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Assembly variation analysis generally demands probability distributions of variation sources. However, due to small production volume in aircraft manufacturing, especially prototype manufacturing, the probability distributions are hard to obtain, and only the small-sample data of variation sources can be consulted. Thus, this paper aims to propose a variation analysis method driven by small-sample data for compliant aero-structure assembly.

First, a hybrid assembly variation model, integrating rigid effects with flexibility, is constructed based on the homogeneous transformation and elasticity mechanics. Then, the bootstrap approach is introduced to estimate a variation source based on small-sample data. The influences of bootstrap parameters on the estimation accuracy are analyzed to select suitable parameters for acceptable estimation performance. Finally, the process of assembly variation analysis driven by small-sample data is demonstrated.

A variation analysis method driven by small-sample data, considering both rigid effects and flexibility, is proposed for aero-structure assembly. The method provides a good complement to traditional variation analysis methods based on probability distributions of variation sources.

With the proposed method, even if probability distribution information of variation sources cannot be obtained, accurate estimation of the assembly variation could be achieved. The method is well suited for aircraft assembly, especially in the stage of prototype manufacturing.

A variation analysis method driven by small-sample data is proposed for aero-structure assembly, which can be extended to deal with other similar applications.

To solve the problem of simulation evaluation with small samples, a fresh approach of grey estimation is presented based on classical statistical theory and grey system theory. The purpose of this paper is to make full use of the difference of data distribution and avoid the marginal data being ignored.

Based upon the grey distribution characteristics of small sample data, the definition about a new concept of grey relational similarity measure comes into being. At the same time, the concept of sample weight is proposed according to the grey relational similarity measure. Based on the new definition of grey weight, the grey point estimation and grey confidence interval are studied. Then the improved Bootstrap resampling is designed by uniform distribution and randomness as an important supplement of the grey estimation. In addition, the accuracy of grey bilateral and unilateral confidence intervals is introduced by using the new grey relational similarity measure approach.

The new small sample evaluation method can realize the effective expansion and enrichment of data and avoid the excessive concentration of data. This method is an organic fusion of grey estimation and improved Bootstrap method. Several examples are used to demonstrate the feasibility and validity of the proposed methods to illustrate the credibility of some simulation data, which has no need to know the probability distribution of small samples.

This research has completed the combination of grey estimation and improved Bootstrap, which makes more reasonable use of the value of different data than the unimproved method.

With the development of deep learning-based analytical techniques, increased research has focused on fatigue data analysis methods based on deep learning, which are gaining in popularity. However, the application of deep neural networks in the material science domain is mainly inhibited by data availability. In this paper, to overcome the difficulty of multifactor fatigue life prediction with small data sets,

A multiple neural network ensemble (MNNE) is used, and an MNNE with a general and flexible explicit function is developed to accurately quantify the complicated relationships hidden in multivariable data sets. Moreover, a variational autoencoder-based data generator is trained with small sample sets to expand the size of the training data set. A comparative study involving the proposed method and traditional models is performed. In addition, a filtering rule based on the R2 score is proposed and applied in the training process of the MNNE, and this approach has a beneficial effect on the prediction accuracy and generalization ability.

A comparative study involving the proposed method and traditional models is performed. The comparative experiment confirms that the use of hybrid data can improve the accuracy and generalization ability of the deep neural network and that the MNNE outperforms support vector machines, multilayer perceptron and deep neural network models based on the goodness of fit and robustness in the small sample case.

The experimental results imply that the proposed algorithm is a sophisticated and promising multivariate method for predicting the contact fatigue life of a coating when data availability is limited.

A data generated model based on variational autoencoder was used to make up lack of data. An MNNE method was proposed to apply in the small data case of fatigue life prediction.

The purpose of this paper is to introduce error ellipse into the bootstrap method to improve the reliability of small samples and the credibility of the S-N curve.

Based on the bootstrap method and the reliability of the original samples, two error ellipse models are proposed. The error ellipse model reasonably predicts that the discrete law of expanded virtual samples obeys two-dimensional normal distribution.

By comparing parameters obtained by the bootstrap method, improved bootstrap method (normal distribution) and error ellipse methods, it is found that the error ellipse method achieves the expansion of sampling range and shortens the confidence interval, which improves the accuracy of the estimation of parameters with small samples. Through case analysis, it is proved that the tangent error ellipse method is feasible, and the series of S-N curves is reasonable by the tangent error ellipse method.

