Journal articles: 'Closed-form dynamic model'

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Bascetta, Luca, Gianni Ferretti, and Bruno Scaglioni. "Closed form Newton–Euler dynamic model of flexible manipulators." Robotica 35, no. 5 (November 17, 2015): 1006–30. http://dx.doi.org/10.1017/s0263574715000934.

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SUMMARYIn this paper, a closed-form dynamic model of flexible manipulators is developed, based on the Newton–Euler formulation of motion equations of flexible links and on the adoption of the spatial vector notation. The proposed model accounts for two main innovations with respect to the state of the art: it is obtained in closed form with respect to the joints and modal coordinates (including the quadratic velocity terms) and motion equations of the whole manipulator can be computed for any arbitrary shape of the links and any possible link cardinality starting from the output of several commercial (finite element analysis) FEA codes. The Newton–Euler formulation of motion equations in terms of the joint and elastic variables greatly improves the simulation performances and makes the model suitable for real-time control and active vibration damping. The model has been compared with literature benchmarks obtained by the classical multibody approach and further validated by comparison with experiments collected on an experimental manipulator.

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De Luca, A., and B. Siciliano. "Closed-form dynamic model of planar multilink lightweight robots." IEEE Transactions on Systems, Man, and Cybernetics 21, no. 4 (1991): 826–39. http://dx.doi.org/10.1109/21.108300.

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Hafner, Christian M., and Oliver Linton. "AN ALMOST CLOSED FORM ESTIMATOR FOR THE EGARCH MODEL." Econometric Theory 33, no. 4 (August 22, 2016): 1013–38. http://dx.doi.org/10.1017/s0266466616000256.

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The exponential GARCH (EGARCH) model introduced by Nelson (1991) is a popular model for discrete time volatility since it allows for asymmetric effects and naturally ensures positivity even when including exogenous variables. Estimation and inference are usually done via maximum likelihood. Although some progress has been made recently, a complete distribution theory of MLE for EGARCH models is still missing. Furthermore, the estimation procedure itself may be highly sensitive to starting values, the choice of numerical optimization algorithm, etc. We present an alternative estimator that is available in a simple closed form and which could be used, for example, as starting values for MLE. The estimator of the dynamic parameter is independent of the innovation distribution. For the other parameters we assume that the innovation distribution belongs to the class of Generalized Error Distributions (GED), profiling out its parameter in the estimation procedure. We discuss the properties of the proposed estimator and illustrate its performance in a simulation study and an empirical example.

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Huang, Qilin, Yong Wang, Zhipu Huo, and Yudong Xie. "Nonlinear Dynamic Analysis and Optimization of Closed-Form Planetary Gear System." Mathematical Problems in Engineering 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/149046.

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A nonlinear purely rotational dynamic model of a multistage closed-form planetary gear set formed by two simple planetary stages is proposed in this study. The model includes time-varying mesh stiffness, excitation fluctuation and gear backlash nonlinearities. The nonlinear differential equations of motion are solved numerically using variable step-size Runge-Kutta. In order to obtain function expression of optimization objective, the nonlinear differential equations of motion are solved analytically using harmonic balance method (HBM). Based on the analytical solution of dynamic equations, the optimization mathematical model which aims at minimizing the vibration displacement of the low-speed carrier and the total mass of the gear transmission system is established. The optimization toolbox in MATLAB program is adopted to obtain the optimal solution. A case is studied to demonstrate the effectiveness of the dynamic model and the optimization method. The results show that the dynamic properties of the closed-form planetary gear transmission system have been improved and the total mass of the gear set has been decreased significantly.

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Kachani, S., Y. Oumanar, and N. Raissi. "A closed-form solution for a dynamic pricing model with reference price effect." Applied Mathematical Sciences 8 (2014): 1693–701. http://dx.doi.org/10.12988/ams.2014.4119.

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Chen, I.-Ming, and Guilin Yang. "Automatic Model Generation for Modular Reconfigurable Robot Dynamics." Journal of Dynamic Systems, Measurement, and Control 120, no. 3 (September 1, 1998): 346–52. http://dx.doi.org/10.1115/1.2805408.

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In control and simulation of a modular robot system, which consists of standardized and interconnected joint and link units, manual derivation of its dynamic model needs tremendous effort because these models change all the time as the robot geometry is altered after module reconfiguration. This paper presents a method to automate the generation of the closed-form equation of motion of a modular robot with arbitrary degrees-of-freedom and geometry. The robot geometry we consider here is branching type without loops. A graph technique, termed kinematic graphs and realized through assembly incidence matrices (AIM) is introduced to represent the module assembly sequence and robot geometry. The formulation of the dynamic model is started with recursive Newton-Euler algorithm. The generalized velocity, acceleration, and forces are expressed in terms of linear operations on se(3), the Lie algebra of the Euclidean group SE(3). Based on the equivalence relationship between the recursive formulation and the closed-form Lagrangian formulation, the accessibility matrix of the kinematic graph of the robot is used to assist the construction of the closed-form equation of motion of a modular robot. This automatic model generation technique can be applied to the control of rapidly reconfigurable robotic workcells and other automation equipment built around modular components that require accurate dynamic models.

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Cheng, S. P., and N. C. Perkins. "Closed-Form Vibration Analysis of Sagged Cable/Mass Suspensions." Journal of Applied Mechanics 59, no. 4 (December 1, 1992): 923–28. http://dx.doi.org/10.1115/1.2894062.

