@article{timofeeva_ul shougat_pankow_peters_2024, title={Accelerating imaging frequency in high-speed polarization imaging through data modeling}, volume={63}, ISSN={["1560-2303"]}, DOI={10.1117/1.OE.63.4.043103}, abstractNote={We develop a new processing algorithm for the analysis of high-speed quantitative polarized light microscopy measurements. The measurements are obtained using a high-speed rotating polarizing component and a camera, collecting images at several polarizer angles per rotation. The technique uses data from less than the full quarter-waveplate rotation and then performs an optimal fit of the measured data to the expected response curves. Thus, it allows to increase the effective frame rate of the alignment angle and retardation maps due to the reduction in required images. Due to the complexity of the intensity response curves, a particle swarm optimization method is applied. The algorithm addresses the motion error in high-speed polarization imaging while still using multiple polarization angles for the reconstruction. We apply the algorithm to two example cases: quasi-static loading of a tensile coupon and quality inspection of a polymer fiber during rapid motion. The results demonstrate that increasing the reconstructions per second (i.e., decreasing the number of polarization angles per reconstruction) does not significantly decrease the quality of the reconstructions until ∼2.5 times the increase in reconstructions per second is achieved. Therefore, the developed algorithm is an effective method to increase the effective polarization imaging rate without complex hardware modifications.}, number={4}, journal={OPTICAL ENGINEERING}, author={Timofeeva, Anastasia and Ul Shougat, Md Raf E. and Pankow, Mark and Peters, Kara}, year={2024}, month={Apr} }
 @article{ul shougat_alonso_rahman_peters_2024, title={Interaction of Lamb waves and sensors in structural health monitoring of carbon fiber composite}, volume={12951}, ISBN={["978-1-5106-7208-6"]}, ISSN={["1996-756X"]}, DOI={10.1117/12.3010936}, abstractNote={Carbon fiber composites have gained widespread popularity as advanced composite materials, finding their widespread applications across industries like aerospace, automobile, transportation, and health care. This popularity stems from their unique mechanical, electrical, and thermal properties. However, it is imperative to acknowledge that the structural integrity of these composites can undergo deterioration over time, mainly due to factors such as fatigue, impact damage, and aging. Hence, there is a burning need for a reliable method to monitor the health of these carbon fiber composite structures to prevent potential failure. The main goal of this research is to investigate the specific measurement issues when implementing a structural health monitoring approach for these composite plates by employing the guided Lamb wave technique. It is well known that the orientation of the fiber within a layered carbon fiber composite plate affects the propagation characteristics of Lamb waves. On the other hand, the sensors on and potentially embedded in the plates also interact with the Lamb wave in a dynamic manner. Using a micro-3D Laser doppler vibrometer, this research explores the microscopic interaction among the sensors, local fiber orientation and texture, and Lamb waves in these carbon fiber composite plates. Such insight can potentially lead us to a more viable means of interpreting the output of sensors and guided Lamb waves to detect defects within these composites.}, journal={HEALTH MONITORING OF STRUCTURAL AND BIOLOGICAL SYSTEMS XVIII}, author={Ul Shougat, Md Raf E. and Alonso, Joseph and Rahman, Waliur and Peters, Kara}, year={2024} }
 @article{ul shougat_li_perkins_2024, title={Multiplex-free physical reservoir computing with an adaptive oscillator}, volume={109}, ISSN={["2470-0053"]}, DOI={10.1103/PhysRevE.109.024203}, abstractNote={Nonlinear oscillators can often be used as physical reservoir computers, in which the oscillator's dynamics simultaneously performs computation and stores information. Typically, the dynamic states are multiplexed in time, and then machine learning is used to unlock this stored information into a usable form. This time multiplexing is used to create virtual nodes, which are often necessary to capture enough information to perform different tasks, but this multiplexing procedure requires a relatively high sampling rate. Adaptive oscillators, which are a subset of nonlinear oscillators, have plastic states that learn and store information through their dynamics in a human readable form, without the need for machine learning. Highlighting this ability, adaptive oscillators have been used as analog frequency analyzers, robotic controllers, and energy harvesters. Here, adaptive oscillators are considered as a physical reservoir computer without the cumbersome time multiplexing procedure. With this multiplex-free physical reservoir computer architecture, the fundamental logic gates can be simultaneously calculated through dynamics without modifying the base oscillator.}, number={2}, journal={PHYSICAL REVIEW E}, author={Ul Shougat, Md Raf E. and Li, Xiaofu and Perkins, Edmon}, year={2024}, month={Feb} }
