Energy Consumption Prediction of Industrial Robots under High-load Dynamic Conditions

doi:10.3969/j.issn.1004-132X.2026.04.018

Abstract

Abstract:

The power of industrial robots under high-load and highly fluctuating processing conditions showed non-stationary and multi-source coupling characteristics， which led to the problems of reduced accuracy and stability of energy consumption prediction models under cross-operation conditions. Multi-source time series data were collected from the self-built processing experimental platform. The heterogeneous data were synchronized and resampled through timestamps， and power tags were constructed using sliding windows. The prediction results of random forest， gradient boosting tree， support vector regression， multi-layer perceptive machine and two fusion structure models under multiple working conditions were compared. The results show that the energy consumption prediction result of the gradient boosting tree + support vector regression fusion model is the best in the working conditions without participation in training， with an average absolute error of 3.73%. The research reveales the predictive characteristics of different models under high-dynamic processing conditions， which may provide technical support for energy efficiency modeling， process optimization and green operations of high-load processing of the industrial robots.

Key words: industrial robot, high-load processing, energy consumption, data-driven, fusion model

摘要：

工业机器人在高负载、强波动加工工况下的功率呈现非平稳和多源耦合特征，导致能耗预测模型在跨工况条件下易出现精度与稳定性下降的问题。基于自主搭建的加工实验平台采集多源时序数据，通过时间戳对异频数据进行同步与重采样处理，利用滑动窗口构建功率标签。对比了随机森林、梯度提高树、支持向量回归、多层感知机及两种融合结构模型在多工况下的预测结果。结果显示梯度提高树+支持向量回归融合模型的能耗预测结果在未参与训练的工况中最优，平均绝对误差为3.73%。研究揭示了不同模型在高动态加工工况下的预测特性，可为工业机器人高负载加工过程的能效建模、工艺优化与绿色运行提供技术支撑。

关键词: 工业机器人, 高负载加工, 能量消耗, 数据驱动, 融合模型

CLC Number:

TP242.2

SUN Yue, HUANG Hui, YIN Fangchen. Energy Consumption Prediction of Industrial Robots under High-load Dynamic Conditions[J]. China Mechanical Engineering, 2026, 37(4): 939-947.

孙悦, 黄辉, 尹方辰. 高负载动态工况下工业机器人的能耗预测[J]. 中国机械工程, 2026, 37(4): 939-947.

Figures/Tables 18

Fig.1 Robotic machining experimental platform

Fig.2 Schematic of the multi-source signal acquisition and storage system

Tab.1 Physical and mechanical properties of white marble

压缩强度/MPa

弯曲强度/MPa

肖氏硬度HSD

体积密度/

（g·cm $- 3$ ）

Tab.1 Physical and mechanical properties of white marble

压缩强度/MPa

弯曲强度/MPa

肖氏硬度HSD

体积密度/

（g·cm $- 3$ ）

吸水率/%

204

14.6

2.85

0.15

Tab.2 Factor levels of machining parameters in the experiment

因素	水平
因素	1	2	3	4	5
主轴转速/（r·min $- 1$ ）	7000	7500	8000	8500	9000
进给速度/（mm·min $- 1$ ）	1200	1500	1800	2100	2400
切削宽度/mm	1.5	2.0	2.5	3.0	3.5
切削深度/mm	1.2	1.6	2.0	2.4	2.8

Tab.2 Factor levels of machining parameters in the experiment

因素	水平
因素	1	2	3	4	5
主轴转速/（r·min $- 1$ ）	7000	7500	8000	8500	9000
进给速度/（mm·min $- 1$ ）	1200	1500	1800	2100	2400
切削宽度/mm	1.5	2.0	2.5	3.0	3.5
切削深度/mm	1.2	1.6	2.0	2.4	2.8

Tab.3 Cutting parameter combinations for verification experiments

组号	主轴转速/（r·min $- 1$ ）	进给速度/（mm·min $- 1$ ）	切削宽度/mm	切削深度/mm
1	7250	1350	1.75	1.4
2	7750	1650	2.25	1.8
3	8250	1950	2.75	2.2
4	8750	2250	3.25	2.6
5	7000	2400	1.50	2.8
6	8500	1200	3.50	1.2
7	9000	1500	2.00	2.0
8	7500	2100	2.50	2.4

Tab.3 Cutting parameter combinations for verification experiments

组号	主轴转速/（r·min $- 1$ ）	进给速度/（mm·min $- 1$ ）	切削宽度/mm	切削深度/mm
1	7250	1350	1.75	1.4
2	7750	1650	2.25	1.8
3	8250	1950	2.75	2.2
4	8750	2250	3.25	2.6
5	7000	2400	1.50	2.8
6	8500	1200	3.50	1.2
7	9000	1500	2.00	2.0
8	7500	2100	2.50	2.4

