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Journal articles on the topic 'Norm parameter'

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Published: 30 May 2022

Last updated: 31 May 2022

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1

Feng, Qingxiang, Qi Zhu, Lin-Lin Tang, and Jeng-Shyang Pan. "L1-norm plus L2-norm sparse parameter for image recognition." Optik 126, no. 23 (December 2015): 4078–82. http://dx.doi.org/10.1016/j.ijleo.2015.08.172.

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2

Rodomanov, Anton, and Yurii Nesterov. "Smoothness Parameter of Power of Euclidean Norm." Journal of Optimization Theory and Applications 185, no. 2 (March 27, 2020): 303–26. http://dx.doi.org/10.1007/s10957-020-01653-6.

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3

Brusdal, Kari, and Trond Mannseth. "Basis Norm Rescaling for Nonlinear Parameter Estimation." SIAM Journal on Scientific Computing 21, no. 6 (January 2000): 2114–25. http://dx.doi.org/10.1137/s1064827598341645.

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4

Ollinaho, P., H. Järvinen, P. Bauer, M. Laine, P. Bechtold, J. Susiluoto, and H. Haario. "Total energy norm in NWP closure parameter optimization." Geoscientific Model Development Discussions 6, no. 4 (December 17, 2013): 6717–40. http://dx.doi.org/10.5194/gmdd-6-6717-2013.

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Abstract. We explore the use of total energy norm in improving numerical weather prediction (NWP) model forecast skill. The Ensemble Prediction and Parameter Estimation System (EPPES) is utilized to estimate ECHAM5 atmospheric GCM closure parameters related to clouds and precipitation. The target criterion in the optimization is the total energy norm of three-day forecast error with respect to the ECMWF operational analyses. The results are summarized as follows: (i) forecast error growth in terms of energy norm is slower in the optimized than in the default model up to day ten forecasts (and beyond), (ii) headline forecast skill scores are improved in the training sample as well as in independent samples, (iii) the decrease of the forecast error energy norm at day three is mainly because of smaller kinetic energy error in the tropics, and (iv) this impact is spread into mid-latitudes at longer ranges and appears as smaller forecast error of potential energy. The interpretation of these results is that the parameter optimization has reduced the model error so that the forecasts remain longer in the vicinity of the analyzed state.

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5

Knauer, Christian, Stefan König, and Daniel Werner. "Fixed-Parameter Complexity and Approximability of Norm Maximization." Discrete & Computational Geometry 53, no. 2 (February 21, 2015): 276–95. http://dx.doi.org/10.1007/s00454-015-9667-0.

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6

Štecha, Jan, Milan Cepák, Jaroslav Pekař, and Daniel Pachner. "SYSTEM PARAMETER ESTIMATION USING TOTAL P-NORM MINIMIZATION." IFAC Proceedings Volumes 38, no. 1 (2005): 1143–48. http://dx.doi.org/10.3182/20050703-6-cz-1902.00192.

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7

Krawczyk-Stańdo, Dorota, and Marek Rudnicki. "Regularization Parameter Selection in Discrete Ill-Posed Problems — The Use of the U-Curve." International Journal of Applied Mathematics and Computer Science 17, no. 2 (June 1, 2007): 157–64. http://dx.doi.org/10.2478/v10006-007-0014-3.

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Regularization Parameter Selection in Discrete Ill-Posed Problems — The Use of the U-CurveTo obtain smooth solutions to ill-posed problems, the standard Tikhonov regularization method is most often used. For the practical choice of the regularization parameter α we can then employ the well-known L-curve criterion, based on the L-curve which is a plot of the norm of the regularized solution versus the norm of the corresponding residual for all valid regularization parameters. This paper proposes a new criterion for choosing the regularization parameter α, based on the so-called U-curve. A comparison of the two methods made on numerical examples is additionally included.

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8

Roisah, Kholis. "Understanding Trade-Related Aspects of Intellectual Property Rights Agreement: From Hard and Soft Law Perspective." Hasanuddin Law Review 3, no. 3 (December 26, 2017): 277. http://dx.doi.org/10.20956/halrev.v3i3.1153.

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Trade-Related Aspects of Intellectual Property Rights (TRIPs) Agree-ment interesting to be understood in the perspective of hard law and soft law. TRIPs Agreement justified as hard or soft law by identifying the norms in the TRIPs agreement. Parameter obligation of TRIPs agreement visible implementation and enforcement of agreement norm with full compliance to fourth of the IPR Convention for the State parties is an indicator of unconditional obligation. Parameters precision TRIPS agreement showed formulation of general obligation setting up the implementation of treaty obligations is regulated in detail and the use of ”shall” term in any norm, describe the imperative norm character and shown indicator as substantial limited of interpretation with the parties might not interpreted. Parameter delegation looked explicitly provision of implementation and enforcement agreement that put an obligation on national authorities of state parties through domestic law and its courts. Parameter obligation, precision as well as delegation showed as high indicator that the TRIPs agreement characterized as hard law.

