Approximate Discrete Model Research Articles

Modular approximate discrete modeling for blisk system with triple closed-loop equivalence method

At present, the lumped-parametric model is often used in the preliminary design of bladed disks. However, the lack of systematic modeling methods leads to high errors. In order to develop the systematic modeling method and improve the equivalence accuracy, this paper considers the comprehensive equivalence from the aspects of natural characteristics, transient forced responses, and steady-state forced responses under aerodynamic excitations. This paper includes two novelties. First, based on the modular equation of blisk system, an approximate discrete model is derived for computational efficiency. Second, a triple closed-loop equivalence method with modal weight optimization is developed innovatively for optimal equivalence parameters. The method can significantly improve the accuracy of element parameters in the lumped-parametric model and achieve the comprehensive equivalence to actual blisk. Compared with the existing equivalence method, the average errors of natural frequencies in the whole mode interval and in the high-density mode interval are reduced by 41.75 % and 36.76 %, respectively. The maximum and average displacement errors of the transient response are reduced by 51.76 % and 58.98 %, respectively. Furthermore, vibration characteristics of the mass and stiffness mistuned blisks are analyzed under traveling wake excitation during acceleration and deceleration processes by approximate discrete model and determined parameters.

A first order continuous timeVARwith random coefficients

This article considers a first order continuous time vector autoregression with random coefficients. We discuss some difficulties that arise when the exact discrete analogue is used for estimating the continuous time parameters and provide an estimation method based on an approximate discrete model. Some expressions for the estimator of the drift parameter matrix, for its approximated bias and for the covariance matrix of the parameter estimates are derived. The finite sample performance of the proposed method is studied by a Monte Carlo experiment. We also illustrate the advantages of our model in an application on the expectations theory of the term structure of interest rates. Results show that the performance of the proposed methodology is good, and allowing for time variation on coefficients results in large reductions in the root mean square error of the parameter estimates.

Stability Effect of Control Weight on Multiloop COT-Controlled Buck Converter With PI Compensator and Small Output Capacitor ESR

Multiloop constant on-time (COT) controlled buck converter uses two weight resistors for sensing inductor current and detecting output voltage in its inner loop. When an output capacitor with a small equivalent series resistance (ESR) is employed, the converter will suffer the risk of instability due to different weight settings of inductor current and output voltage using a proportional-integral (PI) compensation gain in the outer voltage loop. However, no attention has been paid for their stability effects, which are important for designing the inner loop and outer voltage loop. To address these issues, a piecewise linear model is established for multiloop COT-controlled buck converter. Circuit parameter-related bifurcation behaviors and control weight-related dynamical distributions are explored to demonstrate these stability effects. Furthermore, by deriving an approximate discrete model, a control weight-related stability criterion is expressed explicitly, from which stability boundaries for dividing the normally stable and abnormally unstable operation parameter regions are thereby yielded. Besides, control weight-related transient performances under different circuit parameter settings are analyzed. Finally, PSIM circuit simulations and hardware circuit experiments verify the theoretical analysis well.

Discrete model for circular and square rigid tanks with concentric openings – Seismic analysis of a historic water tower

The dynamic characteristics of rigid, cylindrical or square tanks with concentric openings (manholes) are studied using detailed FEM and approximate discrete models. Parametric studies are presented, in the form of practical design charts, for various geometrical configurations. Further on, the dynamic analysis of a historic water tower is attempted, where the hollow cylindrical tank and the supporting structure are modelled in detail. Comparison studies to other approximate analyses are discussed. Seismic analyses of the water tower are performed considering fixed base conditions, the usual design assumption, and complete fluid–structure-soil interaction effects. The dynamic characteristics of the soil are accounted via a simplified frequency-independent mass-spring-damping model for rigid ring foundations.

Análisis por el método de elementos finitos del comportamiento de las pastillas de freno ABS con base de acero y zinc discretizando el elemento continuo utilizando software CAE

En el presente trabajo se realizó el estudio del comportamiento de las pastillas de freno de un sistema ABS utilizando el método de análisis por elementos finitos. Este método esta basado en la transformación de un cuerpo de naturaleza continua en un modelo discreto aproximado, esta transformación se conoce como la discretización del modelo. Por esta razón, una de las acciones más críticas es la de realizar un mallado de calidad, de manera que esto permite mejorar la convergencia de resultados optimizando la carga computacional, lo cual posibilita que el problema pueda ser resuelto en un menor tiempo. El uso de herramientas de software para realizar este tipo de estudio tiene la ventaja de que en el pos procesamiento se puede escoger el tipo de parámetros que se quiere estudiar, en este caso se analizaron variables mecánicas y térmicas que permitieron caracterizar el comportamiento de los materiales de las pastillas. El estudio se efectuó para dos materiales: Trimat MN 1081 que está compuesto de acero y filamentos no ferrosos y Trimat GZC compuesto de fibras de zinc, de esta manera se obtuvieron características importantes de estos materiales, como son el esfuerzo, la deformación, penetración, flujo de calor y energía. En base al método desarrollado y a los resultados obtenidos, se realizará un estudio con materiales alternativos, lo cual permitirá determinar la viabilidad de usarlos en busca de obtener resultados óptimos tanto en características mecánicas como en costos.

