Koopman theory is widely used for data-driven modeling of nonlinear dynamical systems. One of the well-known algorithms that stem from this approach is the Extended Dynamic Mode Decomposition (EDMD), a data-driven algorithm for uncontrolled systems. In this thesis, we will start by discussing the EDMD algorithm. We will discuss how this algorithm encompasses Dynamic Mode Decomposition (DMD), a widely used data-driven algorithm. Then we will extend our discussion to input-output systems and identify ways to extend the Koopman Operator Theory to input-output systems. We will also discuss how various algorithms can be identified as instances of this framework. Special care is given to Wavelet-based Dynamic Mode Decomposition (WDMD). WDMD is a variant of DMD that uses only the input and output data. WDMD does that by generating auxiliary states acquired from the Wavelet transform. We will show how the action of the Koopman operator can be simplified by using the Wavelet transform and how the WDMD algorithm can be motivated by this representation. We will also introduce a slight modification to WDMD that makes it more robust to noise. / Master of Science / To analyze a real-world phenomenon we first build a mathematical model to capture its behavior. Traditionally, to build a mathematical model, we isolate its principles and encode it into a function. However, when the phenomenon is not well-known, isolating these principles is not possible. Hence, rather than understanding its principles, we sample data from that phenomenon and build our mathematical model directly from this data by using approximation techniques. In this thesis, we will start by focusing on cases where we can fully observe the phenomena, when no external stimuli are present. We will discuss how some algorithms originating from these approximation techniques can be identified as instances of the Extended Dynamic Mode Decomposition (EDMD) algorithm. For that, we will review an alternative approach to mathematical modeling, called the Koopman approach, and explain how the Extended DMD algorithm stems from this approach. Then we will focus on the case where there is external stimuli and we can only partially observe the phenomena. We will discuss generalizations of the Koopman approach for this case, and how various algorithms that model such systems can be identified as instances of the EDMD algorithm adapted for this case. Special attention is given to the Wavelet-based Dynamic Mode Decomposition (WDMD) algorithm. WDMD builds a mathematical model from the data by borrowing ideas from Wavelet theory, which is used in signal processing. In this way, WDMD does not require the sampling of the fully observed system. This gives WDMD the flexibility to be used for cases where we can only partially observe the phenomena. While showing that WDMD is an instance of EDMD, we will also show how Wavelet theory can simplify the Koopman approach and thus how it can pave the way for an easier analysis.

This thesis mainly addresses the problems of thermal management in data centers (DCs) through data-driven techniques. For thermal management, a temperature prediction model in the facility is very important, while the thermal modeling based on first principles in DCs is quite difficult due to the complicated air flow and heat transfer. Therefore, we employ multiple data-driven techniques including statistical methods and deep neural networks (DNNs) to represent the thermal dynamics. Then based on such data-driven models, temperature estimation and control are implemented to optimize the thermal management in DCs. The contributions of this study are summarized in the following four aspects: 1) A data-driven model constructed through multiple linear Autoregression exogenous (ARX) models is adopted to describe the thermal behaviors in DCs. On the basis of such data-driven model, an observer of adaptive Kalman filter is proposed to estimate the temperature distribution in DC. 2) Based on the data-driven model proposed in the first work, a data-driven fault tolerant predictive controller considering different actuator faults is developed to regulate the temperature in DC. 3) To improve the modeling accuracy, a deep input convex neural network (ICNN) is adopted to implement thermal modeling in DCs, which is also specifically designed for further control design. Besides, the algorithm of elastic weight consolidation (EWC) is employed to overcome the catastrophic forgetting in continual learning. 4) A novel example reweighting algorithm is utilized to enhance the robustness of ICNN against noisy data and avoid overfitting in the training process. Finally, all the proposed approaches are validated in real experiments or experimental-data-based simulations. / Dissertation / Doctor of Philosophy (PhD) / This thesis mainly investigates the applications of data-driven techniques for thermal management in data centers. The implementations of thermal modeling, temperature estimation and temperature control in data centers are the key contributions in this work. First, we design a data-driven statistical model to describe the complicated thermal dynamics of data center. Then based on the data-driven model, efficient observer and controller are developed respectively to optimize the thermal management in data centers. Moreover, to improve the nonlinear modeling performance in data centers, specific deep input convex neural networks capable of good representation capability and control tractability are adopted. This thesis also proposes two novel strategies to avoid the influence of catastrophic forgetting and noisy data respectively during the training processes. Finally, all the proposed techniques are validated in real experiments or experimental-data-based simulations.

