Robustness Analysis of an Electrohydraulic Steering Control System Based on the Estimated Uncertainty Model

The impossibility of replacing hydraulic drives with other type drives in heavy duty machinery is the main reason for the development of a system for controlling hydraulic power steering. Moreover, the need for remote automatic control of the steering in specific types of mobile machinery leads to significant scientific interest in the design of embedded systems for controlling electro-hydraulic steering units. This article introduces an approach, which has been developed by authors, for robust stability and robust performance analysis of two embedded systems for controlling electro-hydraulic power steering in mobile machinery. It is based on the suggested new more realistic “black box” SIMO model with output multiplicative uncertainty. The uncertainty is obtained by parameters confidence interval and Gauss approximation formula. The embedded control systems used a linear-quadratic Gaussian (LQG) controller and H∞ controller. The synthesis of the controllers was performed on the basis of a nominal part of an uncertainty model. Robust stability and robust performance analyses were performed in the framework of a so-called structured singular value, μ. The obtained theoretical results were experimentally approved by real experiments with both of the developed control systems, which were physically realized as a laboratory test rig.

Designing a single-vendor and multiple-buyers' integrated production inventory model for interval type-2 fuzzy demand and fuzzy rule based deterioration

In this paper, a single-vendor and multiple-buyers' integrated production inventory model is investigated where deterioration rate of the item is assumed to change in accordance with the weather conditions of a particular region. It relies upon the values of certain attributes that have a direct influence on the extent of deterioration. These parameter values are easily forecasted and thereby can be utilized to determine the item depletion rate, which is executed here using Mamdani fuzzy inference scheme. Besides, a nearest interval approximation formula for the defuzzification of interval type-2 fuzzy number (IT2FN) is developed. Its application in the proposed model is brought off by considering imprecise demand patterns at the buyers' locations which are in the form of IT2FNs. The model optimizes the total number of shipments to be made to the buyers within a complete cycle so as to minimize the overall integrated cost incurred. An optimization problem with interval objective function is formulated. A detailed illustration of the theoretical results is further demonstrated with the help of numerical example, followed by sensitivity analysis which provides insights into better decision making.

Structure Dynamic Response of Amphibious Aircraft Induced by Water-Taxiing

The significant dynamic response under the combined impact of aerodynamic and hydrodynamic forces could be likely to appear because of the structural flexibility, when taxiing on the water surface for amphibious aircraft. Meanwhile, the modal characteristics of the structure are also affected by the additional motion of water. These require that the influence of the structural elasticity and the coupling effect between water and structure should be considered in dynamic response analysis of water-taxiing. According to the peculiarities of the amphibious aircraft, structural dynamics model is based on the distribution of stiffness and mass, Virtual Mass Theory is utilized to solve the wet modes on the water surface, rational function approximations of unsteady aerodynamic force in time-domain are constructed by the Minimum-State Approximation Formula, and loose coupling method is employed to simulate the hydrodynamic elastic response under the encounter of amphibian with single wave and repeated waves, respectively. Analysis of dynamic characteristics during the water-taxiing of the amphibious aircraft has been achieved in this work. The results show that wet natural frequencies of the aircraft have different degrees of decline compared with the dry frequencies because of the influence of added water on the hull, and the response amplitude of dynamic loads obtained by using the wet modes have some certain extent decrease compared with the dry modes. The dynamic amplitude of different locations changes in different degree relatives to the center of gravity position, which reflects the influence of structural elasticity. Due to the excitation of single wave and repeated waves, the structural vibration amplitude will increase rapidly, but the amplitude shows a certain divergence trend under the action of repeated waves with a given oscillation frequency, which is more severe for structural strength design.

SPX Calibration of Option Approximations under Rough Heston Model

The volatility of stock return does not follow the classical Brownian motion, but instead it follows a form that is closely related to fractional Brownian motion. Taking advantage of this information, the rough version of classical Heston model also known as rough Heston model has been derived as the macroscopic level of microscopic Hawkes process where it acts as a high-frequency price process. Unlike the pricing of options under the classical Heston model, it is significantly harder to price options under rough Heston model due to the large computational cost needed. Previously, some studies have proposed a few approximation methods to speed up the option computation. In this study, we calibrate five different approximation methods for pricing options under rough Heston model to SPX options, namely a third-order Padé approximant, three variants of fourth-order Padé approximant, and an approximation formula made from decomposing the option price. The main purpose of this study is to fill in the gap on lack of numerical study on real market options. The numerical experiment includes calibration of the mentioned methods to SPX options before and after the Lehman Brothers collapse.

