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Journal articles on the topic 'Affine dependence in the parameter'

Author: Grafiati

Published: 18 February 2023

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1

Cox, Pepijn B., Siep Weiland, and Roland Toth. "Affine Parameter-Dependent Lyapunov Functions for LPV Systems With Affine Dependence." IEEE Transactions on Automatic Control 63, no. 11 (November 2018): 3865–72. http://dx.doi.org/10.1109/tac.2018.2824982.

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2

Walsh, Alex, and James Richard Forbes. "Very Strictly Passive Controller Synthesis With Affine Parameter Dependence." IEEE Transactions on Automatic Control 63, no. 5 (May 2018): 1531–37. http://dx.doi.org/10.1109/tac.2017.2748928.

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3

Feng, Yu. "Positive real control for discrete-time singular systems with affine parameter dependence." Journal of the Franklin Institute 352, no. 3 (March 2015): 882–96. http://dx.doi.org/10.1016/j.jfranklin.2014.11.002.

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4

Rozza, Gianluigi. "Reduced basis methods for Stokes equations in domains with non-affine parameter dependence." Computing and Visualization in Science 12, no. 1 (November 10, 2006): 23–35. http://dx.doi.org/10.1007/s00791-006-0044-7.

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5

Hooshmandi, Kaveh, Farhad Bayat, and Andrzej Bartoszewicz. "Sampled-Data Linear Parameter Variable Approach for Voltage Regulation of DC–DC Buck Converter." Electronics 11, no. 19 (October 6, 2022): 3208. http://dx.doi.org/10.3390/electronics11193208.

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This paper addresses the new method for output voltage regulation of DC–DC buck converter nonlinear systems by a sampled-data linear parameter varying (LPV) controller. For this purpose, an output-error state-space affine LPV model is presented for DC–DC buck converter nonlinear systems. The sampled-data structure of the controller is considered as a time delay in the input, and stabilization conditions are obtained for LPV systems with affine dependence on the parameter by using a parameter-dependent Lyapunov–Krasovskii functional. Then, the design condition of the sampled-data LPV controller with an appropriate sampling period is derived to guarantee that the output voltage of the DC–DC buck converter can be adjusted to the desired voltage. Finally, simulation results are provided to show the validity of the presented approach in practical control applications where there are limitations on the value of the sampling period and the cost of the digital implementation.

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6

Deng, Qirong, Mingtian Li, and Yonghua Yao. "Continuous dependence on parameters of self-affine sets and measures." Chaos, Solitons & Fractals 161 (August 2022): 112309. http://dx.doi.org/10.1016/j.chaos.2022.112309.

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7

Kuti, József, and Péter Galambos. "Affine Tensor Product Model Transformation." Complexity 2018 (2018): 1–12. http://dx.doi.org/10.1155/2018/4073531.

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This paper introduces the novel concept of Affine Tensor Product (TP) Model and the corresponding model transformation algorithm. Affine TP Model is a unique representation of Linear Parameter Varying systems with advantageous properties that makes it very effective in convex optimization-based controller synthesis. The proposed model form describes the affine geometric structure of the parameter dependencies by a nearly minimum model size and enables a systematic way of geometric complexity reduction. The proposed method is capable of exact analytical model reconstruction and also supports the sampling-based numerical approach with arbitrary discretization grid and interpolation methods. The representation conforms with the latest polytopic model generation and manipulation algorithms. Along these advances, the paper reorganizes and extends the mathematical theory of TP Model Transformation. The practical merit of the proposed concept is demonstrated through a numerical example.

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8

Dalila, Khamari, Makouf Abdessalem, Drid Said, and Larbi Chrifi-Alaoui. "Robust linear parameter varying induction motor control with polytopic models." Serbian Journal of Electrical Engineering 10, no. 2 (2013): 335–48. http://dx.doi.org/10.2298/sjee121218008d.

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This paper deals with a robust controller for an induction motor which is represented as a linear parameter varying systems. To do so linear matrix inequality (LMI) based approach and robust Lyapunov feedback controller are associated. This new approach is related to the fact that the synthesis of a linear parameter varying (LPV) feedback controller for the inner loop take into account rotor resistance and mechanical speed as varying parameter. An LPV flux observer is also synthesized to estimate rotor flux providing reference to cited above regulator. The induction motor is described as a polytopic model because of speed and rotor resistance affine dependence their values can be estimated on line during systems operations. The simulation results are presented to confirm the effectiveness of the proposed approach where robustness stability and high performances have been achieved over the entire operating range of the induction motor.

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9

Şahin, İsmail Hakkı, and Coşku Kasnakoğlu. "Control of a small helicopter with linear matrix inequality-based design assuring stability and performance." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 234, no. 3 (September 24, 2019): 624–39. http://dx.doi.org/10.1177/0954410019877699.

