针对极限学习机（extreme learning machine, ELM）预测下肢关节力矩时，随机初始化输入权重和偏置影响模型准确度问题，提出一种基于核极限学习机（kernel based extreme learning machine, KELM）的下肢康复机器人关节力矩预测方法。该方法将高斯核函数与ELM相融合，并采用遗传算法（genetic algorithm, GA）与粒子群优化（particle swarm optimization, PSO）结合的基因粒子群GAPSO对KELM的参数进行优化。首先，采集1位在跑步机上以0.4、0.5、0.6、0.7和0.8 m/s等5个不同速度行走的右下肢偏瘫患者运动数据并对数据进行预处理；其次，通过GAPSO对KELM进行优化，获得最优正则化系数C和核函数宽度参数S，将输出关节力矩与反向生物力学分析计算的关节作比较；最后，利用均方根误差（root mean square error, RMSE）和相关系数P来评价算法优越性。实验结果表明，基于GAPSO优化后的KELM（GAPSO-KELM）算法相对于PSO-KELM算法、KELM算法和ELM算法的平均最大均方根误差分别降低14%、18%、28%，且P除了0.8 m/s右侧踝关节内外翻是0.79外，其余P最小是0.84，GAPSO-KELM算法进一步提高预测精度，使其为康复治疗提供更有效的算法支持。

A kernel based extreme learning machine (KELM) method was proposed for predicting joint moments of lower limb rehabilitation robots to address the problem that random initialization of input weights and bias affect the accuracy of the model when predicting lower limb joint moments by extreme learning machine (ELM). The method integrated Gaussian kernel function with ELM and used genetic algorithm (GA) combined with particle swarm optimization (PSO) of genetic algorithm-particle swarm optimization (GAPSO) to optimize the parameters of KELM. Firstly, the motion data of a patient with right lower limb hemiplegia walking on a treadmill at 5 different speeds of 0.4, 0.5, 0.6, 0.7 and 0.8 m/s were collected and preprocessed. Secondly, the KELM was optimized by GAPSO to obtain the optimal regularization coefficient C and kernel function width parameter S. The output joint moments were compared with the joints calculated by inverse biomechanical analysis. Finally, the root mean square (RMSE) and correlation coefficient (P) were used to evaluate the superiority of the algorithm. The experimental results show that the average maximum root mean square error of KELM algorithm based on GAPSO (GAPSO-KELM) optimization is 14%, 18% and 28% lower than that of PSO-KELM algorithm, KELM algorithm and ELM algorithm, respectively, and the minimum P is 0.84 except for 0.8 m/s right ankle inversion, which is 0.79. The GAPSO-KELM algorithm further improves the prediction accuracy, making it a more effective algorithm support for rehabilitation treatment.