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A theoretical model is presented which describes the three-dimensional nonlinear motion of a sagged cable that supports an array of discrete masses. An asymptotic form of this general model is derived for the linear response of a cable/mass suspension having small equilibrium curvature and horizontal supports. While the asymptotic model remains rich enough to capture dominant sagged cable effects, it is simple enough to permit closed-form analysis. A free vibration analysis is pursued that leads to closed-form solutions for problems which, heretofore, were analyzed using purely numerical methods. Among the advantages of the present method is its ability to pro vide results for: (1) complex mass arrays, (2) high-order modes, and (3) dynamic cable tension. Examples highlight the key role played by mass array symmetry and lead to new conclusions regarding free vibration.

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Hadian, Hamoon, Yasser Amooshahi, and Abbas Fattah. "Kinematics and Dynamics Modeling of a New 4-DOF Cable-Driven Parallel Manipulator." International Journal of Intelligent Mechatronics and Robotics 1, no. 4 (October 2011): 44–60. http://dx.doi.org/10.4018/ijimr.2011100103.

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This paper addresses the kinematics and dynamics modeling of a 4-DOF cable-driven parallel manipulator with new architecture and a typical Computed Torque Method (CTM) controller is developed for dynamic model in SimMechanics. The novelty of kinematic architecture and the closed loop formulation is presented. The workspace model of mechanism’s dynamic is obtained in an efficient and compact form by means of natural orthogonal complement (NOC) method which leads to the elimination of the nonworking kinematic-constraint wrenches and also to the derivation of the minimum number of equations. To verify the dynamic model and analyze the dynamical properties of novel 4-DOF cable-driven parallel manipulator, a typical CTM control scheme in joint-space is designed for dynamic model in SimMechanics.

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Siu, D. P., and G. S. Ladde. "A Multivariate Stochastic Hybrid Model with Switching Coefficients and Jumps: Solution and Distribution." Journal of Probability and Statistics 2011 (2011): 1–20. http://dx.doi.org/10.1155/2011/720614.

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In this work, a class of multidimensional stochastic hybrid dynamic models is studied. The system under investigation is a first-order linear nonhomogeneous system of Itô-Doob type stochastic differential equations with switching coefficients. The switching of the system is governed by a discrete dynamic which is monitored by a non-homogeneous Poisson process. Closed-form solutions of the systems are obtained. Furthermore, the major part of the work is devoted to finding closed-form probability density functions of the solution processes of linear homogeneous and Ornstein-Uhlenbeck type systems with jumps.

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Akhmedov, Odiljon S., Abdulla A. Azamov, and Gafurjan I. Ibragimov. "FOUR–DIMENSIONAL BRUSSELATOR MODEL WITH PERIODICAL SOLUTION." Ural Mathematical Journal 6, no. 1 (July 29, 2020): 3. http://dx.doi.org/10.15826/umj.2020.1.001.

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In the paper, a four-dimensional model of cyclic reactions of the type Prigogine's Brusselator is considered. It is shown that the corresponding dynamical system does not have a closed trajectory in the positive orthant that will make it inadequate with the main property of chemical reactions of Brusselator type. Therefore, a new modified Brusselator model is proposed in the form of a four-dimensional dynamic system. Also, the existence of a closed trajectory is proved by the DN-tracking method for a certain value of the parameter which expresses the rate of addition one of the reagents to the reaction from an external source.

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Ahn, T. Y., K. F. Eman, and S. M. Wu. "Cutting Dynamics Identification by Dynamic Data System (DDS) Modeling Approach." Journal of Engineering for Industry 107, no. 2 (May 1, 1985): 91–94. http://dx.doi.org/10.1115/1.3185988.

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The dynamics of the cutting process have been conventionally characterized in terms of the Dynamic Cutting Force Coefficients (DCFC) which represent its transfer characteristics at discrete frequencies. However, this approach fails to obtain the transfer function of the process in closed analytical form. Anticipating the stochastic nature of the cutting process and the double modulation principle, a two-input one-output multivariate system was postulated for the dynamic cutting process identification model. The Dynamic Data System (DDS) methodology was used to formulate and characterize the dynamic cutting process using Modified Autoregressive Moving Average Vector (MARMAV) models. Subsequently, transfer functions of the inner and outer modulation dynamics of the cutting processes were obtained from the identified models.

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Zhang, Lixin, Jean W. Zu, and Zhichao Hou. "Complex Modal Analysis of Non-Self-Adjoint Hybrid Serpentine Belt Drive Systems." Journal of Vibration and Acoustics 123, no. 2 (November 1, 2000): 150–56. http://dx.doi.org/10.1115/1.1356697.

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A linear damped hybrid (continuous/discrete components) model is developed in this paper to characterize the dynamic behavior of serpentine belt drive systems. Both internal material damping and external tensioner arm damping are considered. The complex modal analysis method is developed to perform dynamic analysis of linear non-self-adjoint hybrid serpentine belt-drive systems. The adjoint eigenfunctions are acquired in terms of the mode shapes of an auxiliary hybrid system. The closed-form characteristic equation of eigenvalues and the exact closed-form solution for dynamic response of the non-self-adjoint hybrid model are obtained. Numerical simulations are performed to demonstrate the method of analysis. It is shown that there exists an optimum damping value for each vibration mode at which vibration decays the fastest.

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Huang, Qi Lin, Yong Wang, Zhi Pu Huo, Jun Gang Wang, and Ruo Yu Sheng. "Free Torsional Vibration Characteristics of a Closed-Form Planetary Gear Set." Applied Mechanics and Materials 300-301 (February 2013): 1042–47. http://dx.doi.org/10.4028/www.scientific.net/amm.300-301.1042.

