arXiv subjects

James S. Welsh

Publications and source records attributed to James S. Welsh.

At least 19 recordsLinked to original sources

arXiv2024

Identification of Additive Continuous-time Systems in Open and Closed loop

When identifying electrical, mechanical, or biological systems, parametric continuous-time identification methods can lead to interpretable and parsimonious models when the model structure aligns with the physical properties of the system. Traditional linear system identification may not consider the most parsimonious model when relying solely on unfactored transfer functions, which typically result from standard direct approaches. This paper presents a novel identification method that delivers additive models for both open and closed-loop setups. The estimators that are derived are shown to be generically consistent, and can admit the identification of marginally stable additive systems. Numerical simulations show the efficacy of the proposed approach, and its performance in identifying a modal representation of a flexible beam is verified using experimental data.

eess.SY↗

arXiv2024

Consistency analysis of refined instrumental variable methods for continuous-time system identification in closed-loop

Refined instrumental variable methods have been broadly used for identification of continuous-time systems in both open and closed-loop settings. However, the theoretical properties of these methods are still yet to be fully understood when operating in closed-loop. In this paper, we address the consistency of the simplified refined instrumental variable method for continuous-time systems (SRIVC) and its closed-loop variant CLSRIVC when they are applied on data that is generated from a feedback loop. In particular, we consider feedback loops consisting of continuous-time controllers, as well as the discrete-time control case. This paper proves that the SRIVC and CLSRIVC estimators are not generically consistent when there is a continuous-time controller in the loop, and that generic consistency can be achieved when the controller is implemented in discrete-time. Numerical simulations are presented to support the theoretical results.

eess.SY↗

arXiv2024

Statistical Analysis of Block Coordinate Descent Algorithms for Linear Continuous-time System Identification

Block coordinate descent is an optimization technique that is used for estimating multi-input single-output (MISO) continuous-time models, as well as single-input single output (SISO) models in additive form. Despite its widespread use in various optimization contexts, the statistical properties of block coordinate descent in continuous-time system identification have not been covered in the literature. The aim of this paper is to formally analyze the bias properties of the block coordinate descent approach for the identification of MISO and additive SISO systems. We characterize the asymptotic bias at each iteration, and provide sufficient conditions for the consistency of the estimator for each identification setting. The theoretical results are supported by simulation examples.

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arXiv2023

On the Relation between Discrete and Continuous-time Refined Instrumental Variable Methods

The Refined Instrumental Variable method for discrete-time systems (RIV) and its variant for continuous-time systems (RIVC) are popular methods for the identification of linear systems in open-loop. The continuous-time equivalent of the transfer function estimate given by the RIV method is commonly used as an initialization point for the RIVC estimator. In this paper, we prove that these estimators share the same converging points for finite sample size when the continuous-time model has relative degree zero or one. This relation does not hold for higher relative degrees. Then, we propose a modification of the RIV method whose continuous-time equivalent is equal to the RIVC estimator for any non-negative relative degree. The implications of the theoretical results are illustrated via a simulation example.

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arXiv2023

Parsimonious Identification of Continuous-Time Systems: A Block-Coordinate Descent Approach

The identification of electrical, mechanical, and biological systems using data can benefit greatly from prior knowledge extracted from physical modeling. Parametric continuous-time identification methods can naturally incorporate this knowledge, which leads to interpretable and parsimonious models. However, some applications lead to model structures that lack parsimonious descriptions using unfactored transfer functions, which are commonly used in standard direct approaches for continuous-time system identification. In this paper we characterize this parsimony problem, and develop a block-coordinate descent algorithm that delivers parsimonious models by sequentially estimating an additive decomposition of the transfer function of interest. Numerical simulations show the efficacy of the proposed approach.

eess.SY↗

arXiv2021

A Comparison of Proton Stopping Power Measured with Proton CT and x-ray CT in Fresh Post-Mortem Porcine Structures

Purpose: Currently, calculations of proton range in proton therapy patients are based on a conversion of CT Hounsfield Units of patient tissues into proton relative stopping power. Uncertainties in this conversion necessitate larger proximal and distal planned target volume margins. Proton CT can potentially reduce these uncertainties by directly measuring proton stopping power. We aim to demonstrate proton CT imaging with complex porcine samples, to analyze in detail three-dimensional regions of interest, and to compare proton stopping powers directly measured by proton CT to those determined from x-ray CT scans. Methods: We have used a prototype proton imaging system with single proton tracking to acquire proton radiography and proton CT images of a sample of porcine pectoral girdle and ribs, and a pig's head. We also acquired close in time x-ray CT scans of the same samples, and compared proton stopping power measurements from the two modalities. In the case of the pig's head, we obtained x-ray CT scans from two different scanners, and compared results from high-dose and low-dose settings. Results: Comparing our reconstructed proton CT images with images derived from x-ray CT scans, we find agreement within 1% to 2% for soft tissues, and discrepancies of up to 6% for compact bone. We also observed large discrepancies, up to 40%, for cavitated regions with mixed content of air, soft tissue, and bone, such as sinus cavities or tympanic bullae. Conclusions: Our images and findings from a clinically realistic proton CT scanner demonstrate the potential for proton CT to be used for low-dose treatment planning with reduced margins.

