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Uniqueness from discrete data in an inverse spectral problem for a pencil of ordinary differential operators

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES 2016年第3期94卷 793-813页

作者： Brown, Malcolm Marletta, Marco Symons, Freddy Cardiff Sch Comp Sci & Informat Queens Bldg5 Parade Cardiff CF24 3AA S Glam Wales Cardiff Sch Math 21-23 Senghennydd Rd Cardiff CF24 4AG S Glam Wales

We prove a pair of uniqueness theorems for an inverse problem for an ordinary differential operator pencil of second order. The uniqueness is achieved from a discrete set of data, namely, the values at the points -n2 nN) of (a physically appropriate generalization of) the Weyl-Titchmarsh m-function m() for the problem. As a corollary, we establish a uniqueness result for a physically motivated inverse problem inspired by Berry and Dennis (Boundary-condition-varying circle billiards and gratings: the Dirichlet singularity', J. Phys. A: Math. Theor. 41 (2008) 135203). To achieve these results, we prove a limit-circle analogue to the limit-point m-function interpolation result of Rybkin and Tuan (A new interpolation formula for the Titchmarsh-Weyl m-function', Proc. Amer. Math. Soc. 137 (2009) 4177-4185);however, our proof, using a Mittag-Leffler series representation of m(), involves a rather different method from theirs, circumventing the A-amplitude representation of Simon (A new approach to inverse spectral theory, I. Fundamental formalism', Ann. Math.(2) 150 (1999) 1029-1057). Uniqueness of the potential then follows by appeal to a Borg-Marenko argument.

关键词： THEOREMS (Mathematics) INVERSE problems (Differential equations) interpolation algorithms DIFFERENTIAL equations OPERATOR theory

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Fuzzy Modeling Vapor Pressure Deficit to Monitoring Microclimate in Greenhouses

Fuzzy Modeling Vapor Pressure Deficit to Monitoring Microcli...

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5th IFAC Conference on Sensing, Control and Automation Technologies for Agriculture (AGRICONTROL)

作者： Cesar Ramos-Fernandez, Julio Balmat, Jean-Francois Antonio Marquez-Vera, Marco Lafont, Frederic Pessel, Nathalie Steed Espinoza-Quesada, Eduardo Univ Politecn Pachuca Carr Pachuca Cd Sahagun Km 20 Zempoala 43830 Hgo Mexico Univ Toulon & Var Aix Marseille Univ CNRS ENSAMLSIS UMR 7296CS 60584 F-83041 Toulon 9 France

Instrumentation to measure microclimate in greet-amuses is a task to developing before starting the identification and control moisture and temperature in greenhouses, a variable which best describe the microclimate and helps prevent fungus and disease risks, is the vapor pressure deficit (VPD), it is measured indirectly by means of two inputs: temperature and humidity, by means the psychrometric chart, and another way is using interpolation models. This paper shows methodology to measure VPD, by using fuzzy modeling type Takagi-Sugeno (T-S). Fuzzy modeling is based on expert and human knowledge, additionally this is combined with mathematical techniques to identify parameters of the antecedents and consequents of IF-THEN fuzzy rules, each IF-THEN fuzzy rule defines a submodel or region of interpolation. In this work, expert knowledge is the information described in psychrometric chart. Modeling learning was performed using air temperature and relative humidity, a set of 8 fuzzy rules was proposed to interpolate the VPD. The results of the fuzzy model are illustrated using measurements of an experimental I greenhouse, and was contrasted with a model well known in the literature. The algorithm of fuzzy modelling VPD, was codified in two platform application real time: C to microcontroller and LabVIEW (TM) thus it is possible measuring the instantaneous VPD. (C) 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： fuzzy sensors interpolation algorithms microclimate monitoring

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Norm and interpolation based absolute stress evaluation in steel members using the Lcr wave

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NDT & E INTERNATIONAL 2023年 137卷

作者： Liu, Yongzhi Long, Zhili Gong, Yunxuan Ju, Jianzhong Wang, Yingzhu Li, Zuohua Liu, Menglong Harbin Inst Technol Shenzhen Dept Mech Engn & Automat Shenzhen 518055 Peoples R China Harbin Inst Technol Shenzhen Dept Civil & Environm Engn Shenzhen 518055 Peoples R China

