The objective of this research is to develop large signal modeling and optimization methods for Capacitive Micromachined Ultrasonic Transducers (CMUTs), especially when they are used in an array configuration. General modeling and optimization methods that cover a large domain of CMUT designs are crucial, as many membrane and array geometry combinations are possible using existing microfabrication technologies. Currently, large signal modeling methods for CMUTs are not well established and nonlinear imaging techniques utilizing linear piezoelectric transducers are not applicable to CMUTs because of their strong nonlinearity. In this work, the nonlinear CMUT behavior is studied, and a feedback linearization method is proposed to reduce the CMUT nonlinearity. This method is shown to improve the CMUT performance for continuous wave applications, such as high-intensity focused ultrasound or harmonic imaging, where transducer linearity is crucial. In the second part of this dissertation, a large signal model is developed that is capable of transient modeling of CMUT arrays with arbitrary electrical terminations. The developed model is suitable for iterative design optimization of CMUTs and CMUT based imaging systems with arbitrary membrane and array geometries for a variety of applications. Finally, a novel multi-pulse method for nonlinear tissue and contrast agent imaging with CMUTs is presented. It is shown that the nonlinear content can be successfully extracted from echo signals in a CMUT based imaging system using a multiple pulse scheme. The proposed method is independent of the CMUT geometry and valid for large signal operation. Experimental results verifying the developed large signal CMUT array model, proposed gap feedback and multi-pulse techniques are also presented.

Mediational analysis quantifies proposed causal mechanisms through which treatments act on outcomes. In the presence of clustered data, conventional multiple regression mediational methods break down, requiring the use of hierarchical linear modeling techniques. As an additional consideration, nonlinear relationships in multilevel mediation models require unique specifications that are ignored if modeled linearly. Improper specification of nonlinear relationships can lead to a consistently overestimated mediated effect. This has direct implications for inferences regarding intervention causality and efficacy. The current investigation examined a specific nonlinear multilevel mediation model parameterization to account for nonlinear relationships in clustered data. A simulation study was conducted to compare linear and nonlinear model specifications in the presence of truly nonlinear data. MacKinnon et al.’s (2007a) empirical-M based PRODCLIN method for estimating the confidence interval surrounding the instantaneous indirect effect was used to compare confidence interval coverage rates surrounding both the linear and nonlinear models’ estimates. Overall, the nonlinear model’s estimates were less biased, more efficient, and produced higher coverage rates than the linear model specification. For conditions containing a true value of zero for the instantaneous indirect effect, bias, efficiency, and coverage rate values were similar for the linear and nonlinear estimators. For conditions with a non-zero value for the instantaneous indirect effect, both the linear and nonlinear models were substantially biased. However, the nonlinear model was always less biased and always produced higher coverage rates than the linear model. The nonlinear model was more efficient than the linear model for all but two design conditions. / text

Sensor network coverage refers to the quality of service provided by a sensor network surveilling a region of interest. So far, coverage problems have been formulated to address area coverage or to maintain line-of-sight visibility in the presence of obstacles (i.e., art-gallery problems). Although very useful in many sensor applications, none of the existing formulations address coverage as it pertains to target tracking by means of multiple sensors, nor do they provide a closed-form function that can be applied to the problem of allocating sensors for the surveilling objective of maximizing target detection while minimizing false alarms. This dissertation presents a new coverage formulation addressing the quality of service of sensor networks that cooperatively detect targets traversing a region of interest, and is readily applicable to the current sensor network coverage formulations. The problem of track coverage consists of finding the positions of <em>n</em> sensors such that the amount of tracks detected by at least <em>k</em> sensors is optimized. This dissertation studies the geometric properties of the network, addressing a deterministic track-coverage formulation and binary sensor models. It is shown that