Emulsion copolymerization of styrene and butyl acrylate in the presence of a chain transfer agent. Part 2: parameters estimability and confidence regions

Accurate estimation of the model parameters is required to obtain reliable predictions of the products end-use properties. However, due to the mathematical model structure and/or to a possible lack of measurements, the estimation of some parameters may be impossible. This paper will focus on the case where the main limitations to the parameters estimability are their weak effect on the measured outputs or the correlation between the effects of two or more parameters. The objective of the method developed in this paper is to determine the subset of the most influencing parameters that can be estimated from the available experimental data, when the complete set of model parameters cannot be estimated. This approach has been applied to the mathematical model of the emulsion copolymerization of styrene and butyl acrylate, in the presence of n-dodecyl mercaptan as a chain transfer agent. In addition, a new approach is used to better assess the true confidence regions and evaluate the accuracy of the parameters estimates in more reliable way

A framework for model reliability and estimability analysis of crystallization processes with multi-impurity multi-dimensional population balance models

The development of reliable mathematical models for crystallization processes may be very challenging due the complexity of the underlying phenomena, the inherent Population Balance Models (PBMs) and the large number of parameters that need to be identified from experimental data. Due to the poor information content of the experiments, the structure of the model itself and correlation between model parameters, the mathematical model may contain more parameters than can be accurately and reliably identified from the available experimental data. A novel framework for parameter estimability for guaranteed optimal model reliability is proposed then validated by a complex crystallization process. The latter is described by a differential algebraic system which involves a multi-dimensional population balance model that accounts for the combined effects of different crystal growth modifiers/impurities on the crystal size and shape distribution of needle-like crystals. Two estimability methods were combined: the first is based on a sequential orthogonalization of the local sensitivity matrix and the second is Sobol, a variance-based global sensitivities technic. The framework provides a systematic way to assess the quality of two nominal sets of parameters: one obtained from prior knowledge and the second obtained by simultaneous identification using global optimization. A cut-off value was identified from an incremental least square optimization procedure for both estimability methods, providing the required optimal subset of model parameters. The implemented methodology showed that, although noisy aspect ratio data were used, the 8 most influential and least correlated parameters could be reliably identified out of twenty-three, leading to a crystallization model with enhanced prediction capability