The uniaxial absolute stress in steel members is a vital indicator for evaluating the performance of steel struc-tures. Non-destructive ultrasonic detection is widely applied in the absolute stress measurement of steel members with the advantages of easy implementation, no limits on materials and high precision. The acquisition algorithm of time-of-flight (TOF), the sampling rate of ultrasonic signal and the processing of outliers determine the ac-curacy of the stress measurement. In this study, we proposed a norm and interpolation based algorithm for absolute stress measurement using the longitudinal critically refracted (Lcr) waves, which improves the accuracy and velocity of the absolute stress measurement. Firstly, the norm was designed to obtain the TOF of the ul-trasonic signal. When only the Lcr wave arose in the ultrasonic signal, the two-norm similarity algorithm was found to be consistent with the cross-correlation-based algorithm and the corresponding theoretical expressions were derived. With the non-Lcr wave in the ultrasonic echo, the two-norm similarity algorithm has stronger anti-interference ability. Secondly, the pchipslopes, spline and linear interpolation algorithms were introduced via which the TOF of ultrasound with low sampling rate reaches the same accuracy as that of high sampling rate signal. Finally, a special class of outliers in TOF was explored, and a threshold based on the number of shift points and the stress feature was proposed to calibrate these outliers to normal values. Experiments demonstrate the proposed algorithm improves the accuracy and velocity of uniaxial absolute stress measurement in structural steel members.

关键词： Non-destructive ultrasonic detection Absolute stress Longitudinal critically refracted wave Norm interpolation algorithms

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Application of Polynomial interpolation for Iterative Complementation of the Missing Nodes in a Regular Network of Squares Used for the Construction of a Digital Terrain Model

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REMOTE SENSING 2024年第6期16卷 999页

作者： Gosciewski, Dariusz Gerus-Gosciewska, Malgorzata Szczepanska, Agnieszka Univ Warmia & Mazury Inst Geodesy & Civil Engn Fac Geoengn Dept Geodesy Oczapowskiego 1 PL-10719 Olsztyn Poland Univ Warmia & Mazury Inst Geodesy & Civil Engn Fac Geoengn Dept Geoinformat & Cartog Heweliusza 12 PL-10720 Olsztyn Poland Univ Warmia & Mazury Inst Spatial Management & Geog Fac Geoengn Dept Socioecon Geog Prawochenskiego 15 PL-10724 Olsztyn Poland

Due to the continuous increase in the volume of spatially located information, the current requirements imposed on the Spatial Information System (SIS) concern increasing data mining capabilities. Modern measurement systems, based on devices which enable the automatic recording of observation results on a mass scale (LiDAR-Light Detection and Ranging, MBES-Multi Beam Echo Sounder, etc.), allow for a very large volume of information on the surface to be measured and acquired in a relatively short time. One of the methods to reduce the volume of data enabling the generation of a model surface is to convert unevenly distributed measurement points into a regular network of squares (GRID). However, the generation of a complete grid is not always possible. In the measurement spectrum, there may be areas where measurement points have not been recorded. Measurement points can also be eliminated by either filtering the erroneously recorded data or eliminating the measured vegetation or the utilities in the area. To address these problems, the current article proposes a method for complementing the missing internal nodes in a regular network of squares using polynomial interpolation algorithms. Moreover, the paper demonstrates the possibilities of using the presented method for adding additional points between the already existing nodes of the network of squares. The application of the methodology presented in this article enables the effective elimination of (or a reduction in) the gaps in the GRID structure, which, in turn, allows such a network of squares to be used to generate a more accurate Digital Terrain Model.

