In order to extract the non-linear fault characteristics of rolling bearings more accurately, a novel nonlinear dynamical analysis method, referred to as the refined composite multi-scale dispersion q-complexity (RCMSDQC), is proposed for fault feature extraction of rolling bearings. To improve further the overall performance of the extreme learning machine (ELM) algorithm, the adaptive whale optimization algorithm (AWOA) is used to determine the input weights and hidden layer biases of the ELM. The RCMSDQC has the advantages of strong feature extraction ability and stability compared to the composite multi-scale weighted permutation entropy (CMSWPE) and composite multi-scale permutation entropy (CMSPE) methods. Furthermore, compared to the whale optimization algorithm, particle swarm optimization, and genetic algorithm, the AWOA shows a superior performance in the benchmark function comparison experiment. Based on the experimental rolling bearing data from the Paderborn University, the performance of the proposed method is further evaluated. The experimental results indicate that the proposed fault diagnosis method can identify the type and severity of rolling bearing faults with an accuracy of 99.1%.

为了更准确地提取滚动轴承的非线性故障特征，提出了一种新颖的非线性动力学分析方法，即精制的复合多尺度色散q-复杂度（RCMSDQC），用于滚动轴承的故障特征提取。为了进一步提高极限学习机（ELM）算法的整体性能，自适应鲸鱼优化算法（AWOA）用于确定ELM的输入权重和隐藏层偏差。与复合多尺度加权置换熵（CMSWPE）和复合多尺度置换熵（CMSPE）方法相比，RCMSDQC具有强大的特征提取能力和稳定性。此外，与鲸鱼优化算法，粒子群优化算法和遗传算法相比，AWOA在基准功能比较实验中显示出优异的性能。基于帕德博恩大学的实验滚动轴承数据，进一步评估了该方法的性能。实验结果表明，所提出的故障诊断方法能够识别出滚动轴承故障的类型和严重性，准确率达到99.1％。