A statistical model for dating uncertainties in Greenland ice core records

<p>Most layer-counting based paleoclimate proxy records have non-negligible uncertainties that arise from both the proxy measurement and the dating processes. Proper knowledge of the dating uncertainties in paleoclimatic ice core records is important for a rigorous propagation to further analyses; for example for identification and dating of stadial-interstadial transitions during glacial intervals, for model-data comparisons in general, or to provide a complete uncertainty quantification of early warning signals. We develop a statistical model that incorporates the dating uncertainties of the Greenland Ice Core Chronology 2005 (GICC05), which includes the uncertainty associated with layer counting. We express the number of layers per depth interval as the sum of a structural component that represents both underlying physical processes and biases in layer counting, described by a linear regression model, and a noise component that represents the internal variation of the underlying physical processes, as well as residual counting errors. We find the residual components to be described well by a Gaussian white noise process that appear to be largely uncorrelated, allowing us to represent the dating uncertainties using a multivariate Gaussian process. This means that we can easily produce simulations as well as incorporate tie-points from other proxy records to match the GICC05 time scale to other chronologies. Moreover, this multivariate Gaussian process exhibits Markov properties which grants a substantial gain in computational efficiency.</p>

Time Varying Loads and White Noise on an SDOF System with Bouc Hysteresis Using Gaussian Closure

In a recent publication [H. Waubke and C. Kasess, Gaussian closure technique applied to the hysteretic Bouc model with nonzero mean white noise excitation, J. Sound Vibr. 382 (2016) 258–273], the response of a single-degree-of-freedom (SDOF) system under Gaussian white noise and a constant dead load is presented. The system has a hysteresis described by Bouc [R. Bouc, Forced vibration of mechanical systems with hysteresis, in Proc. Fourth Conference on Nonlinear Oscillation (Prague, 1967), p. 315]. New is the usage of a slowly time-varying deterministic load added to the Gaussian white noise process. The transient solution is calculated using the Gaussian closure technique together with an explicit time step procedure. All moments in the Gaussian closure technique are evaluated analytically. The results of the Gaussian closure technique are in good agreement with the results from the Monte-Carlo method.

On the Basel Liquidity Formula for Elliptical Distributions

A justification of the Basel liquidity formula for risk capital in the trading book is given under the assumption that market risk-factor changes form a Gaussian white noise process over 10-day time steps and changes to P&L (profit-and-loss) are linear in the risk-factor changes. A generalization of the formula is derived under the more general assumption that risk-factor changes are multivariate elliptical. It is shown that the Basel formula tends to be conservative when the elliptical distributions are from the heavier-tailed generalized hyperbolic family. As a by-product of the analysis, a Fourier approach to calculating expected shortfall for general symmetric loss distributions is developed.

LQG Control of Across-Wind Response of a Tall Building with AMD

Modern tall buildings are more flexible so occur excessive wind-induced vibration resulting in occupant discomfort and structural safety. Many studies to reduce such a wind-induced vibration using a feedback controller and auxiliary devices have been conducted .The optimal control law of linear quadratic Gaussian (LQG) controller is used for reducing the across-wind vibration response of a tall building with an active mass damper (AMD). Fluctuating across-wind load treated as a Gaussian white noise process is simulated numerically in time domain. And using this simulated across-wind load estimated across-wind vibration responses of tall building with AMD using LQG controller.

Active Control of Along-Wind Response of a Tall Building with AMD Using LQR Controller

Most of modern tall buildings using lighter construction materials are more flexible so could be excessive wind-induced vibrations resulting in occupant discomfort and structural unsafety. The optimal control technique for reducing along-wind vibration of a tall building based on the linear quadratic regulator (LQR) is presented in this work. Actively controlled reduced along-wind vibration response is obtained from the tall building installed in an active mass damper (AMD) with a LQR controller. Fluctuating along-wind load is generated using numerical simulation method, which can formulate a stationary Gaussian white noise process. Simulating wind load in the time domain using known spectra data of fluctuating along-wind load is particularly useful for estimation of windinduced vibration which is more or less narrow banded process such as a along-wind response of a tall building. In this work, fluctuating along-wind load acting on a tall building treated as a stationary Gaussian white noise process is simulated numerically using the along-wind load spectra proposed by G. Solari in1992. And using this simulated along-wind load estimated the reduced along-wind vibration response of a tall building installed in an AMD with a LQR controller.

