Thesis (M.S.)--California Polytechnic State University, 2009. / Mode of access: Internet. Title from PDF title page; viewed on June 4, 2009. Major professor: Daniel J. Biezad. "Presented to the faculty California Polytechnic State University, San Luis Obispo." "In partial fulfillment of the requirements for the degree [of] Master of Science in Aerospace Engineering." "May 2009." Includes bibliographical references (p. 110-111). Also available on microfiche.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1973. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliography.

abstract: This thesis considers the application of basis pursuit to several problems in system identification. After reviewing some key results in the theory of basis pursuit and compressed sensing, numerical experiments are presented that explore the application of basis pursuit to the black-box identification of linear time-invariant (LTI) systems with both finite (FIR) and infinite (IIR) impulse responses, temporal systems modeled by ordinary differential equations (ODE), and spatio-temporal systems modeled by partial differential equations (PDE). For LTI systems, the experimental results illustrate existing theory for identification of LTI FIR systems. It is seen that basis pursuit does not identify sparse LTI IIR systems, but it does identify alternate systems with nearly identical magnitude response characteristics when there are small numbers of non-zero coefficients. For ODE systems, the experimental results are consistent with earlier research for differential equations that are polynomials in the system variables, illustrating feasibility of the approach for small numbers of non-zero terms. For PDE systems, it is demonstrated that basis pursuit can be applied to system identification, along with a comparison in performance with another existing method. In all cases the impact of measurement noise on identification performance is considered, and it is empirically observed that high signal-to-noise ratio is required for successful application of basis pursuit to system identification problems. / Dissertation/Thesis / M.A. Mathematics 2012

This thesis concentrates on learning and identification of fuzzy systems, and this thesis is composed about learning fuzzy systems from data for regression and function approximation by constructing complete, compact, and consistent fuzzy systems. Fuzzy systems are prevalent to solve pattern recognition problems and function approximation problems as a result of the good knowledge representation. With the development of fuzzy systems, a lot of sophisticated methods based on them try to completely solve pattern recognition problems and function approximation problems by constructing a great diversity of mathematical models. However, there exists a conflict between the degree of the interpretability and the accuracy of the approximation in general fuzzy systems. Thus, how to properly make the best compromise between the accuracy of the approximation and the degree of the interpretability in the entire system is a significant study of the subject.The first work of this research is concerned with the clustering technique on constructing fuzzy models in fuzzy system identification, and this method is a part of clustering based learning of fuzzy systems. As the determination of the proper number of clusters and the appropriate location of clusters is one of primary considerations on constructing an effectively fuzzy model, the task of the clustering technique aims at recognizing the proper number of clusters and the appropriate location as far as possible, which gives a good preparation for the construction of fuzzy models. In order to acquire the mutually exclusive performance by constructing effectively fuzzy models, a modular method to fuzzy system identification based on a hybrid clustering-based technique has been considered. Due to the above reasons, a hybrid clustering algorithm concerning input, output, generalization and specialization has hence been introduced in this work. Thus, the primary advantage of this work is the proposed clustering technique integrates a variety of clustering properties to positively identify the proper number of clusters and the appropriate location of clusters by carrying out a good performance of recognizing the precise position of each dataset, and this advantage brings fuzzy systems more complete.The second work of this research is an extended work of the first work, and two ways to improve the original work have been considered in the extended work, including the pruning strategy for simplifying the structure of fuzzy systems and the optimization scheme for parameters optimization. So far as the pruning strategy is concerned, the purpose of which aims at refining rule base by the similarity analysis of fuzzy sets, fuzzy numbers, fuzzy membership functions or fuzzy rules. By other means, through the similarity analysis of which, the complete rules can be kept and the redundant rules can be reduced probably in the rule base of fuzzy systems. Also, the optimization scheme can be regarded as a two-layer parameters optimization in the extended work, because the parameters of the initial fuzzy model have been fine tuning by two phases gradation on layer. Hence, the extended work primarily puts focus on enhancing the performance of the initial fuzzy models toward the positive reliability of the final fuzzy models. Thus, the primary advantage of this work consists of the simplification of fuzzy rule base by the similarity-based pruning strategy, as well as more accuracy of the optimization by the two-layer optimization scheme, and these advantages bring fuzzy systems more compact and precise.So far as a perfect modular method for fuzzy system identification is concerned, in addition to positively solve pattern recognition problems and function approximation problems, it should primarily comprise the following features, including the well-understanding interpretability, low-degree dimensionality, highly reliability, stable robustness, highly accuracy of the approximation, less computational cost, and maximum performance. However, it is extremely difficult to meet all of these conditions above. Inasmuch as attaining the highly achievement from the features above as far as possible, the research works of this thesis try to present a modular method concerning a variety of requirements to fuzzy systems identification.