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9

KUBO, Tomohiro. "Lumped-Parameter-Part Control with H^|^infin;-Norm Bound." Transactions of the Society of Instrument and Control Engineers 34, no. 11 (1998): 1744–46. http://dx.doi.org/10.9746/sicetr1965.34.1744.

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10

Hwang, Chyi, Jyh-jia Chen, and Shih-lian Cheng. "H ∞ -Norm Computation for Linear System with Parameter Perturbations." IFAC Proceedings Volumes 30, no. 16 (June 1997): 261–66. http://dx.doi.org/10.1016/s1474-6670(17)42616-4.

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11

Zhang, Hao, and Yingling Peng. "Lp-norm based minimisation algorithm for signal parameter estimation." Electronics Letters 35, no. 20 (1999): 1704. http://dx.doi.org/10.1049/el:19991080.

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12

Shi, Yi Ran, Yan Tao Tian, Lan Xiang Zhu, and Li Fei Deng. "The MUSIC Minimum Norm Method for Linear Polarized Array Parameter Estimation." Applied Mechanics and Materials 411-414 (September 2013): 1559–63. http://dx.doi.org/10.4028/www.scientific.net/amm.411-414.1559.

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This paper used signal Cyclostationarity and MUSIC minimum norm method to estimate DOA and polarization parameters with linear polarization array. Cyclostationarity statistics have the advantage of limiting different frequencies of signal cycle stationary colored noise and inhibit both the minimum norm loop correlation function and estimation error. This paper also verifies the effectiveness of the method through simulation experiments.

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13

GULIN, A., and V. MOROZOVA. "Stability of the Two-parameter Set of Nonlocal Difference Schemes." Computational Methods in Applied Mathematics 9, no. 1 (2009): 79–99. http://dx.doi.org/10.2478/cmam-2009-0005.

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Abstract The paper deals with difference schemes for the heat-conduction equa- tion with nonlocal boundary conditions containing two real parameters. Such schemes have been investigated for some special parameter values, but the general case was not considered previously. The eigenvalue problem arises as a result of variable division and is solved here explicitly. The so-called reality domains were selected on the plane for which all eigenvalues and eigenfunctions are real. It was demon- strated that the difference schemes in question are symmetrizable in reality domains, that is their transition operators are similar to self-adjoint ones. The necessary and sufficient stability conditions for difference schemes under consideration are obtained with respect to the initial data in the specially constructed norm. The equivalence of the above-mentioned norm to the grid L2-norm has been proved.

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14

Ollinaho, P., H. Järvinen, P. Bauer, M. Laine, P. Bechtold, J. Susiluoto, and H. Haario. "Optimization of NWP model closure parameters using total energy norm of forecast error as a target." Geoscientific Model Development 7, no. 5 (September 2, 2014): 1889–900. http://dx.doi.org/10.5194/gmd-7-1889-2014.

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Abstract. We explore the use of dry total energy norm in improving numerical weather prediction (NWP) model forecast skill. The Ensemble Prediction and Parameter Estimation System (EPPES) is utilized to estimate ECHAM5 atmospheric GCM (global circulation models) closure parameters related to clouds and precipitation. The target criterion in the optimization is the dry total energy norm of 3-day forecast error with respect to the ECMWF (European Centre for Medium-Range Weather Forecasts) operational analyses. The results are summarized as follows: (i) forecast error growth in terms of energy norm is slower in the optimized than in the default model up to day 10 forecasts (and beyond), (ii) headline forecast skill scores are improved in the training sample as well as in independent samples, (iii) the decrease of the forecast error energy norm at day three is mainly because of smaller kinetic energy error in the tropics, and (iv) this impact is spread into midlatitudes at longer ranges and appears as a smaller forecast error of potential energy. The interpretation of these results is that the parameter optimization has reduced the model error so that the forecasts remain longer in the vicinity of the analyzed state.

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15

Zhiyong Geng and Lin Huang. "H/sub 2/ norm checking for systems with parameter uncertainties." IEEE Transactions on Automatic Control 45, no. 8 (2000): 1519–22. http://dx.doi.org/10.1109/9.871763.

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16

Wang, Guodong. "Multiplicative Noise Removal Using TVL1 Norm and Adaptive Penalty Parameter." Journal of Information and Computational Science 11, no. 11 (July 20, 2014): 3993–4001. http://dx.doi.org/10.12733/jics20104240.

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17

Karimi, Hamid Reza. "Robust stabilization withH∞performance for a class of linear parameter-dependent systems." Mathematical Problems in Engineering 2006 (2006): 1–15. http://dx.doi.org/10.1155/mpe/2006/59867.