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This article focuses on linear matrix inequality-based controller designs that can achieve stabilization and reference tracking for a small unmanned helicopter at various flight conditions. A nonlinear mathematical model of a small-scale helicopter is constructed. Then trim conditions are found and linearized around different equilibrium points. Local [Formula: see text] controllers are designed at trim conditions based on the local linear models. The pointwise controllers achieve local stability and performance, but fail at stabilization and tracking over the full envelope. A scheduling controller is built by blending the local controller outputs. In addition, grid-based [Formula: see text] controllers are designed at each operating point with common Lyapunov function. This allows controller scheduling between the adjacent design points with guaranteed stability and performance across the design envelope. Based on the family of linear systems which are obtained from the nonlinear model, an affine parameter-dependent model is built to exploit the approximate linear parameter dependency. Then, a parameter-dependent linear parameter varying controller is synthesized for the affine parameter-dependent model. Although local performance is satisfactory for all given design methods, local [Formula: see text] controllers and affine parameter-dependent controller cannot yield satisfactory performance over the full flight envelope apart from the grid-based controller with common Lyapunov function approach.

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10

Ding, Daoxin. "Continuous dependence on parameters of certain self-affine measures, and their singularity." Czechoslovak Mathematical Journal 61, no. 2 (June 2011): 495–508. http://dx.doi.org/10.1007/s10587-011-0068-0.

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11

ARTINESCU, IRINA MARIA, and COSTIN RADU BOLDEA. ""A visual and numerical comparative study of some parallel affine projection algorithms for solving the convex feasibility problem with application to scratch inpainting"." Carpathian Journal of Mathematics 38, no. 2 (February 28, 2022): 299–313. http://dx.doi.org/10.37193/cjm.2022.02.03.

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"The paper compares four variants of algorithms that solve the problem of Convex Feasibility using affine combinations of projections, two classical variants of Parallel Projection Method (PPM) and two modified variants that involve variable weight, in terms of their effectiveness in inpainting a convex polygon, as well as in terms of their convergence in a finite a number of step. We also present a numerical study of the dependence of the efficiency and the execution speed of these algorithms on the shape of the inpainted convex set, as well as on the values of the relaxation parameter."

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12

Queslel, J. P., and J. E. Mark. "Theoretical Equilibrium Moduli and Swelling Extents for Elastomers Crosslinked in Solution." Rubber Chemistry and Technology 63, no. 1 (March 1, 1990): 46–55. http://dx.doi.org/10.5254/1.3538241.

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Abstract Equilibrium elongation moduli and swelling properties have been calculated for amorphous polymer networks prepared in a diluted reference state of polymer volume fraction υ2C. The three molecular elasticity theories employed are based on (i) an idealized affine deformation model (in which the constraints on junction fluctuations are infinite), (ii) an idealized phantom chain model (in which the constraints are absent), and (iii) the more realistic Flory-Erman theory (in which the constraints vary with crosslinking conditions, degree of swelling, and extent of elongation). A discussion of the dependence of the constraint parameter κ on υ2C is given, and is applied to the calculation of stress-strain isotherms in elongation specifically for cis-polyisoprene cured with dicumyl peroxide. The experimental dependence of κ on υ2C investigated by Erman and Mark was found to be similar to the dependence of the plateau modulus on dilution, and this is consistent with the constrained contour model proposed by Erman and Monnerie.

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13

LI, MING, and S. C. LIM. "MODELING NETWORK TRAFFIC USING CAUCHY CORRELATION MODEL WITH LONG-RANGE DEPENDENCE." Modern Physics Letters B 19, no. 17 (July 30, 2005): 829–40. http://dx.doi.org/10.1142/s0217984905008864.

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Much attention has been given to the long-range dependence and fractal properties in network traffic engineering, and these properties are also widely observed in many fields of science and technologies. Traffic time series is conventionally characterized by its fractal dimension D, which is a measure for roughness, and by the Hurst parameter H, which is a measure for long-range dependence, see for examples (Refs. 10–12). Each property has been traditionally modeled and explained by self-affine random functions, such as fractional Gaussian noise (FGN)1,10–13,18,22–28 and fractional Brownian motion (FBM),6,7 where a linear relationship between D and H, say D = 2 - H for one-dimensional series, links the two properties. The limitation of single parameter models (e.g., FGN) in long-range dependent (LRD) traffic modeling has been noticed as can be seen from Refs. 1, 18 and 25. Hence, models which can provide good fitting of LRD traffic for both short-term lags and long-term ones are worth studying due to the importance of accurate models of traffic in network communications.13 This letter utilizes a statistical model called the Cauchy correlation model to model LRD traffic. This model characterizes D and H separately, and it allows any combination of two within the constraint of LRD condition. It is a new power-law correlation model for LRD traffic modeling with its local and global behavior decoupling. Its flexibility in data modeling in comparison with a single parameter model of FGN is briefly discussed, and applications to LRD traffic modeling demonstrated.

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14

Weng, Z., R. J. Patton, and P. Cui. "Active fault-tolerant control of a double inverted pendulum." Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 221, no. 6 (September 1, 2007): 895–904. http://dx.doi.org/10.1243/09596518jsce367.

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This paper proposes an active fault-tolerant control scheme based on a gain-scheduled H∞ design strategy. Under the assumption that the effects of faults on the system can be of affine parameter dependence, a reconfigurable robust H∞ controller is developed. The resulting controller is a function of the fault effect factors, which can be derived online from the residual vector of the fault detection and isolation (FDI) mechanism. To demonstrate the effectiveness of the proposed method, a non-linear double inverted pendulum system with a fault in the motor tachometer loop is considered. The adaptive fault-tolerant controller recovers well from the unstable system with loop failure.

