A new modal-based damage location indicator

Vibration-based damage detection techniques use the change in modal data as an indicator to assess damages in the structure. Knowing the structural dynamic characteristics of the healthy and damaged structure, the estimation of the damage location and severity is possible by solving an inverse problem. This paper presents a mathematical expression relating damage location and depth to the frequency shifts of the bending vibration modes. This expression permits the extraction of a series of coefficients that characterize each damage location and are independent of the damage severity. The vector aggregating these coefficients for a given location constitutes a Damage Location Indicator (DLI) that unambiguously characterizes the position of a geometrical discontinuity in the beam. A set of vectors typifying all locations along the beam may be used as patters opposable to the damage signature found by measurements. The similarity between the signature and one of the patterns indicates the location of damage

Wavefront Curvature Sensing from Image Projections

This research outlines the development and simulation of a signal processing approach to real time wavefront curvature sensing in adaptive optics. The signal processing approach combines vectorized Charge Coupled Device (CCD) read out with a wavefront modal estimation technique. The wavefront sensing algorithm analyzes vector projections of image intensity data to provide an estimate of the wavefront phase as a combination of several low order Zernike polynomial modes. This wavefront sensor design expands on an existing idea for vector based tilt sensing by providing the ability to compensate for additional modes. Under the proposed wavefront sensing approach, the physical wavefront sensor would be replaced by a pair of imaging devices capable of generating vector projections of the image data. Using image projections versus two-dimensional image data allows for faster CCD read out and decreased read noise

Stochastic Sensor Scheduling via Distributed Convex Optimization

In this paper, we propose a stochastic scheduling strategy for estimating the states of N discrete-time linear time invariant (DTLTI) dynamic systems, where only one system can be observed by the sensor at each time instant due to practical resource constraints. The idea of our stochastic strategy is that a system is randomly selected for observation at each time instant according to a pre-assigned probability distribution. We aim to find the optimal pre-assigned probability in order to minimize the maximal estimate error covariance among dynamic systems. We first show that under mild conditions, the stochastic scheduling problem gives an upper bound on the performance of the optimal sensor selection problem, notoriously difficult to solve. We next relax the stochastic scheduling problem into a tractable suboptimal quasi-convex form. We then show that the new problem can be decomposed into coupled small convex optimization problems, and it can be solved in a distributed fashion. Finally, for scheduling implementation, we propose centralized and distributed deterministic scheduling strategies based on the optimal stochastic solution and provide simulation examples.Comment: Proof errors and typos are fixed. One section is removed from last versio

Topology and Geometry of the CfA2 Redshift Survey

We analyse the redshift space topology and geometry of the nearby Universe by computing the Minkowski functionals of the Updated Zwicky Catalogue (UZC). The UZC contains the redshifts of almost 20,000 galaxies, is 96% complete to the limiting magnitude m_Zw=15.5 and includes the Center for Astrophysics (CfA) Redshift Survey (CfA2). From the UZC we can extract volume limited samples reaching a depth of 70 hMpc before sparse sampling dominates. We quantify the shape of the large-scale galaxy distribution by deriving measures of planarity and filamentarity from the Minkowski functionals. The nearby Universe shows a large degree of planarity and a small degree of filamentarity. This quantifies the sheet-like structure of the Great Wall which dominates the northern region (CfA2N) of the UZC. We compare these results with redshift space mock catalogues constructed from high resolution N-body simulations of two Cold Dark Matter models with either a decaying massive neutrino (tauCDM) or a non-zero cosmological constant (LambdaCDM). We use semi-analytic modelling to form and evolve galaxies in these dark matter-only simulations. We are thus able, for the first time, to compile redshift space mock catalogues which contain galaxies, along with their observable properties, rather than dark matter particles alone. In both models the large scale galaxy distribution is less coherent than the observed distribution, especially with regard to the large degree of planarity of the real survey. However, given the small volume of the region studied, this disagreement can still be a result of cosmic variance.Comment: 14 pages including 10 figures. Accepted for publication in Monthly Notice