physics.med-ph↗

arXiv2021

Consistency Analysis of the Closed-loop SRIVC Estimator

The Consistency of the Closed-Loop Simplified Refined Instrumental Variable method for Continuous-time system (CLSRIVC) is analysed based on sampled data. It is proven that the CLSRIVC estimator is not consistent when a continuous-time controller is used in the closed-loop.

eess.SY↗

arXiv2021

Consistent identification of continuous-time systems under multisine input signal excitation

For many years, the Simplified Refined Instrumental Variable method for Continuous-time systems (SRIVC) has been widely used for identification. The intersample behaviour of the input plays an important role in this method, and it has been shown recently that the SRIVC estimator is not consistent if an incorrect assumption on the intersample behaviour is considered. In this paper, we present an extension of the SRIVC algorithm that is able to deal with continuous-time multisine signals, which cannot be interpolated exactly through hold reconstructions. The proposed estimator is generically consistent for any input reconstructed through zero or first-order-hold devices, and we show that it is generically consistent for continuous-time multisine inputs as well. The statistical performance of the proposed estimator is compared to the standard SRIVC estimator through extensive simulations.

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arXiv2021

Analysis of characteristics of images acquired with a prototype clinical proton radiography system

Verification of patient specific proton stopping powers obtained in the patient treatment position can be used to reduce the distal margins needed in particle beam planning. Proton radiography can be used as a pre-treatment instrument to verify integrated stopping power consistency with the treatment planning CT. Although a proton radiograph is a pixel by pixel representation of integrated stopping powers, the image may also be of high enough quality and contrast to be used for patient alignment. This investigation qualifies the accuracy and image quality of a prototype proton radiography system on a clinical proton delivery system. We have developed a clinical prototype proton radiography system designed for integration into efficient clinical workflows. We tested the images obtained by this system for water-equivalent thickness (WET) accuracy, image noise, and spatial resolution. We evaluated the WET accuracy by comparing the average WET and rms error in several regions of interest (ROI) on a proton radiograph of a custom peg phantom. We measured the spatial resolution on a CATPHAN Line Pair phantom and a custom edge phantom by measuring the 10% value of the modulation transfer function (MTF). In addition, we tested the ability to detect proton range errors due to anatomical changes in a patient with a customized CIRS pediatric head phantom and inserts of varying WET placed in the posterior fossae of the brain. We took proton radiographs of the phantom with each insert in place and created difference maps between the resulting images. Integrated proton range was measured from an ROI in the difference maps.

physics.med-ph↗

arXiv2021

Technical Note: A fast and monolithic prototype clinical proton radiography system optimized for pencil beam scanning

Purpose: To demonstrate a proton imaging system based on well-established fast scintillator technology to achieve high performance with low cost and complexity, with the potential of a straightforward translation into clinical use. Methods: The system tracks individual protons through one (X, Y) scintillating fiber tracker plane upstream and downstream of the object and into a 13 cm-thick scintillating block residual energy detector. The fibers in the tracker planes are multiplexed into silicon photomultipliers (SiPMs) to reduce the number of electronics channels. The light signal from the residual energy detector is collected by 16 photomultiplier tubes (PMTs). Only four signals from the PMTs are output from each event, which allows for fast signal readout. A robust calibration method of the PMT signal to residual energy has been developed to obtain accurate proton images. The development of patient-specific scan patterns using multiple input energies allows for an image to be produced with minimal excess dose delivered to the patient. Results: The calibration of signals in the energy detector produces accurate residual range measurements limited by intrinsic range straggling. We measured the water-equivalent thickness (WET) of a block of solid water (physical thickness of 6.10 mm) with a proton radiograph. The mean WET from all pixels in the block was 6.13 cm (SD 0.02 cm). The use of patient-specific scan patterns using multiple input energies enables imaging with a compact range detector. Conclusions: We have developed a prototype clinical proton radiography system for pretreatment imaging in proton radiation therapy. We have optimized the system for use with pencil beam scanning systems and have achieved a reduction of size and complexity compared to previous designs.

physics.med-ph↗

arXiv2020

Efficiency Analysis of the Simplified Refined Instrumental Variable Method for Continuous-time Systems

In this paper, we derive the asymptotic Cramér-Rao lower bound for the continuous-time output error model structure and provide an analysis of the statistical efficiency of the Simplified Refined Instrumental Variable method for Continuous-time systems (SRIVC) based on sampled data.It is shown that the asymptotic Cramér-Rao lower bound is independent of the intersample behaviour of the noise-free system output and hence only depends on the intersample behaviour of the system input. We have also shown that, at the converging point of the SRIVC algorithm, the estimates do not depend on the intersample behaviour of the measured output. It is then proven that the SRIVC estimator is asymptotically efficient for the output error model structure under mild conditions. Monte Carlo simulations are performed to verify the asymptotic Cramér-Rao lower bound and the asymptotic covariance of the SRIVC estimates.