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15

Himmelsbach, Matthias, and Andreas Kroll. "On Optimal Test Signal Design and Parameter Identification Schemes for Dynamic Takagi-Sugeno Fuzzy Models Using the Fisher Information Matrix." International Journal of Fuzzy Systems 24, no. 2 (November 21, 2021): 1012–24. http://dx.doi.org/10.1007/s40815-021-01185-9.

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AbstractThis paper is concerned with the analysis of optimization procedures for optimal experiment design for locally affine Takagi-Sugeno (TS) fuzzy models based on the Fisher Information Matrix (FIM). The FIM is used to estimate the covariance matrix of a parameter estimate. It depends on the model parameters as well as the regression variables. Due to the dependency on the model parameters good initial models are required. Since the FIM is a matrix, a scalar measure of the FIM is optimized. Different measures and optimization goals are investigated in three case studies.

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16

Kong, Martin. "On the Impact of Affine Loop Transformations in Qubit Allocation." ACM Transactions on Quantum Computing 2, no. 3 (September 30, 2021): 1–40. http://dx.doi.org/10.1145/3465409.

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Most quantum compiler transformations and qubit allocation techniques to date are either peep-hole focused or rely on sliding windows that depend on a number of external parameters including the topology of the quantum processor. Thus, global optimization criteria are still lacking. In this article, we explore the synergies and impact of affine loop transformations in the context of qubit allocation and mapping. With this goal in mind, we designed and implemented AXL , a domain specific language and source-to-source compiler for quantum circuits that can be directly described with affine relations. We conduct an extensive evaluation spanning circuits from the recently introduced QUEKO benchmark suite, eight quantum circuits taken from the literature, three distinct coupling graphs, four affine transformations (including the Pluto dependence distance minimization and Feautrier’s minimum latency algorithms), four qubit allocators, and two back-end quantum compilers. Our results demonstrate that affine transformations using global optimization criteria can cooperate effectively in several scenarios with quantum qubit mapping algorithms to reduce the circuit depth, size and allocation time.

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17

Prud’homme, C., D. V. Rovas, K. Veroy, L. Machiels, Y. Maday, A. T. Patera, and G. Turinici. "Reliable Real-Time Solution of Parametrized Partial Differential Equations: Reduced-Basis Output Bound Methods." Journal of Fluids Engineering 124, no. 1 (November 2, 2001): 70–80. http://dx.doi.org/10.1115/1.1448332.

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We present a technique for the rapid and reliable prediction of linear-functional outputs of elliptic (and parabolic) partial differential equations with affine parameter dependence. The essential components are (i) (provably) rapidly convergent global reduced-basis approximations—Galerkin projection onto a space WN spanned by solutions of the governing partial differential equation at N selected points in parameter space; (ii) a posteriori error estimation—relaxations of the error-residual equation that provide inexpensive yet sharp and rigorous bounds for the error in the outputs of interest; and (iii) off-line/on-line computational procedures methods which decouple the generation and projection stages of the approximation process. The operation count for the on-line stage in which, given a new parameter value, we calculate the output of interest and associated error bound, depends only on N (typically very small) and the parametric complexity of the problem; the method is thus ideally suited for the repeated and rapid evaluations required in the context of parameter estimation, design, optimization, and real-time control.

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18

REPIN, SERGEY I. "ERRORS OF FINITE ELEMENT METHOD FOR PERFECTLY ELASTO-PLASTIC PROBLEMS." Mathematical Models and Methods in Applied Sciences 06, no. 05 (August 1996): 587–604. http://dx.doi.org/10.1142/s0218202596000237.

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This paper discusses convergence of the finite element method for variational problems of the Hencky plasticity theory. To obtain a priori convergence estimates we use the method of “double approximation”. In the framework of this approach perfectly elastoplastic problem is approximated by some regularized problem. Hence, finite element solutions of the regularized problem depend on the regularization parameter δ and the mesh parameter h. For these solutions we obtain a projection type error estimate. This estimate is a sum of the two parts which represent the errors of regularization and discretization, respectively. Then we prove that under some assumptions on the external data the minimizer of the regularized problem and the maximizer of its dual problem possess additional differentiability properties and deduce the corresponding estimates which explicitly depend on the parameter δ. This makes it possible to prove that there is a dependence between δ and h such that piecewise-affine continuous approximations of the regularized problems generate a sequence of tensor valued functions which converges to the exact solution of the Hencky plasticity problem.

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19

Lipnitskii, A. V. "On the singular and higher characteristic exponents of an almost periodic linear differential system with an affine dependence on a parameter." Differential Equations 42, no. 3 (March 2006): 369–79. http://dx.doi.org/10.1134/s0012266106030074.

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20

GREPL, MARTIN A. "CERTIFIED REDUCED BASIS METHODS FOR NONAFFINE LINEAR TIME-VARYING AND NONLINEAR PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS." Mathematical Models and Methods in Applied Sciences 22, no. 03 (March 2012): 1150015. http://dx.doi.org/10.1142/s0218202511500151.