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We focus on the issue of robust stabilization withH∞performance for a class of linear time-invariant parameter-dependent systems under norm-bounded nonlinear uncertainties. By combining the idea of polynomially parameter-dependent quadratic Lyapunov functions and linear matrix inequalities formulations, some parameter-independent conditions with high precision are given to guarantee robust asymptotic stability and robust disturbance attenuation of the linear time-invariant parameter-dependent system in the presence of norm-bounded nonlinear uncertainties. The parameter-dependent state-feedback control is designed based on the Hamilton-Jacobi-Isaac (HJI) method. The applicability of the proposed design method is illustrated in a simple example.

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18

Xenophontos, Christos. "A Parameter Robust Finite Element Method for Fourth Order Singularly Perturbed Problems." Computational Methods in Applied Mathematics 17, no. 2 (April 1, 2017): 337–49. http://dx.doi.org/10.1515/cmam-2016-0045.

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AbstractWe consider fourth order singularly perturbed problems in one-dimension and the approximation of their solution by the h version of the finite element method. In particular, we use piecewise Hermite polynomials of degree ${p\geq 3}$ defined on an exponentially graded mesh. We show that the method converges uniformly, with respect to the singular perturbation parameter, at the optimal rate when the error is measured in both the energy norm and a stronger, ‘balanced’ norm. Finally, we illustrate our theoretical findings through numerical computations, including a comparison with another scheme from the literature.

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19

Zhu, Wei-Bo, Bin Shuai, and Shi-Hang Zhang. "The Linguistic Interval-Valued Intuitionistic Fuzzy Aggregation Operators Based on Extended Hamacher T-Norm and S-Norm and Their Application." Symmetry 12, no. 4 (April 23, 2020): 668. http://dx.doi.org/10.3390/sym12040668.

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Linguistic interval-valued intuitionistic fuzzy sets, as an extension of interval-valued intuitionistic fuzzy sets, have strong practical value in the management of complex uncertainty system with qualitative evaluation information. This study focuses on the development of several linguistic interval-valued intuitionistic fuzzy Hamacher (LIVIFH) aggregation operators based on the extended Hamacher t-norm and s-norm. First, the extended Hamacher t-norm and s-norm, which are applicable to linguistic information environment, are applied to define the linguistic interval-valued intuitionistic fuzzy Hamacher operational laws. Second, based on the proposed operational laws, this study defines the linguistic interval-valued intuitionistic fuzzy Hamacher weighted average (LIVIFHWA) operator and the linguistic interval-valued intuitionistic fuzzy Hamacher weighted geometric (LIVIFHWG) operator, and then investigates their properties. Furthermore, the degeneracy and monotonicity of the proposed operators with respect to the adjustable parameter are explored. Finally, a multiple attribute group decision-making (MAGDM) approach is developed based on the proposed LIVIFH aggregation operators, and then this approach is applied to a supplier selection problem. Parameter analysis indicates that the adjustable parameter in the proposed LIVIFH aggregation operators could reflect the attitudes of decision makers. The LIVIFHWA operator would be more appropriate to optimistic decision makers, and the LIVIFHWG operator to pessimistic decision makers. In addition, as the adjustable parameter increasing, both attitudes tend to be neutral. The proposed method is also compared with two other approaches to show its feasibility and efficiency.

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20

Wang, Lingqian, Hui Zhou, Yufeng Wang, Bo Yu, Yuanpeng Zhang, Wenling Liu, and Yangkang Chen. "Three-parameter prestack seismic inversion based on L1-2 minimization." GEOPHYSICS 84, no. 5 (September 1, 2019): R753—R766. http://dx.doi.org/10.1190/geo2018-0730.1.

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Prestack inversion has become a common approach in reservoir prediction. At present, the critical issue in the application of seismic inversion is the estimation of elastic parameters in the thin layers and weak reflectors. To improve the resolution and the accuracy of the inversion results, we introduced the difference of [Formula: see text] and [Formula: see text] norms as a nearly unbiased approximation of the sparsity of a vector, denoted as the [Formula: see text] norm, to the prestack inversion. The nonconvex penalty function of the [Formula: see text] norm can be decomposed into two convex subproblems via the difference of convex algorithm, and each subproblem can be solved efficiently by the alternating direction method of multipliers. Compared with the [Formula: see text] norm regularization, the [Formula: see text] minimization can reconstruct reflectivities more accurately. In addition, the [Formula: see text]-[Formula: see text] predictive filtering was introduced to guarantee the lateral continuity of the location and the amplitude of the reflectivity series. The generalized linear inversion and [Formula: see text]-[Formula: see text] predictive filtering are combined for stable elastic impedance inversion results, and three parameters of P-wave velocity, S-wave velocity, and density can be inverted with the Bayesian linearized amplitude variation with offset inversion. The inversion results of synthetic and real seismic data demonstrate that the proposed method can effectively improve the resolution and accuracy of the inversion results.

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21

Turk, D., J. Gillis, G. Pipeleers, and J. Swevers. "Identification of linear parameter-varying systems: A reweightedℓ2,1-norm regularization approach." Mechanical Systems and Signal Processing 100 (February 2018): 729–42. http://dx.doi.org/10.1016/j.ymssp.2017.07.054.