Dynamic stability analysis of torsional vibrations of a shaft system connected by a Hooke׳s joint through a continuous system model

Stability of parametrically excited torsional vibrations of a shaft system composed of two torsionally elastic shafts interconnected through a Hooke׳s joint is studied. The shafts are considered to be continuous (distributed-parameter) systems and an approximate discrete model for the torsional vibrations of the shaft system is derived via a finite element scheme. The stability of the solutions of the linearized equations of motion, consisting of a set of Mathieu–Hill type equations, is examined by means of a monodromy matrix method and the results are presented in the form of a Strutt–Ince diagram visualizing the effects of the system parameters on the stability of the shaft system.

Runge–Kutta model-based adaptive predictive control mechanism for non-linear processes

This paper proposes a novel non-linear model predictive control mechanism for non-linear systems. The idea behind the mechanism is that the so-called Runge–Kutta model of a continuous-time non-linear system can be regarded as an approximate discrete model and employed in a generalized predictive control loop for prediction and derivative calculation purposes. Additionally, the Runge–Kutta model of the system is used for state estimation in the extended Kalman filter framework and online parameter adaptation. The proposed method has been tested on two different non-linear systems. Simulation results have revealed the effectiveness of the proposed method for different cases.

A Runge-Kutta Model Based Adaptive Predictive Controller for Nonlinear Systems

The aim of this paper is to illustrate the application of the previously proposed [1] Runge-Kutta (RK) model based nonlinear model predictive control method to the Continuously Stirred Tank Reactor (CSTR) system. The method utilizes the so-called Runge-Kutta model of a continuous-time nonlinear system as an approximate discrete model and employes it in the Model Predictive Control (GPC) loop. In the proposed method, the RK model is not only used for control purposes, but also it is utilized for state estimation in the Extended Kalman Filter (EKF) framework and on-line parameter adaptation. The results show the effectiveness of the method in control, state estimation and parameter adaptation tasks.

Stability Analysis of FPGA-Based Control of Brushless DC Motors and Generators Using Digital PWM Technique

Brushless dc (BLDC) drives have received significant attention, owing to their high efficiency, electromagnetic interference, and high mechanical reliability due to the absence of brushes in commercial, residential, and industrial applications. In generating mode, they are very suitable for small wind and hydro generator applications, as well as integrated starter alternators in hybrid electric vehicles. This paper discusses digital pulsewidth modulation control for a BLDC drive in both motoring and generating modes of operation. This control strategy is simple and robust, requires no current sensors, and is not computationally intensive. Owing to these attributes, the technique can be implemented on a low-cost field-programmable gate array. This paper investigates potential stability issues due to the simplicity of this control under various conditions of load disturbances and also owing to the reduction in processor capability. Lyapunov stability criteria have been used to analyze the closed-loop stability of the system. Furthermore, an approximate discrete model has been developed, and the stability of the system is analyzed to ensure closed-loop operation under various sets of loads, speeds, and input voltages. Simulation and experimental results have been presented to verify the claims.

Fault-tolerant control for a class of nonlinear sampled-data systems via a Euler approximate observer

In this paper, a fault-tolerant control (FTC) scheme is developed for a class of nonlinear sampled-data systems. First, a Euler approximate discrete model is used to describe the plant under the sampling. Under this model, an observer-based fault estimation method is proposed. To guarantee the accuracy of both the state and fault estimation values, the conditions to make the approximate model consistent with the exact model are presented. Then, an active fault-tolerant controller, which has a constraint condition for the sampling time, is designed to make the faulty system stable. Finally, an inverted pendulum is used to show the efficiency of the proposed method.

The transfer-matrix and max-plus algebra method for global combinatorial optimization: Application to cyclic and polyhedral water clusters

A new method for the combinatorial optimization of quasi-one-dimensional systems is presented. This method is in close analogy with the well-known transfer-matrix method. The method allows for the calculation of the lowest energy levels of the system. However, when finding the ground and some low-lying states of large complex systems, this method is more economical when compared to the standard transfer-matrix method. The method presented here is based on max-plus algebra, which has maximization and addition as its basic arithmetic operations. For the explanation of this method we use cyclic water clusters as simple examples. The efficiency of the max-plus-algebraic method is demonstrated in the course of global combinatorial optimization of hydrogen bond arrangements in large polyhedral water clusters with fixed positions of the oxygen atoms. The energy of the clusters is estimated using approximate discrete models for the intermolecular interactions.

