Prediction of Three-dimensional Machined Surface Topography of KDP Crystals Based on Deep Learning

doi:10.3969/j.issn.1004-132X.2025.10.021

Abstract

Abstract:

The surface morphology of potassium dihydrogen phosphate（KH₂PO₄， KDP） machined by single point diamond turning was the research objects. The low， mid， and high-frequency wavelengths and amplitudes of the three-dimensional surface were extracted by CWT and power spectral density（PSD） as sample sets. Cutting parameters were treated as key variables， and bi-directional long short-term memory （BiLSTM）， gated recurrent units（GRU）， random forest（RF）， and convolutional neural network（CNN） were developed to predict the wavelengths and amplitudes of different frequency bands， ultimately enabling the prediction of the three-dimensional machined surface topography. The results indicate that the BiLSTM model demonstrate superior prediction performance for mid and high-frequency wavelengths， as well as low and high-frequency amplitudes， with average percentage errors of 2.14% and 3.03% for mid and high-frequency wavelengths， and 4.62% and 7.19% for low and high-frequency amplitudes， respectively. The GRU model excelles in predicting low-frequency wavelengths and mid-frequency amplitudes， with errors of 3.83% and 5.68%. The predicted three-dimensional surface topography closely matches experimental results from the validation sets. The correspondence between cutting parameters and the three-dimensional machined surface of KDP crystals was revealed by combining continuous wavelet transform， power spectral density， and deep learning methods and the correctness was verified.

Key words: potassium dihydrogen phosphate（KDP） crystal, surface topography, deep learning, continuous wavelet transform（CWT）

摘要：

以单点金刚石车削加工磷酸二氢钾（KH₂PO₄，KDP）的已加工表面形貌为研究对象，采用连续小波变换和功率谱密度方法提取已加工KDP晶体三维形貌的低频、中频、高频的波长和幅值作为样本集，将切削参数作为关键变量，建立双向长短期神经网络（BiLSTM）、门循环单元（GRU）、随机森林网络（RF）和卷积神经网络（CNN）分别预测已加工KDP晶体各频段的波长和幅值，最终实现三维已加工表面形貌的预测。结果表明，BiLSTM模型对中频和高频波长、低频和高频幅值的预测结果最优，预测结果误差均值分别为2.14%和3.03%、4.62%和7.19%；GRU网络对低频波长和中频幅值的的预测结果最优，预测结果误差均值分别为3.83%和5.68%；由深度学习模型预测的高频、中频、低频的幅值和波长所生成KDP晶体的三维已加工表面形貌与验证集的实验结果高度一致，验证了结合连续小波、功率谱密度与深度学习方法建立切削参数与KDP晶体三维已加工表面的对应关系的正确性。

关键词: KDP晶体, 表面形貌, 深度学习, 连续小波变换

CLC Number:

TH161

Zulong YAN, Qilong PANG, Jianlong XIONG. Prediction of Three-dimensional Machined Surface Topography of KDP Crystals Based on Deep Learning[J]. China Mechanical Engineering, 2025, 36(10): 2329-2334.

闫祖龙, 庞启龙, 熊建龙. 基于深度学习的KDP晶体三维已加工表面形貌预测[J]. 中国机械工程, 2025, 36(10): 2329-2334.

Figures/Tables 9

References 20

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验证集	进给量 f/（μm·r^-1）	主轴转速 n/（r·min^-1）	切削深度 a_p/μm
1	12	900	9
2	12	1200	3
3	12	1500	3
4	8	900	3

验证集	进给量 f/（μm·r^-1）	主轴转速 n/（r·min^-1）	切削深度 a_p/μm
1	12	900	9
2	12	1200	3
3	12	1500	3
4	8	900	3

模型	组别	波长/μm			幅值/nm
模型	组别	低频	中频	高频	低频	中频	高频
真实值	1	221.47	62.52	13.12	5.11	23.16	4.11
	2	217.35	91.44	18.72	7.84	16.58	5.04
	3	272.73	100.62	21.35	8.54	31.12	8.86
	4	208.09	94.75	15.12	6.69	14.97	3.67
BiLSTM	1	214.75	65.49	13.71	5.09	22.43	3.36
	2	231.48	93.85	17.98	7.58	15.07	5.15
	3	263.74	99.58	21.77	8.68	34.31	8.67
	4	213.27	94.91	14.86	6.35	15.25	3.86
GRU	1	231.63	75.26	15.06	4.86	21.75	2.56
	2	222.59	91.86	16.68	10.90	17.06	5.84
	3	271.01	103.35	21.76	8.33	27.59	8.50
	4	217.89	90.74	16.19	4.96	15.34	3.44
RF	1	274.08	52.19	20.82	6.46	12.09	5.16
	2	294.61	54.01	23.98	13.25	17.70	8.27
	3	260.16	50.22	18.62	5.04	43.72	3.65
	4	274.01	52.12	20.81	6.49	12.09	3.81
CNN	1	276.62	71.8	17.81	8.51	18.01	6.06
	2	272.95	76.37	18.36	12.49	19.08	6.11
	3	272.92	76.37	18.36	6.87	43.91	4.08
	4	274.73	73.14	17.85	8.56	17.45	3.27

模型	组别	波长/μm			幅值/nm
模型	组别	低频	中频	高频	低频	中频	高频
真实值	1	221.47	62.52	13.12	5.11	23.16	4.11
	2	217.35	91.44	18.72	7.84	16.58	5.04
	3	272.73	100.62	21.35	8.54	31.12	8.86
	4	208.09	94.75	15.12	6.69	14.97	3.67
BiLSTM	1	214.75	65.49	13.71	5.09	22.43	3.36
	2	231.48	93.85	17.98	7.58	15.07	5.15
	3	263.74	99.58	21.77	8.68	34.31	8.67
	4	213.27	94.91	14.86	6.35	15.25	3.86
GRU	1	231.63	75.26	15.06	4.86	21.75	2.56
	2	222.59	91.86	16.68	10.90	17.06	5.84
	3	271.01	103.35	21.76	8.33	27.59	8.50
	4	217.89	90.74	16.19	4.96	15.34	3.44
RF	1	274.08	52.19	20.82	6.46	12.09	5.16
	2	294.61	54.01	23.98	13.25	17.70	8.27
	3	260.16	50.22	18.62	5.04	43.72	3.65
	4	274.01	52.12	20.81	6.49	12.09	3.81
CNN	1	276.62	71.8	17.81	8.51	18.01	6.06
	2	272.95	76.37	18.36	12.49	19.08	6.11
	3	272.92	76.37	18.36	6.87	43.91	4.08
	4	274.73	73.14	17.85	8.56	17.45	3.27