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A purely torsional dynamic model of closed-form planetary gear set is developed to investigate its natural frequency and free vibration modes. The closed-form planetary gear set considered consists of two-stage planetary gear connected by high-speed carrier and ring gear. Three identical planet gears are equally spaced in each stage. Based on the precondition, the natural modes are classified into three types of vibration modes: overall modes，high-speed planet mode and low-speed planet mode

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Xin, X., C. Chicone, and Z. Chen. "Analyical Solutions for Failure Evolution With a Nonlinear Local Damage Model." Journal of Applied Mechanics 68, no. 6 (November 10, 2000): 835–43. http://dx.doi.org/10.1115/1.1406956.

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The partitioned-modeling and similarity methods are applied in this paper to derive a closed-form solution for localized dynamic failure problems, with a nonlinear local damage model. The initial point of the localization is taken as the point at which the type of governing differential equation transforms from being hyperbolic to elliptic for dynamic case due to material damage. The evolution of localization is represented by a moving material surface of discontinuity between the elliptic domain and hyperbolic domain. A closed-form solution for a static loading case is also given as a complementary note to show evolution of the localized failure. The effects of model parameters on the structural response are investigated, and the evolution of relevant field variables is illustrated to demonstrate the essential feature of the localized failure evolution.

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Miller, Brad A., and Itzhak Green. "Semi-Analytical Dynamic Analysis of Spiral-Grooved Mechanical Gas Face Seals." Journal of Tribology 125, no. 2 (March 19, 2003): 403–13. http://dx.doi.org/10.1115/1.1510876.

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A novel semi-analytical formulation is presented for the linearized dynamic analysis of spiral-grooved mechanical gas face seals. The linearized rotordynamic properties of the gas film are numerically computed and then represented analytically by a constitutive model consisting of a cosine modified Prony series. The cosine modification enables the Prony series to characterize the gas film properties of face seals in applications with large compressibility numbers. The gas film correspondence principle is then employed to couple the constitutive model to the dynamics of the mechanical face seal. Closed-form solutions are presented for the transient natural response to initial velocity conditions, the steady-state response to rotor runout and initial stator misalignment, the transmissibility ratios, and the stability threshold. Results from the closed-form solutions are all within a few percent of the results from a full nonlinear numerical simulation.

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Mohamed, Samer A., Shady A. Maged, and Mohammed I. Awad. "A performance comparison between closed form and numerical optimization solutions for humanoid robot walking pattern generation." International Journal of Advanced Robotic Systems 18, no. 4 (July 1, 2021): 172988142110297. http://dx.doi.org/10.1177/17298814211029774.

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This article presents the modeling process of the lower part of a humanoid biped robot in terms of kinematic/dynamic states and the creation of a full dynamic simulation environment for a walking robot using MATLAB/Simulink. This article presents two different approaches for offline walking pattern generation: one relying on a closed-form solution of the linear inverted pendulum model (LIPM) mathematical model and another that considers numerical optimization as means of desired output trajectory following for a cart table state-space model. This article then investigates the possibility of introducing solution-dependent modifications to both approaches that could increase the reliability of basic walking pattern generation models in terms of smooth single support–double support phase transitioning and power consumption optimization. The algorithms were coded into offline walking pattern generators for NAO humanoid robot as a valid example and the two approaches were compared against each other in terms of stability, power consumption, and computational effort as well as against their basic unmodified counterparts.

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Chang, T. P. "Stochastic Dynamic Response of a Simplified Nonlinear Fluid Model for Viscoelastic Materials." Journal of Mechanics 28, no. 2 (May 8, 2012): 365–72. http://dx.doi.org/10.1017/jmech.2012.41.

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AbstractIn the present study, we propose a simplified nonlinear fluid model to characterize the complex nonlinear response of some viscoelastic materials. Recently, the viscoelastic modeling has been utilized by many researchers to simulate some parts of human body in bioengineering and to represent many material properties in mechanical engineering, electronic engineering and construction engineering. Occasionally it is almost impossible to evaluate the constant parameters in the model in the deterministic sense, therefore, the damping coefficient of the dashpot and the spring constants of the linear and nonlinear springs are considered as stochastic to model the stochastic properties of the viscoelastic materials. After some transformations, the closed-form solution can be obtained for the mean value of the displacement of the simplified nonlinear fluid model, subjected to constant rate of displacement. Based on the closed-form solution, the proposed method generates the stochastic dynamic response of the simplified nonlinear model, which plays an important role in performing the reliability analysis of the nonlinear system.

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Lieh, Junghsen, and Imtiaz-ul Haque. "Symbolic Closed-Form Modeling and Linearization of Multibody Systems Subject to Control." Journal of Mechanical Design 113, no. 2 (June 1, 1991): 124–32. http://dx.doi.org/10.1115/1.2912760.

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Symbolic closed-form equation formulation and linearization for constrained multibody systems subject to control are presented. The formulation is based on the principle of virtual work. The algorithm is recursive, automatically eliminates the constraint forces and redundant coordinates, and generates the nonlinear or linear dynamic equations in closed-form. It is derived with respect to principal body coordinates and a moving reference frame that allows one to generate the dynamic equations for multibody systems moving along curved track or road. The output equations may be either in syntactically correct FORTRAN form or in the form as derived by hand. A procedure that simplifies the trigonometric expressions, linearizes the geometric nonlinearities, and converts the linearized equations in state-space form is included. Several examples have been used to validate the procedure. Included is a simulation using a seven-DOF automobile ride model with active suspensions.

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Lazzati, Natalia, and Amilcar A. Menichini. "A Dynamic Approach to the Dividend Discount Model." Review of Pacific Basin Financial Markets and Policies 18, no. 03 (September 2015): 1550018. http://dx.doi.org/10.1142/s0219091515500186.

