Academic literature on the topic 'Non-polynomial dependence'
Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles
Consult the lists of relevant articles, books, theses, conference reports, and other scholarly sources on the topic 'Non-polynomial dependence.'
Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.
You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.
Journal articles on the topic "Non-polynomial dependence"
1
Severa, Libor, Jaroslav Buchar, Šárka Nedomová, and Květoslava Šustová. "Rheological profile of raw whey." Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis 58, no. 1 (2010): 167–74. http://dx.doi.org/10.11118/actaun201058010167.
Full textAbstract:
The results of raw whey rheological behavior investigation – particularly viscosity, dependence on temperature, time, and share rate, are presented. The whey samples have been examined under temperature ranging from 17 to 90 °C and under share rate ranging from 0.34 to 68 s−1. The measurements have been performed using rotary digital viscometer (concentric cylinders geometry). The material was found to be temperature dependent (non-linearly), time dependent and shear thinning. Received data have been successfully characterized by several mathematical models (power, exponential, and polynomial) in MATLAB® software with satisfying correlations between experimental and computed results. Following correlations have been achieved: temperature dependence with r2= 0.993 using polynomial model, time dependence with r2= 0.985 using power model, and shear thinning behavior r2= 0.998 using power model. The results are quite useful for practical design of technological equipment such as pumps and piping.
2
Stanciu, Ioana. "Study of Rheological Behavior of Olive Oil Used as Biodegradable Lubricant." Oriental Journal Of Chemistry 37, no. 5 (October 30, 2021): 1248–51. http://dx.doi.org/10.13005/ojc/370533.
Full textAbstract:
In this article, based on experimental data, we obtained three dependence relations of dynamic viscosity versus temperature by polynomial and exponential fitting. The correlation coefficients have values close to unity which proves that the obtained relations accurately describe the non-Newtonian behavior of olive oil.
3
Kharitonov, I. A., Regina V. Rodyakina, and A. L. Goncharov. "Investigation of Magnetic Properties of Various Structural Classes Steels in Weak Magnetic Fields Characteristic for Generation of Thermoelectric Currents in Electron Beam Welding." Solid State Phenomena 299 (January 2020): 1201–7. http://dx.doi.org/10.4028/www.scientific.net/ssp.299.1201.
Full textAbstract:
The results of studies of magnetic and thermoelectric properties of pearlite, martensitic and austenitic steels, as well as cobalt and nickel based alloys are presented. The magnetization curves for materials from among the studied ones, as well as dependences of absolute thermoelectric power on the material temperature, are obtained. It was found that for ferromagnetic substances in weak magnetic fields the dependence of magnetic induction on the magnetic field strength is non-linear. This allows to conclude that magnetic permeability of such medium is not a constant, but can be described, for example, by a third-order polynomial.
4
Ramesh, K. P., J. Ramakrishna, K. S. Suresh, and C. Raghavendra Rao. "Pressure Dependence of the Chlorine NQR in Chloro Pyridines." Zeitschrift für Naturforschung A 55, no. 1-2 (February 1, 2000): 111–16. http://dx.doi.org/10.1515/zna-2000-1-219.
Full textAbstract:
The 35CI NQR frequency (υQ) and spin lattice relaxation time (T1 ) in 2,6-dichloropyridine, 2 amino 3,5-dichloropyridine and 6 chloro 2-pyridinol have been measured as a function of pressure up to 5.1 kbar at 300 K, and the data have been analysed to estimate the temperature coefficients of the NQR frequency at constant volume. All the three compounds show a non linear variation of the NQR frequency with pressure which can be described by a 2nd order polynomial in pressure. The rate of change of the NQR frequency with pressure is positive and decreases with increasing pressure. The spin lattice relaxation time T1, in all the three compounds shows a small increase with pressure, indicating that the relaxation is mainly due to the torsional motions.
5
MARCOLLI, MATILDE, and JESSICA SU. "ARITHMETIC OF POTTS MODEL HYPERSURFACES." International Journal of Geometric Methods in Modern Physics 10, no. 04 (March 6, 2013): 1350005. http://dx.doi.org/10.1142/s0219887813500059.
