CNC machine tools play an important role in the equipment manufacturing industry， and their reliability level has become the bottleneck restricting the development of the industry. Reliability modeling of NC machine tools is the basis of reliability engineering. A comprehensive review on the state of the reliability modeling technology research is given. Reliability models are mainly divided into four categories： reliability modeling method based on fault time data， reliability modeling method based on multi-source hierarchical information set， reliability modeling method based on performance degradation data and process reliability modeling method based on dynamic characteristic parameters. The research process and technical progress of various modeling methods are analyzed. On the basis of affirming the obvious progress made in the reliability modeling method and technology of CNC machine tools， this paper analyzes and points out the existing problems and shortcomings of the research work， and discusses the trends and hotspots of the reliability modeling research of CNC machine tools. Finally， the development trend of reliability modeling methods and technology of CNC machine tools is prospected from the perspective of reliability modeling development law、engineering application and industry demand.

The maintenance and repair of electromechanical equipment such as aerospace equipment， high-grade CNC machine tools and wind power generation equipment directly affect its comprehensive efficiency and service life. Health assessment is the basis of maintenance strategy formulation and maintenance resource management. It is the premise of predictive maintenance， fault prediction and health management. The traditional health assessment method has the disadvantages of relying too much on expert experience， unable to process large-scale data and low accuracy， which is difficult to meet the needs of modern electromechanical equipment health management technology. On the basis of combing and analyzing the latest research results of health status assessment of electromechanical equipment at home and abroad， this paper summarizes the research progress and development trend of health assessment of electromechanical equipment from four key links： signal acquisition， feature extraction， health status division and health assessment； The challenges faced by the related technologies of health assessment of electromechanical equipment are pointed out； Finally， the solutions and development trends to deal with these challenges are discussed.

Aiming at multiple types of faults and unknown fault reasons of tool magazine， this paper established a Bayesian network of the circular tool magazine system based on fault tree analysis of the tool magazine. The prior probability and conditional probability of nodes in the Bayesian network are solved by using a batch of fault data. Based on the analysis of node importance of the Bayesian network， it is found that the cutter body motor， the positioning key of ATC and the body of ATC are the weak links in the circular tool magazine. In addition， based on the analysis of the posterior failure rate of the parent node， the failure of tool changing components and tool storage components are the main cause of tool loss in the tool library. If tool loss occurs， the tool arm and cutter head motor should be overhauled first.

Aiming at the problem of inconsistent feature distribution of rolling bearing vibration data collected under variable operating conditions and difficulty in obtaining the labels of the samples to be identified， a sub-domain adaptive deep transfer learning fault diagnosis method was proposed. Firstly， to make full use of the image feature extraction capabilities of the convolutional neural network （CNN）， the rolling bearing vibration signal was used to generate an image data set using continuous wavelet transform （CWT）.Secondly， the common feature extraction of the source domain and the target domain adopted the ResNet-50 model structure of improved image set pre-training， and the sub-domain adaptive metric introduced the local maximum mean discrepancy （LMMD） criterion. This metric is used for sub-domain adaptation by calculating pseudo-labels in the target domain to match the conditional distribution distance， thereby reducing the difference in the distribution of sub-categories of faults under different working conditions and improving the accuracy of model diagnosis. Finally， experiments on two public variable-condition rolling bearing fault data sets verify that the proposed method has an average recognition accuracy of about 99%. Compared with the results of different transfer learning methods， the effectiveness and superiority of the proposed method are demonstrated.

Aiming at the problem of low accuracy and unstable performance of the fault diagnosis model of rolling bearing in noise environment conditions， This paper proposes a stable anti?noise fault diagnosis neural network SAFDNN model. The model uses the original vibration data signal as input. First， the CNN is used to extract the characteristics of the data signal， and then the BiLSTM is used to fully extract the sequence characteristics of the data signal， and then the attention mechanism is added for feature fusion and automatically pay attention to the relevant information of each data signal， improving the diagnostic performance of the model， and finally performing feature classification through the fully connected layer and Softmax layer. The experimental results show that SAFDNN can maintain a higher fault recognition accuracy and better stability of the diagnosis effect under the condition of adding additional noise with different signal?to?noise ratios.

