Field-programmable analog array (FPAA) based four-state adaptive oscillator for analog frequency analysis.

Adaptive oscillators are a subset of nonlinear oscillators that can learn and encode information in dynamic states. By appending additional states onto a classical Hopf oscillator, a four-state adaptive oscillator is created that can learn both the frequency and amplitude of an external forcing frequency. Analog circuit implementations of nonlinear differential systems are usually achieved by using operational amplifier-based integrator networks, in which redesign procedures of the system topology is time consuming. Here, an analog implementation of a four-state adaptive oscillator is presented for the first time as a field-programmable analog array (FPAA) circuit. The FPAA diagram is described, and the hardware performance is presented. This simple FPAA-based oscillator can be used as an analog frequency analyzer, as its frequency state will evolve to match the external forcing frequency. Notably, this is done without any analog-to-digital conversion or pre-processing, making it an ideal frequency analyzer for low-power and low-memory applications.

Genetic algorithm shape optimization to manipulate the nonlinear response of a clamped-clamped beam.

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.

A Hopf physical reservoir computer.

Physical 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.