Optimization Model Construction Method of CNC Milling Energy Efficiency Based on Specific Energy Values and ELM-AdaBoost under Small Samples

doi:10.3969/j.issn.1004-132X.2026.04.006

Abstract

Abstract:

Aiming at the problems of high cost of energy efficiency data acquisition in CNC milling processes and low prediction accuracy of traditional CNC milling energy efficiency model under small sample data， an energy efficiency optimization model was proposed based on specific energy values and extreme learning machine（ELM）-adaptive enhancement algorithm（AdaBoost）. The experimental data were obtained through orthogonal experimental design， a mechanism model was constructed based on specific energy value， combined ELM and AdaBoost to form ELM-AdaBoost data model， and finally integrated the energy efficiency prediction model， which might guarantee the prediction accuracy while effectively reduce the model's demands for data volume. The energy efficiency optimization models were established with the objectives of minimum specific energy value and minimum machining costs， and the optimal processing parameters were solved and optimized by non-dominated sorting genetic algorithm Ⅱ and entropy weight-TOPSIS， and the machining experiments were conducted to verify the feasibility of the proposed method.

Key words: CNC milling, specific energy value, energy efficiency optimization, small sample learning

摘要：

针对数控铣削过程能效数据采集成本高、传统数控铣削能效模型在小样本数据下预测精度低的问题，提出了一种基于比能值和极限学习机（ELM）-自适应增强算法（AdaBoost）的能效优化模型。通过正交试验设计获取试验数据，构建基于比能值的机理模型，结合ELM与AdaBoost形成ELM-AdaBoost数据模型，最后集成能效预测模型，在保证预测精度的同时有效减少模型对数据量的需求。建立以最小比能值和最低加工成本为目标的能效优化模型，通过非支配排序遗传算法Ⅱ和熵权- TOPSIS进行最优工艺参数求解与优化，加工试验验证了提出方法的可行性。

关键词: 数控铣削, 比能值, 能效优化, 小样本学习

CLC Number:

TP391

BAO Hong, YANG Shuo, YAO Hang, LI Yapeng. Optimization Model Construction Method of CNC Milling Energy Efficiency Based on Specific Energy Values and ELM-AdaBoost under Small Samples[J]. China Mechanical Engineering, 2026, 37(4): 821-830.

鲍宏, 杨硕, 姚航, 李亚鹏. 小样本下基于比能值和ELM-AdaBoost的数控铣削能效优化模型构建方法[J]. 中国机械工程, 2026, 37(4): 821-830.