Full textAbstract:
We consider Potts model hypersurfaces defined by the multivariate Tutte polynomial of graphs (Potts model partition function). We focus on the behavior of the number of points over finite fields for these hypersurfaces, in comparison with the graph hypersurfaces of perturbative quantum field theory defined by the Kirchhoff graph polynomial. We give a very simple example of the failure of the "fibration condition" in the dependence of the Grothendieck class on the number of spin states and of the polynomial countability condition for these Potts model hypersurfaces. We then show that a period computation, formally similar to the parametric Feynman integrals of quantum field theory, arises by considering certain thermodynamic averages. One can show that these evaluate to combinations of multiple zeta values for Potts models on polygon polymer chains, while silicate tetrahedral chains provide a candidate for a possible occurrence of non-mixed Tate periods.
6
Bréhier, Charles-Edouard. "Approximation of the invariant distribution for a class of ergodic SPDEs using an explicit tamed exponential Euler scheme." ESAIM: Mathematical Modelling and Numerical Analysis 56, no. 1 (January 2022): 151–75. http://dx.doi.org/10.1051/m2an/2021089.
Full textAbstract:
We consider the long-time behavior of an explicit tamed exponential Euler scheme applied to a class of parabolic semilinear stochastic partial differential equations driven by additive noise, under a one-sided Lipschitz continuity condition. The setting encompasses nonlinearities with polynomial growth. First, we prove that moment bounds for the numerical scheme hold, with at most polynomial dependence with respect to the time horizon. Second, we apply this result to obtain error estimates, in the weak sense, in terms of the time-step size and of the time horizon, to quantify the error to approximate averages with respect to the invariant distribution of the continuous-time process. We justify the efficiency of using the explicit tamed exponential Euler scheme to approximate the invariant distribution, since the computational cost does not suffer from the at most polynomial growth of the moment bounds. To the best of our knowledge, this is the first result in the literature concerning the approximation of the invariant distribution for SPDEs with non-globally Lipschitz coefficients using an explicit tamed scheme.
7
WOLF, THOMAS. "A comparison of four approaches to the calculation of conservation laws." European Journal of Applied Mathematics 13, no. 2 (April 2002): 129–52. http://dx.doi.org/10.1017/s0956792501004715.
Full textAbstract:
The paper compares computational aspects of four approaches to compute conservation laws of single Differential Equations (DEs) or systems of them, ODEs and PDEs. The only restriction, required by two of the four corresponding computer algebra programs, is that each DE has to be solvable for a leading derivative. Extra constraints for the conservation laws can be specified. Examples include new conservation laws that are non-polynomial in the functions, that have an explicit variable dependence and families of conservation laws involving arbitrary functions. The following equations are investigated in examples: Ito, Liouville, Burgers, Kadomtsev–Petviashvili, Karney–Sen–Chu–Verheest, Boussinesq, Tzetzeica, Benney.
8
MATAR, S., J. TEICHMANN, and P. MOHN. "MAGNETOVOLUME EFFECTS IN Fe3Pt." International Journal of Modern Physics B 07, no. 01n03 (January 1993): 691–94. http://dx.doi.org/10.1142/s0217979293001451.
Full textAbstract:
Equilibrium values of the energy for the magnetic and non-magnetic structures were derived for Fe3Pt using the scalar relativistic ASW method. The stable ground state is found to be ferromagnetic. Calculations were extended to obtain total energy curves as a function of moment and volume via the FSM method. Results were fitted using a polynomial in M and V within a Landau-Ginzburg model of spin fluctuations. Relevant properties to Invar such as the magnetic contribution to the thermal expansion coefficient and the critical pressure for the disappearance of magnetism and its pressure dependence were derived.
9
Wang, Haopeng, Xueyan Liu, Panos Apostolidis, and Tom Scarpas. "Non-Newtonian Behaviors of Crumb Rubber-Modified Bituminous Binders." Applied Sciences 8, no. 10 (September 29, 2018): 1760. http://dx.doi.org/10.3390/app8101760.
Full textAbstract:
Crumb rubber-modified bitumen (CRMB) has been utilized in the asphalt paving industry for decades due to its various benefits. The complex interaction between bitumen and crumb rubber as well as the addition of warm-mix additives makes the typical laws of Newtonian fluids insufficient to describe the behaviors of highly modified bituminous binders. To systematically explore the non-Newtonian behaviors of CRMB, a dynamic shear rheometer was utilized to apply shear loading on the samples at various temperatures and shear rates. Results show that the viscosity of different binders are highly temperature- and shear rate-dependent, while highly modified binders exhibit more obvious shear-thinning behaviors at certain temperatures. With the help of zero shear viscosity and yield stress, the shear-thinning behaviors of non-Newtonian binders can be sufficiently characterized. The Arrhenius equation is invalid to describe viscosity-temperature characteristics of bitumen in the non-Newtonian region. A second-order polynomial function was proposed to characterize the viscosity-temperature dependence with a high correlation degree.