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We derive a dynamic model of the firm with endogenous investment and leverage ratio within the framework of the dividend discount model (DDM). Our valuation model incorporates two relevant components, namely, managerial flexibility and long-run growth. We dispense with any utility specification capturing the preferences of shareholders and obtain closed-form solutions for the firm problem. A standard parameterization suggests that the value of the real options and long-run growth opportunities can easily represent more than 8% and 10% of share price, respectively. We also find that these two components of the stock price are both complements and countercyclical. We finally identify industries where valuation models that do not incorporate these features can lead to considerable underpricing of securities.

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PETKOV, VLADIMIR P. "DELEGATED MANAGEMENT IN DYNAMIC DUOPOLIES." International Game Theory Review 12, no. 02 (June 2010): 93–114. http://dx.doi.org/10.1142/s0219198910002544.

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This paper studies the commitment value of delegation in a model of dynamic competition. We argue that separating ownership and control delivers an instantaneous first-mover advantage. Thus, delegation would enable an oligopolistic firm to increase its equilibrium profit relative to direct management. We focus on remuneration strategies that provide managers with intertemporal production incentives: future wages depend on current effort. Their composition and functional form are endogenously determined by the requirement for Markov perfection. For the case of linear-quadratic payoffs, we obtain a closed-form solution for the equilibrium wage strategies which is independent of industry structure.

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Alexander, R. M., S. T. Noah, and C. G. Franck. "Parametric Identification of a Vibratory System With a Clearance." Journal of Vibration and Acoustics 115, no. 1 (January 1, 1993): 25–32. http://dx.doi.org/10.1115/1.2930310.

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An analytical and experimental investigation of a vibratory system with a clearance was conducted. A finite element model and an equivalent single-degree-of-freedom closed-form solution were used to determine the dynamic parameters and response of an experimental structure interacting with a gap. The closed-form solution is obtained by taking advantage of the piecewise linearity of the system. Results from these solution methods are in agreement with experimental data. The results also suggest that the closed-form solution approximates the response of the experimental structure with accuracy greater than that of the finite element model. The closed-form solution was also used to determine the gap size of the structure. The parameter identification procedure utilized in this study appears to be simple to use and can be readily extended to other types of piecewise-linear multi-degree-of-freedom systems.

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Duckworth, J. Kate, and Mihail Zervos. "An investment model with entry and exit decisions." Journal of Applied Probability 37, no. 02 (June 2000): 547–59. http://dx.doi.org/10.1017/s0021900200015734.

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We consider an investment model which generalizes a number of models that have been studied in the literature. The model involves entry and exit decisions as well as decisions relating to production scheduling. We then address the problem of its valuation from the standpoint of the dynamic programming approach. Our analysis results in a closed form analytic solution that can take qualitatively different forms depending on parameter values.

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Duckworth, J. Kate, and Mihail Zervos. "An investment model with entry and exit decisions." Journal of Applied Probability 37, no. 2 (June 2000): 547–59. http://dx.doi.org/10.1239/jap/1014842558.

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We consider an investment model which generalizes a number of models that have been studied in the literature. The model involves entry and exit decisions as well as decisions relating to production scheduling. We then address the problem of its valuation from the standpoint of the dynamic programming approach. Our analysis results in a closed form analytic solution that can take qualitatively different forms depending on parameter values.

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Yu, Xing, Yanyin Li, and Zhongkai Wan. "Dynamic Currency Futures and Options Hedging Model." Mathematical Problems in Engineering 2019 (July 1, 2019): 1–11. http://dx.doi.org/10.1155/2019/8074384.

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In this paper, we consider a risk averse competitive firm that adopts currency futures and options for hedging purpose. Based on the assumption of unbiased markets of currency futures and options, we propose the optimal hedging model in dynamic setting. By using two-stage optimization method, we prove that it is desirable for the prudent enterprise to buy exchange rate options to hedge currency risk. Furthermore, we derive the closed-form solutions of the multiperiod hedging problem with the quadratic utility function. We investigate an empirical study incorporated into GARCH-t prediction on the efficiency of hedging with currency futures and options. The empirical results demonstrate that hedging with currency futures and options can reduce the silver export firm’s risk exposure. Profits and the effective boundaries are compared in three cases: hedging with futures and options synchronously, only with futures and without any hedge. The results of multiple comparisons among different hedging strategies show that hedging with linear and nonlinear derivatives is advisable for the export firm.

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YU, MEI, HIROSHI INOUE, SATORU TAKAHASHI, and JIANMING SHI. "DYNAMIC PORTFOLIO SELECTION WITH UNCERTAINTY." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 17, no. 02 (April 2009): 237–50. http://dx.doi.org/10.1142/s0218488509005838.

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How to make a prompt decision for uncertainty investment is always a key problem in financial market. In this paper, we present a new dynamic portfolio selection strategy in stock market. The investor is assumed to seek an investment strategy that will maximize his/her final wealth and minimize the total risk. An analytically optimal strategy in closed form is obtained by solving a dynamic programming problem. Some applications are also presented to illustrate this model.

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Kuznetsov, N. V., M. V. Yuldashev, and R. V. Yuldashev. "Analytical-numerical analysis of closed-form dynamic model of Sayano-Shushenskaya hydropower plant: stability, oscillations, and accident." Communications in Nonlinear Science and Numerical Simulation 93 (February 2021): 105530. http://dx.doi.org/10.1016/j.cnsns.2020.105530.

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Huba, Mikulas, and Damir Vrancic. "Extending the Model-Based Controller Design to Higher-Order Plant Models and Measurement Noise." Symmetry 13, no. 5 (May 4, 2021): 798. http://dx.doi.org/10.3390/sym13050798.