Experimental Modal Analysis of Jacket-Type Platforms Using Data-Driven Stochastic Subspace Identification Method

Employing efficient techniques to accurately identify the modal parameters of new and aging offshore structures has been of interest to the offshore industry for decades. Early methods of modal identification were developed for the frequency domain. The new trend is to employ either input-output or output-only time-domain modal identification methods. Under the assumption that the excitation input is a zero-mean Gaussian white noise process, a modern output-only method that allows direct application to the response time series is the data-driven stochastic subspace identification (SSI-data) method. The main objective of this paper is to evaluate the performance of the SSI-data method using the test data measured from a physical model of a realistic offshore jacket-type platform. Response acceleration data associated with three different excitation mechanisms are investigated: impact loading, step relaxation and white noise ground motion. Although the SSI-data method has been theoretically developed, and often perceived to be only valid, for the ambient noise testing environment, it is shown in this study that the SSI-data method also performs well using data from either the impact loading or step relaxation tests.

Optimal stabilization and path-following controls for a bicycle

The article is about stabilizing and path-tracking control of a bicycle by a rider. It is based on previously published work, in which it has been shown how a driver's or rider's preview of the roadway can be combined with the linear dynamics of an appropriate vehicle to yield a problem of discrete-time optimal-linear-control-theory form. In the previous work, it was shown how an optimal ‘driver’ converts path preview sample values, modelled as deriving from a Gaussian white-noise process, into steering control inputs to cause the vehicle to follow the previewed path. The control compromises between precision and ease, to an extent that is controllable through choice of weights in the optimal control calculations. Research into the dynamics of bicycles has yielded a benchmark model, with equations of motion firmly established by extensive cross-checking. Model predictions have been verified for modest speeds by experimental testing. The established optimal linear preview stabilizing and tracking control theory is now brought together with the benchmark bicycle description to yield optimal controls for the bicycle for variations in speed and performance objectives. The resulting controls are installed in the bicycle, giving a virtual rider-controlled system, and frequency responses of the rider-controlled system are calculated to demonstrate tracking capability. Then path-tracking simulations are used to illustrate the behaviour of the controlled system. Tight and loose controls, representing different balances between tracking accuracy and control effort, are calculated and illustrated through the simulations.

Driver Steering Control and a New Perspective on Car Handling Qualities

The article is about steering control of cars by drivers, concentrating on following the lateral profile of the roadway, which is presumed visible ahead of the car. It builds on previously published work, in which it was shown how the driver's preview of the roadway can be combined with the linear dynamics of a simple car to yield a problem of discrete-time optimal-linear-control-theory form. In that work, it was shown how an optimal ‘driver’ of a linear car can convert the path preview sample values, modelled as deriving from a Gaussian white-noise process, into steering wheel displacement commands to cause the car to follow the previewed path with an attractive compromise between precision and ease. Recognizing that real roadway excitation is not so rich in high frequencies as white-noise, a low-pass filter is added to the system. The white-noise sample values are filtered before being seen by the driver. Numerical results are used to show that the optimal preview control is unaltered by the inclusion of the low-pass filter, whereas the feedback control is affected diminishingly as the preview increases. Then, using the established theoretical basis, new results are generated to show time-invariant optimal preview controls for cars and drivers with different layouts and priorities. Tight and loose controls, representing different balances between tracking accuracy and control effort, are calculated and illustrated through simulation. A new performance criterion with handling qualities implications is set up, involving the minimization of the preview distance required. The sensitivities of this distance to variations in the car design parameters are calculated. The influence of additional rear wheel steering is studied from the viewpoint of the preview distance required and the form of the optimal preview gain sequence. Path-following simulations are used to illustrate relatively high-authority and relatively low-authority control strategies, showing manoeuvring well in advance of a turn under appropriate circumstances. The results yield new insights into driver steering control behaviour and vehicle design optimization. The article concludes with a discussion of research in progress aimed at a further improved understanding of how drivers control their vehicles.