Framework For Parameter Estimation Research Articles

Critical state soil mechanics analysis of the constant cell volume triaxial test

SummaryWe have developed a critical state, stress‐strain analysis that predicts the entire sequence of states from start to the end of a constant cell volume triaxial test in p‐q‐v‐ɛz, space, where p is the spherical stress, q is the deviator stress, v is the specific volume and ɛz is the axial strain. The analysis requires five soil properties to be specified, these being the critical state properties (M, λ and κ) and two elastic properties (any two of E, η, G and K—all four can be found from any two).In order to test the analysis, properties taken mostly from one series of constant cell volume triaxial tests are used to simulate the behaviour in a second test series. In both series the two soils (a sand loam and a clay loam) were tested at several different water contents. The first (property estimation) series of tests was performed using large samples, whereas the second (verification) series involved small samples. The behaviour is quite different in the two series. The elastic property E was not determined in the first series of tests but was estimated from the second series. Furthermore, for three very wet samples, λ had to be estimated by fitting the analysis to the data. The verification was not therefore fully independent of the input test data, particularly for the three wet samples. The stress strain analysis simulated the behaviour of both series of tests in all four dimensions of the p‐q‐v‐ɛz space. The match in p‐q‐v space was good for all samples. On a q‐ɛz plane, the value of q was under‐estimated for several samples, but for most of the samples the match was good on this plane. The analysis was generally as good as, and sometimes better than, a previous analysis that deals only with the end point of the test in p‐q‐v space. The previous analysis did not take account of the elastic properties. The stress‐strain analysis therefore seems to offer a useful framework for parameter estimation from constant cell volume triaxial tests. This extends the usefulness of the test itself, as the elastic properties may now be accounted for. The success of the analysis also strengthens the record of success of the critical state concept for unsaturated soils.

Blind equalization and estimation of FIR communications channels using fractional sampling

We consider the problem of blind estimation and equalization of digital communication finite impulse response (FIR) channels using fractionally spaced samples. Fractionally sampled data are cyclostationary rather than stationary. The problem is cast into a mathematical framework of parameter estimation for a vector stationary process with single input (information sequence) and multiple outputs, by using a time-series representation of a cyclostationary process. The channel parameters are estimated by first estimating various subchannels using the second- and the fourth-order cumulant function of the received data, and then appropriately aligning and scaling them. The estimated channel impulse response is then used to construct a linear equalizer. Two illustrative simulation examples using four- and 16-QAM signals are presented where effect of symbol-timing-phase offset is studied via simulations.

Parameter estimation in a structural acoustic system with fully nonlinear coupling conditions

A methodology for estimating physical parameters in a class of structural acoustic systems is presented. The general model under consideration consists of an interior cavity which is separated from an exterior disturbance by an enclosing elastic structure. Piezoceramic patches are bonded to or embedded in the structure; these can be used both as actuators and sensors in applications ranging from the control of interior noise levels to the determination of structural flaws through nondestructive evaluation techniques. The presence and excitation of the patches, however, changes the geometry and material properties of the structure as well as involves unknown patch parameters, thus necessitating the development of parameter estimation techniques which are applicable in this coupled setting. In developing a framework for approximation, parameter estimation and implementation, strong consideration is given to the fact that the input operator is unbonded due to the discrete nature of the patches. Moreover, the model is weakly nonlinear as a result of the coupling mechanism between the structural vibrations and the interior acoustic dynamics. Within this context, an illustrating model is given, well-posedness and approximation results are discussed and an applicable parameter estimation methodology is presented. The scheme is then illustrated through several numerical examples with simulations modeling a variety of commonly used structural acoustic techniques for system excitation and data collection.

Determination of Particle Collision Efficiencies for Flocculent Transport Models

The object of this study is to investigate the data needs for accurate estimation of particle collision efficiencies ({alpha}). Batch flocculation and vertical flocculent settling studies were conducted on aquatic sediment particles in the size range of 2--80 {mu}m in diameter. Dynamic particle-size distribution data sets were generated using a 256-category binary-collision-based flocculent settling model and subsequently compressed into 128, 64, 32, 16, 8, and 4 logarithmically varying particle-diameter categories. A previously developed parameter-estimation framework was used to estimate {alpha} values from the compressed data sets. Variability in the {alpha} estimates indicates that it is not an artifact of the experimental data. The residual function value after 20 estimation iterations increased with the discretization levels, indicating shallower residual function slopes. Parameter estimate accuracy was unaffected by the levels of data sparsity considered. Increased random noise resulted in consistently lower estimated collision efficiencies. Rate of convergence was unaffected by random noise but decreased with data sparsity levels. Particle water column residence times were significantly overestimated using four category distributions.