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We present reduced basis approximations and associated a posteriori error bounds for parabolic partial differential equations involving (i) a nonaffine dependence on the parameter and (ii ) a nonlinear dependence on the field variable. The method employs the Empirical Interpolation Method in order to construct "affine" coefficient-function approximations of the "nonaffine" (or nonlinear) parametrized functions. We consider linear time-invariant as well as linear time-varying nonaffine functions and introduce a new sampling approach to generate the function approximation space for the latter case. Our a posteriori error bounds take both error contributions explicitly into account — the error introduced by the reduced basis approximation and the error induced by the coefficient function interpolation. We show that these bounds are rigorous upper bounds for the approximation error under certain conditions on the function interpolation, thus addressing the demand for certainty of the approximation. As regards efficiency, we develop an offline–online computational procedure for the calculation of the reduced basis approximation and associated error bound. The method is thus ideally suited for the many-query or real-time contexts. Numerical results are presented to confirm and test our approach.

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21

Šiljak, Dragoslav D., and Matija D. Šiljak. "Nonnegativity of uncertain polynomials." Mathematical Problems in Engineering 4, no. 2 (1998): 135–63. http://dx.doi.org/10.1155/s1024123x98000763.

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The purpose of this paper is to derive tests for robust nonnegativity of scalar and matrix polynomials, which are algebraic, recursive, and can be completed in finite number of steps. Polytopic families of polynomials are considered with various characterizations of parameter uncertainty including affine, multilinear, and polynomic structures. The zero exclusion condition for polynomial positivity is also proposed for general parameter dependencies. By reformulating the robust stability problem of complex polynomials as positivity of real polynomials, we obtain new sufficient conditions for robust stability involving multilinear structures, which can be tested using only real arithmetic. The obtained results are applied to robust matrix factorization, strict positive realness, and absolute stability of multivariable systems involving parameter dependent transfer function matrices.

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22

Casenave, Fabien, Nissrine Akkari, Alexandre Charles, and Christian Rey. "Nonintrusive approximation of parametrized limits of matrix power algorithms – application to matrix inverses and log-determinants." ESAIM: Mathematical Modelling and Numerical Analysis 53, no. 1 (January 2019): 219–48. http://dx.doi.org/10.1051/m2an/2018048.

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We consider in this work quantities that can be obtained as limits of powers of parametrized matrices, for instance the inverse matrix or the logarithm of the determinant. Under the assumption of affine dependence in the parameters, we use the Empirical Interpolation Method (EIM) to derive an approximation for powers of these matrices, from which we derive a nonintrusive approximation for the aforementioned limits. We derive upper bounds of the error made by the obtained formula. Finally, numerical comparisons with classical intrusive and nonintrusive approximation techniques are provided: in the considered test-cases, our algorithm performs well compared to the nonintrusive ones.

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23

Skytsiouk, Volodymyr, and Tatiana Klotchko. "DETERMINATION OF DIAGNOSTIC SIGNS OF MULTIPLE SCLEROSIS USING TONTOR STEP MODEL." Bulletin of Kyiv Polytechnic Institute. Series Instrument Making, no. 64(2) (December 24, 2022): 93–100. http://dx.doi.org/10.20535/1970.64(2).2022.270036.

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The conducted theoretical studies provide a basic thesis regarding the creation of a generalized concept of diagnosis of the signs of multiple sclerosis, which should determine the parameters of the distortion of the idealized model of the body system by the real nature of the disease and the state of the object. The work presents an analytical model for determining the onset of the disease using the TONTOR step model. The proposed method provides the doctor with information, excluding the subjective factor, while the results of such information technology significantly increase the accuracy of determining the early stage of the disease. Purpose of work consists in modeling the diagnostic signs of appearance of multiple sclerosis at an early stage of development, and appearance of moment of action's onset of this pathology by analysis methods. With this method of modeling, we have the opportunity to use affine and conformal transformations, which were considered earlier. In this case, the chord should be perceived as a directional vector with location accuracy. A circle is a consequence of an affine transformation. Thus, we have the opportunity to set the coordinates of the points of the trajectory and the circle in an unambiguous correspondence. In addition, since the real motion along the trajectory is characterized by oscillatory processes, the affine transformation of the model can be imagined as an exponential curve. The proposed physical and mathematical information processing models will help determine the main points of creating the principles of operation of technical integrated diagnostic tools. The basis is a vector model for determining the state of biological objects, which will allow information signals to be determined with help of integrated TONTOR sensors and TONTOR step model. As a result, the study of the nature of this functional dependence will provide analytical dependences in digital form, will allow the creation of a computer-integrated hardware solution that will eliminate subjectivity in diagnostics according to the "bad - good" principle.

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24

Brignone, Riccardo, Christoph Gerhart, and Eva Lütkebohmert. "Arbitrage-free Nelson–Siegel model for multiple yield curves." Mathematics and Financial Economics 16, no. 2 (October 6, 2021): 239–66. http://dx.doi.org/10.1007/s11579-021-00308-y.

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AbstractWe propose an affine term structure model that allows for tenor-dependence of yield curves and thus for different risk categories in interbank rates, an important feature of post-crisis interest rate markets. The model has a Nelson–Siegel factor loading structure and thus economically well interpretable parameters. We show that the model is tractable in terms of estimation and provides good in-sample fit and out-of-sample forecasting performance. The proposed model is arbitrage-free across maturities and tenors, and thus perfectly suited for risk management and pricing purposes. We apply our framework to the pricing of caplets in order to illustrate its practical applicability and its suitability for stress testing.