Fig.3 Overall flowchart of the energy consumption prediction method for industrial robots

Fig.4 Flowchart of multi-source signal synchronization and power label construction

Fig.5 Comparison between raw power signal and sliding-window averaged power under a typical condition

Fig.6 Flowchart of feature construction and data processing

Fig.7 Integrated model structure

Tab.4 Core hyperparameter configurations of regression models

模型	关键参数	最终取值	参数说明
RF	n_estimators	150	弱学习器数量
	max_depth	9	单棵树最大深度
	min_samples_split	10	内部节点最小划分样本数
	min_samples_leaf	1	叶节点最小样本数
GBRT	n_estimators	120	弱学习器数量
	learning_rate	0.3	学习率
	max_depth	3	单棵树最大深度
	min_child_weight	1	子节点最小样本权重
	subsample	0.6	行采样比例
	colsample_bytree	0.9	列采样比例
SVR	C	100	惩罚系数
	gamma	0.001	RBF核函数宽度
	epsilon	0.1	不敏感区间宽度
MLP	hidden_layer_sizes	（100，）	最优隐藏层结构
	alpha	1.0	L2正则化系数
	learning_rate_init	0.01	初始学习率
RF+ SVR、GBRT+SVR	第一层模型参数	同上	RF或GBRT的最优参数
RF+ SVR、GBRT+SVR	第二层模型参数	SVR（C=100，γ=0.001，ε=0.1）	仅对第一层预测残差建模

Fig.8 Power prediction curves and error profiles of six models under a typical machining condition

Fig.9 Power prediction performance of different models on the training set

Tab.5 Error metrics of different models for energy prediction on the training set

模型名	平均绝对误差	标准差
RF	8.96	12.92
GBRT	9.83	9.98
SVR	13.11	12.65
MLP	4.91	6.40
RF+SVR	14.58	16.35
GBRT+SVR	8.09	10.50

Fig.10 Violin-box plots of relative energy prediction errors for different models

Fig.11 Scatter plot comparing measured and predicted energy consumption on the validation set

Fig.12 Absolute energy prediction errors of different models under eight validation conditions

Tab.6 Error metrics of different models in the energy consumption verification and prediction task

模型名	MAE	RMSE	最小误差	最大误差
RF	4.74	6.01	$-$ 7.86	9.36
GBRT	5.35	7.26	$-$ 13.81	6.06
SVR	11.95	13.81	$-$ 22.2	8.58
MLP	67.77	67	$-$ 75.91	$-$ 60.62
RF+SVR	5.94	7.62	$-$ 12.97	9.61
GBRT+SVR	3.73	4.73	$-$ 4.52	6.08

Tab.6 Error metrics of different models in the energy consumption verification and prediction task

模型名	MAE	RMSE	最小误差	最大误差
RF	4.74	6.01	$-$ 7.86	9.36
GBRT	5.35	7.26	$-$ 13.81	6.06
SVR	11.95	13.81	$-$ 22.2	8.58
MLP	67.77	67	$-$ 75.91	$-$ 60.62
RF+SVR	5.94	7.62	$-$ 12.97	9.61
GBRT+SVR	3.73	4.73	$-$ 4.52	6.08

