Identifiability of hybrid system models

This paper addresses the challenging problem of designing an adaptive feedback strategy for the stabilization of a class of nonlinearly parameterized uncertain systems in discrete time. The nonlinear least squares (NLS) algorithm is applied to estimate the unknown parameters, and a sufficient condition is proposed to ensure the strong consistency of the estimator. Based on the NLS algorithm, the global stability of the system is achieved under the output feedback design.

It is important to improve the depth resolution in depth-resolved wavenumber-scanning interferometry (DRWSI) owing to the limited range of wavenumber scanning. In this work, a new nonlinear iterative least-squares algorithm called the wavenumber-domain least-squares algorithm (WLSA) is proposed for evaluating the phase of DRWSI. The simulated and experimental results of the Fourier transform (FT), complex-number least-squares algorithm (CNLSA), eigenvalue-decomposition and least-squares algorithm (EDLSA), and WLSA were compared and analyzed. According to the results, the WLSA is less dependent on the initial values, and the depth resolution δz is approximately changed from δz to δz/6. Thus, the WLSA exhibits a better performance than the FT, CNLSA, and EDLSA.

Arc welding is still the dominant welding process in industry and a major challenge in this context is robotisation and automation, which require sensor based adaptive control. Therefore, the present paper describes the application of neural network technology for gas metal arc welding control. A system based on a multilayer feed forward network has been developed for modelling and online adjustment of welding parameters appropriate to guarantee a certain degree of quality in the field of butt joint welding with full penetration when the gap varies during the welding process. It has been shown that operating in an open loop, the developed system can tackle gap variations relevant to many welding situations. However, to improve robustness to uncertainties, disturbances, etc. a closed loop control system based on a 'single neuron self-learning proportional, sum, and differential' control algorithm, which compensates for non-monitorial changes in welding conditions by feeding back information on the realised front bead geometry, has also been developed and tested. The Levenberg–Marquardt algorithm for non-linear least squares has been used with a back propagation algorithm for training the neural networks, and a Bayesian regularisation technique has been successfully applied for minimising the risk of inexpedient overtraining.

Oriented patterns in an image often carry important information about the scene represented. Rao and Jain developed a technique to analyze images with oriented texture using phase portraits, where the parameters of a planar first-order phase portrait are locally estimated using a nonlinear least-squares algorithm. The method gives accurate results, but is computationally expensive. Shu and Jain proposed a faster linear method for the estimation of the parameters of the phase portrait. However, their formulation leads to the minimization of a different error measure, which is not as robust as the nonlinear least-squares procedure in the presence of noise, and also makes the implicit assumption that the orientation field was truly generated by a phase portrait model (with an extra weighting factor to compensate for noise sensitivity). We propose a new derivation of Shu and Jain's linear estimator that leads to similar estimation equations, while making explicit the nature of the error measure. Our procedure includes an iterative scheme, of which Shu and Jain's linear estimator is a particular case. We show that our estimator is more robust to noise than Shu and Jain's linear estimator.

The Air Force Wright Research and Development Center and the Arnold Engineering Development Center are continuing a program for measuring optical effects of satellite material outgassing products on cryo-optic surfaces. This paper presents infrared (4000 to 700 cm-1) transmittance data for contaminant films condensed on a 77 K geranium window. From the transmittance data, the contaminant film refractive and absorptive indices (n, k) were derived using an analytical thin-film interference model with a nonlinear least-squares algorithm. To date 19 materials have been studied with the optical contants determined for 13 of those. The materials include adhesives, paints, composites, films, and lubricants. This program is continuing and properties for other materials will be available in the future.

Analysis of multi-component fluorescence emission by phase-sensitive detection using one modulation frequency

A method is presented to measure the magnetic field vector in prominences by means of the polarimetric observations in the D3 line of He obtained with the High Altitude Observatory Stokes polarimeter. The characteristics of the observed Stokes profiles are discussed. The theory of the Hanle effect is reformulated in the representation of the irreducible tensors of the density matrix, and is generalized to derive the circular polarization profiles across the spectral line in terms of the intensity and direction of the prominence magnetic field. The circular polarization profile so deduced can be employed to obtain useful information which adds to that carried by the linear polarization observations. A non-linear least-squares algorithm is proposed to derive the measurement of the magnetic field from the observations, and a consistency check is suggested to test the adequacy of the theoretical model to describe the physics of the He I atomic excitation in prominences.

A permeability measurement system is developed to quantify the inter-pore connectivity of tissue engineering scaffolds. It uses dry air as the fluid medium and allows rapid measurement operations. The paper analyses the fluid phenomena in porous structures, providing a theoretical background for the developed system. A nonlinear least-squares algorithm is developed to estimate the effective porosity, from which the intrinsic permeability is derived based on the mean pore size of the scaffold. It is shown that the flow in the measurement operations does not have to be within Darcy's region. The developed system can be used to characterize tissue engineering scaffolds with a wide range of permeability values.