Model-based optimization of batch- and continuous crystallization processes

Crystallization is an important separation process, extensively used in most chemical industries and especially in pharmaceutical manufacturing, either as a method of production or as a method of purification or recovery of solids. Typically, crystallization can have a considerable impact on tuning the critical quality attributes (CQAs), such as crystal size and shape distribution (CSSD), purity and polymorphic form, that impact the final product quality performance indicators and inherent end-use properties, along with the downstream processability. Therefore, one of the critical targets in controlled crystallization processes, is to engineer specific properties of the final product. The purpose of this research is to develop systematic computer-aided methodologies for the design of batch and continuous mixed suspension mixed product removal (MSMPR) crystallization processes through the implementation of simulation models and optimization frameworks. By manipulating the critical process parameters (CPPs), the achievable range of CQAs and the feasible design space (FDS) can be identified. Paracetamol in water and potassium dihydrogen phosphate (KDP) in water are considered as the model chemical systems.The studied systems are modeled utilizing single and multi-dimensional population balance models (PBMs). For the batch crystallization systems, single and multi-objective optimization was carried out for the determination of optimal operating trajectories by considering mean crystal size, the distribution s standard deviation and the aspect ratio of the population of crystals, as the CQAs represented in the objective functions. For the continuous crystallization systems, the attainable region theory is employed to identify the performance of multi-stage MSMPRs for various operating conditions and configurations. Multi-objective optimization is also applied to determine a Pareto optimal attainable region with respect to multiple CQAs. By identifying the FDS of a crystallization system, the manufacturing capabilities of the process can be explored, in terms of mode of operation, CPPs, and equipment configurations, that would lead to the selection of optimum operation strategies for the manufacturing of products with desired CQAs under certain manufacturing and supply chain constraints. Nevertheless, developing reliable first principle mathematical models for crystallization processes can be very challenging due to the complexity of the underlying phenomena, inherent to population balance models (PBMs). Therefore, a novel framework for parameter estimability for guaranteed optimal model reliability is also proposed and implemented. Two estimability methods are combined and compared: the first is based on a sequential orthogonalization of the local sensitivity matrix and the second is Sobol, a variance-based global sensitivities technic. The framework provides a systematic way to assess the quality of two nominal sets of parameters: one obtained from prior knowledge and the second obtained by simultaneous identification using global optimization. A multi-dimensional population balance model that accounts for the combined effects of different crystal growth modifiers/ impurities on the crystal size and shape distribution of needle-like crystals was used to validate the methodology. A cut-off value is identified from an incremental least square optimization procedure for both estimability methods, providing the required optimal subset of model parameters. In addition, a model-based design of experiments (MBDoE) methodology approach is also reported to determine the optimal experimental conditions yielding the most informative process data. The implemented methodology showed that, although noisy aspect ratio data were used, the eight most influential and least correlated parameters could be reliably identified out of twenty-three, leading to a crystallization model with enhanced prediction capability. A systematic model-based optimization methodology for the design of crystallization processes under the presence of multiple impurities is also investigated. Supersaturation control and impurity inclusion is combined to evaluate the effect on the product's CQAs. To this end, a morphological PBM is developed for the modelling of the cooling crystallization of pure KDP in aqueous solution, as a model system, under the presence of two competitive crystal growth modifiers/ additives: aluminum sulfate and sodium hexametaphosphate. The effect of the optimal temperature control with and without the additives on the CQAs is presented via utilizing multi-objective optimization. The results indicate that the attainable size and shape attributes, can be considerably enhanced due to advanced operation flexibility. Especially it is shown that the shape of the KDP crystals can be affected even by the presence of small quantity of additives and their morphology can be modified from needle-like to spherical, which is more favourable for processing. In addition, the multi-impurity PBM model is extended by the utilization of a high-resolution finite volume (HR-FV) scheme, instead of the standard method of moments (SMOM), in order for the full reconstruction and dynamic modelling of the crystal size and shape distribution to be enabled. The implemented methodology illustrated the capabilities of utilizing high-fidelity computational models for the investigation of crystallization processes in impure media for process and product design and optimization purposes

Electrode-Specific Degradation Diagnostics for Lithium-Ion Batteries with Practical Considerations