On blind identifiability of multipath channels using fractional sampling and second-order cyclostationary statistics

The problem of blind identifiability of digital communication multipath channels using fractionally spaced samples is considered. Fractionally sampled data are cyclostationary rather than stationary. The problem is cast into a mathematical framework of parameter estimation for a vector stationary process with single input (information sequence) and multiple outputs, by using a time-series representation of a cyclostationary process. A necessary and sufficient condition for channel identifiability from the correlation function of the vector stationary process is derived. This result provides an alternative but equivalent statement of an existing result. Using this result, it is shown that certain class of multipath channels cannot be identified from the second-order statistics irrespective of how the sampling rate is chosen. >

Estimation of skew angle in text-image analysis bySLIDE: Subspace-based line detection

A new signal processing method is developed for estimating the skew angle in text document images. Detection of the skew angle is an important step in text processing tasks such as optical character recognition (OCR) and computerized filing. Based on a recently introduced multiline-fitting algorithm, the proposed method reformulates the skew detection problem into a special parameter-estimation framework such that a signal structure similar to the one in the field of sensor array processing is obtained. In this framework, straight lines in an image are modeled as wavefronts of propagating planar waves. Certain measurements are defined in this virtual propagation environment such that the large amount of coherency that exists between the locations of the pixels on parallel lines is exploited to enhance a subspace in the space spanned by the measurements. The well-studied techniques of sensor array processing (e.g., the ESPRIT algorithm) are then exploited to produce a closed form and high-resolution estimate for the skew angle.

Robust statistical methods of 2D and 3D image description

In this paper the problem of image feature extraction is considered with emphasis on developing methods which are resilient in the presence of data contamination. The issue of robustness of estimation procedures has received considerable attention in the statistics community [1–3] but its results are only recently being applied to specific image analysis tasks [4–7]. In this paper we show how the design of robust methods applies to image description tasks posed within a statistical hypothesis testing and parameter estimation framework. The methodology is illustrated by applying it to finding robust, optimal estimation kernels for line detection and edge detection. We then discuss the relationship of these optimal solutions to both the well established Hough Transform technique and the standard estimation kernels developed in the statistics literature. The application of standard robust kernels to image analysis tasks is illustrated by two examples which involve circular arc detection in gray-level imagery and planar surface segmentation in depth data. Robust methods are found to be effective general tools for generating 2D and 3D image descriptions.

Sensor array processing techniques for super resolution multi-line-fitting and straight edge detection

A signal processing method is developed for solving the problem of fitting multiple lines in a two-dimensional image. It formulates the multi-line-fitting problem in a special parameter estimation framework such that a signal structure similar to the sensor array processing signal representation is obtained. Then the recently developed algorithms in that formalism can be exploited to produce super-resolution estimates for line parameters. The number of lines may also be estimated in this framework. The signal representation used can be generalized to handle problems of line fitting and of straight edge detection. Details of the proposed algorithm and several experimental results are presented. The method exhibits considerable computational speed superiority over existing single- and multiple-line-fitting algorithms such as the Hough transform method. Potential applications include road tracking in robotic vision, mask wafer alignment in semiconductor manufacturing, aerial image analysis, text alignment in document analysis, and particle tracking in bubble chambers.

Adaptive Models in Decentralized Optimizing Control

A model based technique is presented for the decentralized or large scale optimizing control problem when the system is composed of interconnected subsystems. For each subsystem, separable output and interaction adaptive models are used within a framework of integrated system optimisation and parameter estimation. The output model describes the behaviour of the outputs in response to the subsystem controls while the interaction model describes the behaviour of the subsystem interactions after the subsystem control signals have been transmitted around the system. Each model contains parameters which are estimated as part of a parameter estimation procedure and which account for subsystem uncertainties. By solving the system optimality conditions, the technique provides optimum process operation.

Estimation of population pharmacokinetic parameters using destructively obtained experimental data: a simulation study of the one-compartment open model.

A simulation study of the one-compartment open pharmacokinetic model has been made. The population pharmacokinetic parameters which characterize the population of drug residues over time are assumed to be stochastic. A general theoretical model framework for parameter estimation via the method of extended least squares is presented. Formulas approximating the required mean and variance time functions are developed and subsequently used in the simulation study. The effects of four different designs in four different animal populations are presented. The simulated data are those of the single observation per animal per time point type. The characterizing population pharmacokinetic parameters have been analyzed for bias and reliability in both a naive and second-order mean model. Recommendations for choosing an appropriate sampling design are included.