10
Ruska, Ruslana. "MODELLING THE DYNAMICS OF PENSION CONTRIBUTIONS ACCUMULATION IN NON-GOVERNMENTAL PENSION FUNDS." Economic Analysis, no. 28(4) (2018): 106–13. http://dx.doi.org/10.35774/econa2018.04.106.
Full textAbstract:
Introduction. Pension provision in any country depends both on the state of the national economy and on the state regulation of social processes. The solidarity pension system in Ukraine does not provide a decent standard of living. Alternative, which allows creating an additional source of pension benefits, which are guaranteed by the state, and reducing the financial burden on the state, are non-state pension funds. Non-state pension funds provide non-state pension provision services by individualizing the accumulation of funds. Their main purpose is to ensure that people receive additional mandatory state pension insurance payments. After analysing different approaches to improving the system of non-state pension funds, the main indicators influencing pension payments are revealed. Purpose. The article aims to model the dynamics of key indicators, on which the payment of pensions in non-state pension funds depends. Methodology. In the process of writing a paper, we have used a number of scientific methods. The system approach is used as one of the main methods of scientific research. The MARSPline module is a component of Data Mining technology in the application package Statistica, techniques of mathematical modelling, in particular approximating polynomials in the process of modelling the dynamics of receipts and payments. The use of actuarial methods helps show how to determine the accumulated amount on individual accounts of participants in non-state pension funds. Results. Different methods and approaches to the evaluation of the activity of non-state pension funds have been analysed. The use of the sixth grade polynomial has made it possible to follow the dynamics of contracting for subsequent periods. It is determined by actuarial methods of accumulated amount on individual pension accounts with different options for contributing and charges interest thereon, allowing depositors to predict the amount of their investments. Using the MARSPline module Statistics program is constructed: a regression model of the dependence of a retirement asset on one person from contributions and investments of investments; Dependence of pension payments on contributions to individual accounts, income from investment of assets, expenses and the number of paid pensions, which allows calculation of future payments to participants, is revealed. The application of the fourth-level approximation polynomial makes it possible to determine the amounts of future retirement benefits in dynamics.
Dissertations / Theses on the topic "Non-polynomial dependence"
1
Botsiura, O. A., I. P. Zakharov, and V. Semenikhin. "Instrumental uncertainties accounting in identification of nonpolynomial calibration dependence." Thesis, "Софттрейд", 2020. https://openarchive.nure.ua/handle/document/18994.
Full textAbstract:
The problem of constructing a calibration dependence of measuring instruments is solved using a measuring experiment, during which values are measured with some uncertainties. According to the obtained values of the measured quantities for a given type of dependence, its identification is carried out. The most common method for solving the identification problem is the least squares method, which is well implemented for polynomial dependencies. In metrological practice, one often has to deal with the case when identifying a nonlinear calibration dependence, an increase in the degree of the polynomial within reasonable limits does not lead to a significant decrease in the approximation error. In this case, the transformation of the original dependence into a linear dependence is applied by changing the variables. The parameters of the linearized dependence are subsequently found using the least square method.
Uncertainty of identification of linearized dependence is considered, which consists of two components - approximation uncertainty and instrumental uncertainty. The first component is known using the least square method. When finding the second component, two cases are considered: when the values of the input variable are known exactly or with corresponding uncertainties. This paper discusses the solution to the problem of the uncertainty evaluation of the non-polynomial dependence identification taking into account the uncertainties of the measured values.
2
Deschatre, Thomas. "Dependence modeling between continuous time stochastic processes : an application to electricity markets modeling and risk management." Thesis, Paris Sciences et Lettres (ComUE), 2017. http://www.theses.fr/2017PSLED034/document.