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22

Kleffe, Jürgen, and Ragnar Norberg. "Minimum Norm Estimation Under Parameter Constraints with an Application to Insurance." Statistics 31, no. 3 (January 1998): 215–34. http://dx.doi.org/10.1080/02331889808802637.

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23

Phoenix, Austin A., Dustin Bales, Rodrigo Sarlo, and Pablo Tarazaga. "Improved model correlation through optimal parameter ranking using model reduction algorithms: Augmenting engineering judgment." Journal of Vibration and Control 24, no. 20 (October 9, 2017): 4716–39. http://dx.doi.org/10.1177/1077546317733906.

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As the complexity and scales of dynamic models increase, novel and efficient model correlation methodologies are vital to the development of accurate models. Classically, to correlate a Finite Element Model (FEM) such that it matches a dynamic test, an experienced engineer chooses a small subset of input parameters that are surmised to be crucial, sensitive and/or possibly erroneous. The operator will then use engineering judgment, or a model updating technique to update the selected subset of parameters until the error between the FEM and the test article is reduced to within a set bound. To reduce the intricacy and difficulty of model correlation, a methodology is proposed to provide a quantitative parameter importance ranking using a model reduction algorithm applied to a parameter sensitivity analysis. Four model reduction algorithms are studied in this effort, the Discrete Empirical Interpolation Method (SVD-DEIM), Q-DEIM, Projection Coefficient and finally Weighted Projection Coefficient. These model reduction methods identify and rank critical parameters, enabling the selection of a minimum set of critical correlation parameters. This reduced set of parameters results in reduced computational resources and engineering effort required to generate a correlated model. The insight gained using these methods is essential in developing an optimal, reduced parameter set that provides high correlation capability with minimal iterative costs. To evaluate the proposed parameter selection methodology, a representative set of academic and industry experts provided their engineering judgment for comparison with the methodology presented. A comprehensive investigation of the robustness of this methodology is performed on a simple cantilever beam for demonstration. The scale of the model has expressly been chosen to allow for all potential ranking variations to be evaluated so that these ranking methods can be understood relative to the true optimal ranking. The ranking robustness to incorrect engineering judgment, resulting in uncertainty in the assumed size of the design space and, therefore, the error bounds, is investigated. The methodology presented identifies the most useful parameters for correlation, enabling a straightforward and computationally efficient model correlation approach as compared with other methods. To quantify the ranking quality, a metric, the Correlation Norm Error, is developed. For the problem discussed, blind random assessments result in a Correlation Norm Error of 413.3. Engineering judgment has been shown to improve upon blind random assessments, reducing the Correlation Norm Error to 334.3. The best performing model reduction method, Q-DEIM using 10 FEM runs as the input, was able to identify the optimal ranking correctly, reducing the Correlation Norm Error to zero.

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24

Fang, Chen, Jiang Hong Shi, Kun Yu Li, and Zheng Wang. "State Feedback Robust H_∞Control for Generalized Discrete System and Simulation." Applied Mechanics and Materials 467 (December 2013): 621–26. http://dx.doi.org/10.4028/www.scientific.net/amm.467.621.

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For a class of uncertain generalized discrete linear system with norm-bounded parameter uncertainties, the state feedback robust control problem is studied. One sufficient condition for the solvability of the problem and the state feedback robust controller are obtained in terms of linear matrix inequalities. The designed controller guarantees that the closed-loop systems is regular, causal, stable and satisfies a prescribed norm bounded constraint for all admissible uncertain parameters under some conditions. The result of the normal discrete system can be regarded as a particular form of our conclusion. A simulation example is given to demonstrate the effectiveness of the proposed method.

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25

Shi, Long, and Haiquan Zhao. "$$L_{1}$$ L 1 -norm constrained normalized subband adaptive filter algorithm with variable norm-bound parameter and improved version." Signal, Image and Video Processing 11, no. 5 (November 30, 2016): 865–71. http://dx.doi.org/10.1007/s11760-016-1033-z.

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26

Schmid, H., M. P. Nash, A. A. Young, O. Röhrle, and P. J. Hunter. "A Computationally Efficient Optimization Kernel for Material Parameter Estimation Procedures." Journal of Biomechanical Engineering 129, no. 2 (September 21, 2006): 279–83. http://dx.doi.org/10.1115/1.2540860.

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Estimating material parameters is an important part in the study of soft tissue mechanics. Computational time can easily run to days, especially when all available experimental data are taken into account. The material parameter estimation procedure is examplified on a set of homogeneous simple shear experiments to estimate the orthotropic constitutive parameters of myocardium. The modification consists of changing the traditional least-squares approach to a weighted least-squares. This objective function resembles a L2-norm type integral which is approximated using Gaussian quadrature. This reduces the computational time of the material parameter estimation by two orders of magnitude.