The error ellipse methods can lay a technical foundation for life prediction of products and have a progressive significance for the quality evaluation of products.

This study aims to achieve long-term prediction on a specific monotonic data series of atmospheric corrosion rate vs time.

This paper presents a new method, used to the collected corrosion data of carbon steel provided by the China Gateway to Corrosion and Protection, that combines non-linear gray Bernoulli model (NGBM(1,1) with genetic algorithm to attain the purpose of this study.

Results of the experiments showed that the present study’s method is more accurate than other algorithms. In particular, the mean absolute percentage error (MAPE) and the root mean square error (RMSE) of the proposed method in data sets are 9.15 per cent and 1.23 µm/a, respectively. Furthermore, this study illustrates that model parameter can be used to evaluate the similarity of curve tendency between two carbon steel data sets.

Corrosion data are part of a typical small-sample data set, and these also belong to a gray system because corrosion has a clear outcome and an uncertainly occurrence mechanism. In this work, a new gray forecast model was proposed to achieve the goal of long-term prediction of carbon steel in China.

The purpose of this paper is to analyze parameters that influence direct maintenance cost (DMC) in the civil aircraft operational phase. Reducing direct maintenance cost of civil aircrafts is one of the important ways to improve economy. DMC prediction can provide decision support for the optimization of the design parameters optimization to realize the objection in decreasing the maintenance cost, and it can also improve the aircraft competitiveness.

The paper analyzes some parameters comprehensively, which influence DMC in the civil aircraft’s operational phase. Based on the analysis of the influential parameters and the characteristics of data in the period of civil aircraft’s designing period, the paper presents prediction support method based on fuzzy support vector machine (FSVM) and realizes quantitative forecast of DMC in the aircraft design phase.

The paper presents the process of DMC analysis and model in the aircraft design phase, the DMC prediction model is used in newly developed aircrafts.

The numerical examples using B737NP fleet data in the paper have proved the effectiveness of the proposed method.

The paper establishes the prediction model of civil aircraft DMC based on FSVM. The model can handle fuzzy data and small sample data which contain noise. The results prove that the method can satisfy the demand of the real data in civil aircraft designing.

Based on climate issues and carbon emissions, this study aims to promote low-carbon consumption and compel consumers to actively shift to energy-saving appliances. In this big data era, online reviews in social and electronic commerce (e-commerce) websites contain valuable product information, which can facilitate firm business strategies and consumer comparison shopping. This study is designed to advance existing research on energy-saving refrigerators by incorporating machine learning models in the analysis of online reviews to provide valuable suggestions to e-commerce platform managers and manufacturers to effectively understand the psychological cognition of consumers.

This study proposes an online e-commerce review mining and management strategy model based on “data acquisition and cleaning, data mining and analysis and strategy formation” through multiple machine learning methods, namely, Bayes networks, support vector machine (SVM), latent Dirichlet allocation (LDA) and importance–performance analysis (IPA), to help managers.

Based on a case study of one of the largest e-commerce platforms in China, this study linguistically analyzes 29,216 online reviews of energy-saving refrigerators. Results indicate that the energy-saving refrigerator features that consumers are generally satisfied with are, in sequential order, logistics, function, price, outlook, after-sales service, brand, quality and space. This study also identifies ten topics with 100 keywords by analyzing 18 different refrigerator models. Finally, based on the IPA, this study allocates different priorities to the features and provides suggestions from the perspective of consumers, the government and manufacturers.

In terms of limitations, future research may focus on the following points. First, the topics identified in this study derive from specific points in time and reviews; thus, the topics may change with the text data. A machine learning-based online review analysis platform could be developed in the future to dynamically improve consumer satisfaction. Moreover, given that consumers' needs may change over time, e-commerce platform types and consumer characteristics, such as user profiles, can be incorporated into the model to effectively analyze trends in consumers' perceived dimensions.

This study fills the gap in previous research in this field, which uses small-sample data for qualitative analysis, while integrating management ideas and proposes an online e-commerce review mining and management strategy model based on machine learning methods. Moreover, this study considers how consumers' emotional and thematic preferences for products affect their purchase decision-making from the perspective of their psychological perception and linguistically analyzes online reviews of energy-saving refrigerators using the proposed mining model. Through the improved IPA model, this study provides optimizing strategies to help e-commerce platform managers and manufacturers.