Data-driven model predictive control framework of semicontinuous distillation process / Distillation technology is one of the most sought-after operations in the chemical process industries. Countless research has been done in the past to reduce the cost associated with distillation technology. As a result of process intensification, a semicontinuous distillation system is proposed as an alternative for purifying the n-component mixture (n>=3) which has the advantage over both batch and continuous process for low to medium production rates. A traditional distillation setup requires n-1 columns to separate the components to the desired purity. However, a semicontinuous system performs the same task by integrating a distillation column with n-2 middle vessel (storage tank). Consequently, with lower capital cost, the total annualized cost (TAC) per tonne of feed processed is less for a semicontinuous system compared to a traditional setup for low to medium throughput. Yet, the operating cost of a semicontinuous system exceed those of the conventional continuous setup. Semicontinuous system exhibits a non-linear dynamic behavior with a cyclic steady state and has three modes of operation. The main goal of this thesis is to reduce the operating cost per tonne of feed processed which leads to lower TAC per tonne of feed processed using a model predictive control (MPC) scheme compared to the existing PI configuration This work proposes a novel multi-model technique using subspace identification to identify a linear model for each mode of operation without attaining discontinuity. Subsequently, the developed multi-model framework was implemented in a shrinking horizon MPC architecture to reduce the TAC/tonne of feed processed while maintaining the desired product purities at the end of each cycle. The work uses Aspen Plus Dynamics simulation as a test bed to simulate the semicontinuous system and the shrinking horizon MPC scheme is formulated in MATLAB. VBA is used to communicate the inputs from MPC in MATLAB to the process in Aspen Plus Dynamics. / Thesis / Master of Science in Chemical Engineering (MSChE)

A power grid network is an interconnected network of coupled devices that generate, transmit and distribute power to consumers. These complex and usually large-scale systems have high dimensional models that are computationally expensive to simulate especially in real time applications, stability analysis, and control design. Model order reduction (MOR) tackles this issue by approximating these high dimensional models with reduced high-fidelity representations. When the internal description of the models is not available, the reduced representations are constructed by data. In this dissertation, we investigate four problems regarding the MOR and data-driven modeling of the power networks model, particularly the swing equations. We first develop a parametric MOR approach for linearized parametric swing equations that preserves the physically-meaningful second-order structure of the swing equations dynamics. Parameters in the model correspond to variations in operating conditions. We employ a global basis approach to develop the parametric reduced model. We obtain these local bases by $mathcal{H}_2$-based interpolatory model reduction and then concatenate them to form a global basis. We develop a framework to enrich this global basis based on a residue analysis to ensure bounded $mathcal{H}_2$ and $mathcal{H}_infty$ errors over the entire parameter domain. Then, we focus on nonlinear power grid networks and develop a structure-preserving system-theoretic model reduction framework. First, to perform an intermediate model reduction step, we convert the original nonlinear system to an equivalent quadratic nonlinear model via a lifting transformation. Then, we employ the $mathcal{H}_2$-based model reduction approach, Quadratic Iterative Rational Krylov Algorithm (Q-IRKA). Using a special subspace structure of the model reduction bases resulting from Q-IRKA and the structure of the underlying power network model, we form our final reduction basis that yields a reduced model of the same second-order structure as the original model. Next, we focus on a data-driven modeling framework for power network dynamics by applying the Lift and Learn approach. Once again, with the help of the lifting transformation, we lift the snapshot data resulting from the simulation of the original nonlinear swing equations such that the resulting lifted-data corresponds to a quadratic nonlinearity. We then, project the lifted data onto a lower dimensional basis via a singular value decomposition. By employing a least-squares measure, we fit the reduced quadratic matrices to this reduced lifted data. Moreover, we investigate various regularization approaches. Finally, inspired by the second-order sparse identification of nonlinear dynamics (SINDY) method, we propose a structure-preserving data-driven system identification method for the nonlinear swing equations. Using the special structure on the right-hand-side of power systems dynamics, we choose functions in the SINDY library of terms, and enforce sparsity in the SINDY output of coefficients. Throughout the dissertation, we use various power network models to illustrate the effectiveness of our approaches. / Doctor of Philosophy / Power grid networks are interconnected networks of devices responsible for delivering electricity to consumers, e.g., houses and industries for their daily needs. There exist mathematical models representing power networks dynamics that are generally nonlinear but can also be simplified