the tracks detected by a network of heterogeneous omnidirectional sensors are the geometric transversals of non-translates families of disks. A novel methodology based on cones and convex analysis is presented for representing and measuring sets of transversals as closed-form functions of the sensors positions and ranges. As a result, the problem of optimally deploying a sensor network with the aforementioned objectives can be formulated as an optimization problem subject to mission dynamics and constraints. The sensor placement problem, in which the sensors are placed such that track coverage is maximized for a fixed sensor network, is formulated as a nonlinear program and solved using sequential quadratic programming. The sensor deployment, involving a dynamic sensor network installed on non-maneuverable sonobuoys deployed in the ocean, is formulated as an optimization problem subject to inverse dynamics. Both a finite measure of the cumulative coverage provided by a sensor network over a fixed period of time and the oceanic-induced current velocity field are accounted for in order to optimize the dynamic sensor network configuration. It is shown that a state-space representation of the motions of the individual sensors subject to the current vector field can be derived from sonobuoys oceanic drift models and obtained from CODAR measurements. Also considered in the sensor model are the position-dependent acoustic ranges of the sensors due to the effects from heterogenous environmental conditions, such as ocean bathymetry, surface temporal variability, and bottom properties. A solution is presented for the initial deployment scheme of the non-maneuverable sonobuoys subject to the ocean's current, such that sufficient track coverage is maintained over the entire mission. As sensor networks are subject to random disturbances due to unforseen heterogenous environmental conditions propagated throughout the sensors trajectories, the optimal initial positions solution is evaluated for robustness through Monte Carlo simulations. Finally, the problem of controlling a network of maneuverable underwater vehicles, each equipped with an onboard acoustic sensor is formulated using optimal control theory. Consequently, a new optimal control problem is presented that integrates sensor objectives, such as track coverage, with cooperative path planning of a mobile sensor network subject to time-varying environmental dynamics. / Dissertation

General anesthesia is a drug-induced reversible state where neuromuscular blockade (NMB), hypnosis, and analgesia (jointly denoted by depth of anesthesia - DoA) are guaranteed. This thesis concerns mathematical modeling and feedback control of the effect of the muscle relaxants atracurium and rocuronium, the hypnotic propofol, and the analgesic remifentanil. It is motivated by the need to reduce incidences of awareness and overdose-related post-operative complications that occur in standard clinical practice. A major challenge for identification in closed-loop is the poor excitation provided by the feedback signal. This applies to the case of drugs administered in closed-loop. As a result, the standard models for the effect of anesthetics appear to be over-parameterized. This deteriorates the result of system identification and prevents individualized control. In the first part of the thesis, minimally parameterized models for the single-input single-output NMB and the multiple-input single-output DoA are developed, using real data. The models have a nonlinear Wiener structure: linear time-invariant dynamics cascaded with a static nonlinearity. The proposed models are shown to improve identifiability as compared to the standard ones. The second part of the thesis presents system identification methods for Wiener systems: a batch prediction error method, and two recursive techniques, one based on the extended Kalman filter, and another based on the particle filter. Algorithms are given for both the NMB and the DoA using the minimally parameterized models. Nonlinear adaptive controllers are proposed in the third part of the thesis. Using the model parameter estimates from the extended Kalman filter, the controller performs an online inversion of the Wiener nonlinearity. A pole-placement controller or a linear quadratic Gaussian controller is used for the linearized system. Results show good reference tracking performance both in simulation and in real trials. Relating to patient safety, the existence of undesirable sustained oscillations as consequence of Andronov-Hopf bifurcations for a NMB PID-controlled system is analyzed. Essentially the same bifurcations are observed in the standard and the minimally parameterized models, confirming the ability of the latter to predict the nonlinear behavior of the closed-loop system. Methods to design oscillation-free controllers are outlined.