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25

Chrostowski, Robert, and Filippo Mangolini. "On the nature and propagation of errors in roughness parameters obtained from spectral analysis of atomic force microscopy topographic images." Journal of Vacuum Science & Technology A 40, no. 5 (September 2022): 053204. http://dx.doi.org/10.1116/6.0001998.

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Scale-dependent surface roughness strongly affects critical surface properties of materials, including adhesion, wettability, and optical/thermal properties. As a particular example, tuning the ratio of the true to nominal area—a parameter that depends on the root mean square (RMS) local slope of the finest scales of topography—is an effective approach to tailor the wetting characteristics of solid surfaces. While power spectral density (PSD) analysis of atomic force microscopy (AFM) topographic images allows for directly assessing the scale-dependence of surface roughness, this approach to analyze AFM height maps requires power-law modeling and extrapolation of a PSD with inherently non-normal error distributions. Here, we use a Monte Carlo approach based on synthetic AFM images of known input power-law parameters to (1) evaluate the accuracy of fitting techniques based on the expected distribution of the PSD; (2) evaluate the error propagation from the standard errors of the fitted power-law parameters to the computed RMS slope and area ratio; and (3) evaluate the statistical power of various PSD regression techniques when differentiating surfaces. The results indicated that standard error for ordinary least squares on a log-log PSD (log OLS) underpredicts the observed variance by [Formula: see text]50%. This underprediction can be eliminated by implementing a log-link gamma regression. Moreover, when propagating the standard error to derived parameters (e.g., the RMS slope), the propagated error is generally conservative relative to the observed variance and closely predicts the observed variance when extrapolating to the finest scale. This result demonstrates the possibility of accurately estimating roughness parameters that are critical for evaluating surface phenomena on the basis of fitting and extrapolating AFM data using self-affine models. Finally, our results provided evidence for the possibility of statistically differentiating surfaces with similar power-law parameters when using weighted gamma regression with a mean of 10 images, as opposed to unweighted log-OLS that requires as many as 10 000 images to differentiate images.

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26

Møller, Ingelise, Bo H. Jacobsen, and Niels B. Christensen. "Rapid inversion of 2-D geoelectrical data by multichannel deconvolution." GEOPHYSICS 66, no. 3 (May 2001): 800–808. http://dx.doi.org/10.1190/1.1444969.

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Modern geoelectrical data acquisition systems can record more than 100 000 data values per field day. Despite the growth in computer power and the development of more efficient numerical algorithms, interpreting such data volumes remains a nontrivial computational task. We present a 2-D one‐pass inversion procedure formulated as a multichannel deconvolution. It is based on the equation for the electrical potential linearized under the Born approximation, and it makes use of the 2-D form of the Fréchet derivatives evaluated for the homogeneous half‐space. The inversion is formulated in the wavenumber domain so that the 2-D spatial problem decouples into many small 1-D problems. The resulting multichannel deconvolution algorithm is very fast and memory efficient. The inversion scheme is stabilized through covariance matrices representing the stochastic properties of the earth resistivity and data errors. The earth resistivity distribution is assumed to have the statistical characteristics of a two‐parameter, self‐affine fractal. The local apparent amplitude and fractal dimension of the earth resistivity are estimated directly from geoelectrical observations. A nonlinearity error covariance matrix is added to the conventional measurement error covariance matrix. The stochastic model for the dependence of nonlinearity error on electrode configuration as well as resistivity amplitude and fractal dimension is determined pragmatically through nonlinear simulation experiments. Tests on synthetic examples and field cases including well control support the conclusion that for long data profiles this method automatically produces linearized resistivity estimates which faithfully resolve the main model features.

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27

Polák, Martin. "The Influence of Changing Hydropower Potential on Performance Parameters of Pumps in Turbine Mode." Energies 12, no. 11 (June 1, 2019): 2103. http://dx.doi.org/10.3390/en12112103.

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Pumps as turbines (PAT) are used as an alternative to water turbines in small hydropower plants. The same devices can also be used for energy recovery in water distribution networks. They can replace pressure reduction valves that often lead to energy loss. However, PATs lack the parts that regulate flow so that when a hydropower potential change occurs, efficiency is reduced, as is economic gain. This article summarizes the influence of changing hydropower potential on PAT efficiency and presents comparisons of experimental results with the commonly used predictive model stemming from the theory of physical similarity, which presumes constant PAT efficiency. Our research indicates that the deviation between the model and the real power output calculation at varying potentials was minimal. Similarly, the affine parabola can be used to determine the relationship between total head and flow rate. Other relationships differ from reality the more the PAT efficiency changes. The flow rate and total head dependence on shaft speed are the main factors when setting the optimum operational parameters at varying hydropower potentials. Therefore, a change in efficiency must be included in predictive calculations to correctly optimize PAT operation. The problem is that a change in efficiency cannot be reliably predicted in advance, especially in the case of small-scale devices. For this reason, further research on the issue of changes in PAT efficiency is necessary.