Figures/Tables 16

Fig.1 CNC milling energy efficiency prediction model

Fig.2 ELM-AdaBoost algorithm workflow

Fig.5 On-site data recording

Tab.1 Experimental factors and levels

因素

水平

主轴转速

n/（r·min $- 1$ ）

进给速度

$f$ /（mm·min $- 1$ ）

切削深度

$a p$ /mm

切削宽度

$a e$ /mm

Tab.1 Experimental factors and levels

因素

水平

主轴转速

n/（r·min $- 1$ ）

进给速度

$f$ /（mm·min $- 1$ ）

切削深度

$a p$ /mm

切削宽度

$a e$ /mm

8000

300

0.3

0.4

12000

500

0.4

0.6

16000

700

0.5

0.8

Tab.2 Orthogonal experimental data and validation experimental data

	序号	$n$ /（r·min $- 1$ ）	$f$ /（mm·min $- 1$ ）	$a p$ /mm	$a e$ /mm	$P c u t$ /W	$E T$ /J	$y t /$ （J·min $- 3$ ）
正交试验数据	1	8000	300	0.3	0.4	30.57	121 759.28	704.63
	2	8000	300	0.4	0.6	48.82	95 628.21	415.05
	3	8000	300	0.5	0.8	63.00	75 476.30	262.07
	4	8000	500	0.3	0.6	36.68	58 066.80	336.03
	5	8000	500	0.4	0.8	58.61	45 414.65	197.11
	6	8000	500	0.5	0.4	61.73	83 466.15	289.81
	7	8000	700	0.3	0.8	49.03	32 819.48	189.93
	8	8000	700	0.4	0.4	56.42	66 991.44	290.76
	9	8000	700	0.5	0.6	72.60	46 316.31	160.82
	10	12000	700	0.3	0.4	52.21	68 030.51	393.70
	11	12000	700	0.4	0.6	74.47	47 819.03	207.55
	12	12000	700	0.5	0.8	96.58	40 465.02	140.50
	13	12000	300	0.3	0.6	45.93	98 112.71	567.78
	14	12000	300	0.4	0.8	66.84	77 578.61	336.71
	15	12000	300	0.5	0.4	68.16	147 238.63	511.25
	16	12000	500	0.3	0.8	55.86	47 618.55	275.57
	17	12000	500	0.4	0.4	65.27	85 197.74	369.78
	18	12000	500	0.5	0.6	74.63	65 194.28	226.37
	19	16000	500	0.3	0.4	57.20	96 004.48	555.58
	20	16000	500	0.4	0.6	80.08	69 366.09	301.07
	21	16000	500	0.5	0.8	103.95	51 632.60	179.28
	22	16000	700	0.3	0.6	70.05	50 263.52	290.88
	23	16000	700	0.4	0.8	92.39	43 175.49	187.39
	24	16000	700	0.5	0.4	94.76	76 325.80	265.02
	25	16000	300	0.3	0.8	59.211	82 548.89	477.71
	26	16000	300	0.4	0.4	66.14	162 941.87	707.21
	27	16000	300	0.5	0.6	86.43	99 241.13	344.59
验证试验数据	1	13300	500	0.45	0.60	76.52	67 254.62	259.47
	2	9600	350	0.35	0.30	40.66	160 578.43	796.52
	3	16500	750	0.35	0.80	87.37	34 405.06	170.66
	4	15200	650	0.30	0.75	65.34	46 377.79	268.39
	5	11500	550	0.40	0.30	59.67	113 172.48	491.2
	6	7500	500	0.50	0.60	60.79	67 959.36	235.97
	7	17800	700	0.40	0.50	90.22	63 295.49	274.72
	8	14000	300	0.30	0.50	50.70	109 026.43	630.94
	9	10000	600	0.25	0.80	45.18	43 542.72	302.38
	10	12600	450	0.50	0.40	74.10	113 765.76	395.02
	11	11000	700	0.30	0.80	58.86	39 410.50	228.07
	12	14500	350	0.50	0.50	83.24	103 219.20	358.4
	13	15700	650	0.35	0.70	78.18	43 637.27	225.87
	14	11300	550	0.35	0.70	67.62	68 419.27	242.61
	15	9800	400	0.40	0.35	50.75	164 858.37	757.97
	16	13800	550	0.50	0.60	93.26	62 083.56	209.60
	17	10500	650	0.30	0.75	54.35	41 581.85	265.70
	18	14200	350	0.35	0.55	59.78	116 059.78	668.93
	19	13000	500	0.50	0.45	21.23	73 658.75	275.05
	20	12100	600	0.45	0.35	70.90	114 362.32	523.64
	21	17000	700	0.40	0.80	97.28	39 557.68	182.63
	22	14900	400	0.40	0.60	73.34	86 143.65	334.41

Tab.2 Orthogonal experimental data and validation experimental data

	序号	$n$ /（r·min $- 1$ ）	$f$ /（mm·min $- 1$ ）	$a p$ /mm	$a e$ /mm	$P c u t$ /W	$E T$ /J	$y t /$ （J·min $- 3$ ）
正交试验数据	1	8000	300	0.3	0.4	30.57	121 759.28	704.63
	2	8000	300	0.4	0.6	48.82	95 628.21	415.05
	3	8000	300	0.5	0.8	63.00	75 476.30	262.07
	4	8000	500	0.3	0.6	36.68	58 066.80	336.03
	5	8000	500	0.4	0.8	58.61	45 414.65	197.11
	6	8000	500	0.5	0.4	61.73	83 466.15	289.81
	7	8000	700	0.3	0.8	49.03	32 819.48	189.93
	8	8000	700	0.4	0.4	56.42	66 991.44	290.76
	9	8000	700	0.5	0.6	72.60	46 316.31	160.82
	10	12000	700	0.3	0.4	52.21	68 030.51	393.70
	11	12000	700	0.4	0.6	74.47	47 819.03	207.55
	12	12000	700	0.5	0.8	96.58	40 465.02	140.50
	13	12000	300	0.3	0.6	45.93	98 112.71	567.78
	14	12000	300	0.4	0.8	66.84	77 578.61	336.71
	15	12000	300	0.5	0.4	68.16	147 238.63	511.25
	16	12000	500	0.3	0.8	55.86	47 618.55	275.57
	17	12000	500	0.4	0.4	65.27	85 197.74	369.78
	18	12000	500	0.5	0.6	74.63	65 194.28	226.37
	19	16000	500	0.3	0.4	57.20	96 004.48	555.58
	20	16000	500	0.4	0.6	80.08	69 366.09	301.07
	21	16000	500	0.5	0.8	103.95	51 632.60	179.28
	22	16000	700	0.3	0.6	70.05	50 263.52	290.88
	23	16000	700	0.4	0.8	92.39	43 175.49	187.39
	24	16000	700	0.5	0.4	94.76	76 325.80	265.02
	25	16000	300	0.3	0.8	59.211	82 548.89	477.71
	26	16000	300	0.4	0.4	66.14	162 941.87	707.21
	27	16000	300	0.5	0.6	86.43	99 241.13	344.59
验证试验数据	1	13300	500	0.45	0.60	76.52	67 254.62	259.47
	2	9600	350	0.35	0.30	40.66	160 578.43	796.52
	3	16500	750	0.35	0.80	87.37	34 405.06	170.66
	4	15200	650	0.30	0.75	65.34	46 377.79	268.39
	5	11500	550	0.40	0.30	59.67	113 172.48	491.2
	6	7500	500	0.50	0.60	60.79	67 959.36	235.97
	7	17800	700	0.40	0.50	90.22	63 295.49	274.72
	8	14000	300	0.30	0.50	50.70	109 026.43	630.94
	9	10000	600	0.25	0.80	45.18	43 542.72	302.38
	10	12600	450	0.50	0.40	74.10	113 765.76	395.02
	11	11000	700	0.30	0.80	58.86	39 410.50	228.07
	12	14500	350	0.50	0.50	83.24	103 219.20	358.4
	13	15700	650	0.35	0.70	78.18	43 637.27	225.87
	14	11300	550	0.35	0.70	67.62	68 419.27	242.61
	15	9800	400	0.40	0.35	50.75	164 858.37	757.97
	16	13800	550	0.50	0.60	93.26	62 083.56	209.60
	17	10500	650	0.30	0.75	54.35	41 581.85	265.70
	18	14200	350	0.35	0.55	59.78	116 059.78	668.93
	19	13000	500	0.50	0.45	21.23	73 658.75	275.05
	20	12100	600	0.45	0.35	70.90	114 362.32	523.64
	21	17000	700	0.40	0.80	97.28	39 557.68	182.63
	22	14900	400	0.40	0.60	73.34	86 143.65	334.41