There has been much recent research on the control of complex sound fields in enclosed vibrating structures via active control techniques. Active Structural Acoustic Control (ASAC) has shown much promise for reducing interior cabin noise in aircraft by applying control forces directly to the fuselage structure. Optimal positioning of force actuators for ASAC presents a challenging problem however, because a detailed knowledge of the structural-acoustic coupling in the fuselage is required. This work is concerned with the development of a novel experimental technique for examining the forced harmonic vibrations of an aircraft fuselage and isolating the acoustically well-coupled motions that cause significant interior noise. The developed system identification technique is itself based upon an active control system, which is used to approximate the disturbance noise field in the cabin and apply an inverse excitation to the fuselage structure. The resulting shell vibrations are recorded and used to optimally locate piezoelectric (PZT) actuators on the fuselage for ASAC testing. Experiments for this project made use of a Cessna Citation III aircraft fuselage test rig. Tests were performed at three harmonic disturbance frequencies, including an acoustic resonance, an off-resonance, and a structural resonance case. In all cases, the new system identification technique successfully isolated a simplified, low-magnitude vibration pattern from the total structural response caused by a force disturbance applied at the fuselage's rear engine mount. These measured well-coupled vibration components were used for positioning candidate piezoelectric actuators on the fuselage shell. A genetic algorithm search provided an optimal subset of actuators for use in an ASAC system. ASAC tests confirmed the importance of actuator location, as the optimal sets outperformed alternate groupings in all test cases. In addition, significant global control was achieved, with sound level reductions observed throughout the passenger cabin with virtually no control spillover. / Master of Science

Parameter estimation is a pivotal task across various domains such as system identification, statistics, and machine learning. The literature presents numerous estimation procedures, many of which are backed by well-studied asymptotic properties. In the contemporary landscape, highly advanced digital twins (DTs) offer the capability to faithfully replicate real systems through proper tuning. Leveraging these DTs, data-driven estimators can alleviate challenges inherent in traditional methods, notably their computational cost and sensitivity to initializations. Furthermore, traditional estimators often rely on sensitive data, necessitating protective measures. In this thesis, we consider data-driven and privacy-preserving approaches to parameter estimation that overcome many of these challenges. The first part of the thesis delves into an exploration of modern data-driven estimation techniques, focusing on the two-stage (TS) approach. Operating under the paradigm of inverse supervised learning, the TS approach simulates numerous samples across parameter variations and employs supervised learning methods to predict parameter values. Divided into two stages, the approach involves compressing data into a smaller set of samples and the second stage utilizes these samples to predict parameter values. The simplicity of the TS estimator underscores its interpretability, necessitating theoretical justification, which forms the core motivation for this thesis. We establish statistical frameworks for the TS estimator, yielding its Bayes and minimax versions, alongside developing an improved minimax TS variant that excels in computational efficiency and robustness to distributional shifts. Finally, we conduct an asymptotic analysis of the TS estimator. The second part of the thesis introduces an application of data-driven estimation methods, that includes the TS and neural network based approaches, in the design of tuning rules for PI controllers. Leveraging synthetic datasets generated from DTs, we train machine learning algorithms to meta-learn tuning rules, streamlining the calibration process without manual intervention. In the final part of the thesis, we tackle scenarios where estimation procedures must handle sensitive data. Here, we introduce differential privacy constraints into the Bayes point estimation problem to protect sensitive information. Proposing a unified approach, we integrate the estimation problem and differential privacy constraints into a single convex optimization objective, thereby optimizing the accuracy-privacy trade-off. In cases where both observations and parameter spaces are finite, this approach reduces to a tractable linear program which is solvable using off-the-shelf solvers. In essence, this thesis endeavors to address computational and privacy concerns within the realm of parameter estimation. / Skattning av parametrar utgör en fundamental uppgift inom en mängd fält, såsom systemidentifiering, statistik och maskininlärning. I litteraturen finns otaliga skattningsmetoder, utav vilka många understödjs av välstuderade asymptotiska egenskaper. Inom dagens forskning erbjuder noggrant kalibrerade digital twins (DTs) möjligheten att naturtroget återskapa verkliga system. Genom att utnyttja dessa DTs kan data-drivna skattningsmetoder minska problem som vanligtvis drabbar traditionella skattningsmetoder, i synnerhet problem med beräkningsbörda och känslighet för initialiseringvillkor. Traditionella skattningsmetoder kräver dessutom ofta känslig data, vilket leder till ett behov av skyddsåtgärder. I den här uppsatsen, undersöker vi data-drivna och integritetsbevarande parameterskattningmetoder som övervinner många av de nämnda problemen.  