Explaining a phenomenon often requires identification of an underlying relationship between two variables. However, it is common practice in psychological research to sample only a few values of an independent variable. Young, Cole, and Sutherland (2012) showed that this practice can impair model selection in between-subject designs. The current study expands that line of research to within-subjects designs. In two Monte Carlo simulations, model discrimination under systematic sampling of 2, 3, or 4 levels of the IV was compared with that under random uniform sampling and sampling from a Halton sequence. The number of subjects, number of observations per subject, effect size, and between-subject parameter variance in the simulated experiments were also manipulated. Random sampling out-performed the other methods in model discrimination with only small, function-specific costs to parameter estimation. Halton sampling also produced good results but was less consistent. The systematic sampling methods were generally rank-ordered by the number of levels they sampled.

This thesis addresses the problem of identifying nonlinear dynamic systems from a machine learning perspective. In this context, very little is assumed to be known about the system under investigation, and the only source of information comes from input/output measurements on the system. It corresponds to the black-box modeling approach. Numerous strategies and models have been proposed over the last decades in the machine learning field and applied to modeling tasks in a straightforward way. Despite of this variety, the methods can be roughly categorized into global and local modeling approaches. Global modeling consists in fitting a single regression model to the available data, using the whole set of input and output observations. On the other side of the spectrum stands the local modeling approach, in which the input space is segmented into several small partitions and a specialized regression model is fit to each partition. The first contribution of the thesis is a novel supervised global learning model, the Minimal Learning Machine (MLM). Learning in MLM consists in building a linear mapping between input and output distance matrices and then estimating the nonlinear response from the geometrical configuration of the output points. Given its general formulation, the Minimal Learning Machine is inherently capable of operating on nonlinear regression problems as well as on multidimensional response spaces. Naturally, its characteristics make the MLM able to tackle the system modeling problem. The second significant contribution of the thesis represents a different modeling paradigm, called Regional Modeling (RM), and it is motivated by the parsimonious principle. Regional models stand between the global and local modeling approaches. The proposal consists of a two-level clustering approach in which we first partition the input space using the Self-Organizing Map (SOM), and then perform clustering over the prototypes of the trained SOM. After that, regression models are built over the clusters of SOM prototypes, or regions in the input space. Even though the proposals of the thesis can be thought as quite general regression or supervised learning models, the performance assessment is carried out in the context of system identification. Comprehensive performance evaluation of the proposed models on synthetic and real-world datasets is carried out and the results compared to those achieved by standard global and local models. The experiments illustrate that the proposed methods achieve accuracies that are comparable to, and even better than, more traditional machine learning methods thus offering a valid alternative to such approaches. / This thesis addresses the problem of identifying nonlinear dynamic systems from a machine learning perspective. In this context, very little is assumed to be known about the system under investigation, and the only source of information comes from input/output measurements on the system. It corresponds to the black-box modeling approach. Numerous strategies and models have been proposed over the last decades in the machine learning field and applied to modeling tasks in a straightforward way. Despite of this variety, the methods can be roughly categorized into global and local modeling approaches. Global modeling consists in fitting a single regression model to the available data, using the whole set of input and output observations. On the other side of the spectrum stands the local modeling approach, in which the input space is segmented into several small partitions and a specialized regression model is fit to each partition. The first contribution of the thesis is a novel supervised global learning model, the Minimal Learning Machine (MLM). Learning in MLM consists in building a linear mapping between input and output distance matrices and then estimating the nonlinear response from the geometrical configuration of the output points. Given its general formulation, the Minimal Learning Machine is inherently capable of operating on nonlinear regression problems as well as on multidimensional response spaces. Naturally, its characteristics make the MLM able to tackle the system modeling problem. The second significant contribution of the thesis represents a different modeling paradigm, called Regional Modeling (RM), and it is motivated by the parsimonious principle. Regional models stand between the global and local modeling approaches. The proposal consists of a two-level clustering approach in which we first partition the input space using the Self-Organizing Map (SOM), and then perform clustering over the prototypes of the trained SOM. After that, regression models are built over the clusters of SOM prototypes, or regions in the input space. Even though the proposals of the thesis can be thought as quite general regression or supervised learning models, the performance assessment is carried out in the context of system identification. Comprehensive performance evaluation of the proposed models on synthetic and real-world datasets is carried out and the results compared to those achieved by standard global and local models. The experiments illustrate that the proposed methods achieve accuracies that are comparable to, and even better than, more traditional machine learning methods thus offering a valid alternative to such approaches.