 @article{ul shougat_kennedy_perkins_2023, title={A Self-Sensing Shape Memory Alloy Actuator Physical Reservoir Computer}, volume={7}, ISSN={["2475-1472"]}, DOI={10.1109/LSENS.2023.3270704}, abstractNote={A self-sensing shape memory alloy actuator is harnessed as a computational resource by utilizing it as a physical reservoir computer. Physical reservoir computing is a machine learning technique that takes advantage of the dynamics of a physical system for computation. Compared to recurrent neural networks, this architecture can be both fast and efficient with a cheaper training procedure. A shape memory alloy actuator is designed, fabricated, and tested for processing information. Voltage variation along the shape memory alloy wire is used as the reservoir's nodes. The physical reservoir is then used to predict the future trajectory of the actuator's end effector under various driving signals. This self-prediction method is also reconfigurable, as demonstrated by training the reservoir for one waveform but testing it for a different one. A nonlinear autoregressive moving average prediction task was also used to highlight the physical reservoir computer's abilities. Following this methodology, the soft actuator can be used for actuation and computation at the same time without altering its design.}, number={5}, journal={IEEE SENSORS LETTERS}, author={Ul Shougat, Md Raf E. and Kennedy, Scott and Perkins, Edmon}, year={2023}, month={May} }
 @article{ul shougat_li_shao_mcgarvey_perkins_2023, title={Hopf physical reservoir computer for reconfigurable sound recognition}, volume={13}, ISSN={["2045-2322"]}, DOI={10.1038/s41598-023-35760-x}, abstractNote={AbstractThe Hopf oscillator is a nonlinear oscillator that exhibits limit cycle motion. This reservoir computer utilizes the vibratory nature of the oscillator, which makes it an ideal candidate for reconfigurable sound recognition tasks. In this paper, the capabilities of the Hopf reservoir computer performing sound recognition are systematically demonstrated. This work shows that the Hopf reservoir computer can offer superior sound recognition accuracy compared to legacy approaches (e.g., a Mel spectrum + machine learning approach). More importantly, the Hopf reservoir computer operating as a sound recognition system does not require audio preprocessing and has a very simple setup while still offering a high degree of reconfigurability. These features pave the way of applying physical reservoir computing for sound recognition in low power edge devices.}, number={1}, journal={SCIENTIFIC REPORTS}, author={Ul Shougat, Md Raf E. and Li, XiaoFu and Shao, Siyao and McGarvey, Kathleen and Perkins, Edmon}, year={2023}, month={May} }
 @article{kennedy_ul shougat_perkins_2023, title={Robust self-sensing shape memory alloy actuator using a machine learning approach}, volume={354}, ISSN={["1873-3069"]}, DOI={10.1016/j.sna.2023.114255}, abstractNote={Shape memory alloys are metal alloys that have multiple crystalline states, which can be accessed through heating and cooling. These actuators have several attractive properties, such as a high strength-to-weight ratio, robustness, and compact structure. Added to this, shape memory alloys have a self-sensing property. However, shape memory alloy wires typically have a low contraction of only ∼4%–5%. To overcome this shortcoming, shape memory alloy actuators can use a passive base layer in a morphing configuration to amplify the deformation. By including voltage probes at the base of a unimorph shape memory alloy actuator, self-sensing of the actuator’s configuration can be achieved, without encumbering the actuator with extra mass or wires. Due to the compact nature of this actuator, the voltage probes are necessarily close together, which drastically increases the errors of the estimated deformations. To correct these large errors, a machine learning approach is used to unlock this self-sensing ability for a compact shape memory alloy actuator. Of note, this approach, instead of being a black box method, builds on a self-sensing theory of shape memory alloys. This method of self-sensing with machine learning calibration is capable of predicting the location of the end of the actuator with less than 3% error, even for large deformations.}, journal={SENSORS AND ACTUATORS A-PHYSICAL}, author={Kennedy, Scott and Ul Shougat, Md Raf E. and Perkins, Edmon}, year={2023}, month={May} }