Li-ion batteries inevitably degrade with cyclic usage and storage time. Close to end-of-life batteries can no longer meet their performance requirements and the likelihood of occurring catastrophic failures increases. Thus, an accurate diagnosis of their state of health over long-term use has become a critical function for reliable and safe battery management systems, especially for vehicle electrification and large scale energy storage systems. Degradation of batteries is typically quantified at the cell level with capacity loss and power fade, however different usage conditions and environmental factors can contribute to the degradation of batteries differently. Therefore, typical cell-level lumped degradation metrics are not sufficient to give a full explanation of battery state of health. This dissertation presents approaches for the diagnosis of electrode-specific degradation of Li-ion batteries considering a variety of practical aspects in real-world applications such as the half-cell potential change, the partial data availability, data acquisition method, and practical charging rate. The electrode-specific degradation diagnosis is performed by model-based identification of the individual electrode state-of-health (eSOH) parameters, electrode capacity and utilization range. The advancements contributed by this dissertation are summarized as follows. First, a novel diagnostic algorithm is proposed by combining the terminal voltage fitting process with the peak alignment method to improve electrode parameter estimation confidence. The proposed method addresses the half-cell potential change of the positive electrode due to the chemical aging of the metal oxide. The diagnostic result is experimentally verified with large-format prismatic commercial cells. The second practical consideration is partial data availability. In practice, the full range of OCV measurement is not obtainable without the designated offline diagnostic test. With the limited data, the accuracy of parameter estimation becomes questionable. Therefore, the achievable estimation error bound is analyzed with respect to partial data windows through the Cramer-Rao Bound and confidence interval. The result shows that the eSOH estimation improves when a data window includes slope changes of electrode half-cell potential. This fundamental limitation is applied in data-driven approach to provide data-requirements for machine learning of battery cycle life prediction. Third, continued from the partial window idea, a time-optimal current profile is proposed to enable direct measurement of pseudo-OCV data for the desired range without a long relaxation period. By allowing bi-directional charging, the proposed time-optimal control problem identifies a proper sequence of charge/discharge pulses and successfully reduces total data acquisition time by more than 60% in both simulation and experiment, showing a possible way to implement the developed OCV-based electrode degradation diagnostic algorithm. Fourth, the feasibility of the electrode-specific degradation diagnostics is studied for real-world charging conditions where the typical charging current rate is usually higher (e.g. C/5) than C/20 of pseudo-OCV data. With increasing charging rates, the individual electrode's electrochemical features is obscured, and the overpotential due to internal resistance needs to be estimated concurrently, making the eSOH estimation challenging. An adaptive algorithm with a data selection strategy is proposed to deal with the estimation of both resistance and electrode SOH parameters. Lastly, the potential of the physics-guided machine learning approaches is explored with two case studies for Li-ion battery degradation diagnostics and prognostics.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/168114/1/suhaklee_1.pd

Modeling, Parameter Identification, and Degradation-Conscious Control of Polymer Electrolyte Membrane (PEM) Fuel Cells

Polymer electrolyte membrane (PEM) fuel cells are touted as zero-emission alternatives to internal combustion engines for automotive applications. However, high cost and durability issues have hindered their commercialization. Therefore, significant research efforts are underway to better understand the scientific aspects of PEM fuel cell operation and engineer its components for improved lifetime and reduced cost. Most of the research in this area has been focused on material development. However, as demonstrated by Toyota's fuel cell vehicle, intelligent control strategies may lead to significantly improved durability of the fuel cell stack even with existing materials. Therefore, it seems that the outstanding issues can be better resolved through a combination of improved materials and effective control strategies. Accordingly, this dissertation aims to develop a model-based control strategy to improve performance and durability of PEM fuel cell systems for automotive applications. To this end, the dissertation first develops a physics-based and computationally efficient model for online estimation purposes. The need for such a model arises from the fact that detailed information about the internal states of the cell is required to develop effective control strategies for improved performance and durability, and such information is rarely available from direct measurements. Therefore, a software sensor must be developed to provide the required signals for a control system. To this end, this work utilizes spatio-temporal decoupling of the underlying problem to develop a model that can estimate water and temperature distributions throughout an operating fuel cell in a computationally efficient manner. The model is shown to capture a variety of complex physical phenomena, while running at least an order of magnitude faster than real time for dynamically changing conditions. The model is also validated with extensive experimental measurements under different operating conditions that are of interest for automotive applications. Furthermore, the dissertation extensively explores the sensitivity of the model predictions to a variety of parameters. The sensitivity results are used to study the parameter identifiability problem in detail. The challenges associated with parameter identification in such a large-scale physics-based model are highlighted and a model parameterization framework is proposed to address them. The proposed framework consists of three main components: (1) selecting a subset of model parameters for identification, (2) optimally designing experiments that are maximally informative for parameter identification, and (3) designing a multi-step identification algorithm that ensures sufficient regularization of the inverse problem. These considerations are shown to lead to effective model parameterization with limited experimental measurements. Finally, the dissertation uses a version of the proposed model to develop a degradation-conscious model-predictive control (MPC) framework to enhance the performance and durability of PEM fuel cell systems. In particular, a reduced-order model is developed for control design, which is then successively linearized about the current operating point to enable use of linear control design techniques that offer significant computational advantages. A variety of constraints on system safety and durability are considered and simulation case studies are conducted to evaluate the framework's utility in maximizing performance while respecting the durability constraints. It is also shown that the linear MPC framework employed here can generate the optimal control commands faster than real time. Therefore, the proposed framework is expected to be implementable in practical applications and contribute to extending the lifetime of fuel cell systems.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/155288/1/goshtasb_1.pd