Abstract Oversampling data converters based on Delta-Sigma modulation are a popular solution for modern high-resolution applications. In the design of digital-to-analog or analog-to-digital Delta-sigma converters there are common obstacles due to the difficulties on predicting and verifying their performance. Being a highly nonlinear system, a Delta-Sigma modulator’s (DSM) quantization noise and therefore the spurious tones are difficult to analyze and predict. Multi-bit DACs can be used to improve the performance and linearize the behavior of DSMs. However, this will give rise to the need for linearizing the multi-bit DAC. A popular DAC linearization method, data weighted averaging (DWA) shapes the DAC mismatch noise spectrum. There are many variants of DWA, for low-pass and band-pass DSMs. This thesis proposes a generalization which integrates a few published variants into one, broader DWA scheme. The generalization enables expanding the tone-suppression studies into a larger concept. The performance of one- or multibit DSMs is usually verified by simulations. This thesis proposes a simulation-based qualification (characterization) method that can be used to repeatedly verify and compare the performance of multibit DSM with a DAC mismatch shaping or scrambling scheme. The last contribution of this thesis is a very simple model for tonal behavior. The model enables accurate prediction of spurious tones from both DSMs and DWA-DACs. The model emulates the tone behavior by its true birth-mechanism: frequency modulation. The proposed prediction model for tone-behavior can be used for developing new tone-cancelation methods. Based on the model, a DWA linearization method is also proposed. / Tiivistelmä Delta-Sigma modulaatio on suosituin tekniikka ylinäytteistävissä datan muuntimissa. Riippumatta toteutustarkoituksesta (analogia-digitaali- tai digitaali-analogia-muunnos), Delta-Sigma (DS) modulaatiossa on yleisesti tunnettuja käyttäytymisen ennustamiseen liittyviä ongelmia. Nämä ongelmat ovat peräisin modulaattorin luontaisesta epälineaarisuudesta: DS-muunnin on nimittäin vahvasti epälineaarinen takaisinkytketty systeemi, jonka harhatoistojen ennustaminen ja analysointi on erittäin hankalaa. Yksibittisestä monibittiseen DS-muuntimeen siirryttäessä muuntimen suorituskyky paranee, ja muuntimen kohinakäyttäytyminen on lineaarisempaa. Tämä kuitenkin kostautuu tarpeena linearisoida DS-muuntimen digitaali-analogia (D/A) muunnin. Tällä hetkellä tunnetuin linearisointimenetelmä on nimeltään DWA (data weighted averaging) algoritmi. Tässä työssä DWA:lle ja sen lukuisille varianteille esitellään eräänlainen yleistys, jonka avulla algoritmia voidaan soveltaa sekä alipäästö- että kaistanpäästö-DS-muuntimelle. Kuten tunnettua, DS-modulaattorin analyyttinen tarkastelu on raskasta. Yksi- ja monibittisten DS-muuntimien suunnitellun käyttäytymisen varmistaminen tapahtuukin yleensä simulointien avulla. Työssä esitetään simulointiperiaate, jolla voidaan kvalifioida (karakterisoida) monibittinen DS-muunnin. Tarkemmin, kvalifioinnin kohteena on DWA:n kaltaiset D/A -muuntimien linearisointimentelmät. Kyseessä on pyrkimys ennen kaikkea toistettavaan menetelmään, jolla eri menetelmiä voidaan verrata nopeasti ja luotettavasti. Tämän väitöstyön viimeinen kontribuutio on matemaattinen malli harhatoistojen syntymekanismille. Mallilla sekä DS-muunnoksen että DWA-D/A -muunnokseen liittyvät harhatoistot voidaan ennustaa tarkasti. Harhatoistot mallinnetaan yksinkertaisella havaintoihin perustuvalla FM-modulaatiokaavalla. Syntymekanismin mallinnus mahdollistaa DS-muuntimien ennustettavuuden ja täten auttaa harhatoiston kumoamismenetelmien kehittämistä. Työssä esitetään yksi matemaattisen mallin avulla kehitetty DWA-D/A -muunnoksen linearisointimenetelmä.