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27

Patanavijit, Vorapoj. "Comparative Experimental Exploration of Robust Norm Functions for Iterative Super Resolution Reconstructions under Noise Surrounding." ECTI Transactions on Electrical Engineering, Electronics, and Communications 13, no. 2 (July 1, 2015): 83–98. http://dx.doi.org/10.37936/ecti-eec.2015132.171036.

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In DIP (Digital Image Processing) research society, the multi-frame SRR (Super Resolution Reconstruction) algorithm has grown to be the momentous theme in the last ten years because of its cost effectiveness and its superior spectacle. Consequently, for a multi-frame SRR algorithm which is commonly comprised of a Bayesian ML (Maximum Likelihood) approach and a regularization technique into the unify SRR framework, numerous robust norm functions (which have both redescending and non-redescending influence functions) have been commonly comprised in the unify SRR framework for increasingly against noise or outlier. First, this paper presents the mathematical model of several iterative SRR based on Bayesian ML (Maximum Likelihood) approach and a regularization technique. Three groups of robust norm functions (a zero-redescending influence function (Tukey’s Biweight, Andrew’s Sine and Hampel), a nonzero-redescending influence function (Lorentzian, Leclerc, Geman&McClure, Myriad and Meridian) and a non-redescending influence function (Huber)) are mathematically incorporated into the SRR framework. The close form solutions of the SRR framework based on these robust norm functions have been concluded. Later, the experimental section utilizes two standard images of Lena and Susie (40th) for pilot studies and fraudulent noise patterns of noiseless, AWGN, Poisson, Salt&Pepper, and Speckle of several magnitudes are used to contaminate these two standard images. In order to acquire the maximum PSNR, the comparative experimental exploration has been done by comprehensively tailoring all experimental parameters such as step-size, regularization parameter, norm constant parameter.

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Liu, Yang, Gongliu Yang, Qingzhong Cai, and Lifen Wang. "A New Norm-Observed Calibration Method Based on Improved Differential Evolution Algorithm for SINS." Mathematical Problems in Engineering 2021 (January 29, 2021): 1–14. http://dx.doi.org/10.1155/2021/6684119.

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It is vital for a strapdown inertial navigation system (SINS) to be calibrated before normal use. In this paper, a new kind of norm-observed calibration method is proposed. Considering that the norm of the output of accelerometers and gyroscopes can be exactly the norm of local acceleration of gravity and Earth rotation angular velocity, respectively, optimization function about all-parameter calibration and the corresponding 24-position calibration path is established. Differential evolutionary algorithm (DE) is supposed to be the best option in parameter identification due to its strong search and fast convergence abilities. However, the high-dimensional individual vector from calibration error equations restrains the algorithm’s optimum speed and accuracy. To overcome this drawback, improved DE (IDE) optimization is specially designed: First, current “DE/rand/1” and “DE/current-to-best/1” mutation strategies are combined as one with complementary advantages and overall balance during the whole optimization process. Next, with the increase of the evolutionary generation, the mutation factor can adjust itself according to the convergence situation. Multiple identification tests prove that our IDE optimization has rapid convergence and high repeatability. Besides, certain motivation of external angular velocity is added to the gyroscope calibration, and a series of dynamic observation paths is formed, further improving the optimization accuracy. The final static navigation experiment shows that SINS with calibration parameters solved by IDE has better performance over other identification methods, which further explains that our novel method is more accurate and reliable in parameter identification.

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29

Dai, Zhifeng. "A Closer Look at the Minimum-Variance Portfolio Optimization Model." Mathematical Problems in Engineering 2019 (August 26, 2019): 1–8. http://dx.doi.org/10.1155/2019/1452762.

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Recently, by imposing the regularization term to objective function or additional norm constraint to portfolio weights, a number of alternative portfolio strategies have been proposed to improve the empirical performance of the minimum-variance portfolio. In this paper, we firstly examine the relation between the weight norm-constrained method and the objective function regularization method in minimum-variance problems by analyzing the Karush–Kuhn–Tucker conditions of their Lagrangian functions. We give the range of parameters for the two models and the corresponding relationship of parameters. Given the range and manner of parameter selection, it will help researchers and practitioners better understand and apply the relevant portfolio models. We apply these models to construct optimal portfolios and test the proposed propositions by employing real market data.

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30

Yang, Ai-Li. "Scaled norm minimization method for computing the parameters of the HSS and the two-parameter HSS preconditioners." Numerical Linear Algebra with Applications 25, no. 4 (March 14, 2018): e2169. http://dx.doi.org/10.1002/nla.2169.

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31

Guo, Jiangfeng, Ranhong Xie, Youlong Zou, Guowen Jin, Lun Gao, and Chenyu Xu. "A new method for NMR data inversion based on double-parameter regularization." GEOPHYSICS 83, no. 5 (September 1, 2018): JM39—JM49. http://dx.doi.org/10.1190/geo2017-0394.1.

