selection of reference genome sequences of ARS1.2 for cattle, EquCab3.0 for horse and vicPac2 for alpaca with a low E-value using TBLASTn 2) removing gaps for these sequences 3) alignment of obtained sequences using examined algorithms 4) matching the quality of aligned sequences with sequences of reference genomes by more software. The time of computation was archived for the whole analysis. The seven programs were utilized, each based on different alignment algorithms, namely: ClustalO, ClustalW, Kalign, MAFFT, MUSCLE, Probcons and T-Coffee.Results: The result obtained in this study showed that the fastest is progressive algorithms such as Kalign or MUSCLE-FAST. Moreover, the iterative algorithms like MAFFT and MUSCLE revealed a higher quality of the alignment. The T-Coffee and Probcons programs were computational cost-effective; simultaneously, they were generating a medium-quality calculation in a relatively long time. The best quality of alignment was shown by iterative variants of the MAFFT program; however, the speed of the calculations was relatively low. The fastest algorithm was Kalign, making alignment much faster than the competitors, but achieving average results in the quality of the alignment. The average speed ratio concerning the quality of the analyzed algorithms was obtained by the progressive version of MAFFT, NS1.Conclusions: We conclude that the results of this study can be used to re-alignment of variant primers in new livestock genome releases.

Disturbance rejection based on iterative learning control with extended state observer for a four-degree-of-freedom hybrid magnetic bearing system

Iterative learning control (ILC) is an iterative control strategy which calculates a new input according to the error in previous cycles. It is widely used in industries with repetitive operations. Since magnetic bearing systems can be considered as running in a repetitive task, the ILC could be applied. Hence, this paper proposes a modified iterative learning control (ILC) strategy for a four degree-of-freedom (DOF) hybrid magnetic bearing system to reject the disturbance based on an extended state observer (ESO). The feasibility of applying the ILC to the four-DOF magnetic bearing system is analyzed firstly. It is proved that the tracking error can converge by selecting suitable controller parameters. Secondly, to accurately obtain the uncertainties in the operation process, an ESO is designed. As for a repetitive rotation process, the iteration variant disturbance may have a certain influence on the performance of the system which is not usually considered. Therefore, the iteration variant disturbance is introduced and the effectiveness is derived. Finally, simulations and experiments are carried out to demonstrate the effectiveness of the proposed method. The classical proportion-integration-differentiation (PID) control and an existing proposed neural network inverse (NNI) control are implemented for comparison. The results show that the proposed strategy can achieve better reference tracking and disturbance suppression ability than PID and NNI control.

Iterative Suzuki-Miyaura Cross-coupling/Bromo-desilylation Reaction Sequences for the Assembly of Chemically Well-defined, Acyclic Oligopyrrole/Benzenoid Hybrids Embodying Mixed Modes of Connectivity.

Syntheses of a range of chemically well-defined oligopyrrole/benzenoid hybrids are described using tandem Suzuki-Miyaura cross-coupling/bromo-desilyation reaction sequences for linking borylated pyrroles, halogenated pyrroles and/or dibromobenzenes to one another. By such means, including iterative variants, a range of all α-linked, all β-linked oligopyrroles as well as certain combinations thereof have been assembled, some of them for the first time. The conductivities of iodine-treated thin films formed from certain such systems have been determined.

Do all roads lead to Rome? Understanding the role of initialization in iterative back-translation

Back-translation provides a simple yet effective approach to exploit monolingual corpora in Neural Machine Translation (NMT). Its iterative variant, where two opposite NMT models are jointly trained by alternately using a synthetic parallel corpus generated by the reverse model, plays a central role in unsupervised machine translation. In order to start producing sound translations and provide a meaningful training signal to each other, existing approaches rely on either a separate machine translation system to warm up the iterative procedure, or some form of pre-training to initialize the weights of the model. In this paper, we analyze the role that such initialization plays in iterative back-translation. Is the behavior of the final system heavily dependent on it? Or does iterative back-translation converge to a similar solution given any reasonable initialization? Through a series of empirical experiments over a diverse set of warmup systems, we show that, although the quality of the initial system does affect final performance, its effect is relatively small, as iterative back-translation has a strong tendency to convergence to a similar solution. As such, the margin of improvement left for the initialization method is narrow, suggesting that future research should focus more on improving the iterative mechanism itself.