Assessing the relationships between Nationalism, Ethnocentrism, and Individualism in Flanders using Bergstrom's approximate discrete model

Although Nationalism, Ethnocentrism, and Individualism in Flanders have been the subject of several studies before, a longitudinal analysis has not been performed on all three concepts simultaneously nor have their relationships and the direction of their relationships been studied in continuous time. In this study we performed a continuous‐time state‐space analysis on panel data collected from 1274 subjects, in the years 1991, 1995 and 1999. The LISREL program is used for estimating the approximate discrete model (ADM), and for comparison, also the exact discrete model (EDM) is estimated by means of the Mx program. Details of continuous time modeling, especially the EDM and ADM, are dealt with. Individualism and Ethnocentrism turn out to be connected in a moderately strong feedback relationship with the effect from Individualism towards Ethnocentrism somewhat stronger than that in the opposite direction. Both Individualism and Ethnocentrism have small effects on Nationalism. The autoregression functions, cross‐lagged effect functions, and mean predictions are shown.

Concurrent material and structural optimization of hollow plate with truss-like material

In this paper, optimum stress distribution for hollow plates composed of linear cellular materials (LCMs), a kind of truss-like material, is investigated. To reduce the computational cost, we model the material as micropolar continua representation. Two classes of design variables, relative density, and cell-size distribution of truss-like materials are to be determined by optimization under given total material volume constraint. And the concurrent designs of material and structure are obtained for three different optimization formulations. For the first formulation, we aim at the minimization of the maximum stress that appears at the initial uniform design; for the second formulation, we minimize the highest stress within the specified point set. As the yield strength of truss-like material is dependent on the relative material density, we minimize the ratio of stress over the corresponding yield strength along the hole boundary in our third formulation, which maximizes the strength reserve and seems more rational. The numerical results for the three objectives validate the concurrent optimization method proposed in this paper. And the influence of ply angle (angle between the principle direction of material and the axes of the system’s coordinates) on the optimum result is discussed. The dependence of optimum design on finite element meshes is also investigated. An approximate discrete model is established to verify the method proposed in this paper, and the stress concentration near a hole is reduced significantly.

ON THE STABILITY OF AN ACCURATE DISCRETE-TIME MODEL OF THE DCM BOOST CONVERTER

An accurate discrete-time model of a voltage-fed boost converter, which operates under the discontinuous mode (DCM), is derived. Based on this, bifurcation and chaos analysis is carried out to obtain a relationship equation of parameters, which exactly determines the ranges of parameters for the steady operation of the boost converter. Compared with an existing approximate discrete model, the proposed model has unique merits in exhibiting and explaining the boost converter's non-linear phenomena.

Surface refractive index field estimation from multiple radars

Retrieval of surface layer refractivity via the method of Fabry et al. (1997) is considered. A mathematical framework is constructed, and signal processing algorithms are derived that facilitate refractivity retrieval from the returns from multiple radars viewing a common geographical area. In particular, an approximate discrete model is derived to relate the measured phases to the surface layer refractivity fields, and a modified least squares estimation algorithm is then proposed for the resulting, often ill‐conditioned, inversion problem. Because the measurement technique is subject to modulo 2π uncertainties which impact retrievals, a novel algorithm which jointly estimates the unwrapped phases and refractive index (RI) field is also provided. Numerical results indicate the effectiveness of the derived algorithms in both the single‐ and multiple‐radar cases, as well as clearly establishing that having multiple views of the same geographical area from separate radars provides for significant improvement of the RI field estimates.

Vibration of an Eccentrically Clamped Annular Plate

Small amplitude vibration of an eccentric annular plate, which is free along its outer edge and clamped along the interior, is investigated through experimental and analytical methods. A disk with this geometry, or a stacked array in which the clamping and symmetry axes of each disk are nominally coincident, is common in data storage and brake systems applications. In the present case, the geometric imperfections on the boundary can have important implications for the disk’s dynamic response. Changes that occur in the natural frequency spectrum, the mode shapes, and the free response under eccentric mounting are studied through laboratory measurements and an approximate discrete model of the plate. The natural frequencies and modes are found through global discretization of the Kamke quotient for a classical thin plate. For the axisymmetric geometry, the natural frequencies of the “sine” and “cosine” vibration modes for a specified number of nodal diameters are repeated. With increasing eccentricity, on the other hand, each pair of repeated frequencies splits at a rate that depends on the number of nodal diameters. Over a range of clamping and eccentricity ratios, the model’s predictions are compared to the measured results.