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Nuclear magnetic resonance (NMR) technology plays a significant role in petroleum exploration. NMR data can be processed using inversion methods to reflect the relaxation information of all the components. We have developed a new double-parameter regularization (DPR) method for the inversion of NMR data, whose regularization terms consist of Tikhonov regularization and maximum entropy regularization. The objective function for the DPR method was solved using the Levenberg-Marquardt method, the proportional coefficient of the regularization parameter was obtained using an iteration procedure, and the optimum regularization parameter of the DPR method was selected using an S-curve. The relationship between the optimum regularization parameter and the signal-to-noise ratio (S/N) of the data was evaluated. Moreover, we compared the results of the NMR inversion obtained from the norm smooth method, the maximum entropy method, and the DPR method for simulated data. We evaluated how the proportional coefficient of the regularization parameter affected the inverted [Formula: see text] distributions and processed field NMR log data for a tight sandstone reservoir using the DPR method. The results indicated that the optimum regularization parameter for the DPR method gradually decreases with increasing data S/N. The accuracy is higher for the DPR method than for the norm smooth method and the maximum entropy method under low-S/N conditions. It is of great importance to select the proportional coefficient for the DPR method. The inverted [Formula: see text] distributions are similar for the DPR method and the norm smooth method when the proportional coefficient is small, and this is similar for the DPR method and the maximum entropy method when the proportional coefficient is large.

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32

BESALÚ, MIREIA, and DAVID NUALART. "ESTIMATES FOR THE SOLUTION TO STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY A FRACTIONAL BROWNIAN MOTION WITH HURST PARAMETER H ∈ (⅓, ½)." Stochastics and Dynamics 11, no. 02n03 (September 2011): 243–63. http://dx.doi.org/10.1142/s0219493711003267.

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In this paper we establish precise estimates for the supremum norm for the solution of a dynamical system driven by a Hölder continuous function of order between ⅓ and ½ using the techniques of fractional calculus. As an application we deduce the existence of moments for the solutions to stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H ∈(⅓, ½) and we obtain an estimate for the supremum norm of the Malliavin derivative.

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33

Bai, Yuanqiang, and Karolos M. Grigoriadis. "Damping parameter design optimization in structural systems using an explicit norm bound." Journal of Sound and Vibration 319, no. 3-5 (January 2009): 795–806. http://dx.doi.org/10.1016/j.jsv.2008.06.046.

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34

Van Huffel, S., Haesun Park, and J. B. Rosen. "Formulation and solution of structured total least norm problems for parameter estimation." IEEE Transactions on Signal Processing 44, no. 10 (1996): 2464–74. http://dx.doi.org/10.1109/78.539031.

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35

Wu, Fen, Xin Hua Yang, Andy Packard, and Greg Becker. "Induced L2-norm control for LPV systems with bounded parameter variation rates." International Journal of Robust and Nonlinear Control 6, no. 9-10 (November 1996): 983–98. http://dx.doi.org/10.1002/(sici)1099-1239(199611)6:9/10<983::aid-rnc263>3.0.co;2-c.

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36

Wu, Ligang, Peng Shi, and Xiaojie Su. "Hankel-norm model approximation for LPV systems with parameter-varying time delays." International Journal of Systems Science 41, no. 10 (September 6, 2010): 1173–85. http://dx.doi.org/10.1080/00207720903171753.

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37

Owens, D. H. "Multivariable norm optimal and parameter optimal iterative learning control: a unified formulation." International Journal of Control 85, no. 8 (August 2012): 1010–25. http://dx.doi.org/10.1080/00207179.2012.673136.

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38

Wei, Zhiliang, Ning Fu, Siyi Jiang, Xiaodong Li, and Liyan Qiao. "Parameter Measurement of LFM Signal With FRI Sampling and Nuclear Norm Denoising." IEEE Transactions on Instrumentation and Measurement 71 (2022): 1–17. http://dx.doi.org/10.1109/tim.2022.3158986.

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39

Wang, Yan Ru, Mao Yu Zhang, Jun Wu Dai, Mai Tong, and George C. Lee. "3D Temporal Characteristics of Scale Model Responses in Shaking Table Test." Advanced Materials Research 163-167 (December 2010): 3977–80. http://dx.doi.org/10.4028/www.scientific.net/amr.163-167.3977.

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In this paper, we present the analysis on 3D temporal characteristics of a scale model for high-rise structure. Based on the parameter of instantaneous tangential acceleration aT, normal acceleration aN, Euclidean norm of acceleration vector |a|, Euclidean norm of velocity vector |v|, temporal curvature κ, κt, Some interesting relationships and information in depth between them would be obtain.

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Shi, Yuewu, Wei Wang, Zhizhen Zhu, and Xin Nie. "The Parameter Estimation of Double Exponential Pulse Based on a Least Infinity Norm Fitting Method." Journal of Physics: Conference Series 2083, no. 4 (November 1, 2021): 042002. http://dx.doi.org/10.1088/1742-6596/2083/4/042002.