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28

Li, An-Bo, Hao Chen, Xiao-Feng Du, Guo-Kai Sun, and Xian-Yu Liu. "Parametric Modeling Method for 3D Symbols of Fold Structures." ISPRS International Journal of Geo-Information 11, no. 12 (December 13, 2022): 618. http://dx.doi.org/10.3390/ijgi11120618.

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Most fabrication methods for three-dimensional (3D) geological symbols are limited to two types: directly increasing the dimensionality of a 2D geological symbol or performing appropriate modeling for an actual 3D geological situation. The former can express limited vertical information and only applies to the three-dimensional symbol-making of point mineral symbols, while the latter weakens the difference between 3D symbols and 3D geological models and has several disadvantages, such as high dependence on measured data, redundant 3D symbol information, and low efficiency when displayed in a 3D scene. Generating a 3D geological symbol is represented by the process of constructing a 3D geological model. This study proposes a parametric modeling method for 3D fold symbols according to the complexity and diversity of the fold structures. The method involves: (1) obtaining the location of each cross-section in the symbol model, based on the location parameters; (2) constructing the middle cross-section, based on morphological parameters and the Bezier curve; (3) performing affine transformation according to the morphology of the hinge zone and the middle section to generate the sections at both ends of the fold; (4) generating transition sections of the 3D symbol model, based on morphing interpolation; and (5) connecting the point sets of each transition section and stitching them to obtain a 3D fold-symbol model. Case studies for different typical fold structures show that this method can eliminate excessive dependence on geological survey data in the modeling process and realize efficient, intuitive, and abstract 3D symbol modeling of fold structures based on only a few parameters. This method also applies to the 3D geological symbol modeling of faults, joints, intrusions, and other geological structures and 3D geological modeling of typical geological structures with a relatively simple spatial morphology.

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29

Fernandez, Bastien, and Fanni M. Sélley. "Conditioning problems for invariant sets of expanding piecewise affine mappings: application to loss of ergodicity in globally coupled maps." Nonlinearity 35, no. 8 (July 6, 2022): 3991–4042. http://dx.doi.org/10.1088/1361-6544/ac640f.

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Abstract We propose a systematic approach to the construction of invariant union of polytopes (IUP) in expanding piecewise affine mappings whose linear components are isotropic scalings. The approach relies on using empirical information embedded in trajectories in order to infer, and then to solve, a so-called conditioning problem for some generating collection of polytopes. A conditioning problem consists of a series of requirements on the polytopes’ localisation and on the dynamical transitions between these elements. The core element of the approach is a reformulation of the problem as a set of piecewise linear inequalities for some matrices which encapsulate geometric constraints. In that way, the original topological puzzle is converted into a standard problem in computational geometry. This transformation involves an optimisation procedure that ensures that both problems are equivalent. As a proof of concept, the approach is applied to the study of the loss of ergodicity in basic examples of globally coupled maps. The study explains, completes and substantially extends previous achievements about asymmetric IUP in these systems. Comparison with the numerics reveals sharp existence conditions depending on the map parameters, and accurate fits of the empirical ergodic components. In addition, this application also reveals unanticipated features about conditioning problem solutions, especially as the dependence on the set of admissible face directions is concerned.

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Grima, Cyril, Nathaniel E. Putzig, Bruce A. Campbell, Matthew Perry, Sean P. S. Gulick, Russell C. Miller, Aaron T. Russell, et al. "Investigating the Martian Surface at Decametric Scale: Population, Distribution, and Dimension of Heterogeneity from Radar Statistics." Planetary Science Journal 3, no. 10 (October 1, 2022): 236. http://dx.doi.org/10.3847/psj/ac9277.

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Abstract Building on one decade of theory and methodology maturation, we investigate the coherent and incoherent components of the response of the Martian surface to nadir-looking orbital radar. We apply a reflectometry technique known as radar statistical reconnaissance to Mars Reconnaissance Orbiter Shallow Radar data over a test region with a large dynamic range in echo strength. This technique provides a set of statistical parameters describing the heterogeneity of the surface and near-surface structure, presumably at a scale of ∼15 m. We discuss the physical meanings of these parameters related to surface and near-surface properties. Most (but not all) investigated terrains have a dominantly coherent surface return, a characteristic that is not necessarily indicative of a smooth surface. The observed behavior of the coherent and incoherent power components of the echo matches signal growth with increasing surface roughness. This finding allows us to identify smooth and level terrains that we use as a reference to approximate the surface height and slope variations of other regions. Nearly systematic mismatches between the SHARAD and MOLA-pulse-width roughness illustrate the complementarity of these data sets from their respective sensitivity range, and advocate for the use of self-affine radar backscattering models to account for roughness variations at different scales. Our methodology provides a wealth of surface properties assessment based on radar scattering with quasi-global coverage, without a dependence on other data, and at a decametric horizontal scale relevant to subregional geology investigation and landing site reconnaissance.

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31

Weijia Shang, E. Hodzic, and Zhigang Chen. "On uniformization of affine dependence algorithms." IEEE Transactions on Computers 45, no. 7 (July 1996): 827–40. http://dx.doi.org/10.1109/12.508321.

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32

Jing, Naihuan, and Honglian Zhang. "Two-parameter twisted quantum affine algebras." Journal of Mathematical Physics 57, no. 9 (September 2016): 091702. http://dx.doi.org/10.1063/1.4962722.