To improve the accuracy of parameter prediction for small-sample data, considering the existence of error in samples, the error circle is introduced to analyze original samples.

The influence of surface roughness on fatigue life is discussed. The error circle can treat the original samples and extend the single sample, which reduces the influence of the sample error.

The S-N curve obtained by the error circle method is more reliable; the S-N curve of the Bootstrap method is more reliable than that of the Maximum Likelihood Estimation (MLE) method.

The parameter distribution and characteristics are statistically obtained based on the surface roughness, surface roughness factor and intercept constant. The original sample is studied by an error circle and discussed using the Bootstrap and MLE methods to obtain corresponding S-N curves. It provides a more trustworthy basis for predicting the useful life of products.

For the studies whose purposes are to evaluate the relationship between industrial characteristics and innovation activities of the enterprises, there are some limitations in the measures of industrial characteristics and using traditional statistical techniques. The purpose of this paper is to investigate the relationship between industrial characteristics and innovation capabilities within Chinese high-tech industries using grey system theory. The research results show that grey system theory is suitable to investigate the relationship between industrial characteristics and innovation capabilities within Chinese high-tech industries.

This paper proposes the measures of industrial characteristics and innovation capabilities of high-tech enterprises. First, based on the data on Chinese large and medium-sized high-tech enterprises for the period of 2011-2013, this paper applies grey relational analysis to identify the relatively most important indexes on affecting innovation capabilities of Chinese high-tech enterprises. Second, based on the results from grey relational analysis, this study draws a ranking of the five Chinese high-tech industries in terms of innovation capabilities by grey decision making. Finally, based on the results from grey decision making, this study applies GM (0, N) model to investigate the relationship between industrial characteristics and innovation capabilities within Chinese high-tech industries.

The results of this study show that in the evaluation indexes system of innovation capabilities of high-tech enterprises, personnel in R & D institutions, R & D personnel, internal expenditure on R & D, expenditure on new product development, expenditure on technology imports, expenditure on technology renovation, and expenditure on technology assimilation and absorption are relatively most important elements affecting innovation capabilities of Chinese high-tech enterprises. In addition, the two top ranking on innovation capabilities are manufacture of electronic equipment and communication equipment, and manufacture of medicines. At last, the findings indicate that in the measures of industrial characteristics, the three top ranking on affecting innovation capabilities of Chinese high-tech enterprises are R & D intensity, technology absorption intensity of indigenous high-tech enterprises and foreign-invested enterprises size. The opening level is in the middle position. Technology intensity, market concentration, and state-owned enterprises size are the three bottom ranking on affecting innovation capabilities of Chinese high-tech enterprises.

This study has some limitations. First, this study is limited to Chinese high-tech industries. The findings may not be applicable to other countries’ high-tech industries. Further studies with other countries’ high-tech industries could be extended and examined how industrial characteristics affect innovation capabilities of the firms in these industries. Second, the measures of industrial characteristics proposed in this study are somewhat theoretically weak. In the future, the authors will further improve the current analysis, and develop the measures of industrial characteristics. Finally, with the advent of the more data with the consistent statistical coverage released by China’s National Bureau of Statistics during the more continuous years, other methods, such as panel data regression model in econometrics could be used to evaluate the relationship between industrial characteristics and innovation capabilities within Chinese high-tech industries. By then, the scholars can compare the results from grey system theory and those from panel data regression model in econometrics.

Appropriate industrial environment is favorable for Chinese high-tech enterprises to feed their innovation capabilities. Scientific evaluation on the relationship between industrial characteristics and innovation capabilities within Chinese high-tech industries is of great significance for Chinese high-tech enterprises in exerting technological catch-up and promoting their competitive advantage. The purposed measures of industrial characteristics and innovation capabilities of high-tech enterprises in this paper, and combined methodology based on grey system theory could be applied to evaluate the relationship between industrial characteristics and innovation capabilities of Chinese high-tech enterprises.

This paper proposes the measures of industrial characteristics and innovation capabilities of high-tech enterprises, and uses grey system theory to evaluate the relationship between industrial characteristics and innovation capabilities within Chinese high-tech industries.