Recent emphasis has been placed on merging regional forest inventory data with satellite-based information both to improve the efficiency of estimates of population totals, and to produce regional maps of forest variables. There are numerous ways in which forest class and structure variables may be modeled as functions of remotely sensed variables, yet surprisingly little work has been directed at surveying modem statistical techniques to determine which tools are best suited to the tasks given multiple objectives and logistical constraints. Here, a series of analyses to compare nonlinear and nonparametric modeling techniques for mapping a variety of forest variables, and for stratification of field plots, was conducted using data in the Interior Western United States. The analyses compared four statistical modeling techniques for predicting two discrete and four continuous forest inventory variables. The modeling techniques include generalized additive models (GAMs), classification and regression trees (CARTs), multivariate adaptive regression splines (MARS), and artificial neural networks (ANNs). Alternative stratification schemes were also compared for estimating population totals. The analyses were conducted within six ecologically different regions using a variety of satellite-based predictor variables. The work resulted in the development of an objective modeling box that automatically models spatial response variables as functions of any assortment of predictor variables through the four nonlinear or nonparametric modeling techniques. In comparing the different modeling techniques, all proved themselves workable in an automated environment, though ANNs were more problematic. When their potential mapping ability was explored through a simple simulation, tremendous advantages were seen in use of MARS and ANN for prediction over GAMs, CART, and a simple linear model. However, much smaller differences were seen when using real data. In some instances, a simple linear approach worked virtually as well as the more complex models, while small gains were seen using more complex models in other instances. In real data runs, MARS performed (marginally) best most often for binary variables, while GAMs performed (marginally) best most often for continuous variables. After considering a subjective "ease of use" measure, computing time and other predictive performance measures, it was determined that MARS had many advantages over other modeling techniques. In addition, stratification tests illustrated cost-effective means to improve precision of estimates of forest population totals. Finally, the general effect of map accuracy on the relative precision of estimates of population totals obtained under simple random sampling compared to that obtained under stratified random sampling was established and graphically illustrated as a tool for management decisions.

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The design of nonlinear adaptive control systems for reducing vibration transmission in applications such as transportation systems is discussed. The systems studied include suspension systems, such as those used in vehicles, employing nonlinear magneto-rheological (MR) dampers that are controlled to provide improved vibration isolation. Magneto-rheological dampers use a novel class of smart fluid whose apparent viscosity changes as it is exposed to a magnetic field. The developed adaptive control scheme is designed to deal with the nonlinearities and uncertainties that commonly arise in most suspension applications. Some of the nonlinearities that are considered include time-varying characteristics, displacement-dependent effects, and hysterisis damping of magneto-rheological dampers. The uncertainties include mass and stiffness variations that can commonly occur in a suspension system. A number of nonlinear analytical models are developed and used in numerical simulation to evaluate the validity and effectiveness of the developed adaptive controllers. Further, the results of the numerical study are used in an experimental evaluation of the controllers on a seat suspension for heavy vehicles. The analytical and experimental evaluation both indicate the effectiveness of the proposed adaptive control technique in controlling vibration transmission in the presence of both system nonlinearities and uncertainties. The manuscript will provide a detail account of the modeling, dynamic analysis, adaptive control development, and testing that was performed throughout this study. / Ph. D.