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33

Giblin, P. J., and P. A. Holtom. "Affine-Distance symmetry sets." MATHEMATICA SCANDINAVICA 93, no. 2 (December 1, 2003): 247. http://dx.doi.org/10.7146/math.scand.a-14422.

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The affine distance symmetry set (ADSS) of a plane curve is an affinely invariant analogue of the euclidean symmetry set (SS) [7], [6]. We list all transitions on the ADSS for generic 1-parameter families of plane curves. We show that for generic convex curves the possible transitions coincide with those for the SS but for generic non-convex curves, further transitions occur which are generic in 1-parameter families of bifurcation sets, but are impossible in the euclidean case. For a non-convex curve there are also additional local forms and transitions which do not fit into the generic structure of bifurcation sets at all. We give computational and experimental details of these.

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34

Jianhong, Wang. "Zonotope parameter identification for piecewise affine systems." Journal of Systems Engineering and Electronics 31, no. 5 (October 2020): 1077–84. http://dx.doi.org/10.23919/jsee.2020.000060.

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35

Kadyrov, A., and M. Petrou. "Affine Parameter Estimation from the Trace Transform." IEEE Transactions on Pattern Analysis and Machine Intelligence 28, no. 10 (October 2006): 1631–45. http://dx.doi.org/10.1109/tpami.2006.198.

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36

Jianwang, Hong, and Ricardo A. Ramirez-Mendoza. "Zonotope parameter identification for piecewise affine system." Systems Science & Control Engineering 8, no. 1 (January 1, 2020): 232–40. http://dx.doi.org/10.1080/21642583.2020.1737845.

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37

Alkhoury, Ziad, Mihály Petreczky, and Guillaume Mercère. "Identifiability of affine linear parameter-varying models." Automatica 80 (June 2017): 62–74. http://dx.doi.org/10.1016/j.automatica.2017.01.029.

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38

Barczy, Mátyás, Leif Döring, Zenghu Li, and Gyula Pap. "On parameter estimation for critical affine processes." Electronic Journal of Statistics 7 (2013): 647–96. http://dx.doi.org/10.1214/13-ejs786.

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39

Popova, Evgenija, Lyubomir Kolev, and Walter Krämer. "A Solver for Complex-Valued Parametric Linear Systems." Serdica Journal of Computing 4, no. 1 (March 31, 2010): 123–32. http://dx.doi.org/10.55630/sjc.2010.4.123-132.

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This work reports on a new software for solving linear systems involving affine-linear dependencies between complex-valued interval parameters. We discuss the implementation of a parametric residual iteration for linear interval systems by advanced communication between the system Mathematica and the library C-XSC supporting rigorous complex interval arithmetic. An example of AC electrical circuit illustrates the use of the presented software.

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DELIUS, GUSTAV W., MARK D. GOULD, JON R. LINKS, and YAO-ZHONG ZHANG. "ON TYPE I QUANTUM AFFINE SUPERALGEBRAS." International Journal of Modern Physics A 10, no. 23 (September 20, 1995): 3259–81. http://dx.doi.org/10.1142/s0217751x95001571.

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The type I simple Lie superalgebras are sl(m|n) and osp(2|2n). We study the quantum deformations of their untwisted affine extensions Uq[sl(m|n)(1)] and Uq[osp(2|2n)(1)]. We identify additional relations between the simple generators (“extra q Serre relations”) which need to be imposed in order to properly define Uq[sl(m|n)(1)] and Uq[osp(2|2n)(1)]. We present a general technique for deriving the spectral-parameter-dependent R matrices from quantum affine superalgebras. We determine the R matrices for the type I affine superalgebra Uq[sl(m|n)(1)] in various representations, thereby deriving new solutions of the spectral-parameter-dependent Yang-Baxter equation. In particular, because this algebra possesses one-parameter families of finite-dimensional irreps, we are able to construct R matrices depending on two additional spectral-parameter-like parameters, providing generalizations of the free fermion model.

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41

Şahin, Ismail Hakki, and Coşku Kasnakoğlu. "An Affine Parameter Dependent Controller of an Helicopter for Various Forward Velocity Conditions." Applied Mechanics and Materials 789-790 (September 2015): 1067–72. http://dx.doi.org/10.4028/www.scientific.net/amm.789-790.1067.

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In this paper, we address the design of a controller that accomplishes stabilization and reference tracking at various flight conditions by using linear helicopter models. The suggested controller is in the form of an H-infinity gain-scheduler, and is used for stabilization and reference tracking for the 4 axis (heave, pitch, roll and yaw) autopilot. Based on the linear models given for the Puma helicopter, an approximate affine parameter dependent model has been built. Then, a linear parameter dependent controller is synthesized which stabilizes the affine parameter dependent helicopter model. By doing so, a single controller achieves stabilization and reference tracking of a family of linear models by scheduling the controller gains based on the online measurement of the scheduling parameter, which is the forward velocity. Moreover, the affine parameter dependent controller is fitted into the linear models. It is observed that this single parameter dependent controller successfully stabilizes a family of linear helicopter model at different forward flight conditions.

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Ren, Weizheng, Wei He, and Yansong Cui. "An Improved Fast Affine Motion Estimation Based on Edge Detection Algorithm for VVC." Symmetry 12, no. 7 (July 8, 2020): 1143. http://dx.doi.org/10.3390/sym12071143.