Control of Lithium-Ion Battery Warm-up from Sub-zero Temperatures

The archetype of rechargeable technology, Li-ion batteries have over the last decade benefited from improvements in material science through increased energy and power density. Although widely adopted, these batteries suffer from significant performance degradation at low temperatures, posing a challenge for automotive applications, especially during vehicle start-up. This begs the question: if one was to seek an energy optimal warm-up strategy, how would it look? Moreover, if as much as 22% of reduction in range of electric vehicles is attributable to onboard battery heating systems, would an optimal heating strategy alleviate this energy drain and at what drawback? This thesis addresses these questions. To that end, we pose and solve two energy-optimal warm-up strategies in addition to developing tools that will enable one to make prudent decisions on whether warm-up is feasible if the battery energy state falls too low. In this dissertation, we address the four main aspects of control design modeling, control, verification and adaptation. There are two primary control strategies that are designed in this dissertation and tools to analyze them are developed. The first warm-up scenario involves a receding horizon optimal control problem whose objective trades-offs increase in battery's temperature by self-heating against energy expended. The shape of battery current is restricted to be bi-directional pulses that charge and discharge the cell at relatively high frequencies via an external capacitor. The optimal control problem solves for the amplitude of the pulse train and the results clarify issues associated with capacitor size, time and lost energy stored. The second control policy is deduced by solving an optimal discharge control problem for the trajectory of power that could self-heat the cell and at the same time feed an external heater whilst minimizing the loss in state of charge. Batteries inevitably age as they are used and consequently their dynamics also change. Since both proposed methods are model based, the last of part of this dissertation proposes a novel augmented-state-space partitioning technique which can be used to design cascaded nonlinear estimators. Using this partitioning technique, the relative average estimability of the different states of the electrical and thermal model is studied and Dual Extended Kalman Filters are built and validated in simulations. All the methods developed are demonstrated via a combination of simulation and experiments on Iron Phosphate or Nickel Manganese Cobalt Li-ion battery cell which have high power capability and could be used in replacement of 12V starter batteries or 48V start-stop applications.PHDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/136964/1/elemsn_1.pd

Advanced Diagnostics for Lithium-ion Batteries: Decoding the Information in Electrode Swelling