Aiming at the problems of traditional fault diagnosis model with many parameters， long training， long detection time， poor noise resistance and not suitable for online real-time diagnosis， the paper puts forward the rolling bearing fault diagnosis method based on residual connection and one-dimensional separable convolution（1D-RSCNN）， and constructs an embedded system consisting of Jetson Nano and signal acquisition circuit. The model dimensions are compressed with 1D separable convolution and global average pooling to improve the computational efficiency of traditional convolution， and wide convolution cores， Dropout is introduced into the residual network to improve the tolerance of noise through. The test results show that the diagnostic accuracy of this method is as high as 99.92%. Compared with other models， the diagnosis accuracy is high， the real-time is good， the anti-jamming ability is strong， and it is suitable for the real-time detection of motor bearing fault.

In view of the difficulty of feature extraction and low classification accuracy in the diagnosis of rolling bearing multiple faults， this paper starts from the two aspects of effective feature extraction and fault classification accuracy， and combines the method of variational modal decomposition （VMD） and extreme learning machine （ELM）. An adaptive method for diagnosing multiple faults of rolling bearings is presented. Aiming at the situation that VMD parameters need to be manually set in advance， which leads to poor signal decomposition， the Gray Wolf Algorithm （GWO） is proposed to optimize VMD to achieve adaptively obtaining the best decomposition parameters k and α. Furthermore， in order to overcome the problem of low classification accuracy of a single ELM model and unstable classification results， an integrated extreme learning machine （IELM） is proposed to realize the classification and recognition of multiple faults， and improve the accuracy and stability of fault classification. First， use GWO to optimize VMD and obtain the best decomposition parameters adaptively； Secondly， select and extract the time-frequency feature vector of the modal signal； Finally， input the feature vector into IELM for training and classification. Experiments show that this method can adaptively decompose signals and produce the best decomposing effect， realizing accurate early warning and identification of rolling bearing faults.

The difficulties of failure data collection and operation data changeability hinder the application of fault diagnosis methods to turrets. Hence， an anomaly detection method using non-failure data and considering the change of working conditions was proposed for detecting turrets’ anomaly state during operation. The method studied the judgment principle of abnormal data through the multivariate Gaussian distribution（MGD） and the deviation characteristic associated with working conditions. First， the key working conditions and signal characteristics in different turret working processes were determined through statistical analysis. Second， some methods like linear regression， information gain， and generalized regression neural network were selected to model their relationships， respectively. Following that， the deviation of observation from the given signal characteristics is calculated. Finally， the operation data from turret normal state were used to train the model. Many experiments under different working conditions and abnormal simulation were conducted to verify that the proposed model can eliminate the influence of working conditions on abnormal judgment compared to the traditional MGD model.

Aiming at the problems existing in the traditional FMEA of CNC machine tools， such as the unreasonable distribution of expert weight and risk factor weight， and the insufficient robustness of the calculation model of risk coefficient（RPN）， an improved FMEA method based on multi-attribute group decision-making is proposed. Firstly， interval number is introduced to represent the risk factor of machine tool failure mode； Secondly， considering the subjective and objective weights of experts， according to the consistency principle， the comprehensive weights of experts are calculated， and the weighted average operator（WAA） is used to determine the comprehensive evaluation matrix of fault mode； Thirdly， the interval number entropy method is used to determine the weight of risk factors， and the improved risk priority number （IRPN） calculation model is used to obtain the failure mode risk value； Finally， combined with interval number distance measure， the optimal and worst interval number improved TOPSIS method is used to rank the risk of failure mode. Taking a machining center as an example， the rationality and effectiveness of the method are verified.

In order to solve the shortcomings of traditional failure mode and effect analysis（FMEA）， an improved FMEA method based on interval triangular fuzzy number and grey correlation analysis method is proposed and applied to the risk analysis of spindle system of machining center. Firstly， interval-triangular fuzzy numbers are used to evaluate the level of failure modes and the relative importance of risk factors. Secondly， the weight of risk factors is calculated by fuzzy AHP. Finally， the failure modes are sorted by GRA method. The example results show that FM2（oil leakage） is the failure mode with the highest risk priority. Compared with the other two schemes， this method can sort the failure modes more effectively and reasonably.