Första delen av uppsatsen är en undersökning av moderna data-drivna skattningtekniker, med fokus på två-stegs-metoden (TS). Som metod inom omvänd övervakad maskininlärning, simulerar TS en stor mängd data med ett stort urval av parametrar och tillämpar sedan metoder från övervakad inlärning för att förutsäga parametervärden. De två stegen innefattar datakomprimering till en mindre mängd, varefter den mindre mängden data används för parameterskattning. Tack vare sin enkelhet och tydbarhet lämpar sig två-stegs-metoden väl för teoretisk analys, vilket är uppsatsens motivering. Vi utvecklar ett statistiskt ramverk för två-stegsmetoden, vilket ger Bayes och minimax-varianterna, samtidigt som vi vidareutvecklar minimax-TS genom en variant med hög beräkningseffektivitet och robusthet gentemot skiftade fördelningar. Slutligen analyserar vi två-stegs-metodens asymptotiska egenskaper.  Andra delen av uppsatsen introducerar en tillämpning av data-drivna skattningsmetoder, vilket innefattar TS och neurala nätverk, i designen och kalibreringen av PI-regulatorer. Med hjälp av syntetisk data från DTs tränar vi maskininlärningsalgoritmer att meta-lära sig regler för kalibrering, vilket effektiverar kalibreringsprocessen utan manuellt ingripande.  I sista delen av uppsatsen behandlar vi scenarion då skattningsprocessen innefattar känslig data. Vi introducerar differential-privacy-begränsningar i Bayes-punktskattningsproblemet för att skydda känslig information. Vi kombinerar skattningsproblemet och differential-privacy-begränsningarna i en gemensam konvex målfunktion, och optimerar således avvägningen mellan noggrannhet och integritet. Ifall både observations- och parameterrummen är ändliga, så reduceras problemet till ett lätthanterligt linjärt optimeringsproblem, vilket löses utan vidare med välkända metoder.  Sammanfattningsvis behandlar uppsatsen beräkningsmässiga och integritets-angelägenheter inom ramen för parameterskattning. / <p>QC 20240306</p>

Single Particle Tracking (SPT) plays an important role in the study of physical and dynamic properties of biomolecules moving in their native environment. To date, many algorithms have been developed for localization and parameter estimation in SPT. Though the performance of these methods is good when the signal level is high and the motion model simple, they begin to fail as the signal level decreases or model complexity increases. In addition, the inputs to the SPT algorithms are sequences of images that are cropped from a large data set and that focus on a single particle. This motivates us to seek machine learning tools to deal with that initial step of extracting data from larger images containing multiple particles. This thesis makes contributions to both data extraction question and to the problem of state and parameter estimation. First, we build upon the Expectation Maximization (EM) algorithm to create a generic framework for joint localization refinement and parameter estimation in SPT. Under the EM-based scheme, two representative methods are considered for generating the filtered and smoothed distributions needed by EM: Sequential Monte Carlo - Expectation Maximization (SMC-EM), and Unscented - Expectation Maximization (U-EM). The selection of filtering and smoothing algorithms is very flexible so long as they provide the necessary distributions for EM. The versatility and reliability of EM based framework have been validated via data-intensive modeling and simulation where we considered a variety of influential factors, such as a wide range of {\color{red}Signal-to-background ratios (SBRs)}, diffusion speeds, motion blur, camera types, image length, etc. Meanwhile, under the EM-based scheme, we make an effort to improve the overall computational efficiency by simplifying the mathematical expression of models, replacing filtering/smoothing algorithms with more efficient ones {\color{purple} (trading some accuracy for reduced computation time)}, and using parallel computation and other computing techniques. In terms of localization refinement and parameter estimation in SPT, we also conduct an overall quantitative comparison among EM based methods and standard two-step methods. Regarding the U-EM, we conduct transformation methods to make it adapted to the nonlinearities and complexities of measurement model. We also extended the application of U-EM to more complicated SPT scenarios, including time-varying parameters and additional observation models that are relevant to the biophysical setting. The second area of contribution is in the particle detection and extraction