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The article extends a model-based controller design to higher-order systems, focusing on the speed and shapes of the closed loop responses, including the noise attenuation. It shows that, to obtain simple but reliable results, it is necessary to pay attention to the initial process identification and modelling and also to modify the target closed-loop transfer functions, which must remain causal. To attenuate high initial control signal peaks, appropriate pre-filters are introduced. In order to work with as few parameters as possible, all higher-order transfer functions (process models, target closed loops, pre-filters and noise-attenuation filters) are selected in the form of binomial filters with multiple time constants. Consequently, the so-called “half-rule”, used to reduce too complex process transfer functions, has been modified accordingly. Because derived controllers can lead to different transient dynamics depending on the context of use, the article recalls the need to introduce dynamic classes of control to clarify the mission of individual types of controllers. Consequently, also the performance evaluation using the total variation (TV) criterion had to be refined. Indeed, in its original version, TV is not suitable to distinguish between reasonable and excessive control effort due to improper tuning and noise. The modified TVs allow evaluating higher order systems with multiple changes in direction of their control signal increase without contributing to the excessive control increments. The advantages of the proposed modifications, compared to the traditional approaches, are made clear through simulation examples.

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Richardson, T., M. Lowenberg, C. Jones, and A. Dubs. "Dynamic gain scheduled control of a Hawk scale model." Aeronautical Journal 111, no. 1121 (July 2007): 461–69. http://dx.doi.org/10.1017/s0001924000004723.

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Abstract When designing flight control laws using linearisations of an aircraft model about different flight conditions, some form of scheduling of the resultant gains will often be required to implement the controller over wide operating regions. In practice, the controller gains are often scheduled against relatively slowly-varying system states such as altitude or velocity. However, it may also be desirable to schedule gains against rapidly-varying states such as angle-of-attack, thereby generating a cyclic dependence through hidden coupling terms. Previous published work at Bristol has developed a numerical method of accounting for this dependence when scheduling state feedback gains against coupled states. The resulting ‘dynamic gain schedule’ is shown to significantly improve the transient response of the aircraft model during rapid manoeuvring and to reduce the chances of control surface actuator position limit saturation. In this paper, the novel design process, using eigenstructure assignment, is applied to a mathematical second-order longitudinal aircraft model which represents an approximate BAe Hawk wind-tunnel model. The dynamic gain scheduled controller is shown to work extremely well in practice when applied to the closed-loop experimental rig. Despite the highly nonlinear characteristics of the model aerodynamics and tailplane actuation system, as well as unmodelled high turbulence levels, dynamic gain scheduling demonstrates stable closed loop control even in regions where the nonlinearities are such that conventional gain scheduling fails to produce a stable response.

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Yue, H., H. Wang, and J. Zhang. "Shaping of molecular weight distribution by iterative learning probability density function control strategies." Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 222, no. 7 (October 8, 2008): 639–53. http://dx.doi.org/10.1243/09596518jsce584.

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A mathematical model is developed for the molecular weight distribution (MWD) of free-radical styrene polymerization in a simulated semi-batch reactor system. The generation function technique and moment method are employed to establish the MWD model in the form of Schultz—Zimm distribution. Both static and dynamic models are described in detail. In order to achieve the closed-loop MWD shaping by output probability density function (PDF) control, the dynamic MWD model is further developed by a linear B-spline approximation. Based on the general form of the B-spline MWD model, iterative learning PDF control strategies have been investigated in order to improve the MWD control performance. Discussions on the simulation studies show the advantages and limitations of the methodology.

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Feng, Yan Bo, and Tao Sun. "Dynamic Analysis of Wafer Slicing by Using Multi Wire Saw." Key Engineering Materials 419-420 (October 2009): 421–24. http://dx.doi.org/10.4028/www.scientific.net/kem.419-420.421.

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Multi wire saw is the important basis of integrate circuit, optoelectronic, photovoltaic industry, and it becomes a promising technology for semiconductor wafer production because of its advantage of slicing large ingot into thin wafers with high efficiency and good quality. In the process of moving, the inevitable wiresaw vibration is directly related to the whole process with both benefit and harm. This paper analyses the wire vibration behavior in cutting area, the dynamic model is built by modeling the interaction between the dynamics of wire and hydrodynamic characteristics of slurry flow, available modal analysis provides closed form expressions for the steady state response, obtain the vibration of wire subject to different process parameters on wire saw manufacturing process.

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Subedi, Dipendra, Ilya Tyapin, and Geir Hovland. "Dynamic Modeling of Planar Multi-Link Flexible Manipulators." Robotics 10, no. 2 (May 11, 2021): 70. http://dx.doi.org/10.3390/robotics10020070.

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A closed-form dynamic model of the planar multi-link flexible manipulator is presented. The assumed modes method is used with the Lagrangian formulation to obtain the dynamic equations of motion. Explicit equations of motion are derived for a three-link case assuming two modes of vibration for each link. The eigenvalue problem associated with the mass boundary conditions, which changes with the robot configuration and payload, is discussed. The time-domain simulation results and frequency-domain analysis of the dynamic model are presented to show the validity of the theoretical derivation.

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Azha Mohd Annuar, Khalil, Nik Azran Ab. Hadi, Mohamad Haniff Harun, Mohd Firdaus Mohd Ab. Halim, Siti Nur Suhaila Mirin, and Arman Hadi Azahar. "Dynamic modelling and analysis of 3D overhead gantry crane system." International Journal of Engineering & Technology 7, no. 3 (July 4, 2018): 1257. http://dx.doi.org/10.14419/ijet.v7i3.10099.

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The overhead gantry crane systems are extensively used in harbours and factories for transportation of heavy loads. The crane speeding up, required for motion, always induces undesirable load swing. This writings present dynamic modelling of a 3D overhead gantry crane sys-tem based on closed-form equations of motion. By using the Lagrange technique, a 3D overhead gantry crane system nonlinear dynamic model is deriving. Then perform a linearization process to obtain a linear model dynamic system. Finally, simulation results systems re-sponses of the derived nonlinear and linear model are presented showing the accuracy and performance of both model.