In order to improve the positioning accuracy of ball screw pair， a double-nut ball screw load distribution model considering the geometric error of the ball under the compound load is proposed in this paper. The distribution of all ball contact loads under the compound action of different coaxial and radial loads is analyzed. On this basis， the influence of ball geometric error on dynamic and static contact load distribution is analyzed. The simulation results show that the load distribution model proposed in this paper has good reference significance for improving the position accuracy prediction and positioning error compensation of ball screw pair.

In order to obtain the relative optimal test configuration considering multiple optimization objectives in the optimization design of accelerated degradation test， a multi-objective optimization design method of constant stress accelerated degradation test is proposed. The accelerated degradation model is established based on gamma process， and the unknown parameters are solved by maximum likelihood estimation method. Considering the model fitting accuracy and life estimation accuracy， a multi-objective optimization model is constructed. The model is solved by NSGA-II， and a Pareto frontier set considering multiple optimization objectives is established. The relative proportion of each objective function in Pareto frontier set is calculated based on the value of single objective optimization objective function. On this basis， the Analytic Hierarchy Process is used to make expert decision on the accelerated degradation test to be carried out， and the weight value of each objective function is obtained. Taking the minimum error between the relative proportion of the objective function and the weight value of the objective function as the evaluation standard， the relatively optimal test configuration in the Pareto front set is selected. Finally， the effectiveness of the proposed method is verified by the accelerated degradation test data of carbon film resistance.

In order to make full use of the time series correlation characteristics of signals and enhance the model's ability to mine data information comprehensively， thereby further improving the diagnostic accuracy of CNN.This paper proposes a new gearbox fault diagnosis model， which combines CNN with Gated Recurrent Unit （GRU）， which is good at dealing with data timing correlation characteristics. CNN extracts the spatial features of data by end-to-end， and uses the extracted features as the input of GRU to further extract the spatiotemporal features. Finally， the spatiotemporal features extracted by GRU are used as the input of softmax for fault identification. The experimental results show of two groups of gearbox experimental data show that the average fault diagnosis accuracy can reach 99.86% and 99.85% respectively and compared with other models， the results show that the model is superior and effective.

Based on the consideration of the tool error and its dimensional error， the dimensional accuracy prediction of the processed parts does not meet the actual use requirements， and a membership function model that couples fuzzy intervals and fuzzy weights is proposed. This model takes into account the fact that the proportion of various influencing factors in the processing process is not fixed， and it also dynamically characterizes the changes in the contribution of various influencing factors in the processing process. In addition， considering that the size of the actual part processing size is mostly fuzzy value， this paper regards the part size as a possibility distribution and constructs a new reliability prediction model combined with the fuzzy membership function. After comparing the predicted value with the experimental data， it is found that the accuracy of the reliability analysis of the machining accuracy has been significantly improved.

Taking the geometric errors as the research object， this paper presents an approach for the error allocation of CNC machine tool based on the vector projection response surface. Based on the multi-body system theory， a comprehensive error model of machine tool was established to reveal the quantitative relationship between the machining accuracy and geometric errors of the machine tool； by applying the vector projection response surface method， a machining accuracy reliability model was developed to predict and evaluate the machining ability of machine tools， then a machining accuracy reliability sensitivity model was proposed to sequence the influence of distribution parameters of geometric errors on the machining accuracy reliability， and therefore it conducted the identification and optimization of the geometric errors which have larger affect to the machining accuracy reliability. Hence， a general approach for the error allocation of machine tools was formed to realize the reasonable optimization of the geometric error parameters and overall improvement of machining ability of machine tool. The proposed approach was implemented to a four-axis CNC machining center， and the results verified the effectiveness and competitiveness of the approach.

A fault diagnosis method of NC turret based on particle swarm optimization and support vector machine （PSO-SVM） is proposed. Firstly， the NC turret is divided into five subsystems， and a working cycle is divided into four time sequences T1， T2， T3 and T4. Secondly， the feature extraction methods of vibration， motor current， oil pressure and proximity switch signal in different time sequences of NC turret are explored. Finally， fault diagnosis method of NC turret based on PSO-SVM was proposed， and NC turret fault tests were carried out in different time sequences. According to the fault data， support vector machine （SVM） and PSO-SVM fault diagnosis methods are compared and verified. The results show that the fault diagnosis accuracy of T2， T3 and T4 are increased by 28%， 23% and 5%， respectively， which verifies the validity of the proposed fault diagnosis method. The fault diagnosis method proposed in this paper is not only suitable for NC turret， but also provides a new idea for the fault diagnosis of other complex electromechanical system.