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Abstract This paper presents an estimation method of double exponential pulse (DEP) between the physical parameters rise time (t r), full width at half maximum amplitude (t FWHM) and the mathematical parameters α, β. A newly fitting method based on the least infinity norm criterion is proposed to deal with the estimation problem of DEP. The calculation process and equation of parameters of this method is proposed based on an m-th-order polynomial fitting model. This estimation method is compared with the least square method by the same data and fitting function. The results show that the maximum estimation error of parameters of double exponential pulse obtained by the least infinity norm method is 1.5 %.

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Jafar, Adnan, Aamer Iqbal Bhatti, SM Ahmad, and Nisar Ahmed. "Robust gain-scheduled linear parameter-varying control algorithm for a lab helicopter: A linear matrix inequality–based approach." Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 232, no. 5 (March 4, 2018): 558–71. http://dx.doi.org/10.1177/0959651818759861.

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The control performance of aerial vehicles can be easily affected by measurement error in sensor output, dynamic model error, model parameter variation, parametric uncertainty, external disturbance, and dynamic coupling. This article presents a design of robust linear parameter-varying control technique with induced L2-norm performance combined with linear matrix inequality pole region constraints for a lab-scale helicopter. A linear parameter-varying disturbance rejection observer is constructed that characterizes the L2-norm performance of the linear parameter-varying system, which enables to estimate state information not only in the presence of external disturbance but also in case of fault occurrence or unavailability of some sensor output. Therefore, the proposed robust linear parameter-varying control scheme has the tendency to provide an adaptive control solution for stability proof and robust tracking performance. The performance of the proposed technique is confirmed both in simulation and in real time. Compared to conventional output feedback H∞ control technique, the proposed control technique yields a good tracking performance in the presence of disturbance, parameter variation, and dynamic coupling.

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Qu, Na, Jianhui Wang, Jinhai Liu, and Zhonghai Li. "Composite Fire Detection System Using Sparse Representation Method." Mathematical Problems in Engineering 2017 (2017): 1–8. http://dx.doi.org/10.1155/2017/6784764.

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This paper proposes that fire parameter data of smoke, temperature, and CO is fused by sparse representation algorithm. It designs a kind of overcomplete dictionary and obtains the sparse solution of fire recognition through L1 norm, L3/4 norm, L1/2 norm, and L1/4 norm, respectively, in order to select more suitable norm type. A comprehensive classification method is proposed for fire identification. The simulation results show that L1 norm and L3/4 norm are used to obtain the solution with remarkable sparsity and high accuracy. The comprehensive classification method is more effective than minimum residual method and sum of weight coefficients method. This paper uses DSP TMS320F28022 as the core chip, TC72 as the temperature sensor, MQ-7 as the CO gas sensor, and MQ-9 as the smoke sensor to design the hardware of fire detection system. Code Composer Studio (CCS) software is used to compile and debug the program. Proteus software is used to load the program into the hardware circuit for joint simulation. The simulation results show that system design is feasible.

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Wagner, Rosemarie, and Kai Heinlein. "Strukturanalyse von biaxialen Zugversuchen an textilen Flächengebilden/Structural Analysis of biaxial tension tests for textiles." Bauingenieur 94, no. 10 (2019): 386–94. http://dx.doi.org/10.37544/0005-6650-2019-10-72.

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Zusammenfassung Seit ungefähr sechs Jahren gibt es auf europäischer und nationaler Ebene die Bestrebungen das Prüfverfahren zur Untersuchung des zweiachsigen Spannungs-Dehnungs-Verhalten beschichteter Gewebe in ein Standardwerk zu fassen. Hierzu gehört das Bestimmen von Werkstoff-Parametern in ebenen Spannungs-Verzerrungs-Zustand als Eingabegröße in jede numerische Strukturanalyse und für die Ermittlung von Zuschnitten. Zur Bestimmung der Zugsteifigkeiten für einen ebenen Spannungs-Verzerrungs-Zustand von beschichteten Geweben liegt seit Februar 2019 eine nationale Norm vor. In dieser stehen Versuchseinrichtungen und Verfahren nebeneinander, denen eine Einordnung in die Grundlagen der Mechanik und Strukturanalyse fehlt. Beschichtete Gewebe sind inhomogene und anisotrope Verbundwerkstoffe, bestehend aus einzelnen Fadenscharen, die über Webtechniken im losen Verband gehalten und durch Beschichtungen gegen Umwelteinflüsse geschützt werden. Werkstoff-Parametern werden in biaxialen Zugversuchen bestimmt, indem die Eigenschaften für die jeweilige Fadenrichtung homogeniert und linearisiert werden. Es wird aufgezeigt wie sich die homogenen Werkstoff-Parameter des unbeschichteten Gewebes aus dem Fadenverhalten ableiten. Der Einfluss der Probengeometrie auf das Last-Verformungs-Verhalten wird an zwei Beispielen dargestellt. Abschließend werden vier Verfahren zur Bestimmung der Werkstoff-Parameter nach der aktuellen Norm an den derselben Versuchsreihe gegenübergestellt und interpretiert.