Lithium-ion batteries exhibit mechanical expansion and contraction during cycling, consisting of a reversible intercalation-induced expansion and an irreversible expansion as the battery ages. Prior experimental studies have shown that mechanical expansion contains valuable information that correlates strongly with cell aging. However, a number of fundamental questions remain on the usability of the expansion measurement in practice. For example, it is necessary to determine whether the expansion measurements provide information that can help the estimation of the electrode state of health (eSOH), given limits on data availability and sensor noise in the field. Furthermore, the viability of using expansion for cell diagnostics also needs more investigation considering the broad range of aging conditions in real-world applications. This dissertation focuses on the experimental and modeling study of the expansion measurements during aging in order to assess its ability in helping battery diagnostics. To this end, mechanistic voltage and expansion models based on the underlying physics of phase transitions are developed. For the first time, the identifiability of eSOH parameters is explored by incorporating the expansion/force measurement. It is shown that the expansion measurements enhance the estimation of eSOH parameters, especially with a limited data window, since it has a better signal-to-noise ratio compared to the voltage. Moreover, the increased identifiability is closely related to the phase transitions in the electrodes. A long-term experimental aging study of the expansion of the graphite/NMC pouch cells is conducted under a variety of conditions such as temperature, charging rate, and depth of discharge. The goals here are to validate the results of the identifiability analysis and record the reversible and irreversible expansion correlated with capacity loss for informing the electrochemical models. Firstly, the advantages of the expansion concerning the eSOH identifiability are confirmed. Secondly, the results of the expansion evolution reveal that the features in the reversible expansion are an excellent indicator of health and, specifically, capacity retention. The expansion feature is robust to charge conditions. Namely, it is mostly insensitive to the hysteresis effects of the various initial state of charge, and it is detectable at higher C-rates up to 1C. Additionally, the expansion feature occurs near the half-charged point and therefore diagnostics can be performed more often during naturalistic use cases. Thus, the expansion measurement facilitates more frequent capacity checks in the field. Furthermore, an electrochemical and expansion model suitable for model-based estimation is developed. In particular, a multi-particle modeling approach for the graphite electrode is considered. It is demonstrated that the new model is able to capture the peak smoothing effect observed in the differential voltage at higher C-rates above C/2. Model parameters are identified using experimental data from the graphite/NMC pouch cell. The proposed model produces an excellent fit for the observed electric and mechanical swelling response of the cells and could enable physics-based data-driven degradation studies at practical charging rates. Finally, a fast-charging method based on the constant current constant voltage (CC-CV) charging scheme, called CC-CVησT (VEST), is developed. The new approach is simpler to implement and can be used with any model to impose varying levels of constraints on variables pertinent to degradation, such as plating potential and mechanical stress. The capabilities of the new CC-CVησT charging are demonstrated using the physics-based model developed in this dissertation.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/169953/1/pmohtat_1.pd

Parameter Estimation of Complex Systems from Sparse and Noisy Data

Mathematical modeling is a key component of various disciplines in science and engineering. A mathematical model which represents important behavior of a real system can be used as a substitute for the real process for many analysis and synthesis tasks. The performance of model based techniques, e.g. system analysis, computer simulation, controller design, sensor development, state filtering, product monitoring, and process optimization, is highly dependent on the quality of the model used. Therefore, it is very important to be able to develop an accurate model from available experimental data. Parameter estimation is usually formulated as an optimization problem where the parameter estimate is computed by minimizing the discrepancy between the model prediction and the experimental data. If a simple model and a large amount of data are available then the estimation problem is frequently well-posed and a small error in data fitting automatically results in an accurate model. However, this is not always the case. If the model is complex and only sparse and noisy data are available, then the estimation problem is often ill-conditioned and good data fitting does not ensure accurate model predictions. Many challenges that can often be neglected for estimation involving simple models need to be carefully considered for estimation problems involving complex models. To obtain a reliable and accurate estimate from sparse and noisy data, a set of techniques is developed by addressing the challenges encountered in estimation of complex models, including (1) model analysis and simplification which identifies the important sources of uncertainty and reduces the model complexity; (2) experimental design for collecting information-rich data by setting optimal experimental conditions; (3) regularization of estimation problem which solves the ill-conditioned large-scale optimization problem by reducing the number of parameters; (4) nonlinear estimation and filtering which fits the data by various estimation and filtering algorithms; (5) model verification by applying statistical hypothesis test to the prediction error. The developed methods are applied to different types of models ranging from models found in the process industries to biochemical networks, some of which are described by ordinary differential equations with dozens of state variables and more than a hundred parameters