by linear dynamics. Usually, these models are complex and large-scale and therefore take a long time to simulate. Hence, obtaining models of much smaller dimension that can capture the behavior of the original systems with an acceptable accuracy is a necessity. In this dissertation, we focus on approximation of power networks model through the swing equations. First, we study the linear parametric power network model whose operating conditions depend on parameters. We develop an algorithm to replace the original model with a model of smaller dimension and the ability to perform in different operating conditions. Second, given an explicit representation of the nonlinear power network model, we approximate the original model with a model of the same structure but smaller dimension. In the cases where the mathematical models are not available but only time-domain data resulting from simulation of the model is at hand, we apply an already developed framework to infer a model of a small dimension and a specific nonlinear structure: quadratic dynamics. In addition, we develop a framework to identify the nonlinear dynamics while maintaining their original physically-meaningful structure.

In this dissertation, I extend the analysis of human dynamics to human movements in online activities. My work starts with a discussion of the human information foraging process based on three large collections of empirical search click-through logs collected in different time periods. With the analogy of viewing the click-through on search engine result pages as a random walk, a variety of quantities like the distributions of step length and waiting time as well as mean-squared displacements, correlations and entropies are discussed. Notable differences between the different logs reveal an increased efficiency of the search engines, which is found to be related to the vanishing of the heavy-tailed characteristics of step lengths in newer logs as well as the switch from superdiffusion to normal diffusion in the diffusive processes of the random walks. In the language of foraging, the newer logs indicate that online searches overwhelmingly yield local searches, whereas for the older logs the foraging processes are a combination of local searches and relocation phases that are power-law distributed. The investigation highlights the presence of intermittent search processes in online searches, where phases of local explorations are separated by power-law distributed relocation jumps. In the second part of this dissertation I focus on an in-depth analysis of online gambling behaviors. For this analysis the collected empirical gambling logs reveal the wide existence of heavy-tailed statistics in various quantities in different online gambling games. For example, when players are allowed to choose arbitrary bet values, the bet values present log-normal distributions, meanwhile if they are restricted to use items as wagers, the distribution becomes truncated power laws. Under the analogy of viewing the net change of income of each player as a random walk, the mean-squared displacement and first-passage time distribution of these net income random walks both exhibit anomalous diffusion. In particular, in an online lottery game the mean-squared displacement presents a crossover from a superdiffusive to a normal diffusive regime, which is reproduced using simulations and explained analytically. This investigation also reveals the scaling characteristics and probability reweighting in risk attitude of online gamblers, which may help to interpret behaviors in economic systems. This work was supported by the US National Science Foundation through grants DMR-1205309 and DMR-1606814. / Ph. D. / Humans are complex, meanwhile understanding the complex human behaviors is of crucial importance in solving many social problems. In recent years, socio physicists have made substantial progress in human dynamics research. In this dissertation, I extend this type of analysis to human movements in online activities. My work starts with a discussion of the human information foraging process. This investigation is based on empirical search logs and an analogy of viewing the click-through on search engine result pages as a random walk. With an increased efficiency of the search engines, the heavy-tailed characteristics of step lengths disappear, and the diffusive processes of the random walkers switch from superdiffusion to normal diffusion. In the language of foraging, the newer logs indicate that online searches overwhelmingly yield local searches, whereas for the older logs the foraging processes are a combination of local searches and relocation phases that are power-law distributed. The investigation highlights the presence of intermittent search processes in online searches, where phases of local explorations are separated by power-law distributed relocation jumps. In the second part of this dissertation I focus on an in-depth analysis of online gambling behaviors, where the collected empirical gambling logs reveal the wide existence of heavy-tailed statistics in various quantities. Using an analogy of viewing the net change of income of each player as a random walk, the mean-squared displacement and first-passage time distribution of these net income random walks exhibit anomalous diffusion. This investigation also reveals the scaling characteristics and probability reweighting in risk attitude of online gamblers, which may help to interpret behaviors in economic systems. This work was supported by the US National Science Foundation through grants DMR-1205309 and DMR-1606814.

