Asymptotic Performance for Delayed Exponential Process

International audienceThe damped and delayed sinusoidal (DDS) model can be defined as the sum of sinusoids whose waveforms can be damped and delayed. This model is suitable for compactly modeling short time events. This property is closely related to its ability to reduce the time-support of each sinusoidal component. In this correspondence, we derive exact and approximate asymptotic Cramér–Rao bounds (CRBs) for the DDS model. This analysis shows that this model has better, or at least similar, theoretical performance than the well-known exponentially damped sinusoidal (EDS) model. In particular, the performance in the DDS case is significantly improved compared to that of the EDS for closely spaced sinusoids thanks to the nonzero time delays. Consequently, we can exploit the advantageous properties of the DDS model and, in the same time, we can keep high theoretical model parameter estimation accuracy

Damped and delayed sinuosidal model for transient modeling

International audienceIn this work, we present the Damped and De- layed Sinusoidal (DDS) model, a generalization of the sinu- soidal model. This model takes into account an angular fre- quency, a damping factor, a phase, an amplitude and a time- delay parameter for each component. Two algorithms are introduced for the DDS parameter estimation using a sub- band processing approach. Finally, we derive the Cramer- Rao Bound (CRB) expression for the DDS model and a simulation-based performance analysis in the context of a noisy fast time-varying synthetic signal and in the audio transient signal modeling context

Target Recognition Using Late-Time Returns from Ultra-Wideband, Short-Pulse Radar

The goal of this research is to develop algorithms that recognize targets by exploiting properties in the late-time resonance induced by ultra-wide band radar signals. A new variant of the Matrix Pencil Method algorithm is developed that identifies complex resonant frequencies present in the scattered signal. Kalman filters are developed to represent the dynamics of the signals scattered from several target types. The Multiple Model Adaptive Estimation algorithm uses the Kalman filters to recognize targets. The target recognition algorithm is shown to be successful in the presence of noise. The performance of the new algorithms is compared to that of previously published algorithms

Robustness and Accuracy Bounds of Model-based Structural Health Monitoring

The strength and stiffness of structures degrade with time due to a combination of external forces and environmental conditions. A vehicular bridge, an offshore platform, a ship hull, or a wind turbine are examples of structures that for decades must endure cumulative degradation of their mechanical properties due to cyclic loading. Fatigue-induced damage typically starts at the exterior surface of the component unless microscopic or macroscopic imperfections are present in the material\u27s structure. Structural Health Monitoring (SHM) provides a scientific non-destructive framework to estimate the structure\u27s current state and remaining service life. In many model-based structural health monitoring applications, the models are linear, and commonplace is to formulate them based on modal parameters. The research in this dissertation addresses the implications of model uncertainty to system identification and state estimation. Specifically, determining the highest achievable accuracy in the presence of noise in the measurements, unmeasured excitations, and environmental conditions. The main contributions of this dissertation are summarized as follows: i) derivation of exact mathematical expressions to compute the minimum achievable variance of the identified frequencies and damping ratios from noisy vibration measurements due to initial conditions or external forces, and ii) the development of a weighted sensitivity-based finite element model updating framework to a large scale model of a partially instrumented bridge. Additionally, the dissertation explores the robustness of the Kalman filter in structural dynamics for fatigue monitoring applications. The dissertation presents recent developments in the feasibility of using global acceleration measurements to assess the level of composite action on operational bridge decks with unknown girder-slab connection stiffness. Our efforts focused on the 58N Bridge constructed in 1963 located on Interstate 89 in Richmond, Vermont, United States. The Bridge has a three-span continuous deck with two build-up outer girders spanning a total length of 558 feet (170.08 m). A portion of the bridge deck was monitored with uni-directional accelerometers and dynamic strain sensors distributed at various locations. Intermittently, for over two years, with measured temperatures ranging from 15F to 87F, data was acquired. This data was used to update a finite element model of the deck. The updated model displayed improved prediction capabilities with respect to the original model. Such an updated model can be used as a baseline model for stress analysis

Maximum Likelihood Estimation of Exponentials in Unknown Colored Noise for Target Identification in Synthetic Aperture Radar Images

This dissertation develops techniques for estimating exponential signals in unknown colored noise. The Maximum Likelihood (ML) estimators of the exponential parameters are developed. Techniques are developed for one and two dimensional exponentials, for both the deterministic and stochastic ML model. The techniques are applied to Synthetic Aperture Radar (SAR) data whose point scatterers are modeled as damped exponentials. These estimated scatterer locations (exponentials frequencies) are potential features for model-based target recognition. The estimators developed in this dissertation may be applied with any parametrically modeled noise having a zero mean and a consistent estimator of the noise covariance matrix. ML techniques are developed for a single instance of data in colored noise which is modeled in one dimension as (1) stationary noise, (2) autoregressive (AR) noise and (3) autoregressive moving-average (ARMA) noise and in two dimensions as (1) stationary noise, and (2) white noise driving an exponential filter. The classical ML approach is used to solve for parameters which can be decoupled from the estimation problem. The remaining nonlinear optimization to find the exponential frequencies is then solved by extending white noise ML techniques to colored noise. In the case of deterministic ML, the computationally efficient, one and two-dimensional Iterative Quadratic Maximum Likelihood (IQML) methods are extended to colored noise. In the case of stochastic ML, the one and two-dimensional Method of Direction Estimation (MODE) techniques are extended to colored noise. Simulations show that the techniques perform close to the Cramer-Rao bound when the model matches the observed noise

Maximum Likelihood Estimation of Exponentials in Unknown Colored Noise for Target in Identification Synthetic Aperture Radar Images

This dissertation develops techniques for estimating exponential signals in unknown colored noise. The Maximum Likelihood ML estimators of the exponential parameters are developed. Techniques are developed for one and two dimensional exponentials, for both the deterministic and stochastic ML model. The techniques are applied to Synthetic Aperture Radar SAR data whose point scatterers are modeled as damped exponentials. These estimated scatterer locations exponentials frequencies are potential features for model-based target recognition. The estimators developed in this dissertation may be applied with any parametrically modeled noise having a zero mean and a consistent estimator of the noise covariance matrix. ML techniques are developed for a single instance of data in colored noise which is modeled in one dimension as 1 stationary noise, 2 autoregressive AR noise and 3 autoregressive moving-average ARMA noise and in two dimensions as 1 stationary noise, and 2 white noise driving an exponential filter. The classical ML approach is used to solve for parameters which can be decoupled from the estimation problem. The remaining nonlinear optimization to find the exponential frequencies is then solved by extending white noise ML techniques to colored noise. In the case of deterministic ML, the computationally efficient, one and two-dimensional Iterative Quadratic Maximum Likelihood IQML methods are extended to colored noise. In the case of stochastic ML, the one and two-dimensional Method of Direction Estimation MODE techniques are extended to colored noise. Simulations show that the techniques perform close to the Cramer-Rao bound when the model matches the observed noise