Full textAbstract:
Cette thèse traite de problèmes de dépendance entre processus stochastiques en temps continu. Ces résultats sont appliqués à la modélisation et à la gestion des risques des marchés de l'électricité.Dans une première partie, de nouvelles copules sont établies pour modéliser la dépendance entre deux mouvements Browniens et contrôler la distribution de leur différence. On montre que la classe des copules admissibles pour les Browniens contient des copules asymétriques. Avec ces copules, la fonction de survie de la différence des deux Browniens est plus élevée dans sa partie positive qu'avec une dépendance gaussienne. Les résultats sont appliqués à la modélisation jointe des prix de l'électricité et d'autres commodités énergétiques. Dans une seconde partie, nous considérons un processus stochastique observé de manière discrète et défini par la somme d'une semi-martingale continue et d'un processus de Poisson composé avec retour à la moyenne. Une procédure d'estimation pour le paramètre de retour à la moyenne est proposée lorsque celui-ci est élevé dans un cadre de statistique haute fréquence en horizon fini. Ces résultats sont utilisés pour la modélisation des pics dans les prix de l'électricité.Dans une troisième partie, on considère un processus de Poisson doublement stochastique dont l'intensité stochastique est une fonction d'une semi-martingale continue. Pour estimer cette fonction, un estimateur à polynômes locaux est utilisé et une méthode de sélection de la fenêtre est proposée menant à une inégalité oracle. Un test est proposé pour déterminer si la fonction d'intensité appartient à une certaine famille paramétrique. Grâce à ces résultats, on modélise la dépendance entre l'intensité des pics de prix de l'électricité et de facteurs exogènes tels que la production éolienneIn this thesis, we study some dependence modeling problems between continuous time stochastic processes. These results are applied to the modeling and risk management of electricity markets. In a first part, we propose new copulae to model the dependence between two Brownian motions and to control the distribution of their difference. We show that the class of admissible copulae for the Brownian motions contains asymmetric copulae. These copulae allow for the survival function of the difference between two Brownian motions to have higher value in the right tail than in the Gaussian copula case. Results are applied to the joint modeling of electricity and other energy commodity prices. In a second part, we consider a stochastic process which is a sum of a continuous semimartingale and a mean reverting compound Poisson process and which is discretely observed. An estimation procedure is proposed for the mean reversion parameter of the Poisson process in a high frequency framework with finite time horizon, assuming this parameter is large. Results are applied to the modeling of the spikes in electricity prices time series. In a third part, we consider a doubly stochastic Poisson process with stochastic intensity function of a continuous semimartingale. A local polynomial estimator is considered in order to infer the intensity function and a method is given to select the optimal bandwidth. An oracle inequality is derived. Furthermore, a test is proposed in order to determine if the intensity function belongs to some parametrical family. Using these results, we model the dependence between the intensity of electricity spikes and exogenous factors such as the wind production
3
Sundström, David. "On specification and inference in the econometrics of public procurement." Doctoral thesis, Umeå universitet, Nationalekonomi, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-121681.
Full textAbstract:
In Paper [I] we use data on Swedish public procurement auctions for internal regularcleaning service contracts to provide novel empirical evidence regarding green publicprocurement (GPP) and its effect on the potential suppliers’ decision to submit a bid andtheir probability of being qualified for supplier selection. We find only a weak effect onsupplier behavior which suggests that GPP does not live up to its political expectations.However, several environmental criteria appear to be associated with increased complexity,as indicated by the reduced probability of a bid being qualified in the postqualificationprocess. As such, GPP appears to have limited or no potential to function as an environmentalpolicy instrument. In Paper [II] the observation is made that empirical evaluations of the effect of policiestransmitted through public procurements on bid sizes are made using linear regressionsor by more involved non-linear structural models. The aspiration is typically to determinea marginal effect. Here, I compare marginal effects generated under both types ofspecifications. I study how a political initiative to make firms less environmentally damagingimplemented through public procurement influences Swedish firms’ behavior. Thecollected evidence brings about a statistically as well as economically significant effect onfirms’ bids and costs. Paper [III] embarks by noting that auction theory suggests that as the number of bidders(competition) increases, the sizes of the participants’ bids decrease. An issue in theempirical literature on auctions is which measurement(s) of competition to use. Utilizinga dataset on public procurements containing measurements on both the actual and potentialnumber of bidders I find that a workhorse model of public procurements is bestfitted to data using only actual bidders as measurement for competition. Acknowledgingthat all measurements of competition may be erroneous, I propose an instrumental variableestimator that (given my data) brings about a competition effect bounded by thosegenerated by specifications using the actual and potential number of bidders, respectively.Also, some asymptotic results are provided for non-linear least squares estimatorsobtained from a dependent variable transformation model. Paper [VI] introduces a novel method to measure bidders’ costs (valuations) in descending(ascending) auctions. Based on two bounded rationality constraints bidders’costs (valuations) are given an imperfect measurements interpretation robust to behavioraldeviations from traditional rationality assumptions. Theory provides no guidanceas to the shape of the cost (valuation) distributions while empirical evidence suggeststhem to be positively skew. Consequently, a flexible distribution is employed in an imperfectmeasurements framework. An illustration of the proposed method on Swedishpublic procurement data is provided along with a comparison to a traditional BayesianNash Equilibrium approach.