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Wrana, Bogumił. "Dynamics Coefficient for Two-Phase Soil Model." Studia Geotechnica et Mechanica 36, no. 2 (February 28, 2015): 51–56. http://dx.doi.org/10.2478/sgem-2014-0020.

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Abstract The paper investigates a description of energy dissipation within saturated soils-diffusion of pore-water. Soils are assumed to be two-phase poro-elastic materials, the grain skeleton of which exhibits no irreversible behavior or structural hysteretic damping. Description of motion and deformation of soil is introduced as a system of equations consisting of governing dynamic consolidation equations based on Biot theory. Selected constitutive and kinematic relations for small strains and rotation are used. This paper derives a closed form of analytical solution that characterizes the energy dissipation during steady-state vibrations of nearly and fully saturated poro-elastic columns. Moreover, the paper examines the influence of various physical factors on the fundamental period, maximum amplitude and the fraction of critical damping of the Biot column. Also the so-called dynamic coefficient which shows amplification or attenuation of dynamic response is considered.

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Ladde, Gangarm S., and Youngsoo Seol. "Lévy-type nonlinear stochastic dynamic model, method and analysis." Stochastics and Dynamics 19, no. 05 (August 19, 2019): 1950033. http://dx.doi.org/10.1142/s0219493719500333.

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In this work, we consider a prototype stochastic dynamic model for dynamic processes in biological, chemical, economic, financial, medical, military, physical and technological sciences. The dynamic model is described by Lévy-type nonlinear stochastic differential equation. The model validation is established by the usage of Lyapunov-like function. The basic innovative idea is to transform a nonlinear Lévy-type nonlinear stochastic differential into a simpler stochastic differential equation that is easily tested for the existence and uniqueness theorem. Using the nature of Lyapunov-like function, the existence and uniqueness of solution of the original Lévy-type nonlinear stochastic differential equation is established. The main idea of the proof is based on the property of the one-to-one and onto transformation. As the byproduct of the analysis, it is shown that the closed-form implicit solution of transformed stochastic differential equation is a positive martingale. Furthermore, using the change of measure, a Girsanov-type theorem for Lévy-type nonlinear stochastic dynamic model is established.

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Bashkirtseva, Irina, Ekaterina Ekaterinchuk, and Lev Ryashko. "Stochastic Sensitivity Analysis and Noise-Induced Chaos in 2D Logistic-Type Model." International Journal of Bifurcation and Chaos 26, no. 04 (April 2016): 1650053. http://dx.doi.org/10.1142/s021812741650053x.

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We study the dynamics of stochastically forced 2D logistic-type discrete model. Under random disturbances, stochastic trajectories leaving deterministic attractors can form complex dynamic regimes that have no analogue in the deterministic case. In this paper, we analyze an impact of the random noise on 2D logistic-type model in the bistability zones with coexisting attractors (equilibria, closed invariant curves, discrete cycles). For the constructive probabilistic analysis of the random states distribution around such attractors, a stochastic sensitivity functions technique and method of confidence domains are used. For the considered model, on the base of the suggested approach, a phenomenon of noise-induced transitions between attractors and the generation of chaos are analyzed.

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Swanson, Eric T. "Risk Aversion and the Labor Margin in Dynamic Equilibrium Models." American Economic Review 102, no. 4 (June 1, 2012): 1663–91. http://dx.doi.org/10.1257/aer.102.4.1663.

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The household's labor margin has a substantial effect on risk aversion, and hence asset prices, in dynamic equilibrium models even when utility is additively separable between consumption and labor. This paper derives simple, closed-form expressions for risk aversion that take into account the household's labor margin. Ignoring this margin can dramatically overstate the household's true aversion to risk. Risk premia on assets priced with the stochastic discount factor increase essentially linearly with risk aversion, so measuring risk aversion correctly is crucial for asset pricing in the model.

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Leung, Tim, and Raphael Yan. "Optimal dynamic pairs trading of futures under a two-factor mean-reverting model." International Journal of Financial Engineering 05, no. 03 (September 2018): 1850027. http://dx.doi.org/10.1142/s2424786318500275.

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We study the problem of dynamically trading a pair of futures contracts. We consider a two-factor mean-reverting model, where the spot price tends to evolve around its stochastic equilibrium that is also mean-reverting. We derive the futures price dynamics and determine the optimal futures trading strategy by solving a utility maximization problem. By analyzing the associated Hamilton–Jacobi–Bellman equation, we solve the utility maximization explicitly and provide the optimal trading strategies in closed form. Our strategies are applied to volatility (VIX) futures trading, and illustrated in a series of numerical examples.

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Madsen, Jens Koed, Richard Bailey, Ernesto Carrella, and Philipp Koralus. "Analytic Versus Computational Cognitive Models: Agent-Based Modeling as a Tool in Cognitive Sciences." Current Directions in Psychological Science 28, no. 3 (March 29, 2019): 299–305. http://dx.doi.org/10.1177/0963721419834547.

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Computational cognitive models typically focus on individual behavior in isolation. Models frequently employ closed-form solutions in which a state of the system can be computed if all parameters and functions are known. However, closed-form models are challenged when used to predict behaviors for dynamic, adaptive, and heterogeneous agents. Such systems are complex and typically cannot be predicted or explained by analytical solutions without application of significant simplifications. In addressing this problem, cognitive and social psychological sciences may profitably use agent-based models, which are widely employed to simulate complex systems. We show that these models can be used to explore how cognitive models scale in social networks to calibrate model parameters, to validate model predictions, and to engender model development. Agent-based models allow for controlled experiments of complex systems and can explore how changes in low-level parameters impact the behavior at a whole-system level. They can test predictions of cognitive models and may function as a bridge between individually and socially oriented models.