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Korosteleva, Anna. "Changing the Norm of Socium – the Basis of the Communicative Composition of the Film (based on the movie “Nightingale the Robber”)." Stephanos Peer reviewed multilanguage scientific journal 46, no. 2 (March 31, 2021): 58–81. http://dx.doi.org/10.24249/2309-9917-2021-46-2-58-81.

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The research is carried out by the method of semantic communication analysis. The analysis of the communicative composition of a spoken literary text, organized by the communicative parameter of the norm, is presented. The film “Solovey-Razboynik” (“Nightingale the Robber”, Russia, 2012) presents a rare type of a hero capable of changing the society norm, that is, creating and imposing a new norm on the environment. The article analyzes the work of Russian communicative means in dialogues recruited in order to show the process of the hero introducing his own personal norm. The nominative level units perform in the film two aesthetic tasks: 1) they create an alternation of two layers, legend and comics, and 2) they maintain the communication path, also reflecting the change of norms.

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Fuchs, H. V. "DIN 18041:2016 – Eine Norm im raumakustischen „Abseits“?/DIN 18041:2016 – A norm in room acoustic offside?" Lärmbekämpfung 14, no. 04 (2019): 123–32. http://dx.doi.org/10.37544/1863-4672-2019-04-25.

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Die Neufassung der wichtigsten deutschen Norm zur Raumakustik vor 3 Jahren hat zwar den bewerteten Absorptionsgrad aw als untauglichen Einzahlparameter für die Planung eliminiert. Dafür wurde aber der empfohlene Toleranzbereich für die maximal zulässige Nachhallzeit bei Frequenzen unter 250 Hz stark erweitert. Diese und einige andere Änderungen werden einer kritischen Betrachtung hinsichtlich Sprachverstehen und Schallbelastung unterzogen und Berater vor einer unkritischen Anwendung der DIN 18041 in der aktuellen Version gewarnt.   Summary A revision 3 years ago of the most relevant German room acoustics standard has eliminated the inadequate weighted absorption coefficient aw as a planning parameter. In its place, however, the recommended tolerance for the maximum allowed reverberation time below 250 Hz was heavily extended. These and a few other peculiarities are critically reviewed with respect to speech intelligibility and noise generation in communication rooms and consultants warned of an uncritical application of DIN 18041 in its present reading.

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Gallego-Posada, Jose Daniel, and Maria Eugenia Puerta-Yepes. "Internal analysis and optimization applied to parameter estimation under uncertainty." Boletim da Sociedade Paranaense de Matemática 36, no. 2 (April 1, 2018): 107–24. http://dx.doi.org/10.5269/bspm.v36i2.29309.

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We present a methodology through exemplification to perform parameter estimation subject to possible factors of uncertainty. The underlying optimization problem is posed in the framework of the theory of interval-valued optimization. The implementation of numerical procedures required to achieve efficient solutions implied the use of the $\ell_1$ norm instead of usual $\ell_2$ regression. Finally, an implementation using real data was performed, demonstrating the ability of interval analysis to encapsulate uncertainty while facing non-trivial parameter estimation problems.

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Gao, Lei, Chaoqian Li, and Yaotang Li. "A New Upper Bound on the Infinity Norm of the Inverse of Nekrasov Matrices." Journal of Applied Mathematics 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/708128.

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A new upper bound which involves a parameter for the infinity norm of the inverse of Nekrasov matrices is given. And we determine the optimal value of the parameter such that the bound improves the results of Kolotilina, 2013. Numerical examples are given to illustrate the corresponding results.

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Wang, Bao Feng. "Robust Estimation for Discrete Time-Varying Uncertain Systems with Observation Losses in Networked Control System." Applied Mechanics and Materials 336-338 (July 2013): 628–32. http://dx.doi.org/10.4028/www.scientific.net/amm.336-338.628.

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In this paper, we deal with the robust minimum variance filtering problem for discrete time-varying systems with observation losses. The system under consideration is subjected to time-varying norm-bounded parameter uncertainties in both the state and output matrices, and the observation losses are described by a Bernoulli process with a known probability. An upper bound on the variance of the state estimation error is first found under certain probability of missing observations and admissible parameter uncertainties. Then, a robust filter is derived by minimizing the prescribed upper bound in the sense of the matrix norm. It is shown that the desired filter can be obtained in terms of the solutions to two discrete Riccati difference equations.

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Fang, B. Q. "Estimation of the location parameter of the ℓ1-norm symmetric matrix variate distributions." Statistics & Probability Letters 57, no. 3 (April 2002): 269–80. http://dx.doi.org/10.1016/s0167-7152(02)00060-3.

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Musa, Yau Balarabe, and M. Y. Waziri. "Matrix-Norm Approach of Computing Levenberg-Marquardt Reg- ularization Parameter for Nonlinear Equations." Bayero Journal of Pure and Applied Sciences 11, no. 1 (February 7, 2019): 502. http://dx.doi.org/10.4314/bajopas.v11i1.80s.

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