Book chapters on the topic "Non-polynomial dependence"
1
Buchbinder, Iosif L., and Ilya L. Shapiro. "The renormalization group in perturbative quantum gravity." In Introduction to Quantum Field Theory with Applications to Quantum Gravity, 488–93. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198838319.003.0021.
Full textAbstract:
This is a short chapter summarizing the main results concerning the renormalization group in models of pure quantum gravity, without matter fields. The chapter starts with a critical analysis of non-perturbative renormalization group approaches, such as the asymptotic safety hypothesis. After that, it presents solid one-loop results based on the minimal subtraction scheme in the one-loop approximation. The polynomial models that are briefly reviewed include the on-shell renormalization group in quantum general relativity, and renormalization group equations in fourth-derivative quantum gravity and superrenormalizable models. Special attention is paid to the gauge-fixing dependence of the renormalization group trajectories.
2
Buchbinder, Iosif L., and Ilya L. Shapiro. "One-loop renormalization in quantum gravity." In Introduction to Quantum Field Theory with Applications to Quantum Gravity, 474–87. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198838319.003.0020.
Full textAbstract:
This chapter demonstrates the basic methods of one-loop calculations in quantum gravity. Basing its discussion on the general results obtained in chapter 10, it first presents a detailed analysis of the gauge-fixing dependence of one-loop divergences in quantum general relativity and higher-derivative models of quantum gravity. After that, a detailed derivation of divergences in quantum general relativity is given, with the simplest parametrization of the quantum metric and minimal gauge fixing. One-loop divergences in the general (non-conformal) fourth-derivative quantum gravity are then derived in less detail. For a similar calculation in the superrenormalizable polynomial model (superrenormalizable gravity), the chapter just presents and discusses the final result.
Conference papers on the topic "Non-polynomial dependence"
1
Zakharov, Igor, Pavel Neyezhmakov, and Valery Semenikhin. "Identification of Non-Polynomial Calibration Dependence Accounting for Instrumental Uncertainties of Measuring Instruments." In 2021 13th International Conference on Measurement. IEEE, 2021. http://dx.doi.org/10.23919/measurement52780.2021.9446827.
Full text
2
Wagner, Shannon M., and John B. Ferris. "Reduced Order ARIMA Models of 2-D Terrain Profiles Using Singular Value Decomposition." In ASME 2007 International Mechanical Engineering Congress and Exposition. ASMEDC, 2007. http://dx.doi.org/10.1115/imece2007-43388.
Full textAbstract:
The terrain profile is the principal source of vertical excitation to a vehicle’s chassis. To correctly predict the system response an accurate model of the terrain is needed. It is impractical to simulate long data sets; therefore it is necessary to characterize roads so that they can be grouped into sets with similar physical characteristics. The first step is to consider the road to be a realization of an underlying stochastic process. This work develops a method for characterizing non-stationary terrain profiles though ARIMA (autoregressive integrated moving average) modeling and singular value decomposition techniques. It is proposed that the ARIMA coefficients and the distribution of the residual process are jointly dependent functions of the physical characteristics of road profiles. This dependence is then exploited by mapping these dependent functions onto a smaller set of random variables. The resulting number of coefficients required to characterize the terrain is greatly reduced. Examples demonstrate that non-stationary road profiles can be characterized in this manner. Future work in polynomial chaos and ARIMA modeling are discussed within the context of terrain characterization.
3
Gómez-Rodríguez, Carlos, Francesco Sartorio, and Giorgio Satta. "A Polynomial-Time Dynamic Oracle for Non-Projective Dependency Parsing." In Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing (EMNLP). Stroudsburg, PA, USA: Association for Computational Linguistics, 2014. http://dx.doi.org/10.3115/v1/d14-1099.