Fig.6 Comparison of predicted and actual values of the BPNN model

Fig.7 Comparison of predicted and actual values of the SVR model

Fig.8 Comparison of predicted and actual values of the ELM-AdaBoost model

Fig.9 Comparison of predicted and actual values of the mechanistic model

Fig.10 Comparison of predicted and actual values of the energy efficiency prediction model

Tab.3 Comparison of prediction performance for each model

模型	RMSE		MAE		MAPE/%
模型	训练集	测试集	训练集	测试集	训练集	测试集
BPNN 模型	31.1865	83.7857	20.8705	72.9970	5.9269	20.6171
SVR 模型	47.4462	72.6312	35.1507	47.1031	10.0319	11.0563
ELM-AdaBoost	23.7406	45.4189	17.9121	33.9753	5.5810	9.0953
机理模型	27.4273	35.5451	24.2307	29.3955	7.2437	8.4397
能效预测模型	11.9173	23.8684	9.1952	19.8178	2.7215	5.6215

Tab.4 Related parameter values

参数

$n m i n /$

$(r · m i n - 1)$

$n m a x /$

$(r · m i n - 1)$

$f m i n$ $/$

$(m m · m i n - 1)$

$f m a x /$

$(m m · m i n - 1)$

D / m m

η

P m a x / k W

z

[R a] / μ m

[T] / m i n

取值

0.8

1.6

Tab.4 Related parameter values

参数

$n m i n /$

$(r · m i n - 1)$

$n m a x /$

$(r · m i n - 1)$

$f m i n$ $/$

$(m m · m i n - 1)$

$f m a x /$

$(m m · m i n - 1)$

D / m m

取值

2000

24 000

100

5000

2.5

参数

η

P m a x / k W

z

[R a] / μ m

[T] / m i n

取值

0.8

1.6

Fig.11 Pareto front

Tab.5 Ranking results of selected non-dominated solution set

n/ $(r · m i n - 1)$	f/ $(m m · m i n - 1)$	$a p / m m$	$a e / m m$	E_C/ （J $· m m - 3$ ）	C/元	排序
10 400	750	0.50	0.62	142.76	1.725	99
10 700	730	0.45	0.60	168.65	1.416	72
10 500	740	0.46	0.58	160.08	1.453	45
10 600	770	0.43	0.59	173.42	1.392	93
10 500	760	0.48	0.56	155.37	1.504	1
10 600	780	0.52	0.55	151.84	1.539	26

Tab.5 Ranking results of selected non-dominated solution set

n/ $(r · m i n - 1)$	f/ $(m m · m i n - 1)$	$a p / m m$	$a e / m m$	E_C/ （J $· m m - 3$ ）	C/元	排序
10 400	750	0.50	0.62	142.76	1.725	99
10 700	730	0.45	0.60	168.65	1.416	72
10 500	740	0.46	0.58	160.08	1.453	45
10 600	770	0.43	0.59	173.42	1.392	93
10 500	760	0.48	0.56	155.37	1.504	1
10 600	780	0.52	0.55	151.84	1.539	26

Tab.6 Comparison before and after optimization

铣削

因素

$(r · m i n - 1)$

$(m m · m i n - 1)$

a p / m m

a e / m m

E_C/

（J $· m m - 3$ ）

铣削

试验值

Tab.6 Comparison before and after optimization

铣削

因素

$(r · m i n - 1)$

$(m m · m i n - 1)$

a p / m m

a e / m m

E_C/

（J $· m m - 3$ ）

C/元

优化前

12 000

700

0.40

0.60

207.55

1.675

优化后

10 500

760

0.48

0.56

155.37

1.504

铣削

试验值

10 500

760

0.48

0.56

162.81

1.539

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