In this paper, a hierarchical graph attention network (HGAT) 27, 28, 29 was proposed to predict the unknown assembly deviations of the hydraulic equipment, and a derivation gradient matrix is defined for equipment maintenance. And the missing deviations in the assembly are expected to be predicted based on its feature graph. As the development of artificial intelligence, there is a promising branch to generalize the machine learning algorithms 22, 23 to graph domain 24, 25, 26. Besides, the deviations generated in the service stage are not used to guide the product maintenance or improve the tolerance allocation 18.ДЇurthermore, a mechanical assembly can be regard as a feature graph 19, 20, 21. Disregarding deformations, these studies fall within the category of rigid body assembly. Most studies focus on the design stage, and not consider the geometrical feature deviations during usage. However, the existing deviation prediction methods are mainly used for assembly quality control. The sources of fluctuations in the machining process of the workpiece can be identified. 17 proposed a fluctuation evaluation and identification method based on a machining error propagation network. The influence of cumulative deviations of different assembly sequences on product assembly quality can be accurately and effectively evaluated. 16 proposed an assembly sequence deviation propagation model based on the assembly-feature adjacency matrix and geometrical-feature tolerance matrix. It allows designers to evaluate tolerances before the final geometry is defined.

15 proposed a method for tolerance evaluation in product conceptual design stage. The existing research focus on deviation allocation in the product design 9, 10, 11 and assembly stage 12, 13, 14. Data privacy 8 is vital, because the deviations are sensitive and it is necessary to avoid the equipment information leakage derived from the graph models. Here, this research focuses on the privacy-preserving for the assembly deviation prediction. Hence, the graph models 5, a new branch of machine learning method, are proposed to predict the unknown deviations based on the feature graph 6, 7. Complete deviations provide a wealth of guidance information for the assembly maintenance. Because the measurable deviations are limited in the complex assemblies. The existing maintenance methods are almost blind, time-consuming, and laborious. After a long-time usage, the deviations of each part can be very different from the theoretical values due to the deformation away from ideal position 4. Hydraulic equipment plays a significant role in the manufacturing industry 3. Intelligent diagnosis and maintenance of mechanical products is one of the most important part. The PLM (Product-Lifecycle-Management)-oriented value chain collaboration 1, 2 has become the latest way of improving competitiveness in the economy globalization. The effectiveness and superiority of the proposed method are demonstrated by a case study with a four-column hydraulic press. Two privacy-preserving strategies are designed to protect the assembly privacy of node representation and adjacent relationship. A derivation gradient matrix is established to calculate the defined modified necessary index of assembly parts. The hierarchical generalized representation and differential privacy reconstruction techniques are also introduced to generate the graph attention network model for assembly deviation privacy-preserving. A hierarchical graph attention network (HGAT) is established to predict the assembly feature deviations. In this paper, a high-fidelity prediction and privacy-preserving method is proposed based on the observable assembly deviations. However, the actual assembly deviations generated in the service stage can be used to guide the equipment maintenance and tolerance design. Existing deviation prediction methods are mainly used for assembly quality control, which concentrate in the product design and assembly stage. Accurate acquisition and secure transmission of assembly deviation data are the most critical issues for hydraulic equipment manufacturer in the PLM-oriented value chain collaboration. Hydraulic equipment, as a typical mechanical product, has been wildly used in various fields.

Mating press position