L2 Boundedness of Discrete Double Hilbert Transform Along polynomials

We will show $L^{2}$ boundedness of Discrete Double Hilbert Transform along polynomials satisfying some conditions. Double Hilbert exponential sum along polynomials:$\mu(\xi)$ is Fourier multiplier of discrete double Hilbert transform along polynomials. In chapter 1, we define the reverse Newton diagram. In chapter 2, We make approximation formula for the multiplier of one valuable discrete Hilbert transform by study circle method. In chapter 3, We obtain result that $\mu(\xi)$ is bounded by constants if $|D|\geq2$ or all $(m,n)$ are not on one line passing through the origin. We study property of $1/(qt^{n})$ and use circle method (Propsotion 2.1) to calculate sums. We also envision combinatoric thinking about $\mathbb{N}^{2}$ lattice points in j-k plane for some estimates. Finally, we use geometric property of some inequalities about $(m,n)\in\Lambda$ to prove Theorem 3.3. In chapter 4, We obtain the fact that $\mu(\xi)$ is bounded by sums which are related to $\log_{2}({\xi_{1}-a_{1}\slash {q}})$ and $\log_{2}({\xi_{2}-a_{2}\slash {q}})$ and the boundedness of double Hilbert exponential sum for even polynomials with torsion without conditions in Theorem 3.3. We also use $\mathbb{N}^{2}$ lattice points in j-k plane and Proposition 2.1 which are shown in chapter 2 and some estimates to show that Fourier multiplier of discrete double Hilbert transform is bounded by terms about $\log$ and integral this with torsion is bounded by constants.

An analytical approximation formula for the pricing of credit default swaps with regime switching

We derive an analytical approximation for the price of a credit default swap (CDS) contract under a regime-switching Black–Scholes model. To achieve this, we first derive a general formula for the CDS price, and establish the relationship between the unknown no-default probability and the price of a down-and-out binary option written on the same reference asset. Then we present a two-step procedure: the first step assumes that all the future information of the Markov chain is known at the current time and presents an approximation for the conditional price under a time-dependent Black–Scholes model, based on which the second step derives the target option pricing formula written in a Fourier cosine series. The efficiency and accuracy of the newly derived formula are demonstrated through numerical experiments. doi:10.1017/S1446181121000274

Pricing timer options: second-order multiscale stochastic volatility asymptotics

We study the pricing of timer options in a class of stochastic volatility models, where the volatility is driven by two diffusions—one fast mean-reverting and the other slowly varying. Employing singular and regular perturbation techniques, full second-order asymptotics of the option price are established. In addition, we investigate an implied volatility in terms of effective maturity for the timer options, and derive its second-order expansion based on our pricing asymptotics. A numerical experiment shows that the price approximation formula has a high level of accuracy, and the implied volatility in terms of its effective maturity is illustrated. doi:10.1017/S1446181121000249

Lateral resolution limit of laser Doppler vibrometer microscopes for the measurement of surface acoustic waves

The lateral or transverse resolution of single-point interferometers for vibration measurement is especially critical for microelectromechanical systems (MEMS) vibrating up to the gigahertz range. In this regime, the acoustic wavelengths are typically in the range of the size of the laser focus. Thus, a successful vibration measurement requires distinct knowledge about the lateral resolution limit and its dependencies with instrumentation parameters. In this paper, we derive an analytic approximation formula, which allows for estimation of the systematic measurement deviation of the vibration amplitude and, thus, a definition of the lateral resolution limit of single-point interferometers for vibration measurement. Further, a compensation and an optimum numerical aperture are proposed the reduce the measurement deviation. For this, the model includes a laser-interferometer microscope of Mach-Zehnder type with Gaussian laser beams considering the Gouy effect and wavefront curvature. As a measurement scenario, an unidirectional surface acoustic wave (SAW) is regarded. The theoretic findings have been validated in the experiment with a representative vibration measurement on a SAW filter at $$433\,{\mathrm {MHz}}$$ 433 MHz with our heterodyne laser-Doppler interferometer with offset-locked semiconductor lasers. The provided formulas help instrument designers and users to choose suitable instrument parameters, especially the numerical aperture of the utilized microscope objective.

AN ANALYTICAL APPROXIMATION FORMULA FOR THE PRICING OF CREDIT DEFAULT SWAPS WITH REGIME SWITCHING

We derive an analytical approximation for the price of a credit default swap (CDS) contract under a regime-switching Black–Scholes model. To achieve this, we first derive a general formula for the CDS price, and establish the relationship between the unknown no-default probability and the price of a down-and-out binary option written on the same reference asset. Then we present a two-step procedure: the first step assumes that all the future information of the Markov chain is known at the current time and presents an approximation for the conditional price under a time-dependent Black–Scholes model, based on which the second step derives the target option pricing formula written in a Fourier cosine series. The efficiency and accuracy of the newly derived formula are demonstrated through numerical experiments.