We investigate the effect of spatial filtering on the recently proposed data-driven correction reduced order model (DDC-ROM). We compare two filters: the ROM projection, which was originally used to develop the DDC-ROM, and the ROM differential filter, which uses a Helmholtz operator to attenuate the small scales in the input signal. We focus on the following questions: ``Do filtering and differentiation with respect to space variable commute, when filtering is applied to the diffusion term?'' or in other words ``Do we have commutation error (CE) in the diffusion term?" and ``If so, is the commutation error data-driven correction ROM (CE-DDC-ROM) more accurate than the original DDC-ROM?'' If the CE exists, the DDC-ROM has two different correction terms: one comes from the diffusion term and the other from the nonlinear convection term. We investigate the DDC-ROM and the CE-DDC-ROM equipped with the two ROM spatial filters in the numerical simulation of the Burgers equation with different diffusion coefficients and two different initial conditions (smooth and non-smooth). / M.S. / We propose reduced order models (ROMs) for an efficient and relatively accurate numerical simulation of nonlinear systems. We use the ROM projection and the ROM differential filters to construct a novel data-driven correction ROM (DDC-ROM). We show that the ROM spatial filtering and differentiation do not commute for the diffusion operator. Furthermore, we show that the resulting commutation error has an important effect on the ROM, especially for low viscosity values. As a mathematical model for our numerical study, we use the one-dimensional Burgers equations with smooth and non-smooth initial conditions.

Mechanical metamaterials are novel materials that display unique properties from their underlying microstructure topology rather than the constituent material they are made from. Their effective properties displayed at macroscale depend on the design of their microstructural topology. In this work, two classes of mechanical metamaterials are studied within the 2D-space. The first class is made of trusses, referred to as truss-based mechanical metamaterials. These materials are studied through their application to a beam component, where finite element analysis is performed to determine how truss-based microstructures affect the displacement behavior of the beam. This analysis is further subsidized with the development of a graphical user interface, where users can design a beam made of truss-based microstructures to see how their design affects the beam's behavior. The second class of mechanical metamaterial investigated is made of self-assembled structures, called spinodoids. Their smooth topology makes them less prone to high stress concentrations present in truss-based mechanical metamaterials. A large database of spinodoids is generated in this study. Through data-driven modeling the geometry of the spinodoids is coupled with their Young's modulus value to approach inverse design under uncertainty. To see mechanical metamaterials applied to industry they need to be better understood and thoroughly characterized. Furthermore, more tools that specifically help push the ease in the design of these metamaterials are needed. This work aims to improve the understanding of mechanical metamaterials and develop efficient computational design strategies catered solely for them. / Master of Science / Mechanical metamaterials are hierarchical materials involving periodically or aperiodically repeating unit cell arrangements in the microscale. The design of the unit cells allows these materials to display unique properties that are not usually found in traditionally manufactured materials. This will enable their use in a multitude of potential engineering applications. The presented study seeks to explore two classes of mechanical metamaterials within the 2D-space, including truss-based architectures and spinodoids. Truss-based mechanical metamaterials are made of trusses arranged in a lattice-like framework, where spinodoids are unit cells that contain smooth structures resulting from mimicking the two phases that coexist in a phase separation process called spinodal decomposition. In this research, computational design strategies are applied to efficiently model and further understand these sub-classes of mechanical metamaterials.