 @article{ul shougat_perkins_2023, title={The van der Pol physical reservoir computer}, volume={3}, ISSN={["2634-4386"]}, DOI={10.1088/2634-4386/acd20d}, abstractNote={Abstract
               The van der Pol oscillator has historical and practical significance to spiking neural networks. It was proposed as one of the first models for heart oscillations, and it has been used as the building block for spiking neural networks. Furthermore, the van der Pol oscillator is also readily implemented as an electronic circuit. For these reasons, we chose to implement the van der Pol oscillator as a physical reservoir computer (PRC) to highlight its computational ability, even when it is not in an array. The van der Pol PRC is explored using various logical tasks with numerical simulations, and a field-programmable analog array circuit for the van der Pol system is constructed to verify its use as a reservoir computer. As the van der Pol oscillator can be easily constructed with commercial-off-the-shelf circuit components, this PRC could be a viable option for computing on edge devices. We believe this is the first time that the van der Pol oscillator has been demonstrated as a PRC.}, number={2}, journal={NEUROMORPHIC COMPUTING AND ENGINEERING}, author={Ul Shougat, Md Raf E. and Perkins, Edmon}, year={2023}, month={Jun} }
 @article{mollik_kennedy_ul shougat_li_fitzgerald_echols_kirk_silverberg_perkins_2022, title={Discrete element method simulator for joint dynamics: a case study using a red-tailed hawk's hallux digit}, volume={6}, ISSN={["1573-272X"]}, DOI={10.1007/s11044-022-09828-x}, journal={MULTIBODY SYSTEM DYNAMICS}, author={Mollik, Tushar and Kennedy, Scott and Ul Shougat, Md Raf E. and Li, Xiaofu and Fitzgerald, Timothy and Echols, Scott and Kirk, Nick and Silverberg, Larry and Perkins, Edmon}, year={2022}, month={Jun} }
 @article{ul shougat_li_perkins_2022, title={Dynamic effects on reservoir computing with a Hopf oscillator}, volume={105}, ISSN={["2470-0053"]}, DOI={10.1103/PhysRevE.105.044212}, abstractNote={Limit cycle oscillators have the potential to be resourced as reservoir computers due to their rich dynamics. Here, a Hopf oscillator is used as a physical reservoir computer by discarding the delay line and time-multiplexing procedure. A parametric study is used to uncover computational limits imposed by the dynamics of the oscillator using parity and chaotic time-series prediction benchmark tasks. Resonance, frequency ratios from the Farey sequence, and Arnold tongues were found to strongly affect the computation ability of the reservoir. These results provide insights into fabricating physical reservoir computers from limit cycle systems.}, number={4}, journal={PHYSICAL REVIEW E}, author={Ul Shougat, Md Raf E. and Li, XiaoFu and Perkins, Edmon}, year={2022}, month={Apr} }
 @article{mollik_geng_ul shougat_fitzgerald_perkins_2022, title={Genetic algorithm shape optimization to manipulate the nonlinear response of a clamped-clamped beam}, volume={8}, ISSN={["2405-8440"]}, DOI={10.1016/j.heliyon.2022.e11833}, abstractNote={Dynamical systems, which are described by differential equations, can have an enhanced response because of their nonlinearity. As one example, the Duffing oscillator can exhibit multiple stable vibratory states for some external forcing frequencies. Although discrete systems that are described by ordinary differential equations have helped to build fundamental groundwork, further efforts are needed in order to tailor nonlinearity into distributed parameter, continuous systems, which are described by partial differential equations. To modify the nonlinear response of continuous systems, topology optimization can be used to change the shape of the mechanical system. While topology optimization is well-developed for linear systems, less work has been pursued to optimize the nonlinear vibratory response of continuous systems. In this paper, a genetic algorithm implementation of shape optimization for continuous systems is described. The method is very general, with flexible objective functions and very few assumptions; it is applicable to any continuous system. As a case study, a clamped-clamped beam is optimized to have a more nonlinear or less nonlinear vibratory response. This genetic algorithm implementation of shape optimization could provide a tool to improve the performance of many continuous structures, including MEMS sensors, actuators, and macroscale civil structures.}, number={11}, journal={HELIYON}, author={Mollik, Tushar and Geng, Ying and Ul Shougat, Md Raf E. and Fitzgerald, Timothy and Perkins, Edmon}, year={2022}, month={Nov} }