关键词： LiDAR regular network of squares digital terrain model surface modelling interpolation algorithms

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Nudelman interpolation, Parametrizations of Lossless Functions and Balanced Realizations

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IFAC Proceedings Volumes 2004年第21期37卷 345-350页

作者： Jean-Paul Marmorat Martine Olivi CMA BP 93 06902 Sophia-Anipolis Cedex FRANCE phone: 33 4 92 38 19 56 fax: 33 4 92 38 79 98 INRIA BP 93 06902 Sophia-Antipolis Cedex FRANCE phone: 33 4 92 38 78 77 fax: 33 4 92 38 78 58

We investigate the parametrization issue for discrete-time stable all-pass multivariable systems by means of a Schur algorithm involving a Nudel-man interpolation condition. A recursive construction of balanced realizations is associated with it, that possesses a very good numerical behavior. Several atlases of charts or families of local parametrizations are presented and for each atlas a chart selection strategy is proposed. These parametrizations allow for solving optimization problems within the fields of system identification and optimal control.

关键词： Parametrization Inner matrices interpolation algorithms Scattering parameters Differential geometric methods Discrete-time systems Multivariables systems

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Assessment of Similarity of a Set of Impact Response Time Histories

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SAE INTERNATIONAL JOURNAL OF TRANSPORTATION SAFETY 2015年第1期3卷 28-38页

作者： Shi, Yibing Nusholtz, Guy FCA US LLC Auburn Hills MI 48326 USA

Two methods of assessing the similarity of a set of impact test signals have been proposed and used in the literature, which are cumulative variance-based and cross correlation- based. In this study, a normalized formulation unites these two approaches by establishing a relationship between the normalized cumulative variance metric (v), an overall similarity metric, and the normalized magnitude similarity metric (m) and shape similarity metric (s): v=1 - m . s. Each of these ranges between 0 and 1 (for the practical case of signals acquired with the same polarity), and they are independent of the physical unit of measurement. Under generally satisfied conditions, the magnitude similarity m is independent of the relative time shifts among the signals in the set;while the shape similarity s is a function of these. An optimal alignment is defined as the relative shifts corresponding to the minimum of the cumulative variance metric, or equivalently, to the maximum of the shape similarity metric. This system therefore quantifies the similarity of a given set of signals with an "as given" relative time alignment with the following: v = 1- m(p + s(a)), i.e., its overall similarity is partitioned into the shift-invariant normalized magnitude metric m, and the inherent (optimally aligned) normalized shape metric s(a), and a normalized phase metric p which reflects the alignment. An algorithm is provided for automatic search of the optimal shifts for a given set of signals using the cumulative variance as the objective function. The shifts are treated as real numbers instead of integers so that standard continuous variable optimization functions can be used to treat the discrete signals. This is facilitated by an interpolation procedure for shifting a signal with a real-valued time shift. Numerical examples are presented to demonstrate the general effectiveness of the algorithm, and also specific limitations on consistent convergence to the global optimal. Practical measures

关键词： IMPACT response algorithms CRASH testing of automobiles interpolation algorithms INTEGERS MATHEMATICAL optimization

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A New Approach to General interpolation Formulae for Bivariate interpolation

ABSTRACT AND APPLIED ANALYSIS

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ABSTRACT AND APPLIED ANALYSIS 2014年第SI10期000卷 1-11页

作者： Zou, Le Tang, Shuo Hefei Univ Key Lab Network & Intelligent Informat Proc Hefei 230601 Peoples R China Hefei Univ Technol Dept Math Hefei 230039 Peoples R China

General interpolation formulae for bivariate interpolation are established by introducing multiple parameters, which are extensions and improvements of those studied by Tan and Fang. The general interpolation formulae include general interpolation formulae of symmetric branched continued fraction, general interpolation formulae of univariate and bivariate interpolation, univariate block based blending rational interpolation, bivariate block based blending rational interpolation and their dual schemes, and some interpolation form studied by many scholars in recent years. We discuss the interpolation theorem, algorithms, dual interpolation, and special cases and give many kinds of interpolation scheme. Numerical examples are given to show the effectiveness of the method.