<div>The app-based taxi services (ATS) has disrupted the traditional (street-hailing) taxi services (TTS) leading to transformative changes in the urban taxi markets and its impacts on mobility, design and environment. However, the current modeling of these new mobility markets is limited in its understanding of: (1) the underlying factors that influence the growth of the ATS market; (2) the competition of ATS and TTS markets; (3) pricing in the ATS market; (4) system wide tools to understand the impacts of the market. The overarching goal of this dissertation is to address four fundamental processes of taxi system, ranging from demand generation, supply generation and exiting, dynamic pricing generation, and vehicle-passenger matching over road network. This dissertation achieves these goals by using original large scale datasets to characterize disruptive changes in mobility, understand strategic behaviors of stakeholders, and formulate system dynamics.</div><div> </div><div>This dissertation develops various modeling structures and estimation methods, motivated from statistical, econometric, machine learning, and stochastic approaches. First, we adapt multiple econometric models for demand, supply, and platform-exiting (offline) behaviors, including mixture model of spatial lag and Poisson regression and mixture model of spatial lag and panel regression. It is apparent that all proposed econometric models should be corrected with spatial lag due to significant spatial autocorrelations. The results indicate effectiveness of dynamic pricing in controlling demand, however, it also shows no impacts on driver's online and offline behaviors. Then a dynamic pricing generation problem is formulated with multi-class classification. This model is empirically validated for the impacts of demand and supply in dynamic price generation and the significant spatial and temporal heterogeneity. Last, we propose a queueing network consisting of taxi service queues for vehicle-passenger matching and road service queue for vehicle movements at homogeneous spatial units. The method captures stochasticity in vehicle-passenger matching process, and more importantly, formulates the interactions with urban road traffic.</div><div> </div><div>In summary, this dissertation provides a holistic understanding of fundamental processes that govern the rapid rise in ATS markets and in developing quantitative tools for the system wide impacts of this evolving taxi markets. Taken together, these tools are transformative and useful for city agencies to make various decisions in the smart mobility landscape. </div>

According to the World Health Organization, almost all human population (99%) lives in 117 countries with over 6000 cities, where air pollutant concentration exceeds recommended thresholds. The most common, so-called criteria, air pollutants that affect human lives, are particulate matter (PM) and gas-phase (SO2, CO, NO2, O3 and others). Therefore, many countries or regions worldwide have imposed regulations or interventions to reduce these effects. Whenever an intervention occurs, air quality changes due to changes in ambient factors, such as weather characteristics and human activities. One approach for assessing the effects of interventions or events on air quality is through the use of the Weather Normalized Model (WNM). However, current deterministic models struggle to accurately capture the complex, non-linear relationship between pollutant concentrations and their emission sources. Hence, the primary objective of this thesis is to examine the power of machine learning (ML) and deep learning (DL) techniques to develop and improve WNMs. Subsequently, these enhanced WNMs are employed to assess the impact of events on air quality. Furthermore, these ML/DL-based WNMs can serve as valuable tools for conducting exploratory data analysis (EDA) to uncover the correlations between independent variables (meteorological and temporal features) and air pollutant concentrations within the models.  It has been discovered that DL techniques demonstrated their efficiency and high performance in different fields, such as natural language processing, image processing, biology, and environment. Therefore, several appropriate DL architectures (Long Short-Term Memory - LSTM, Recurrent Neural Network - RNN, Bidirectional Recurrent Neural Network - BIRNN, Convolutional Neural Network - CNN, and Gated Recurrent Unit - GRU) were tested to develop the WNMs presented in Paper I. When comparing these DL architectures and Gradient Boosting Machine (GBM), LSTM-based methods (LSTM, BiRNN) have obtained superior results in developing WNMs. The study also showed that our WNMs (DL-based) could capture the correlations between input variables (meteorological and temporal variables) and five criteria contaminants (SO2, CO, NO2, O3 and PM2.5). This is because the SHapley Additive exPlanations (SHAP) library allowed us to discover the significant factors in DL-based WNMs. Additionally, these WNMs were used to assess the air quality changes during COVID-19 lockdown periods in Ecuador. The existing normalized models operate based on the original units of pollutants and are designed for assessing pollutant concentrations under “average” or consistent weather conditions. Predicting pollution peaks presents an even greater challenge because they often lack discernible patterns. To address this, we enhanced the Weather Normalized Models (WNMs) to boost their performance specifically during daily concentration peak conditions. In the second paper, we accomplished this by developing supervised learning techniques, including Ensemble Deep Learning methods, to distinguish between daily peak and non-peak pollutant concentrations. This approach offers flexibility in categorizing pollutant concentrations as either daily concentration peaks or non-daily concentration peaks. However, it is worth noting that this method may introduce potential bias when selecting non-peak values. In the third paper, WNMs are directly applied to daily concentration peaks to predict and analyse the correlations between meteorological, temporal features and daily concentration peaks of air pollutants.