 @article{li_kallepalli_mollik_ul shougat_kennedy_frabitore_perkins_2022, title={The pendulum adaptive frequency oscillator}, volume={179}, ISSN={["1096-1216"]}, DOI={10.1016/j.ymssp.2022.109361}, abstractNote={Adaptive oscillators are a type of nonlinear oscillator that are capable of learning and storing information in plastic states. Here, a typical mechanical pendulum is modified to have an adjustable rod length to create a pendulum adaptive frequency oscillator. Since the resonance frequency of the pendulum is a function of the rod length, this allows the pendulum to learn and encode frequency information from an external source. An experimental pendulum adaptive frequency oscillator is designed and constructed, and its performance is compared to numerical simulations. This nonlinear pendulum was approximated as a Duffing oscillator through the method of multiple scales to determine the physical constants of the experiment by using a curve fit. Utilizing the pendulum adaptive frequency oscillator’s dynamics, this system is able to learn a resonance condition and store this information in the rod length. This causes the system to seek resonance, even with considerable nonlinearity. As pendulums can be used to harvest energy, this type of adaptation could be used to further exploit vibratory energy sources.}, journal={Mechanical Systems and Signal Processing}, author={Li, XiaoFu and Kallepalli, Pawan and Mollik, Tushar and Ul Shougat, Md Raf E and Kennedy, Scott and Frabitore, Sean and Perkins, Edmon}, year={2022}, month={Nov}, pages={109361} }
 @article{ul shougat_li_mollik_perkins_2021, title={A Hopf physical reservoir computer}, volume={11}, ISSN={["2045-2322"]}, DOI={10.1038/s41598-021-98982-x}, abstractNote={AbstractPhysical reservoir computing utilizes a physical system as a computational resource. This nontraditional computing technique can be computationally powerful, without the need of costly training. Here, a Hopf oscillator is implemented as a reservoir computer by using a node-based architecture; however, this implementation does not use delayed feedback lines. This reservoir computer is still powerful, but it is considerably simpler and cheaper to implement as a physical Hopf oscillator. A non-periodic stochastic masking procedure is applied for this reservoir computer following the time multiplexing method. Due to the presence of noise, the Euler–Maruyama method is used to simulate the resulting stochastic differential equations that represent this reservoir computer. An analog electrical circuit is built to implement this Hopf oscillator reservoir computer experimentally. The information processing capability was tested numerically and experimentally by performing logical tasks, emulation tasks, and time series prediction tasks. This reservoir computer has several attractive features, including a simple design that is easy to implement, noise robustness, and a high computational ability for many different benchmark tasks. Since limit cycle oscillators model many physical systems, this architecture could be relatively easily applied in many contexts.}, number={1}, journal={SCIENTIFIC REPORTS}, author={Ul Shougat, Md Raf E. and Li, XiaoFu and Mollik, Tushar and Perkins, Edmon}, year={2021}, month={Sep} }
 @article{li_ul shougat_kennedy_fendley_dean_beal_perkins_2021, title={A four-state adaptive Hopf oscillator}, volume={16}, ISSN={["1932-6203"]}, DOI={10.1371/journal.pone.0249131}, abstractNote={Adaptive oscillators (AOs) are nonlinear oscillators with plastic states that encode information. Here, an analog implementation of a four-state adaptive oscillator, including design, fabrication, and verification through hardware measurement, is presented. The result is an oscillator that can learn the frequency and amplitude of an external stimulus over a large range. Notably, the adaptive oscillator learns parameters of external stimuli through its ability to completely synchronize without using any pre- or post-processing methods. Previously, Hopf oscillators have been built as two-state (a regular Hopf oscillator) and three-state (a Hopf oscillator with adaptive frequency) systems via VLSI and FPGA designs. Building on these important implementations, a continuous-time, analog circuit implementation of a Hopf oscillator with adaptive frequency and amplitude is achieved. The hardware measurements and SPICE simulation show good agreement. To demonstrate some of its functionality, the circuit’s response to several complex waveforms, including the response of a square wave, a sawtooth wave, strain gauge data of an impact of a nonlinear beam, and audio data of a noisy microphone recording, are reported. By learning both the frequency and amplitude, this circuit could be used to enhance applications of AOs for robotic gait, clock oscillators, analog frequency analyzers, and energy harvesting.