Nonlinear dynamics of river runoff elucidated by horizontal visibility graphs

Horizontal Visibility Graphs (HVGs) are a recently developed method to construct networks from time series. The values of the time series are considered as the nodes of the network and are linked to each other if there is no larger value between them, such as they can “see” each other. The network properties reflect the nonlinear dynamics of the time series. For some classes of stochastic processes and for periodic time series, analytical results can be obtained for network-derived quantities such as the degree distribution, the local clustering coefficient distribution, the mean path length, and others. HVGs have the potential to discern between deterministic-chaotic and correlated-stochastic time series. Here, we investigate the sensitivity of the HVG methodology to properties and pre-processing of real-world data, i.e., time series length, the presence of ties, and deseasonalization, using a set of around 150 runoff time series from managed rivers at daily resolution from Brazil with an average length of 65 years. We show that an application of HVGs on real-world time series requires a careful consideration of data pre-processing steps and analysis methodology before robust results and interpretations can be obtained. For example, one recent analysis of the degree distribution of runoff records reported pronounced sub-exponential “long-tailed” behavior of North American rivers, whereas another study of South American rivers showed hyper-exponential “short-tailed” behavior resembling correlated noise. We demonstrate, using the dataset of Brazilian rivers, that these apparently contradictory results can be reconciled by minor differences in data-preprocessing (here: small differences in subtracting the seasonal cycle). Hence, data-preprocessing that is conventional in hydrology (“deseasonalization”) changes long-term correlations and the overall runoff dynamics substantially, and we present empirical consequences and extensive simulations to investigate these issues from a HVG methodological perspective. After carefully accounting for these methodological aspects, the HVG analysis reveals that the river runoff dataset shows indeed complex behavior that appears to stem from a superposition of short-term correlated noise and “long-tailed behaviour,” i.e., highly connected nodes. Moreover, the construction of a dam along a river tends to increase short-term correlations in runoff series. In summary, the present study illustrates the (often substantial) effects of methodological and data-preprocessing choices for the interpretation of river runoff dynamics in the HVG framework and its general applicability for real-world time series.Fil: Lange, Holger. Norwegian Institute of Bioeconomy Research; NoruegaFil: Sippel, Sebastian. Norwegian Institute of Bioeconomy Research; NoruegaFil: Rosso, Osvaldo Aníbal. Instituto Universidad Escuela de Medicina del Hospital Italiano; Argentina. Universidad de Los Andes; Chile. Universidade Federal de Alagoas; Brasil. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Application of asymptotic expansions of maximum likelihood estimators errors to gravitational waves from binary mergers: the single interferometer case

In this paper we describe a new methodology to calculate analytically the error for a maximum likelihood estimate (MLE) for physical parameters from Gravitational wave signals. All the existing litterature focuses on the usage of the Cramer Rao Lower bounds (CRLB) as a mean to approximate the errors for large signal to noise ratios. We show here how the variance and the bias of a MLE estimate can be expressed instead in inverse powers of the signal to noise ratios where the first order in the variance expansion is the CRLB. As an application we compute the second order of the variance and bias for MLE of physical parameters from the inspiral phase of binary mergers and for noises of gravitational wave interferometers . We also compare the improved error estimate with existing numerical estimates. The value of the second order of the variance expansions allows to get error predictions closer to what is observed in numerical simulations. It also predicts correctly the necessary SNR to approximate the error with the CRLB and provides new insight on the relationship between waveform properties SNR and estimation errors. For example the timing match filtering becomes optimal only if the SNR is larger than the kurtosis of the gravitational wave spectrum

Driver behavior classification and lateral control for automobile safety systems

Advanced driver assistance systems (ADAS) have been developed to help drivers maintain stability, improve road safety, and avoid potential collision. The data acquisition equipment that can be used to measure the state and parameter information of the vehicle may not be available for a standard passenger car due to economical and technical limitations. This work focuses on developing three technologies (longitudinal tire force estimation, driver behavior classification and lateral control) using low-cost sensors that can be utilized in ADAS. For the longitudinal tire force estimation, a low cost 1Hz positioning global system (GPS) and a steering angle sensor are used as the vehicle data acquisition equipment. A nonlinear extended two-wheel vehicle dynamic model is employed. The sideslip angle and the yaw rate are estimated by discrete Kalman Filter. A time independent piecewise optimization scheme is proposed to provide time-continuous estimates of longitude tire force, which can be transferred to the throttle/brake pedal position. The proposed method can be validated by the estimation results. Driver behavior classification systems can detect unsafe driver behavior and avoid potentially dangerous situations. To realize this strategy, a machine learning classification method, Gaussian Mixture model (GMM), is applied to classify driver behavior. In this application, a low cost 1Hz GPS receiver is considered as the vehicle data acquisition equipment instead of other more costly sensors (such as steering angle sensor, throttle/brake position sensor, and etc.). Since the driving information is limited, the nonlinear extended two-wheel vehicle dynamic model is adopted to reconstruct the driver behavior. Firstly, the sideslip angle and the yaw rate are calculated since they are not available from the GPS measurements. Secondly, a piecewise optimization scheme is proposed to reproduce the steering angle and the longitudinal force. Finally, a GMM classifier is trained to identify abnormal driver behavior. The simulation results demonstrated that the proposed scenario can detect the unsafe driver behavior effectively. The lateral control system developed in this study is a look-down reference system which uses a magnetic sensor at the front bumper to measure the front lateral displacement and a GPS to measure the vehicle\u27s heading orientation. Firstly, the steering angles can be estimated by using the data provided by the front magnetic sensor and GPS. The estimation algorithm is an observer for a new extended single-track model, in which the steering angle and its derivative are viewed as two state variables. Secondly, the road curvature is determined based on the linear relationship with respect to the steering angle. Thirdly, an accurate and real-time estimation of the vehicle\u27s lateral displacements can be accomplished according to a state observer. Finally, the closed loop controller is used as a compensator for automated steering. The proposed estimation and control algorithms are validated by simulation results. The results showed that this lateral steering control system achieved a good and robust performance for vehicles following or tracking a reference path