With the exponential development of more sustainable automotive powertrains, new gearbox technologies must also be created and tested extensively. Scania employs dynamometer testbeds to conduct such tests, but this plethora of new and rapidly developed gearboxes pose many problems for testbed technicians. Regulating oil temperature during tests is vital and controllers must be developed for each gearbox configuration; this is difficult given system complexity, nonlinear dynamics, and time limitations. Therefore, technicians currently resort to a manually tuned controller based on real-time observations; a time-intensive process with sub-par performance. This master thesis breaks down this predicament into two research questions. The first employs a replicate study to investigate whether linear system identification methods can model the oil conditioning system adequately. A test procedure is developed and executed on one gearbox setup to capture system behavior around a reference point and the resulting models are compared for best fitment. Results from this study show that such data-driven modeling methods can sufficiently represent the system. The second research question investigates whether the derived model can then be used to create a better-performing model-based controller through pole placement design. To draw a comparison between old and new controllers, both are implemented on the testbed PLC while conducting a nominal test procedure varying torque and oil flow. Results from this study show that the developed controller does regulate temperature sufficiently, but the original controller is more robust in this specific test case. / Med den exponentiella utvecklingen av mer hållbara drivlinor i fordonsindustrin måste nya växellådsteknologier skapas och testas på en omfattande skala. Scania använder sig utav dynamometer testbäddar för att utföra sådana tester, men denna uppsjö av nya och snabbt utvecklade växellådor skapar utmaningar för testbäddsteknikerna. Reglering av oljetemperaturen under testerna är avgörande och därmed måste nya regulatorer utvecklas för varje växellådskonfiguration; detta är problematiskt med tanke på systemkomplexitet, olinjär dynamik samt tidsbegränsning. På grund av detta använder sig testbäddsteknikerna för tillfället av en manuell metod för att ta fram parametrarna till regulatorerna baserat på realtidsobservationer vilket är en tidskrävande process som ofta leder till en underpresterande regulator. Det här masterarbetet bryter ner den nämnda problematiken i två forskningsfrågor. Den första behandlar en replikationsstudie för att undersöka om linjära systemidentifikations metoder kan modellera oljekonditioneringssytemet på ett adekvat sätt. En testprocedur utvecklas och utförs på en växellådskonfiguration för att ta fram en modell för systemet kring en referenspunkt. De resulterande modellerna jämförs för att fastställa vilken metod som bäst beskriver systemet. Resultatet från denna studie visar att sådana data-drivna modelleringsmetoder kan beskriva systemet på ett tillfredsställande sätt. Den andra forskningsfrågan undersöker om den härledda modellen kan användas för att skapa en bättre presterande modellbaserad regulator med hjälp av polplaceringsmetoden. För att kunna göra en jämförelse mellan gamla samt nya regulatorer implementeras båda på testbäddens PLC varvid en nominell testprocedur utförs som varierar vridmoment och oljeflöde. Resultatet från denna studie visar att den framtagna regulatorn kan reglera oljetemperaturen på ett tillfredsställande sätt, däremot är den ursprungliga regulatorn mer robust i det behandlade testfallet.