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arXiv2019

Consistency Analysis of the Simplified Refined Instrumental Variable Method for Continuous-time Systems

In this paper, we analyse the consistency of the Simplified Refined Instrumental Variable method for Continuous-time systems (SRIVC). It is well known that the intersample behaviour of the input signal influences the quality and accuracy of the results when estimating and simulating continuous-time models. Here, we present a comprehensive analysis on the consistency of the SRIVC estimator while taking into account the intersample behaviour of the input signal. The main result of the paper shows that, under some mild conditions, the SRIVC estimator is generically consistent. We also describe some conditions when consistency is not achieved, which is important from a practical standpoint. The theoretical results are supported by simulation examples.

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arXiv2018

Aligning Manifolds of Double Pendulum Dynamics Under the Influence of Noise

This study presents the results of a series of simulation experiments that evaluate and compare four different manifold alignment methods under the influence of noise. The data was created by simulating the dynamics of two slightly different double pendulums in three-dimensional space. The method of semi-supervised feature-level manifold alignment using global distance resulted in the most convincing visualisations. However, the semi-supervised feature-level local alignment methods resulted in smaller alignment errors. These local alignment methods were also more robust to noise and faster than the other methods.

cs.LG↗

arXiv2018

An analysis of the SPARSEVA estimate for the finite sample data case

In this paper, we develop an upper bound for the SPARSEVA (SPARSe Estimation based on a VAlidation criterion) estimation error in a general scheme, i.e., when the cost function is strongly convex and the regularized norm is decomposable for a pair of subspaces. We show how this general bound can be applied to a sparse regression problem to obtain an upper bound for the traditional SPARSEVA problem. Numerical results are used to illustrate the effectiveness of the suggested bound.

math.ST↗

arXiv2018

Volterra Kernel Identification using Regularized Orthonormal Basis Functions

The Volterra series is a powerful tool in modelling a broad range of nonlinear dynamic systems. However, due to its nonparametric nature, the number of parameters in the series increases rapidly with memory length and series order, with the uncertainty in resulting model estimates increasing accordingly. In this paper, we propose an identification method where the Volterra kernels are estimated indirectly through orthonormal basis function expansions, with regularization applied directly to the expansion coefficients to reduce variance in the final model estimate and provide access to useful models at previously unfeasible series orders. The higher dimensional kernel expansions are regularized using a method that allows smoothness and decay to be imposed on the entire hyper-surface. Numerical examples demonstrate improved Volterra series estimation up to the 4th order using the regularized basis function method.

eess.SP↗

arXiv2018

An asymptotically optimal indirect approach to continuous-time system identification

The indirect approach to continuous-time system identification consists in estimating continuous-time models by first determining an appropriate discrete-time model. For a zero-order hold sampling mechanism, this approach usually leads to a transfer function estimate with relative degree 1, independent of the relative degree of the strictly proper real system. In this paper, a refinement of these methods is developed. Inspired by indirect PEM, we propose a method that enforces a fixed relative degree in the continuous-time transfer function estimate, and show that the resulting estimator is consistent and asymptotically efficient. Extensive numerical simulations are put forward to show the performance of this estimator when contrasted with other indirect and direct methods for continuous-time system identification.

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arXiv2017

Useful redundancy in parameter and time delay estimation for continuous-time models

This paper proposes an algorithm to estimate the parameters, including time delay, of continuous time systems based on instrumental variable identification methods. To overcome the multiple local minima of the cost function associated with the estimation of a time delay system, we utilise the useful redundancy technique. Specifically, the cost function is filtered through a set of low-pass filters to improve convexity with the useful redundancy technique exploited to achieve convergence to the global minimum of the optimization problem. Numerical examples are presented to demonstrate the effectiveness of the proposed algorithm.

math.ST↗

arXiv2015

Reweighted nuclear norm regularization: A SPARSEVA approach

The aim of this paper is to develop a method to estimate high order FIR and ARX models using least squares with re-weighted nuclear norm regularization. Typically, the choice of the tuning parameter in the reweighting scheme is computationally expensive, hence we propose the use of the SPARSEVA (SPARSe Estimation based on a VAlidation criterion) framework to overcome this problem. Furthermore, we suggest the use of the prediction error criterion (PEC) to select the tuning parameter in the SPARSEVA algorithm. Numerical examples demonstrate the veracity of this method which has close ties with the traditional technique of cross validation, but using much less computations.

math.OC↗