Full text
4
Carobino, Evandro Souto, Renato Pavanello, Rodrigo Batista Tommasini, Debora Junqueira Fonseca, and Leonardo de Oliveira Carvalho. "A Non Linear Finite Element Model to Analyse the Dynamics of Subsea Lifting Operation Using Synthetic Cables." In ASME 2020 39th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/omae2020-18225.
Full textAbstract:
Abstract In the context of subsea lifting many equipment and strategies are employed in order to avoid dynamic instabilities and complex mechanical behaviors during the installation procedures. One of those strategies is the use of synthetic cables to reduce the total sustained weight on the crane and to shift the resonance frequency of the system, leading to reductions of fails risks. This work presents a numerical model intended to predict the dynamic behavior of a cable-equipment system under the influence of the sea waves. The cable is discretized in a finite element mesh which accounts for a nonlinear material model for the elasticity of the cable. The nonlinear elastic law uses a polynomial function to represent the force on the cable as a function of the strain, being able to predict the variation of the stiffness for different load conditions. Further, hydrodynamic forces are considered acting on the equipment and are modeled via Morison’s equation, which introduces a quadratic nonlinear forcing term. The equation of motion is then integrated at the time domain through a Newmark-β predictor-corrector method in order to obtain the dynamic response of the system. Furthermore, an Orcaflex model is constructed using an equivalent linear stiffness representation for the synthetic cable. The results obtained are compared, and the differences between them are highlighted for typical subsea lifting scenarios. In this case, the proposed model can predict non trivial dynamic behaviors of the system such as dependence on the amplitude of the displacement of the lifting point. It is also presented the scenarios where the equivalent linear model is accurate in comparison to the nonlinear one and how the selection of the strain point used to linearize the model affects the dynamics of the system.
5
Lee, Sen Yung, and Shueei Muh Lin. "Dynamic Analysis of Non-Uniform Beams With Time Dependent Elastic Boundary Conditions." In ASME 1995 Design Engineering Technical Conferences collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/detc1995-0283.
Full textAbstract:
Abstract The dynamic response of a non-uniform beam with time dependent elastic boundary conditions is studied by generalizing the method of Mindlin-Goodman and utilizing the exact solutions of general elastically restrained non-uniform beams given by Lee and Kuo. The time dependent elastic boundary conditions for the beam are formulated. A general form of change of dependent variable is introduced and the shifting polynomials of the third order degree, instead of the fifth order degree polynomials taken by Mindlin-Goodman, are selected. The physical meaning of these shifting polynomial functions are explored. Finally, the limiting cases are discussed and several examples are given to illustrate the analysis.
6
Ruge, Peter, and Carolin Trinks. "Dynamics of Infinite Beams Described by Fractional Time Derivatives." In ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/detc2003/vib-48400.
Full textAbstract:
Closed-form solutions of infinite Bernoulli-Euler beams on a viscoelastic foundation are available for harmonic excitations with frequency Ω. For more general time-dependent loadings and beam-systems with local perturbations, for example caused by non-linear effects an overall treatment of the system in the time-domain is highly appropriated. Here the analytical dynamic stiffness of the infinite beam in the frequency-domain is approximated by a rational polynomial in the low frequency-domain and by an irrational part representing the asymptotic behaviour for Ω tending towards infinity. Thus, the corresponding description in the time-domain contains a fractional time derivative part and additonal internal variables due to splitting the rational polynomial into a linear system with respect to Ω.
7
Barbaraci, Gabriele, Alexander H. Pesch, and Jerzy T. Sawicki. "Experimental Investigations of Minimum Power Consumption Optimal Control for Variable Speed AMB Rotor." In ASME 2010 International Mechanical Engineering Congress and Exposition. ASMEDC, 2010. http://dx.doi.org/10.1115/imece2010-40044.
Full textAbstract:
The purpose of this paper is to present a method for development of the optimal speed-dependent control matrix for a rotor supported on active magnetic bearings (AMBs) with the provision of minimum control power consumption over the operating speed range. The speed dependency of the optimal control matrix is the result of the dynamics of rotating machines. Most of published works on optimal control use a stationary optimal control matrix derived for the non-rotating system and thus neglecting the effect of gyroscopic phenomena. This paper employs the minimum energy consumption condition to derive the speed varying optimal control for rotating AMB rotor system. In the presented approach the control matrix is characterized by a second order polynomial matrix with the angular speed as a variable. This leads to a more compact and lower computational burden for controller implementation. Calculations are performed for a 4-axis AMB rotor test rig. Testing with rotor speed ramps is performed and experimental values for power consumption are presented. These results are compared to results with speed invariant optimal control and PID control.
