Entropy is a fundamental concept in the field of information theory. During measurement, conventional entropy measures are susceptible to length and amplitude changes in time series. A new entropy metric, neural network entropy (NNetEn), has been developed to overcome these limitations. NNetEn entropy is computed using a modified LogNNet neural network classification model. The algorithm contains a reservoir matrix of N=19625 elements that must be filled with the given data. The contribution of this paper is threefold. Firstly, this work investigates different methods of filling the reservoir with time series (signal) elements. The reservoir filling method determines the accuracy of the entropy estimation by convolution of the study time series and LogNNet test data. The present study proposes 6 methods for filling the reservoir for time series. Two of them (Method 3 and Method 6) employ the novel approach of stretching the time series to create intermediate elements that complement it, but do not change its dynamics. The most reliable methods for short time series are Method 3 and Method 5. The second part of the study examines the influence of noise and constant bias on entropy values. Our study examines three different time series data types (chaotic, periodic, and binary) with different dynamic properties, Signal to Noise Ratio (SNR), and offsets. The NNetEn entropy calculation errors are less than 10% when SNR is greater than 30 dB, and entropy decreases with an increase in the bias component. The third part of the article analyzes real-time biosignal EEG data collected from emotion recognition experiments. The NNetEn measures show robustness under low-amplitude noise using various filters. Thus, NNetEn measures entropy effectively when applied to real-world environments with ambient noise, white noise, and 1/f noise.

翻译：熵是信息论领域的基本概念。在测量过程中，传统熵度量易受时间序列长度和振幅变化的影响。为克服这些局限性，研究者开发了新熵度量——神经网络熵（NNetEn）。NNetEn熵通过改进的LogNNet神经网络分类模型计算，算法中包含一个需填充给定数据的N=19625个元素的储层矩阵。本文的贡献分为三部分：首先，研究了用时间序列（信号）元素填充储层的不同方法。储层填充方式通过待研究时间序列与LogNNet测试数据的卷积运算，决定了熵估计的精度。本研究提出6种时间序列储层填充方法，其中方法3和方法6采用创新性的时间序列拉伸技术，生成不改变原始动态特性的中间补充元素。对于短时序列，方法3和方法5最为可靠。第二部分探讨噪声和恒定偏差对熵值的影响。研究了三种不同动态特性的时间序列数据类型（混沌、周期和二进制），分析其信噪比（SNR）和偏移量。当信噪比大于30 dB时，NNetEn熵计算误差小于10%，且熵值随偏差分量增大而减小。第三部分分析情感识别实验中采集的实时脑电生物信号数据。NNetEn指标在多种滤波器作用下对低幅值噪声表现出鲁棒性。因此，NNetEn在包含环境噪声、白噪声和1/f噪声的实际应用场景中能有效测量熵值。