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As a newly proposed video coding standard, Versatile Video Coding (VVC) has adopted some revolutionary techniques compared to High Efficiency Video Coding (HEVC). The multiple-mode affine motion compensation (MM-AMC) adopted by VVC saves approximately 15%-25% Bjøntegaard Delta Bitrate (BD-BR), with an inevitable increase of encoding time. This paper gives an overview of both the 4-parameter affine motion model and the 6-parameter affine motion model, analyzes their performances, and proposes improved algorithms according to the symmetry of iterative gradient descent for fast affine motion estimation. Finally, the proposed algorithms and symmetric MM-AMC flame of VTM-7.0 are compared. The results show that the proposed algorithms save 6.65% total encoding time on average, which saves approximately 30% encoding time of affine motion compensation.

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Ghosh, Avishek, Ashwin Pananjady, Adityanand Guntuboyina, and Kannan Ramchandran. "Max-Affine Regression: Parameter Estimation for Gaussian Designs." IEEE Transactions on Information Theory 68, no. 3 (March 2022): 1851–85. http://dx.doi.org/10.1109/tit.2021.3130717.

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44

Bracken, Anthony J., Mark D. Gould, and Yao-Zhong Zhang. "Quantised affine algebras and parameter-dependent R-matrices." Bulletin of the Australian Mathematical Society 51, no. 2 (April 1995): 177–94. http://dx.doi.org/10.1017/s0004972700014040.

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Let Uq(G(1)) be a quantised non-twisted affine Lie algebra with Uq(G) the corresponding quantised simple Lie algebra. Using the previously obtained universal R-matrices for and , explicitly spectral-dependent universal R-matrices for Uq(A1) and Uq(A2) are determined. These spectral-dependent universal R-matrices are evaluated in some concrete representations; well-known results for the fundamental representations are reproduced, and an explicit formula for the spectral-dependent R-matrix associated with the V(3) ⊗ V(6) module is derived, where V(3) and V(6) carry the 3- and 6-dimensional representations of Uq(A2), respectively.

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45

Sung Jun Ban, Chang Woo Lee, and Sang Woo Kim. "Adaptive Regularization Parameter for Pseudo Affine Projection Algorithm." IEEE Signal Processing Letters 16, no. 5 (May 2009): 382–85. http://dx.doi.org/10.1109/lsp.2009.2016479.

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46

Zhang, Liming, and Xuming Huang. "Applications for Affine Invariant Descriptor and Affine Parameter Estimation Based on Two-Source ICA." Journal of Mathematical Modelling and Algorithms 5, no. 4 (March 3, 2006): 505–23. http://dx.doi.org/10.1007/s10852-005-9023-0.

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47

Ganguly, Saswati, Surajit Sengupta, and Peter Sollich. "Statistics of non-affine defect precursors: tailoring defect densities in colloidal crystals using external fields." Soft Matter 11, no. 22 (2015): 4517–26. http://dx.doi.org/10.1039/c5sm00301f.

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Coarse-graining atomic displacements in a solid produces local affine strains and “non-affine” fluctuations. Here we show how a subset of these thermally excited non-affine fluctuations act as defect precursors and suggest how defect probabilities may be altered by an experimentally realisable “external field” conjugate to the global non-affinity parameter..

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48

Jianwang, Hong, Ricardo A. Ramirez-Mendoza, and Xiang Yan. "Statistical Inference for Piecewise Affine System Identification." Mathematical Problems in Engineering 2021 (October 5, 2021): 1–9. http://dx.doi.org/10.1155/2021/4618030.

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This short note studies the problem of piecewise affine system identification, being a special nonlinear system based on our previous contribution on it. Two different identification strategies are proposed to achieve our mission, such as centralized identification and distributed identification. More specifically, for centralized identification, the total observed input-output data are used to estimate all unknown parameter vectors simultaneously without any consideration on the classification process. But for distributed identification, after the whole observed input-output data are classified into their own right subregions, then part input-output data, belonging to the same subregion, are applied to estimate the unknown parameter vector. Whatever the centralized identification and distributed identification, the final decision is to determine the unknown parameter vector in one linear form, so the recursive least squares algorithm and its modified form with the dead zone are studied to deal with the statistical noise and bounded noise, respectively. Finally, one simulation example is used to compare the identification accuracy for our considered two identification strategies.

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Hürlimann, Werner. "From the General Affine Transform Family to a Pareto Type IV Model." Journal of Probability and Statistics 2009 (2009): 1–10. http://dx.doi.org/10.1155/2009/364901.

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The analytical form of general affine transform families with given maximum likelihood estimators for the affine parameters is determined. In this context, the simultaneous maximum likelihood equations of the affine parameters in the generalised Pareto distribution cannot have a common solution. This pathological situation is removed by extending it to a four parameter family, called Pareto type IV model.

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50

Massioni, Paolo, Laurent Bako, and Gérard Scorletti. "Stability of uncertain piecewise-affine systems with parametric dependence." IFAC-PapersOnLine 53, no. 2 (2020): 1998–2003. http://dx.doi.org/10.1016/j.ifacol.2020.12.2508.

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