Look-ahead prediction of spindle thermal errors with on-machine measurement and the cubic exponential smoothing-unscented Kalman filtering-based temperature prediction model of the machine tools

Fu, Guoqiang; Zheng, Yue; Zhou, Linfeng; Lu, Caijiang; Zhang, Li; Wang, Xi; Wang, Tao

doi:10.1016/j.measurement.2023.112536

Cited by 11 publications

(4 citation statements)

References 31 publications

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“…To implement the decoding operation, it is necessary to transform the core tensor

back to the original input space. Here, the inverse MDT transform [ 6 ] is applied to

by reversing the transformation along the time dimension to obtain a second-order core tensor

, as shown in Equation ( 14 ). The core tensor

is then used as the input of decoding to update the network.…”

Section: Proposed Methodsmentioning

confidence: 99%

“…Due to the intermittent characteristics of these demand data, predicting demand relies heavily on time series prediction. Currently, time series prediction methods can be divided into three categories [5]: (1) statistical methods (e.g., exponential smoothing [6] and moving average [7]); (2) machine learning methods (e.g., support vector regression (SVR) [8], random forests (RF) [9], and LightGBM (light gradient boosting machine) [10,11]); and (3) deep learning methods (e.g., recurrent neural networks (RNN) [12] and long short-term memory (LSTM) [13]). These methods are often applicable to time series with strong periodicity and apparent trends.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Robust Interval Prediction of Intermittent Demand for Spare Parts Based on Tensor Optimization

Hong

Ren

et al. 2023

Sensors

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Demand for spare parts, which is triggered by element failure, project schedule and reliability demand, etc., is a kind of sensing data to the aftermarket service of large manufacturing enterprises. Prediction of the demand for spare parts plays a crucial role in inventory management and lifecycle quality management for the aftermarket service of large-scale manufacturing enterprises. In real-life applications, however, demand for spare parts occurs randomly and fluctuates greatly, and the demand sequence shows obvious intermittent distribution characteristics. Additionally, due to factors such as reporting mistakes made by personnel or environmental changes, the actual data of the demand for spare parts are prone to abnormal variations. It is thus hard to capture the evolutional pattern of the demand for spare parts by traditional time series forecasting methods. The reliability of prediction results is also reduced. To address these concerns, this paper proposes a tensor optimization-based robust interval prediction method of intermittent time series for the aftersales demand for spare parts. First, using the advantages of tensor decomposition to effectively mine intrinsic information from raw data, a sequence-smoothing network based on tensor decomposition and a stacked autoencoder is proposed. Tucker decomposition is applied to the hidden features of the encoder, and the obtained core tensor is reconstructed through the decoder, thus allowing us to smooth outliers in the original demand sequence. An alternating optimization algorithm is further designed to find the optimal sequence feature representation and tensor decomposition factors for the extraction of the evolutionary trend of the intermittent series. Second, an adaptive interval prediction algorithm with a dynamic update mechanism is designed to obtain point prediction values and prediction intervals for the demand sequence, thereby improving the reliability of the forecast. The proposed method is validated using the actual aftersales data from a large engineering manufacturing enterprise in China. The experimental results demonstrate that, compared with typical time series prediction methods, the proposed method can effectively grab the evolutionary trend of various intermittent series and improve the accuracy of predictions made with small-sample intermittent series. Moreover, the proposed method provides a reliable elastic prediction interval when distortion occurs in the prediction results, offering a new solution for intelligent planning decisions related to spare parts in practical maintenance.

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“…To implement the decoding operation, it is necessary to transform the core tensor

back to the original input space. Here, the inverse MDT transform [ 6 ] is applied to

by reversing the transformation along the time dimension to obtain a second-order core tensor

, as shown in Equation ( 14 ). The core tensor

is then used as the input of decoding to update the network.…”

Section: Proposed Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Robust Interval Prediction of Intermittent Demand for Spare Parts Based on Tensor Optimization

Hong

Ren

et al. 2023

Sensors

View full text Add to dashboard Cite

show abstract

“…A thermal network compensation model was established by collecting data using resistance temperature detector sensors. Fu et al [13] conducted experimental trials at three xed speeds of 2000, 3000, and 5000, each running for 4 hours. Subsequently, a temperature-sensitive point selection (TPS) network was designed based on self-attention mechanisms, and a gated recurrent unit (GRU) model was developed.…”

