Abstract A theoretical model of amperometric enzyme electrodes has been developed in which chemical amplification occurs in a single enzyme membrane via cyclic substrate conversion. The system is based on non-stationary diffusion equations with a nonlinear factor related to the Michaelis– Menten kinetics of the enzymatic reaction. By solving the nonlinear equations using the AGM technique, simple analytical expressions of concentration substrate, product, and amperometric current response are derived. Further, biosensor sensitivity, resistance, and gain are obtained from the current. MATLAB programming was used to carry out the digital simulation. The analytical results are validated with the numerical results. The effect of substrate concentration, maximum enzymatic rate, and membrane thickness on biosensor response was evaluated.

Abstract Estimating the accurate State of Charge (SOC) of a battery is important to avoid the over/undercharging and protect the battery pack from low cycle life. Current methods of SOC estimation use complex equations in the Extended Kalman Filter (EKF) and the equivalent circuit model. In this paper, we used a Feed Forward Neural Network (FNN) to estimate the SOC value accurately where battery parameters such as current, voltage, and charge are mapped directly to the SOC value at the output. A FNN could self-learn the weights with each training data point and update the model parameters such as weights and bias using a combination of two gradient descents (Adam). This model comprises the Dropout technique, which can have many neural network architectures by dropping the neuron/mode at each epoch/training cycle using the same weights and biases. Our FNN model was trained with data comprising different current rates and tested for different cycling data, for example, 5th, 10th, 20th, and 50th cycles and at a different cutoff voltage (4.5 V). The battery used for estimating the SOC value was a Na-ion based battery, which is highly non-linear, and it was fabricated in a house using Na0.67Fe0.5Mn0.5O2 (NFM) as a cathode and Na metal as a reference electrode. The FNN successfully estimated the SOC value for the highly non-linear nature of the Na-ion battery at different current rates (0.05 C, 0.1 C, 0.5 C, 1 C, 2 C), for different cycling data, and at higher cut-off voltage of –4.5 V Na+, reaching the R2 value of ~0.97–~0.99, ~0.99, and ~0.98, respectively.