problem to create data to feed into the EM-based approaches. Here we build Particle Identification Networks (PINs) covering three different network architectures. The first, \PINCNN{}, is based on a standard Convolutional Neural Network (CNN) structure that has previously been successfully applied in particle detection and localization. The second, \PINRES, uses a Residual Neural Network (ResNet) architecture that is significantly deeper than the CNN while the third, \PINFPN{}, is based on a more advanced Feature Pyramid Network (FPN) that can take advantage of multi-scale information in an image. All networks are trained using the same collection of simulated data created with a range of SBRs and fluorescence emitter densities, as well as with three different Point Spread Functions (PSFs): a standard Born-Wolf model, a model for astigmatic imaging to allow localization in three dimensions, and a model of the Double-Helix engineered PSF. All PINs are evaluated and compared through data-intensive simulation and experiments under a variety of settings. In the final contribution, we link all above together to create an algorithm that takes in raw camera data and produces trajectories and parameter estimates for multiple particles in an image sequence.

Wind observations that are critical for understanding meteorological processes occurring inside of the Earth's atmospheric boundary layer (ABL) are sparse due to limitations of conventional atmospheric sensors. In this dissertation, dynamic systems and estimation theory are combined with experimental methods to exploit the flight envelope of multirotor UAS for wind sensing. The parameters of three quadrotor motion models, consisting of a kinematic particle, a dynamic particle, and a dynamic rigid body models are developed to measure wind velocity in hovering flight. Wind tunnel and steady level flight tests are used to characterize kinematic and dynamic particle models. System identification stepwise regression and output error algorithms are used to determine the model structure and parameter estimates of rigid body models. The comparison of all three models demonstrates the rigid body model to have higher performance resolving slow-varying winds based on a frequency response analysis and field experiments conducted next to a 3-D sonic anemometer. The dissertation also presents an extension of the rigid body wind estimation framework to profile the horizontal components of wind velocity in vertical steady ascending flight. The extension employed system identification to characterize five rigid body models for steady-ascending flight speeds increasing from 0 to 2 m/s in intervals of 0.5~m/s. State observers for wind profiling were synthesized using all five rigid body models. Performance assessments employing wind observations from in situ and remote sensors demonstrated model-based wind profiling results to be be in close agreement with ground-truth wind observations. Finally, the rigid body wind sensing framework developed in this dissertations for multirotor UAS is employed to support science objectives for the Advanced Lagrangian Predictions for Hazards Assessment Project. Quadrotor wind measurements sampled at 10 m above sea level were used to characterize the leeway of a person in water for search and rescue scenarios. Leeway values determined from quadrotor wind measurements were found to be in close to leeway parameters previous published in the literature. This results demonstrates the utility of model-based wind sensing for multirotor UAS for providing wind velocity observations in complex environments where conventional wind observations are not readily available. / Doctor of Philosophy / Wind observations that are critical for understanding meteorological processes occurring inside of the Earth's atmospheric boundary layer (ABL) are sparse due to limitations of conventional atmospheric sensors. In this dissertation, dynamic systems and estimation theory are combined with experimental methods to exploit the flight envelope of multirotor UAS for wind sensing. The parameters of three quadrotor motion models, consisting of a kinematic particle model, a dynamic particle model, and a dynamic rigid body model, are characterized to measure wind velocity in hovering flight. Parameter characterizations are realized using data from wind tunnel, steady level flight tests and system identification experiments. Model-based wind estimations algorithms are developed using the kinematic particle model directly and by synthesizing state observers for the dynamic particle and rigid body models separately. For comparison purposes, the frequency response characteristic of the dynamic particle and rigid body models is examined to determine the range of wind fluctuations that each model can resolve. Performance comparisons demonstrate that the rigid body model to resolve higher wind fluctuations and yield more accurate wind estimates. The dissertation extends the rigid body wind estimation algorithm to estimate wind velocity profiles of the horizontal wind vector. The rigid body wind estimation algorithms is used to answer science questions about about the drift of a person in water.

