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1. When artificial parameter evolution gets real: particle filtering for time-varying parameter estimation in deterministic dynamical systems

   https://doi.org/10.1088/1361-6420/aca55b  

   Arnold, Andrea (December 2022, Inverse Problems)

   Estimating and quantifying uncertainty in unknown system parameters from limited data remains a challenging inverse problem in a variety of real-world applications. While many approaches focus on estimating constant parameters, a subset of these problems includes time-varying parameters with unknown evolution models that often cannot be directly observed. This work develops a systematic particle filtering approach that reframes the idea behind artificial parameter evolution to estimate time-varying parameters in nonstationary inverse problems arising from deterministic dynamical systems. Focusing on systems modeled by ordinary differential equations, we present two particle filter algorithms for time-varying parameter estimation: one that relies on a fixed value for the noise variance of a parameter random walk; another that employs online estimation of the parameter evolution noise variance along with the time-varying parameter of interest. Several computed examples demonstrate the capability of the proposed algorithms in estimating time-varying parameters with different underlying functional forms and different relationships with the system states (i.e. additive vs. multiplicative). 

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2. Determining Parameter Space Margins for Fault Recovery By Inverse Sensitivity Minimization

   Fisher, Michael W.; Hiskens, Ian A (January 2020, 21st Power Systems Computation Conference)

   Power system model parameter values are becoming increasingly uncertain and time-varying. Therefore, it is important to determine the margin in parameter space between a given set of parameter values for which the system will recover from a particular fault, and the nearest parameter values for which it will not recover from that fault. This work presents an efficient method for computing parameter space recovery margins by exploiting the property that the trajectory becomes infinitely sensitive to small changes in parameter value along the operating point’s region of attraction boundary. Consequently, along this boundary the inverse sensitivity of the trajectory approaches zero. The method proceeds by varying parameter values so as to minimize the inverse sensitivity of the system trajectory. Recent results provide theoretical justification for the approach. The efficacy of the method is demonstrated using a modified IEEE 39-bus New England power system test case. 

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3. Pitchfork bifurcation along a slow parameter ramp: Coherent structures in the critical scaling

   https://doi.org/10.1111/sapm.12702  

   Goh, Ryan; Kaper, Tasso_J; Scheel, Arnd (May 2024, Studies in Applied Mathematics)

   Abstract We investigate the slow passage through a pitchfork bifurcation in a spatially extended system, when the onset of instability is slowly varying in space. We focus here on the critical parameter scaling, when the instability locus propagates with speed , where is a small parameter that measures the gradient of the parameter ramp. Our results establish how the instability is mediated by a front traveling with the speed of the parameter ramp, and demonstrate scalings for a delay or advance of the instability relative to the bifurcation locus depending on the sign of , that is on the direction of propagation of the parameter ramp through the pitchfork bifurcation. The results also include a generalization of the classical Hastings–McLeod solution of the Painlevé‐II equation to Painlevé‐II equations with a drift term. 

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4. A Semilinear Parameter-Varying Observer Method for Fabric-Reinforced Soft Robots

   https://doi.org/10.3389/frobt.2021.749591  

   Bui, Phuc D.H.; Schultz, Joshua A. (November 2021, Frontiers in Robotics and AI)

   This paper presents an observer architecture that can estimate a set of configuration space variables, their rates of change and contact forces of a fabric-reinforced inflatable soft robot. We discretized the continuum robot into a sequence of discs connected by inextensible threads; this allows great flexibility when describing the robot’s behavior. At first, the system dynamics is described by a linear parameter-varying (LPV) model that includes a set of subsystems, each of which corresponds to a particular range of chamber pressure. A real-world challenge we confront is that the physical robot prototype exhibits a hysteresis loop whose directions depend on whether the chamber is inflating or deflating. In this paper we transform the hysteresis model to a semilinear model to avoid backward-in-time definitions, making it suitable for observer and controller design. The final model describing the soft robot, including the discretized continuum and hysteresis behavior, is called the semilinear parameter-varying (SPV) model. The semilinear parameter-varying observer architecture includes a set of sub-observers corresponding to the subsystems for each chamber pressure range in the SPV model. The proposed observer is evaluated through simulations and experiments. Simulation results show that the observer can estimate the configuration space variables and their rate of change with no steady-state error. In addition, experimental results display fast convergence of generalized contact force estimates and good tracking of the robot’s configuration relative to ground-truth motion capture data. 

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5. Is contact-line mobility a material parameter?

   https://doi.org/10.1038/s41526-022-00190-y  

   Ludwicki, Jonathan M.; Kern, Vanessa R.; McCraney, Joshua; Bostwick, Joshua B.; Daniel, Susan; Steen, Paul H. (February 2022, npj Microgravity)

   Abstract Dynamic wetting phenomena are typically described by a constitutive law relating the dynamic contact angleθto contact-line velocityU_CL. The so-called Davis–Hocking model is noteworthy for its simplicity and relatesθtoU_CLthrough a contact-line mobility parameterM, which has historically been used as a fitting parameter for the particular solid–liquid–gas system. The recent experimental discovery of Xia & Steen (2018) has led to the first direct measurement ofMfor inertial-capillary motions. This opens up exciting possibilities for anticipating rapid wetting and dewetting behaviors, asMis believed to be a material parameter that can be measured in one context and successfully applied in another. Here, we investigate the extent to whichMis a material parameter through a combined experimental and numerical study of binary sessile drop coalescence. Experiments are performed using water droplets on multiple surfaces with varying wetting properties (static contact angle and hysteresis) and compared with numerical simulations that employ the Davis–Hocking condition with the mobilityMa fixed parameter, as measured by the cyclically dynamic contact angle goniometer, i.e. no fitting parameter. Side-view coalescence dynamics and time traces of the projected swept areas are used as metrics to compare experiments with numerical simulation. Our results show that the Davis–Hocking model with measured mobility parameter captures the essential coalescence dynamics and outperforms the widely used Kistler dynamic contact angle model in many cases. These observations provide insights in that the mobility is indeed a material parameter. 

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