Conditioning Multi-Gaussian Groundwater Flow Parameters to Transient Hydraulic Head and Flowrate Data With Iterative Ensemble Smoothers: A Synthetic Case Study

Over the last decade, data assimilation methods based on the ensemble Kalman filter (EnKF) have been particularly explored in various geoscience fields to solve inverse problems. Although this type of ensemble methods can handle high-dimensional systems, they assume that the errors coming from whether the observations or the numerical model are multivariate Gaussian. To handle existing nonlinearities between the observations and the variables to estimate, iterative methods have been proposed. In this paper, we investigate the feasibility of using the ensemble smoother and two iterative variants for the calibration of a synthetic 2D groundwater model inspired by a real nuclear storage problem in France. Using the same set of sparse and transient flow data, we compare the results of each method when employing them to condition an ensemble of multi-Gaussian groundwater flow parameter fields. In particular, we explore the benefit of transforming the state observations to improve the parameter identification performed by one of the two tested algorithms. Despite the favorable case of a multi-Gaussian parameter distribution considered, we show the importance of defining an ensemble size of at least 200 to obtain sufficiently accurate parameter and uncertainty estimates for the groundwater flow inverse problem considered.

A highly sensitive and specific workflow for detecting rare copy-number variants from exome sequencing data

BackgroundExome sequencing (ES) is a first-tier diagnostic test for many suspected Mendelian disorders. While it is routine to detect small sequence variants, it is not a standard practice in clinical settings to detect germline copy-number variants (CNVs) from ES data due to several reasons relating to performance. In this work, we comprehensively characterized one of the most sensitive ES-based CNV tools, ExomeDepth, against SNP array, a standard of care test in clinical settings to detect genome-wide CNVs.MethodsWe propose a modified ExomeDepth workflow by excluding exons with low mappability prior to variant calling to drastically reduce the false positives originating from the repetitive regions of the genome, and an iterative variant calling framework to assess the reproducibility. We used a cohort of 307 individuals with clinical ES data and clinical SNP array to estimate the sensitivity and false discovery rate of the CNV detection using exome sequencing. Further, we performed targeted testing of the STRC gene in 1972 individuals. To reduce the number of variants for downstream analysis, we performed a large-scale iterative variant calling process with random control cohorts to assess the reproducibility of the CNVs.ResultsThe modified workflow presented in this paper reduced the number of total variants identified by one third while retaining a higher sensitivity of 97% and resulted in an improved false discovery rate of 11.4% compared to the default ExomeDepth pipeline. The exclusion of exons with low mappability removes 4.5% of the exons, including a subset of exons (0.6%) in disease-associated genes which are intractable by short-read next-generation sequencing (NGS). Results from the reproducibility analysis showed that the clinically reported variants were reproducible 100% of the time and that the modified workflow can be used to rank variants from high to low confidence. Targeted testing of 30 CNVs identified in STRC, a challenging gene to ascertain by NGS, showed a 100% validation rate.ConclusionsIn summary, we introduced a modification to the default ExomeDepth workflow to reduce the false positives originating from the repetitive regions of the genome, created a large-scale iterative variant calling framework for reproducibility, and provided recommendations for implementation in clinical settings.

Iterative Decision Feedback Equalization Using Online Prediction

In this article, a new category of soft-input soft-output (SISO) minimum-mean square error (MMSE) finite-impulse response (FIR) decision feedback equalizers (DFEs) with iteration-wise static filters (i.e. iteration variant) is investigated. It has been recently shown that SISO MMSE DFE with dynamic filters (i.e. time-varying) reaches very attractive operating points for high-data rate applications, when compared to alternative turbo-equalizers of the same category, thanks to sequential estimation of data symbols [1]. However the dependence of filters on the feedback incurs high amount of latency and computational costs, hence SISO MMSE DFEs with static filters provide an attractive alternative for computational complexity-performance trade-off. However, the latter category of receivers faces a fundamental design issue on the estimation of the decision feedback reliability for filter computation. To address this issue, a novel approach to decision feedback reliability estimation through online prediction is proposed and applied for SISO FIR DFE with either a posteriori probability (APP) or expectation propagation (EP) based soft feedback. This novel method for filter computation is shown to improve detection performance compared to previously known alternative methods, and finite-length and asymptotic analysis show that DFE with static filters still remains well-suited for high-spectral efficiency applications.

Adaptive iterative learning control for unknown linear time-varying continuous systems

This paper presents a novel model reference adaptive iterative learning control (ILC) for unknown continuous-time linear time-varying systems. The unknown time-varying parameters of the system are neither required to vary slowly nor to have known bounds. The system is not required to be minimum-phase, stable, controllable or observable. The input of the system is determined by a differentiator-free control law. The used reference model is time-invariant and first order and thus choosing its parameters is easily possible, even though, the system under control is high order and time variant. Almost all of the components of the system initial condition can be iteration variant. By introducing a novel kind of Lyapunov function the convergence of the proposed adaptive ILC (AILC) and achieving asymptotic tracking are proved. Also, by rigorous mathematical analysis and with the help of some mathematical key techniques such as Bellman-Gronwall lemma, it is shown that all signals and quantities in the closed-loop system are bounded in the sense of at least one norm. Finally, the effectiveness of the proposed method is verified by two simulation examples.