The use of rotary winged unmanned aerial vehicles in military and civilian applications is rapidly increasing. The primary objective of this study is to develop an automatic flight control system for a radio controlled (RC) helicopter. There is a need for a simple, easy to use methodology to develop automatic flight controllers for first-flight. In order to make the work accessible to new research groups without physical helicopter platforms, a simulation environment is created for validation. The size 30 RC helicopter in AeroSIMRC is treated as the final target platform. A grey box, timedomain system identification method is used to estimate a linear state space model that operates around hover. Identifying the unknown parameters in the model is highly dependent on the initial guess values and the input data. The model is divided into subsystems to make estimation possible. A cascaded controller approach is followed. The helicopter’s fast angular dynamics are separated from the slower translational dynamics. A linear quadratic regulator is used to control the helicopter’s attitude dynamics. An optimised PID outer-loop generates attitude commands from a given inertial position trajectory. The PID controllers are optimised using a simplex search method. An observer estimates the unmeasured states such as blade flapping. The controller is developed in Simulink®, and a plug-in written for AeroSIMRC enables Simulink® to control the simulator through a UDP interface to validate the model and controller. The identified state space model is able to accurately model the flight data from the simulator. The controllers perform well, keeping the helicopter stable even in the presence of considerable disturbances. The attitude controller’s performance is validated using an aeronautical design standard (ADS-33E-PRF) for handling qualities. The trajectory tracking is validated in a series of simulator flight tests. The linear controller is able to sustain stable flight in constant winds of up to 60% of the helicopter’s maximum airspeed. / MIng (Computer and Electronic Engineering), North-West University, Potchefstroom Campus, 2014

The use of rotary winged unmanned aerial vehicles in military and civilian applications is rapidly increasing. The primary objective of this study is to develop an automatic flight control system for a radio controlled (RC) helicopter. There is a need for a simple, easy to use methodology to develop automatic flight controllers for first-flight. In order to make the work accessible to new research groups without physical helicopter platforms, a simulation environment is created for validation. The size 30 RC helicopter in AeroSIMRC is treated as the final target platform. A grey box, timedomain system identification method is used to estimate a linear state space model that operates around hover. Identifying the unknown parameters in the model is highly dependent on the initial guess values and the input data. The model is divided into subsystems to make estimation possible. A cascaded controller approach is followed. The helicopter’s fast angular dynamics are separated from the slower translational dynamics. A linear quadratic regulator is used to control the helicopter’s attitude dynamics. An optimised PID outer-loop generates attitude commands from a given inertial position trajectory. The PID controllers are optimised using a simplex search method. An observer estimates the unmeasured states such as blade flapping. The controller is developed in Simulink®, and a plug-in written for AeroSIMRC enables Simulink® to control the simulator through a UDP interface to validate the model and controller. The identified state space model is able to accurately model the flight data from the simulator. The controllers perform well, keeping the helicopter stable even in the presence of considerable disturbances. The attitude controller’s performance is validated using an aeronautical design standard (ADS-33E-PRF) for handling qualities. The trajectory tracking is validated in a series of simulator flight tests. The linear controller is able to sustain stable flight in constant winds of up to 60% of the helicopter’s maximum airspeed. / MIng (Computer and Electronic Engineering), North-West University, Potchefstroom Campus, 2014