8
Geroulas, Vasileios, Zissimos P. Mourelatos, Vasiliki Tsianika, and Igor Baseski. "Reliability of Nonlinear Vibratory Systems Under Non-Gaussian Loads." In ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/detc2017-67313.
Full textAbstract:
A general methodology is presented for time-dependent reliability and random vibrations of nonlinear vibratory systems with random parameters excited by non-Gaussian loads. The approach is based on Polynomial Chaos Expansion (PCE), Karhunen-Loeve (KL) expansion and Quasi Monte Carlo (QMC). The latter is used to estimate multi-dimensional integrals efficiently. The input random processes are first characterized using their first four moments (mean, standard deviation, skewness and kurtosis coefficients) and a correlation structure in order to generate sample realizations (trajectories). Characterization means the development of a stochastic metamodel. The input random variables and processes are expressed in terms of independent standard normal variables in N dimensions. The N-dimensional input space is space filled with M points. The system differential equations of motion are time integrated for each of the M points and QMC estimates the four moments and correlation structure of the output efficiently. The proposed PCE-KL-QMC approach is then used to characterize the output process. Finally, classical MC simulation estimates the time-dependent probability of failure using the developed stochastic metamodel of the output process. The proposed methodology is demonstrated with a Duffing oscillator example under non-Gaussian load.
9
Huang, Deqing, and Sergei Chernyshenko. "Long-Time Average Cost Control of Polynomial Systems: A Sum-of-Squares-Based Small-Feedback Approach." In ASME 2015 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/dscc2015-9684.
Full textAbstract:
This paper provides a proof of concept of the recent novel idea in the area of long-time average cost control. Meanwhile, a new method of overcoming the well-known difficulty of nonconvexity of simultaneous optimization of a control law and an additional tunable function is given. First, a recently-proposed method of obtaining rigorous bounds of long-time average cost is outlined for the uncontrolled system with polynomials of system state on the right-hand side. In this method the polynomial constraints are relaxed to be sum-of-squares and formulated as semi-definite programs. It was proposed to use the upper bound of long-time average cost as the objective function instead of the time-average cost itself in controller design. In the present paper this suggestion is implemented for a particular system and is shown to give good results. Designing the optimal controller by this method requires optimising simultaneously both the control law and a tunable function similar to the Lyapunov function. The new approach proposed and implemented in this paper for overcoming the inherent non-convexity of this optimisation is based on a formal assumption that the amplitude of control is small. By expanding the tunable function and the bound in the small parameter, the long-time average cost is reduced by minimizing the respective bound in each term of the series. The derivation of all the polynomial coefficients in controller is given in terms of the solvability conditions of state-dependent linear and bilinear inequalities. The resultant sum-of-squares problems are solved in sequence, thus avoiding the non-convexity in optimization.
10
Stappenbelt, Brad, and Krish Thiagarajan. "Vortex-Induced Vibration of Catenary Moored Cylindrical Structures." In ASME 2004 23rd International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2004. http://dx.doi.org/10.1115/omae2004-51164.
Full textAbstract:
Mooring systems utilised for floating structures typically introduce non-linear load-excursion behaviour. This non-linear compliance and the accompanying amplitude dependent natural frequency, influences the Vortex-Induced Vibration (VIV) response of the structure. The application of linear compliance VIV modelling and experimental data has been demonstrated to produce significant uncertainties regarding VIV onset and response prediction of catenary moored cylindrical structures (Bjarke et al. 2003; Dijk et al. 2003). The vortex-induced vibration issues associated with catenary moored cylindrical structures were investigated through non-linearly compliant elastically mounted rigid cylinder experiments. In particular, third order polynomial, hard spring stiffness, (typical of catenary moorings) was considered. The effect on transverse VIV lock-in and vibration amplitudes was examined using a single degree of freedom experimental rig. The experimental rig consisted of a moderately damped, elastically mounted rigid cylinder, restricted in all but the cross-flow direction through use of linear slide mechanism. The linear and cubic compliance components were independently varied over the non-linear compliance ratio of 0 to 0.3. All experimentation was conducted within the stable sub-critical Reynolds number range. The experimental data was compared to numerical results produced by the VIV modelling software package VisFlo. The program utilises a vortex-in-cell discrete vortex numerical method that was modified to allow the inclusion of varying degrees of structural non-linearity.