Section: Introductionmentioning

confidence: 99%

Intermittent multivariate time series spindle thermal error prediction under wide environmental temperature ranges and diverse scenario conditions

Jia,

Zhang,

Shen

et al. 2024

Int J Adv Manuf Technol

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As the integration of mechanical engineering and deep learning elds becomes increasingly intertwined, the application of experimental thermal error modeling in intelligent manufacturing has gained signi cant importance. In this paper, the issue of spindle thermal error is treated as a multivariate time series problem due to the thermal transfer characteristics. This study aims to address the challenge of modeling intermittent multivariate time series spindle thermal errors under a wide range of environmental temperatures and various operational scenarios. To tackle this challenge, a substantial volume of experimental data, capable of effectively re ecting the patterns of spindle thermal error variations, was collected through experiments conducted at multiple speeds and under various operational scenarios.Subsequently, the acquired thermal error data underwent intermittent multivariate time series transformation (IMTS) to suit the serialized deep learning model. The study introduces the Crossformer model into the eld of thermal error modeling for the rst time, which is a variant of the Transformer model. The Crossformer model exhibits remarkable adaptability to temporal aspects while effectively maintaining its focus on data features. Ultimately, this study resulted in the development of the IMTS-CrossformerR experimental thermal error model. Throughout the research, a comprehensive examination of various models was undertaken, including two traditional Transformer models, and other thermal error deep learning and machine learning models. The results indicate that the proposed model outperforms its counterparts across multiple model metrics and predictive capabilities. Particularly noteworthy is its substantial improvement in the Range (± 5) ratio of residual uctuations reaching 95.7%, a key engineering metric. These ndings emphasize the signi cant engineering application value of this research, offering novel methods and insights for the precise prediction of spindle thermal errors in the manufacturing industry.

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“…For non-contact measurement, Liu et al [19] used capacitive displacement sensors to obtain thermal errors along three directions of the spindle. Fu et al [20] employed the fivepoint method and utilized five capacitive displacement sensors to obtain the thermal error of the spindle. Gao et al [21] used a laser interferometer to obtain thermal errors and achieved promising results.…”

Section: Introductionmentioning

confidence: 99%

Modeling and analysis of axial thermal error in machining space of double-swing five-axis machine tool

Wang,

Wu,

Liu

et al. 2023

Int J Adv Manuf Technol

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The axial thermal error of five-axis CNC machine tools is a significant factor affecting the machining accuracy. To predict the axial thermal error during the machining process, a method is proposed to model axial thermal error in the machining space of five-axis machine tools with a double swing table. The comprehensive thermal error model of the machining space is first established, which includes the axial thermal error of the spindle, worktable, and other components. The spindle is then simplified as a rod, and an analytical model for the axial thermal error of the spindle is developed based on the heat transfer governing equations. This model enables the determination of the time-varying behavior of the axial thermal error at different speeds. Furthermore, the worktable is simplified as a circular plate and the analytical model for the axial thermal error of the worktable is established based on the thermal bending differential equation of the small deflection circular plate. This model allows for the determination of the time-space variation of the axial thermal error at different radii of the worktable. Finally, based on the axial comprehensive thermal error field of the five-axis CNC machine tool processing space, the distribution of the axial thermal error in the machine tool processing space under thermal equilibrium conditions is revealed. Experimental verification of the proposed model is conducted on the VMC-C50 double swing five-axis CNC machine tool. The experimental results show that the error between the measured axial thermal error value and the axial comprehensive thermal error model value is within 26.6 %, thus confirming the accuracy of the proposed model.

show abstract

Look-ahead prediction of spindle thermal errors with on-machine measurement and the cubic exponential smoothing-unscented Kalman filtering-based temperature prediction model of the machine tools

Cited by 11 publications

References 31 publications

Robust Interval Prediction of Intermittent Demand for Spare Parts Based on Tensor Optimization

Robust Interval Prediction of Intermittent Demand for Spare Parts Based on Tensor Optimization

Intermittent multivariate time series spindle thermal error prediction under wide environmental temperature ranges and diverse scenario conditions

Modeling and analysis of axial thermal error in machining space of double-swing five-axis machine tool

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