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1. On the Error of Li-ion Battery Parameter Estimation Subject to System Uncertainties

   https://doi.org/10.1149/1945-7111/acbc9c  

   Fogelquist, Jackson; Lai, Qingzhi; Lin, Xinfan (March 2023, Journal of The Electrochemical Society)

   Emerging lithium-ion battery systems require high-fidelity electrochemical models for advanced control, diagnostics, and design. Accordingly, battery parameter estimation is an active research domain where novel algorithms are being developed to calibrate complex models from input-output data. Amidst these efforts, little focus has been placed on the fundamental mechanisms governing estimation accuracy, spurring the question, why is an estimate accurate or inaccurate? In response, we derive a generalized estimation error equation under the commonly adopted least-squares objective function, which reveals that the error can be represented as a combination of system uncertainties (i.e., in model, measurement, and parameter) and uncertainty-propagating sensitivity structures in the data. We then relate the error equation to conventional error analysis criteria, such as the Fisher information matrix, Cramér-Rao bound, and parameter sensitivity, to assess the benefits and limitations of each. The error equation is validated through several uni- and bivariate estimations of lithium-ion battery electrochemical parameters using experimental data. These results are also analyzed with the error equation to study the error compositions and parameter identifiability under different data. Finally, we show that adding target parameters to the estimation without increasing the amount of data intrinsically reduces the robustness of the results to system uncertainties. 

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2. μPMU-Based Temporal Decoupling of Parameter and Measurement Gross Error Processing in DSSE

   https://doi.org/10.3390/electricity2040025  

   Trevizan, Rodrigo D.; Ruben, Cody; Rossoni, Aquiles; Dhulipala, Surya C.; Bretas, Arturo; Bretas, Newton G. (December 2021, Electricity)

   Simultaneous real-time monitoring of measurement and parameter gross errors poses a great challenge to distribution system state estimation due to usually low measurement redundancy. This paper presents a gross error analysis framework, employing μPMUs to decouple the error analysis of measurements and parameters. When a recent measurement scan from SCADA RTUs and smart meters is available, gross error analysis of measurements is performed as a post-processing step of non-linear DSSE (NLSE). In between scans of SCADA and AMI measurements, a linear state estimator (LSE) using μPMU measurements and linearized SCADA and AMI measurements is used to detect parameter data changes caused by the operation of Volt/Var controls. For every execution of the LSE, the variance of the unsynchronized measurements is updated according to the uncertainty introduced by load dynamics, which are modeled as an Ornstein–Uhlenbeck random process. The update of variance of unsynchronized measurements can avoid the wrong detection of errors and can model the trustworthiness of outdated or obsolete data. When new SCADA and AMI measurements arrive, the LSE provides added redundancy to the NLSE through synthetic measurements. The presented framework was tested on a 13-bus test system. Test results highlight that the LSE and NLSE processes successfully work together to analyze bad data for both measurements and parameters. 

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3. Parameter Identifiability and Reduction for Smooth and Nonsmooth Differential-Algebraic Equation Systems

   https://doi.org/10.1109/LCSYS.2024.3521427  

   Abdelfattah, Hesham; Stechlinski, Peter; Eisa, Sameh A (December 2024, IEEE Control Systems Letters)

   We extend the sensitivity rank condition (SERC), which tests for identifiability of smooth input-output systems, to a broader class of systems. Particularly, we build on our recently developed lexicographic SERC (L-SERC) theory and methods to achieve an identifiability test for differential-algebraic equation (DAE) systems for the first time, including nonsmooth systems. Additionally, we develop a method to determine the identifiable and non-identifiable parameter sets. We show how this new theory can be used to establish a (non-local) parameter reduction procedure and we show how parameter estimation problems can be solved. We apply the new methods to problems in wind turbine power systems and glucose-insulin kinetics. 

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4. Immersion and Invariance-based Disturbance Observer and Its Application to Safe Control

   https://doi.org/10.1109/TAC.2024.3416323  

   Wang, Yujie; Xu, Xiangru (January 2024, IEEE Transactions on Automatic Control)

   When the disturbance input matrix is nonlinear, existing disturbance observer design methods rely on the solvability of a partial differential equation or the existence of an output function with a uniformly well-defined disturbance relative degree, which can pose significant limitations. This note introduces a systematic approach for designing an Immersion and Invariance-based Disturbance Observer (IIDOB) that circumvents these strong assumptions. The proposed IIDOB ensures the disturbance estimation error is globally uniformly ultimately bounded by approximately solving a partial differential equation while compensating for the approximation error. Furthermore, by integrating IIDOB into the framework of control barrier functions, a filter-based safe control design method for control affine systems with disturbances is established where the filter is used to generate an alternative disturbance estimation signal with a known derivative. Sufficient conditions are established to guarantee the safety of the disturbed systems. Simulation results demonstrate the effectiveness of the proposed method. 

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5. Parameter estimation from the core-bounce phase of rotating core collapse supernovae in real interferometer noise

   https://doi.org/10.1088/1361-6382/add235  

   Villegas, Laura O; Moreno, Claudia; Pajkos, Michael A; Zanolin, Michele; Antelis, Javier M (April 2025, Classical and Quantum Gravity)

   Abstract We develop and characterize a parameter estimation methodology for rotating core collapse supernovae based on the gravitational wave core bounce phase and real detector noise. Expanding on the evidence from numerical simulations for the deterministic nature of this gravitational wave emission and about the dependence on the ratio $$\beta$$ between rotational kinetic to potential energy, we propose an analytical model for the core bounce component which depends on $$\beta$$ and one phenomenological parameter. We validate the goodness of the model with a pool of representative waveforms. We use the fitting factor adopted in compact coalescing binary searches as a metric to quantify the goodness of the analytical model and the template bank generated by the model presents an average accuracy of 94.4\% when compared with the numerical simulations and is used as the basis for the work. The error for a matched filter frequentist parameter estimation of $$\beta$$ is evaluated. The results obtained considering real interferometric noise and a waveform at a distance of 10 kpc and optimal orientation, for one standard deviation estimation error of the rotation parameter \(\beta\) lie in the range of \(10^{-2}\) to \(10^{-3}\) as \(\beta\) increases. The results are also compared to the scenario where Gaussian recolored data is employed. The analytical model also allows for the first time, to compute theoretical minima in the error for $$\beta$$ for any type of estimator. Our analysis indicates that the presence of rotation would be detectable at 0.5 Mpc for third generation interferometers like CE or ET. 

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