}, number={3}, journal={PLOS ONE}, author={Li, XiaoFu and Ul Shougat, Md Raf E. and Kennedy, Scott and Fendley, Casey and Dean, Robert N. and Beal, Aubrey N. and Perkins, Edmon}, year={2021}, month={Mar} }
 @article{ul shougat_li_mollik_perkins_2021, title={An Information Theoretic Study of a Duffing Oscillator Array Reservoir Computer}, volume={16}, ISSN={["1555-1415"]}, DOI={10.1115/1.4051270}, abstractNote={Abstract
               Typically, nonlinearity is considered to be problematic and sometimes can lead to dire consequences. However, the nonlinearity in a Duffing oscillator array can enhance its ability to be used as a reservoir computer. Machine learning and artificial neural networks, inspired by the biological computing framework, have shown their immense potential, especially in the real-time temporal data processing. Here, the efficacy of a Duffing oscillator array is explored as a reservoir computer by using information theory. To do this, a reservoir computer model is studied numerically, which exploits the dynamics of the array. In this system, the complex dynamics stem from the Duffing term in each of the identical oscillators. The effects of various system parameters of the array on the information processing ability are discussed from the perspective of information theory. By varying these parameters, the information metric was found to be topologically mixed. Additionally, the importance of asynchrony in the oscillator array is also discussed in terms of the information metric. Since such nonlinear oscillators are used to model many different physical systems, this research provides insight into how physical nonlinear oscillatory systems can be used for dynamic computation, without significantly modifying or controlling the underlying dynamical system. To the authors' knowledge, this is the first use of Shannon's information rate for quantifying a reservoir computer of this kind, as well as the first comparison between synchronization phenomena and the computing ability of a reservoir.}, number={8}, journal={Journal of Computational and Nonlinear Dynamics}, author={Ul Shougat, Md. Raf E. and Li, XiaoFu and Mollik, Tushar and Perkins, Edmon}, year={2021}, month={Aug}, pages={081004} }
 @article{li_shougat_mollik_beal_dean_perkins_2021, title={Stochastic effects on a Hopf adaptive frequency oscillator}, volume={129}, ISSN={["1089-7550"]}, DOI={10.1063/5.0050819}, abstractNote={This paper explores the stochastic dynamics of a Hopf adaptive frequency oscillator when driven by noise. Adaptive oscillators are nonlinear oscillators that store information via plastic states. As noise is ubiquitous in physical systems, it is important to gain an understanding of the stochastic effects on adaptive oscillators. Previously, it has been shown that a simplified analysis of the Fokker–Planck equation results in affecting the plastic frequency state of these oscillators. However, when the full Fokker–Planck equation is considered, new behaviors are observed due to changes in oscillation amplitudes in addition to frequencies. The plastic frequency state of these oscillators may benefit from enhanced learning due to small amplitudes of noise, converge to incorrect values for medium amplitudes of noise, and even collapse to zero in the limit of large amplitudes of noise. Interestingly, not all averaged states collapse equally, which leads a two dimensional limit cycle to collapse into single dimensional oscillations when considering the averaged dynamics. These behaviors are compared analytically through the Fokker–Planck equation, numerically using the Euler–Maruyama simulations, and finally validated experimentally using an analog, electronic circuit. These results show that noise can enhance, mislead, or even reduce the dimensionality of the averaged adaptive Hopf oscillator.}, number={22}, journal={JOURNAL OF APPLIED PHYSICS}, author={Li, XiaoFu and Shougat, Md. Raf E. Ul and Mollik, Tushar and Beal, Aubrey N. and Dean, Robert N. and Perkins, Edmon}, year={2021}, month={Jun} }