Solovyeva Elena, Serdyuk Artyom
Department of Electrical Engineering Theory, Saint Petersburg Electrotechnical University "LETI", 197022 St. Petersburg, Russia.
Micromachines (Basel). 2023 Dec 26;15(1):0. doi: 10.3390/mi15010051.
Memristors are devices built on the basis of fourth passive electrical elements in nanosystems. Because of the multitude of technologies used for memristor implementation, it is not always possible to obtain analytical models of memristors. This difficulty can be overcome using behavioral modeling, which is when mathematical models are constructed according to the input-output relationships on the input and output signals. For memristor modeling, piecewise neural and polynomial models with split signals are proposed. At harmonic input signals of memristors, this study suggests that split signals should be formed using a delay line. This method produces the minimum number of split signals and, as a result, simplifies behavioral models. Simplicity helps reduce the dimension of the nonlinear approximation problem solved in behavioral modeling. Based on the proposed method, the piecewise neural and polynomial models with harmonic input signals were constructed to approximate the transfer characteristic of the memristor, in which the current dynamics are described using the Bernoulli differential equation. It is shown that the piecewise neural model based on the feedforward network ensures higher modeling accuracy at almost the same complexity as the piecewise polynomial model.
忆阻器是基于纳米系统中的第四种无源电气元件构建的器件。由于用于忆阻器实现的技术众多，并非总能获得忆阻器的分析模型。使用行为建模可以克服这一困难，行为建模是根据输入和输出信号的输入 - 输出关系构建数学模型。对于忆阻器建模，提出了具有分割信号的分段神经模型和多项式模型。在忆阻器的谐波输入信号情况下，本研究表明应使用延迟线来形成分割信号。这种方法产生的分割信号数量最少，从而简化了行为模型。简单性有助于降低行为建模中求解的非线性逼近问题的维度。基于所提出的方法，构建了具有谐波输入信号的分段神经模型和多项式模型，以逼近忆阻器的传输特性，其中使用伯努利微分方程描述电流动态。结果表明，基于前馈网络的分段神经模型在几乎与分段多项式模型相同的复杂度下确保了更高的建模精度。