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Chang, Hao, Xi-min Rong, Hui Zhao, and Chu-bing Zhang. "Optimal Investment and Consumption Decisions under the Constant Elasticity of Variance Model." Mathematical Problems in Engineering 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/974098.

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We consider an investment and consumption problem under the constant elasticity of variance (CEV) model, which is an extension of the original Merton’s problem. In the proposed model, stock price dynamics is assumed to follow a CEV model and our goal is to maximize the expected discounted utility of consumption and terminal wealth. Firstly, we apply dynamic programming principle to obtain the Hamilton-Jacobi-Bellman (HJB) equation for the value function. Secondly, we choose power utility and logarithm utility for our analysis and apply variable change technique to obtain the closed-form solutions to the optimal investment and consumption strategies. Finally, we provide a numerical example to illustrate the effect of market parameters on the optimal investment and consumption strategies.

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Wen, Yuzhen, and Chuancun Yin. "Solution of Hamilton-Jacobi-Bellman Equation in Optimal Reinsurance Strategy under Dynamic VaR Constraint." Journal of Function Spaces 2019 (January 8, 2019): 1–7. http://dx.doi.org/10.1155/2019/6750892.

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This paper analyzes the optimal reinsurance strategy for insurers with a generalized mean-variance premium principle. The surplus process of the insurer is described by the diffusion model which is an approximation of the classical Cramér-Lunderberg model. We assume the dynamic VaR constraints for proportional reinsurance. We obtain the closed form expression of the optimal reinsurance strategy and corresponding survival probability under proportional reinsurance.

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LI, ZHONG-FEI, KAI W. NG, KEN SENG TAN, and HAILIANG YANG. "OPTIMAL CONSTANT-REBALANCED PORTFOLIO INVESTMENT STRATEGIES FOR DYNAMIC PORTFOLIO SELECTION." International Journal of Theoretical and Applied Finance 09, no. 06 (September 2006): 951–66. http://dx.doi.org/10.1142/s0219024906003883.

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In this paper we propose a variant of the continuous-time Markowitz mean-variance model by incorporating the Earnings-at-Risk measure in the portfolio optimization problem. Under the Black-Scholes framework, we obtain closed-form expressions for the optimal constant-rebalanced portfolio (CRP) investment strategy. We also derive explicitly the corresponding mean-EaR efficient portfolio frontier, which is a generalization of the Markowitz mean-variance efficient frontier.

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Vecer, Jan. "Dynamic Scoring: Probabilistic Model Selection Based on Utility Maximization." Entropy 21, no. 1 (January 8, 2019): 36. http://dx.doi.org/10.3390/e21010036.

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We propose a novel approach of model selection for probability estimates that may be applied in time evolving setting. Specifically, we show that any discrepancy between different probability estimates opens a possibility to compare them by trading on a hypothetical betting market that trades probabilities. We describe the mechanism of such a market, where agents maximize some utility function which determines the optimal trading volume for given odds. This procedure produces supply and demand functions, that determine the size of the bet as a function of a trading probability. These functions are closed form for the choice of logarithmic and exponential utility functions. Having two probability estimates and the corresponding supply and demand functions, the trade matching these estimates happens at the intersection of the supply and demand functions. We show that an agent using correct probabilities will realize a profit in expectation when trading against any other set of probabilities. The expected profit realized by the correct view of the market probabilities can be used as a measure of information in terms of statistical divergence.

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Tkachev, Stepan, Yaroslav Mashtakov, Danil Ivanov, Dmitry Roldugin, and Mikhail Ovchinnikov. "Effect of Reaction Wheel Imbalances on Attitude and Stabilization Accuracy." Aerospace 8, no. 9 (September 6, 2021): 252. http://dx.doi.org/10.3390/aerospace8090252.

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In this paper, the study of stabilization accuracy of a satellite equipped with a set of reaction wheels (RW) is presented. The model of motion takes into account possible static and dynamic reaction wheel imbalances. Due to the complexity of the model, which leads to the numerical issues, the effects of dynamic and static imbalances on inertial stabilization are studied analytically. As a result, estimations of the attitude and stabilization accuracy are presented in closed form.

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BERTARELLI, EMANUELE, RAFFAELE ARDITO, RAFFAELE ARDITO, ALBERTO CORIGLIANO, and ROBERTO CONTRO. "A PLATE MODEL FOR THE EVALUATION OF PULL-IN INSTABILITY OCCURRENCE IN ELECTROSTATIC MICROPUMP DIAPHRAGMS." International Journal of Applied Mechanics 03, no. 01 (March 2011): 1–19. http://dx.doi.org/10.1142/s1758825111000841.

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This work deals with the mechanical response of circular microplates undergoing electrostatic actuation. A one degree-of-freedom model and Finite Element approaches are exploited in a nondimensional framework. First, a quasi-static conventional approach is adopted. From the one degree-of-freedom model a closed form solution for the plate electromechanical problem is obtained for the first time. Then a strong attention is paid to pull-in phenomena in nonlinear dynamics. Dynamic behavior of the structure is explored, leading to the identification of a pull-in loading condition which is dependent on the quality factor Q. The outcomes are discussed and widely compared with those available in the literature for similar microsystems.

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Almeida, Caio Ibsen Rodrigues de. "A Note on the Relation Between Principal Components and Dynamic Factors in Affine Term Structure Models." Brazilian Review of Econometrics 25, no. 1 (May 1, 2005): 89. http://dx.doi.org/10.12660/bre.v25n12005.2673.