关键词： interpolation algorithms BIVARIATE analysis THEOREMS (Mathematics) SYMMETRIC functions POLYNOMIALS

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Tomographic Images Generated from Measurements in Standing Trees Using Ultrasound and Postprocessed Images: Methodological Proposals for Cutting Velocity, interpolation Algorithm and Confusion Matrix Metrics Focusing on Image Quality

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FORESTS 2022年第11期13卷 1935页

作者： Palma, Stella S. S. A. dos Reis, Mariana N. Goncalves, Raquel Univ Estadual Campinas Unicamp Sch Agr Engn FEAGRI BR-13083875 Campinas Brazil

Tomographic images generated by wave propagation are important in tree inspections and can be performed in an economically more accessible way using conventional equipment and postprocessed images, but improvements are necessary to increase image quality, giving greater reliability to the results. The objective of this paper was to present a methodological proposal for the definition of parameters related to image quality produced with tomography using ultrasound equipment and postprocessed images. As a case study, the methodology was applied to five trees of the species Cenostigma pluviosum DC. Gagnon & GP Lewis (Sibipiruna). A total of 1512 tomographic images were constructed from five trees to evaluate the cutting velocity, the interpolation algorithms and the filter application. The photographs of the discs were used to evaluate the theoretical wave propagation routes in the measurement grid and to compare the tomographic images using confusion matrix metrics. The application of the methodology proposed in this species allowed us to conclude that the most appropriate velocity range for cavities inference was up to 40% Vmax and for cavities supplemented with biodeterioration up to 45% Vmax;the best interpolator was the Ellipses method with compensation, with the use of a filter;and the accuracy was the most appropriate metric for evaluating image quality.

关键词： confusion matrix interpolation algorithms tree inspection image filters

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An analysis of processing bulk data with regard to the efficiency of the creation of the GRID structure used in the generation of the digital terrain mode 9

An analysis of processing bulk data with regard to the effic...

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9th International Conference on Environmental Engineering (ICEE)

作者： Gosciewski, Dariusz Univ Warmia & Mazury Fac Geodesy & Land Management Inst Geodesy PL-10957 Olsztyn Poland

ISBN: (纸本)9786094576409

Current survey systems (LiDAR, multibeam echo sounders) allow the automated obtaining of a large amount of surface object measurements in a relatively short time. The large amount of information, survey specificity and the character of the created data sets, as a rule, do not allow them to be used directly for the generation of the digital terrain model (DTM) in spatial information systems (SIS, GIS). The handling of measurement results of this type consists in optimization of set sizes and adaptation of their structure to both the user's requirements and technical processing capabilities. The specificity and universal character of the DTM information layer are an inducement to place particular emphasis on data recording organization and keeping their amount to a minimum. At the same time, it is intended to maintain maximum space description fidelity and its dynamic transformation. Efficient generation of information stored in digital map databases often requires data structure analysis and rationalization of the whole process with regard to processing speed. This paper shows an example of optimizing the efficiency of handling bulk measurement results for DTM creation using the GRID structure. Measurement sets and their processing sequence are also analysed. Methods for selecting the location of measurement points and efficient interpolation algorithms allowing an accurate GRID structure to be generated in a relatively short time are then presented.

关键词： GIS digital terrain model regular GRID structure interpolation algorithms large observation sets

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Simple Interpolating Control

Simple Interpolating Control

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Joint Meeting of the 2nd IFAC Workshop on Linear Parameter Varying Systems (LPVS) / 9th IFAC Symposium on Robust Control Design (ROCOND)

作者： Mercader, Pedro Rubin, Daniel Hoai-Nam Nguyen Bemporad, Alberto Gutman, Per-Olof Technion Israel Inst Technol Fac Civil & Environm Engn IL-3200003 Haifa Israel Technion Israel Inst Technol TASP IL-3200003 Haifa Israel IFP Energies Nouvelles Control Signal & Syst Dept Lyon France IMT Sch Adv Studies Lucca Lucca Italy

We present a new simple approach to extend the admissible region of a saturated control law for discrete-time linear systems under state and input constraints. The approach is based on the interpolation of a given, performance driven, control law and a low-gain controller. The latter is designed such that its admissible set has maximum volume. The interpolation does not require on-line numerical optimization, and an analytical formula for the controller is given. Several numerical examples are presented to illustrate the control technique. (C) 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： Constrained control uncertain linear systems interpolation algorithms predictive control state feedback robust stability

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