Solid Oxide Fuel Cell Hybrid Systems as a Distributed Cogeneration Solution

This paper is on the topic of Solid Oxide Fuel Cell Hybrid Systems as a Distributed Cogeneration Solution. Broadly, the key outcomes of this paper aim to understand the hybrid system solid oxide fuel cell (SOFC) technology combined with micro gas turbine (mGT) plant. To achieve this, research was collated in the Background Information section on the fundamentals of the solid oxide fuel cell variant, interconnected cells that form stacks, stack level operating principles, relevant fuel types and the system’s fuel-flexibility. An overview of gas turbine technology and the principles underpinning operation, and finally hybrid system formed including research into coupling (physical, electrical and thermal) and start-up process of the complete hybrid system was completed. The Methodology was developed in two parts. The first Methodology section demonstrates the system advantages in the context of environmental metrics such as plant/fuel efficiencies, timeof-use, start-up timing and emissions. These are highlighted as key advantages by means of comparison drawn from other relevant generation systems, such as photovoltaic, coal-fired, combined cycle gas turbine and conventional large gas turbine plant. In the second part of the methodology, the system is specified and modelled against defined load and supply factors that affect resulting assessment of the utilisation of this system in the two applications. The Result and Discussion section demonstrates the key outcomes of the Methodology in the context of the Background Information section. Briefly, these include highlighting the efficiency increases that result from combining the SOFC plant with mGT plant, approximated as an increase from 30% as a stand-alone SOFC system, to 55% net electrical efficiency for the SOFC/mGT hybrid (Section 3.2.1), not including further benefits of recuperating thermal energy from the output of the plant as considered in Section 3.4 within ‘Application to UseCases’. Also, the competitive 40 minute start-up time for the SOFC/mGT system (Section 3.2.2) and non-restricted time-of-use advantages (Section 3.2.3) are highlighted. Finally, figures accounting for emissions factors within fuel types combined with plant efficiencies highlighted overall low emissions for the SOFC/mGT as modelled in Section 3.2.4. The results of the second part of the Methodology are detailed within Section 4.0 to assess how the SOFC/mGT system is integrated in hypothetical use-cases, noting assumptions made regarding load and supply factors to achieve this. The sections of the paper, inclusive of all research, modelling and analysis of results, as detailed, support the original aims of the project in terms of understanding the utilisation of highly efficient SOFC/mGT hybrid plant in context to its application as a distributed cogeneration solution. While this system is in early stages as both the Limitations and Further Work section discuss, this particular hybrid may form part of the future energy generation and distribution landscape, with key peak-reduction and time-shift advantages evident

Power Capability Estimation Accounting for Thermal and Electrical Constraints of Lithium-Ion Batteries.

Lithium-ion (Li-ion) batteries have become one of the most critical components in vehicle electrification due to their high specific power and energy density. The performance and longevity of these batteries rely on constraining their operation such that voltage and temperature are regulated within prescribed intervals. Enforcement of constraints on the power capability is a viable solution to protect Li-ion batteries from overheating as well as over-charge/discharge. Moreover, the ability to estimate power capability is vital in formulating power management strategies that account for battery performance limitations while minimizing fuel consumption and emissions. To estimate power capability accounting for thermal and electrical constraints, the characterization of thermal and electrical system behavior is required. In the course of addressing this problem, first, a computationally efficient thermal model for a cylindrical battery is developed. The solution of the convective heat transfer problem is approximated by polynomials with identifiable parameters that have physical meaning. The parameterized thermal model is shown to accurately predict the measured core and surface temperatures. The model-based thermal estimation methodology is augmented for cases of unknown cooling conditions. The proposed method is shown with experimental data to accurately provide estimates of the core temperature even under faults in the cooling system. To jointly account for the thermal and electrical constraints, we utilize time scale separation, and propose a real-time implementable method to predict power capability of a Li-ion battery. The parameterized battery thermal model and estimation algorithms are integrated into a power management system for a series hybrid electric vehicle. An algorithm for sequential estimation of coupled model parameters and states is developed using sensitivity-based parameter grouping. The fully integrated co-simulation of the battery electro-thermal behavior and the on-line adaptive estimators reveal that the power management system can effectively determine power flow among hybrid powertrain components without violating operational constraints.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/107128/1/youngki_1.pd