In view of the existing numerical control machine tool FMECA analysis factors are few， the interaction between factors is not considered and the weight of each factor is the same， the analytic network process（ANP ） and data envelopment analysis（OCD ） model are applied to the study of FMECA in the use stage of numerical control machine tool， with the score of each factor as the input index. Taking economic loss as output index， the OCD model is established and the efficiency value of each failure mode is obtained. Then a new method is proposed to calculate the risk priority number and the damage degree of failure mode is ranked according to RPN. Taking a numerical control machine tool as an example， the influence and effect of the failure modes are analyzed by using the proposed method， and the effectiveness of the proposed method is verified.

In order to solve the problem of low estimation accuracy of some model parameters in the multi stress step stress accelerated degradation test of motorized spindle， a new optimal design method of multi stress step stress accelerated degradation test scheme is proposed in this paper. The sensitivity analysis method and the comprehensive importance of stress are used to determine the weight of each parameter of the acceleration model in the accelerated degradation test， A new optimal design criterion is proposed based on D_{\mathrm{s}}-optimality and parameter weight； the optimization process is given combined with genetic algorithm. Finally， taking the motorized spindle made in China as an example， the accelerated degradation test scheme is optimized， and the results are compared with the existing criteria， verify the effectiveness of the method.

Aiming at diagnosing the misfire fault of engine， a method of misfire diagnosis based on convolutional neural network（CNN） is proposed. The real-time diagnosis system for misfire fault detection of diesel engine is constructed based on STM32 single chip microcomputer. The convolutional neural network for misfire fault diagnosis of diesel engine is written in Microcontroller Unit（MCU） based on STM32CubeMX software. In the experiment the speed signal is collected by using the timer input capture function of single chip microcomputer， and the top dead center signal works as the trigger signal for speed acquisition. The collected speed data is preprocessed and then used as the input of CNN. The test results in the diesel engine bench show that the real-time misfire diagnosis system has high diagnostic accuracy under wide range of speed and load conditions.

At present， sensor signals are widely used to identify and predict the chatter in the milling process of thin-walled parts， but the correlation between the chatter characteristics and the machined surface is not established. In this paper， image processing and pattern recognition technology are used to accurately identify and predict the machining state of thin-walled parts through milling surface images. Firstly， a hybrid filtering scheme is designed to realize the preprocessing of the collected image， then the chatter texture features of the image are extracted through the improved local binary pattern and gray level co-occurrence matrix， and the images collected in the milling process are predicted and recognized by k-nearest neighbor classification algorithm. The experimental results show that the accuracy of the model identification is 95.5% and the average running time of the algorithm is 0.069 s. The experimental results show that the method has high identification accuracy， meets the real-time requirements of chatter prediction and detection， and has good guiding significance for milling state identification and intelligent machining of thin-walled parts.

Based on the traditional FMECA analysis due to the right of indicators and subjective determination of the probability of failure impact， an improved fault analysis method is proposed. Applying the least squares， adjacent matrix， Pagerank， statistical analysis， etc. to evaluate the probability of failure， fault impact， fault repair time， according to which the grey theory is introduced to construct the albino function of each indicator and calculate the evaluation value， form the index evaluation matrix， calculate the index weight based on entropy weighting method， apply the weighted average method to calculate and evaluate the failure risk. Take a domestic processing center as an example for method application， compared with traditional methods to verify the effectiveness of the proposed method.

In view of the lack of unified integrated system framework and algorithm implementation for reliability analysis of CNC equipment in practical application， in this paper， a cyber-physical system based on digital twin is proposed， and the specific framework and algorithm implementation are studied. The closed-loop control from the physical layer to the cyber layer and back to the physical layer can be realized through the 7-step workflow of data acquisition， data processing， digital twin model training and evaluation， model debugging and optimization， model online deployment， reliability analysis， predictive maintenance. The feasibility and effectiveness of the cyber-physical system framework were verified by the reliability experiment of spindle rotation error prediction of CNC equipment. This method can analyze the reliability of CNC equipment， and is helpful to support more effective and scientific predictive maintenance.