References 20

[1]	WANG Enze， LEE C C， LI Yaya. Assessing the Impact of Industrial Robots on Manufacturing Energy Intensity in 38 Countries［J］. Energy Economics， 2022， 105： 105748.
[2]	刘璐，岳彩旭，李子峰，等. 面向切削加工的机床绿色化技术研究进展［J］. 制造技术与机床， 2026（1）： 33-45.
	LIU Lu， YUE Caixu， LI Zifeng， et al. Research Progress on Green Technologies for Machining-oriented Machine Tools［J］. Manufacturing Technology & Machine Tool， 2026（1）： 33-45.
[3]	CHEN Xingzheng， LI Congbo， TANG Ying， et al. Energy Efficient Cutting Parameter Optimization［J］. Frontiers of Mechanical Engineering， 2021， 16（2）： 221-248.
[4]	田威，李鹏程，缪云飞，等. 大型复材薄壁构件工业机器人高精度原位铣边加工新方法［J］. 机械工程学报， 2025， 61（7）： 120-133.
	TIAN Wei， LI Pengcheng， MIAO Yunfei， et al. A New Method for High-precision In-situ Milling Edge Processing of Industrial Robots for Large Composite Thin-walled Components［J］. Journal of Mechanical Engineering， 2025， 61（7）： 120-133.
[5]	CHENG Xuhui， YIN Fangchen， WEN Congwei， et al. Energy Prediction and Optimization for Robotic Stereoscopic Statue Processing［J］. Scientific Reports， 2025， 15： 8544.
[6]	庹军波，彭秋媛，张贤明，等. 工业机器人能耗预测研究［J］. 中国机械工程， 2022， 33（22）： 2727-2732.
	JunboTUO， PENG Qiuyuan， ZHANG Xianming， et al. Energy Consumption Prediction Method for Industrial Robots［J］. China Mechanical Engineering， 2022， 33（22）： 2727-2732.
[7]	GADALETA M， BERSELLI G， PELLICCIARI M， et al. Extensive Experimental Investigation for the Optimization of the Energy Consumption of a High Payload Industrial Robot with Open Research Dataset［J］. Robotics and Computer-Integrated Manufacturing， 2021， 68： 102046.
[8]	HOVGARD M， LENNARTSON B， BENGTSSON K. Applied Energy Optimization of Multi-robot Systems through Motion Parameter Tuning［J］. CIRP Journal of Manufacturing Science and Technology， 2021， 35： 422-430.
[9]	ZHANG Mingyang， YAN Jihong. A Data-driven Method for Optimizing the Energy Consumption of Industrial Robots［J］. Journal of Cleaner Production， 2021， 285： 124862.
[10]	余坼操，朱学军，杨旭东，等. 面向多工位多机器人焊接任务的多目标优化方法［J/OL］. 机械科学与技术. .
	YU Checao， ZHU Xuejun， YANG Xudong， et al. Multi-objective Optimization Method for Multi-station and Multi-Robot Welding Tasks ［J/OL］. Mechanical Science and Technology. .
[11]	ZHOU Jin， YI Hao， CAO Huajun， et al. Structural Decomposition-based Energy Consumption Modeling of Robot Laser Processing Systems and Energy-efficient Analysis［J］. Robotics and Computer-Integrated Manufacturing， 2022， 76： 102327.
[12]	黄吉祥，尹方辰，黄身桂，等. 机器人石材雕刻粗加工能耗建模与优化分析［J］. 华侨大学学报（自然科学版）， 2024， 45（4）： 471-477.
	HUANG Jixiang， YIN Fangchen， HUANG Shengui， et al. Modeling and Optimization Analysis of Energy Consumption in Rough Machining of Robotic Stone Carving［J］. Journal of Huaqiao University （Natural Science）， 2024， 45（4）： 471-477.
[13]	周进. 基于时间尺度函数的工业机器人加工系统节能优化方法与典型应用研究［D］. 重庆：重庆大学， 2022.
	ZHOU Jin. Time-scaling-based Energy-saving Optimization Method and Typical Application Study of Robot Machining System［D］. Chongqing： Chongqing University， 2022.
[14]	栾利强. 考虑变材料去除率过程功率动态特性的石材加工能耗建模研究与应用［D］. 青岛：青岛大学， 2021.
	LUAN Liqiang. Research and Application of Energy Consumption Modeling in Stone Processing Considering Dynamic Characteristics of Process Power for Variable Material Removal Rate ［D］. Qingdao： Qingdao University， 2021.
[15]	梅术龙，谢阳，张超勇，等. 精密铣削机床效能孪生模型构建及动态优化方法［J］. 中国机械工程， 2026， 37（4）： 875-884.
	Mei Shulong， Xie Yang， Zhang Chaoyong， et al. Construction and Dynamic Optimization Method of Efficiency Twin Model for Precision Milling Machine Tools ［J］. China Mechanical Engineering， 2026， 37（4）： 875-884.
[16]	BRILLINGER M， WUWER M， SMAJIC B， et al. Novel Method to Predict the Energy Consumption of Machined Parts in the Design Phase to Attain Sustainability Goals［J］. Journal of Manufacturing Processes， 2023， 101： 1046-1054.
[17]	LIMA R C C， de OLIVEIRA L A V， Da SILVA S P P， et al. A New Proposal for Energy Efficiency in Industrial Manufacturing Systems Based on Machine Learning Techniques［J］. Journal of Manufacturing Systems， 2024， 77： 1062-1076.
[18]	AWAN M R， GONZÁLEZ ROJAS H A， HAMEED S， et al. Machine Learning-based Prediction of Specific Energy Consumption for Cut-off Grinding［J］. Sensors， 2022， 22（19）： 18.
[19]	谢阳，戴逸群，张超勇，等. 融合集成模型与深度学习的机床能耗识别与预测方法［J］. 中国机械工程， 2023， 34（24）： 2963-2974.
	XIE Yang， DAI Yiqun， ZHANG Chaoyong， et al. A Method for Identifying and Predicting Energy Consumption of Machine Tools by Combining Integrated Models and Deep Learning［J］. China Mechanical Engineering， 2023， 34（24）： 2963-2974.
[20]	陶进煊. 基于机理和数据驱动混合的数控铣削能效预测与优化研究［D］. 合肥：合肥工业大学， 2024.
	TAO Jinxuan. Research on Energy Efficiency Prediction and Optimization of CNC Milling Based on Hybrid of Mechanism and Data-drive［D］. Hefei： Hefei University of Technology， 2024.