Determination of residence-time distribution in i.v. tubing of in-line drug delivery system using deconvolution technique

This article presents a new formulation for attitude-independent calibration of three-axis magnetometers. The proposed solution employs a nonlinear least squares (NLLS) estimator that uses the nonlinear sensor model proposed by Foster and Elkaim in the well-known extended two-step (ETS) algorithm. Our solution has a few advantages over ETS and is more straightforward to implement than many subsequent algorithms. It enables the calculation of the calibration parameters’ uncertainties and does not require the assumption that all magnetometer measurements have a constant magnetic field magnitude. The former is essential for evaluating calibration quality, while the latter may be required for on-orbit magnetometer calibration. However, the NLLS has the drawback of requiring an initial parameter estimation to ensure convergence. Therefore, our work presents a new technique to calculate the scale factors and offsets for initializing the NLLS. Simulations and practical implementations demonstrate that our method performs similar to a recently computed analytical solution of the ETS (ETS-A). Furthermore, a Monte Carlo simulation shows that the NLLS algorithm provides a slightly better estimation of the scale factors than the ETS, in addition to the abovementioned advantages.

Among many other uses, positron emission tomography (PET) can be used in studies to estimate the density of a neuroreceptor at each location throughout the brain by measuring the concentration of a radiotracer over time and modeling its kinetics. There are a variety of kinetic models in common usage and these typically rely on nonlinear least-squares (LS) algorithms for parameter estimation. However, PET data often contain artifacts (such as uncorrected head motion) and so the assumptions on which the LS methods are based may be violated. Quantile regression (QR) provides a robust alternative to LS methods and has been used successfully in many applications. We consider fitting various kinetic models to PET data using QR and study the relative performance of the methods via simulation. A data adaptive method for choosing between LS and QR is proposed and the performance of this method is also studied.

Summary New technologies that allow geothermal energy production in colder conditions result in interest for geothermal exploration in low heat flux regions. The Province of Québec, eastern Canada, is such a case. Mapping the Curie point depth (CPD) is appealing as an exploration tool due to the scarcity of the direct data. We have revisited a methodology to estimate the CPD using a fractal source distribution model and aeromagnetic data. Our methodology relies on a statistical model of crustal magnetization having a constant magnetization direction and random magnetization amplitude. The shape of the radial average of the logarithm of the power spectrum of magnetic anomalies is predicted using this model. The model parameters (thickness and depth to the top of the magnetic layer, the fractal exponent β and the constant C’) are obtained by calculating the best fit between the theoretical and observed radial power spectra using a non-linear least-square algorithm. Rather than using a constant value for the fractal exponent β, we propose a new calibration workflow based on heat flux measurements and lithology. This workflow includes the use of normal kriging of heat flux data. Mapping the CPD will help identifying potential areas for further detailed exploration programs.

Hybrid system modeling refers to the construction of system models combining both continuous and discrete dynamics. These models can greatly reduce the complexity of a physical system model by abstracting some of the continuous dynamics of the system into discrete dynamics. Hybrid system models are also useful for describing the interaction between physical processes and computational processes, such as in a digital feedback control system. Unfortunately, hybrid system models poorly capture common software architecture design patterns, such as threads, mobile code, safety, and hardware interfaces. Dealing effectively with these practical software issues is crucial when designing real-world systems. This paper presents a model of a complex control system that combines continuous-state physical system models with rich discrete-state software models in a disciplined fashion. We show how expressive modeling using multiple semantics can be used to address the design difficulties in such a system.

The paper gives an overview of non-linear least square method, and presents GPS satellite pseudorange observation equations, which are usually over-determined because there are only 4 unknowns but normally more than 4 satellites being tracked, resulting in more than 4 pseudorange observation equations. Non-linear least squares(NLS) algorithm to solve pseudorange observation equations in order to find position and clock bias solutions are described in detail. There are three tests designed, one vehicle field test and two simulation tests. There are three NovAtel made GPS receivers being used in vehicle field test, while GSS6560 GPS satellite signal generator being used in simulation tests. By employing a set of differential GPS receivers, it is possible to establish rover station receiver to give a relatively high accurate reference to be compared by NLS and another GPS receiver in the vehicle field test. Results from NLS demonstrate that NLS can achieve high accuracy. Experimental study also shows that NLS algorithm possesses similar accuracy level to that of NovAtel Receiver, which represents world leading level.

Pulse pile-up correction by auto-regression on linear operations (ARLO) method: A comparison with integration-based algorithms