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In econometric applications of the term structure, affine models are among the most used ones. Nevertheless, even presenting a closed form characteristic function, its estimation procedure still presents many points to be understood and difficulties to be removed. In this note, we address one of these points. Suppose we estimate an affine dynamic term structure model, and also apply principal component analysis to the interest rate database available. A very plausible question would inquire about the relation (if any) between the principal components obtained assuming no dynamic restrictions, and the dynamic factors estimated using the proposed term structure model. We answer this question when estimating a standard affine model using zero coupon data. We show that each principal component can be approximated by a linear transformation of the dynamic factors. Although simple, this is an important step to the understanding of the mechanics of dynamic affine term structure models. A numerical example using U.S. zero data illustrates the result

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Yang, Jian Xin, Ben Zhao, and Chun Li Li. "Inverse Kinematics and Dynamics of a 3-DOF Spatial Parallel Manipulator." Applied Mechanics and Materials 229-231 (November 2012): 2280–84. http://dx.doi.org/10.4028/www.scientific.net/amm.229-231.2280.

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Recently the parallel manipulator with less DOFs has attracted industry and academia, but the research on its dynamics is still an open problem. In this paper, the inverse dynamic of a spatial parallel manipulator with two translational degrees of freedom and one rotational degree of freedom is studied based on the Newton-Euler approach. The kinematics analysis is firstly performed in a closed form. The inverse dynamic equation of this manipulator is formulated by using the Lagrange multiplier approach and choosing the Cartesian position and orientation as the generalized coordinates. Finally a numerical example is given for the kinematic and dynamic simulation of this manipulator. The model will be useful to improve the design of the mechanical components and the control algorithm.

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Chasalevris, Athanasios. "An Investigation on the Dynamics of High-Speed Systems Using Nonlinear Analytical Floating Ring Bearing Models." International Journal of Rotating Machinery 2016 (2016): 1–22. http://dx.doi.org/10.1155/2016/7817134.

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The scope of this paper is to investigate the dynamics of a rotor-bearing system of high-speed under recently developed analytical bearing models. The development of a theory that can yield the dynamic response of a high-speed system without short/long bearing approximation and without time-consuming numerical methods for the finite-length bearing model is the outcome of this work. The rotor system is introduced as a rigid body so that the dynamics of the system are influenced only from the nonlinear bearing forces which are introduced with closed form expressions. The outcome is a system of nonlinear equations and its solution produces the dynamic response of the high-speed system using exact analytical solution for the bearing forces. The transient dynamic response of the system is evaluated through the wide range of rotating speed and under different bearing solutions including short bearing approximation, presenting the subsynchronous components that are developed when instabilities occur. Time-frequency analysis of the resulting response time-series is presented and the outcome is compared with that obtained from numerical solution of the bearing lubrication and with the short bearing approximation model.

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Manring, N. D., and R. E. Johnson. "Modeling and Designing a Variable-Displacement Open-Loop Pump." Journal of Dynamic Systems, Measurement, and Control 118, no. 2 (June 1, 1996): 267–71. http://dx.doi.org/10.1115/1.2802313.

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This study develops closed-form equations that may be used to guide the up-front design of a variable-displacement pump. In particular, the initial design of the control actuation system and the controller flow-gain is considered. A dynamic model of the pumping system is also presented and the dynamic effect of parameter variations such as actuator volume, discharge-hose volume, controller flow-gain and system leakage is discussed.

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Montazeri-Gh, Morteza, and Ali Rasti. "Analyzing different numerical linearization methods for the dynamic model of a turbofan engine." Mechanics & Industry 20, no. 3 (2019): 303. http://dx.doi.org/10.1051/meca/2019012.

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State equations of aircraft engine dynamics usually required for controller design, are not available in closed form, so the dynamic models are commonly linearized numerically. Development of model-based controllers for aeroengine in the recent years necessitates the use of accurate linear models. However, there is no comprehensive study about the accuracy of the linear models obtained from nonlinear engine models. In this paper, the accuracy of different numerical linearization methods for linearizing the dynamic model of a turbofan engine is investigated. For this objective, a thermodynamic model of a two-spool turbofan engine is considered and three various numerical linearization methods are defined. The first method is based on the perturbation technique, including ordinary and central difference perturbation. The second one is a system identification method and the third one is tuning the elements of the matrices of the linear state-space model using genetic algorithm. The accuracy analysis of the presented procedures is performed for both single-input and double-input cases. In the single-input case, the fuel mass flow rate and in the double-input, in addition to the fuel, the bleed air taken from between the two compressors are considered as control variables. Finally, by defining different error criterions, the accuracy of the linearization methods is evaluated. The results show that the linear model obtained from system identification and central difference perturbation methods have higher percentage of compliances compared to the others.

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Chang, Hao, and Xi-min Rong. "Dynamic Mean-Variance Model with Borrowing Constraint under the Constant Elasticity of Variance Process." Journal of Applied Mathematics 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/348059.

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This paper studies a continuous-time dynamic mean-variance portfolio selection problem with the constraint of a higher borrowing rate, in which stock price is governed by a constant elasticity of variance (CEV) process. Firstly, we apply Lagrange duality theorem to change an original mean-variance problem into an equivalent optimization one. Secondly, we use dynamic programming principle to get the Hamilton-Jacobi-Bellman (HJB) equation for the value function, which is a more sophisticated nonlinear second-order partial differential equation. Furthermore, we use Legendre transform and dual theory to transform the HJB equation into its dual one. Finally, the closed-form solutions to the optimal investment strategy and efficient frontier are derived by applying variable change technique.

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Journal articles on the topic 'Closed-form dynamic model'

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