Aiming at the problems of weak Complex fault signal and difficult to extract fault features of gearbox in strong noise environment， an improved minimum entropy deconvolution（MED） combined with singular spectrum decomposition（SSD） is proposed to extract fault features. Firstly， margin and power spectrum kurtosis（MPSK） index is constructed to optimize the parameters of MED； Secondly， the improved MED is used as the pre-filter of SSD to make up for the deficiency of SSD； Then the meaningful SSC components are selected by correlation coefficient analysis； Finally， the signal spectrum is analyzed to determine the fault characteristics. The effectiveness and superiority of the proposed method are verified by the Complex fault signal of simulation signal and gearbox test-bed.

This study presents a competitive failure model considering performance degradation failure and fatigue pitting failure. Considering the relationship among the reliability and structural parameters about diameter of the ball， radius of the raceway， contact angel and friction coefficient etc.， the reliability design model is established， and the reliability quantitative design method is proposed.

There is often a mix of random and interval parameters in the design parameters and boundary conditions of spiral bevel gears. Because the measurement space and properties of the two types of uncertain variables are different， the traditional reliability modeling and analysis methods based on probability theory will no longer be applicable. Therefore， a second-order reliability analysis method for hybrid structural analysis with random and interval variables was presented. The limit state function is approximated at the most probable point（MPP） by using the second-order Taylor series expansion method. On this basis， the polar coordinates are introduced and the n-dimensional limit state function is approximately transformed into a new polar coordinate two-dimensional function. By using the gradient vector of the function instead of the failure domain centroid vector， the polar probability density functions of the random variables and the interval variables are derived in polar space. Based on the second-order moment reliability analysis method， the failure probability interval is deduced by the integration method. Finally， the validity of the proposed method is verified by a structural reliability analysis case for spiral bevel gears of a weapon's comprehensive transmission.

Aiming at the problem of difficult to accurately diagnose axle bearing faults in high-speed train under complex operating conditions， this paper proposes a novel design method named Shuffle-SE neural network unit to address this issue. A lightweight neural network called Shuffle-SENet is developed to diagnose high-speed train axle bearing fault on this foundation. The proposed Shuffle-SENet unit is based on the ShufflNet V2 unit. It carries out local optimization of the network structure while retaining lightweight frame， and further integrates the Squeeze-and-Exception（SE） network structure. The proposed network model reduces the need for complex computations while making network operation more efficient and fault diagnosis accuracy significantly improved. In addition， the influence of the Shuffle-SE unit numbers and reduction dimension coefficient of SE unit on the performance of the proposed model is also analyzed in this paper. The experimental results that the proposed method canbe effectively used for fault diagnosis of axle box bearing of the high-speed train under various complex conditions. Compared with the lightweight network models such as MobileNet V2， Shufflenet V1/V2， ResNets， the proposed method guarantees the high efficiency of network operation and greatly improves the diagnostic accuracy of model fault diagnosis. This paper provides a new solution for deep learning technology to be applied in engineering practice and overcome the limitation of high computer hardware demand。

Performance degradation of machine tools affects machining quality and causes other problems. Machining parameters affect the degradation rate. Since the number of machining parameters is often larger than one， the degradation modelling involves multiple variables. A popular modelling method is regression analysis， which has two drawbacks： （a） the accuracy depends on the chosen mean degradation function， and （b） it does not produce the distribution of time to degradation limit. To address these issues， this paper proposes an equivalent processing time based modelling method. The proposed method views each of machining parameters as a stress， uses the product model to combine the machining parameters into a composite stress， and use an accelerated degradation model to combine the composite stress and actual processing time into an equivalent processing time. In such a way， the multivariable degradation modelling problem is simplified into a univariate degradation modelling problem. A real-world example that deals with tool wear is included to illustrate the superiority of the proposed method.

Deep learning has good diagnostic capabilities and generalization capabilities in fault diagnosis， but most of the work is to directly extract signal feature maps from the convolutional layer so that adjacent signal points are not considered， and different sampling frequencies will also affect feature extraction. Therefore， the M2TF-ResNet algorithm was proposed based on the MTF and ResNet18 algorithm. Many experiments were carried out in Case Western Reserve University （CWRU） bearing dataset. Through the verification， it can adapt to the signal feature extraction under different sampling frequencies and avoid over-fitting training. And compared with other fault diagnosis methods， it has more prominent advantages in the diagnosis rate.