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The purpose of this paper is to reveal the changing role of the parameters of the DDGM(1,1) model after multiple transformations in the modeling sequence.

This paper considers DDGM(1,1) model as the research object, adopts the parameter packet technique to analyze the influence of multiple transformations on the modeling accuracy of this model and discusses the quantitative relation of model parameters as multiple transformations in system’s characteristic sequences.

The results of numerical calculation show that the modeling accuracy of DDGM(1,1) model is not affected by multiple transformations in the characteristics sequence of systems.

The paper succeeds in realizing the properties of DDGM(1,1) model by using the method of multiple transformations, which is helpful to understand the modeling mechanism and expand the application range of DDGM(1,1) model.

The study aims to examine the effect of inclusions and inherent microstructure on fatigue behavior of 34Cr2Ni2Mo steel.

Fatigue behavior of 34Cr2Ni2Mo steel was investigated for up to 1E10 cycles.

Results showed that both inclusion and inherent microstructure have an influence on the crack initiation mechanism. Fatigue cracks mostly initiated from inclusions, whereas substrate-induced crack initiations were also observed. Fatigue life of inclusion-induced failures is mostly determined by the location of inclusions rather than the loading stress. The inherent microstructure seems to tolerate inclusions at a lower stress level in very high-cycle regime owing to the absence of internal inclusion-induced failure. For the substrate-induced crack initiations, high-density dislocations are found to be accumulated around the carbide particle-matrix interface, which may be the cause of crack initiation in the inherent structure due to strain localization.

The effect of inclusions and inherent microstructure on fatigue behavior of 34Cr2Ni2Mo steel up to 1E10 cycles.

Highlights

• Fatigue failure occurs even at a lifetime of 5.76E9 cycles.

• Surface inclusion induced premature failures.

• Inherent microstructure tolerates inclusions at lower stress level.

• Internal carbides promote substrate-induced crack initiations.

Fatigue failure occurs even at a lifetime of 5.76E9 cycles.

Surface inclusion induced premature failures.

Inherent microstructure tolerates inclusions at lower stress level.

Internal carbides promote substrate-induced crack initiations.

The equipment manufacturing industry, as a strategic industry of China, is experiencing a transition from imitative innovation to independent innovation. The achievements of independent innovation have not been as good as could have been expected. Based on evolutionary economics, the purpose of this paper is to explore the evolutionary path of the two innovation modes, respectively, and analyze the internal and external factors that hinder the mutation from imitative innovation routine to independent innovation routine. According to the results of the evolutionary game model, several policy suggestions are proposed to promote the transition from imitative innovation to independent innovation.

This paper is based on the concepts of evolutionary economics. Routine, mutation, path dependence and selection are included in the analysis of the evolutionary path of the two innovation modes. Especially, the evolutionary game model of innovation modes selection is established to explain how internal and external conditions work in the transition.

The paper explores the evolutionary path of the transition from imitative innovation to independent innovation in the equipment manufacturing industry of China, and analyses the obstacles and factors (internal path dependence, and the lack of benefit incentive and external mutation conditions such as fiscal support and intellectual property protection) that hinder the mutation from imitative innovation routine to independent innovation routine. The results of the evolutionary game model show that the pursuit of the benefit (innovation return or the profit), as an internal mutation condition, is the most fundamental motivation for independent innovation, while policy incentives, as the external mutation conditions, have a significant impact on the evolutionary transition. According to the results, several policy suggestions are proposed to promote the transition from imitative innovation to independent innovation.

Taking the equipment manufacturing industry as a particular object, this paper tries to explain the evolutionary path and the obstacle factors of the transition from imitative innovation to independent innovation from the perspective of evolutionary economics, involving routine, mutation, path dependence, selection, and so on. The evolutionary game model of innovation modes selection is established to investigate the influence of these factors.

The purpose of this paper is to study the properties of the NGM (1,1,k) prediction model with multiplication transformation and reduce its modeling complexity.

The authors improved this model by putting forward a formula to solve its parameters, building an algorithm for optimizing the NGM (1,1,k) model in terms of the least modeling error and designing a key technology for the implementation of this algorithm. The optimized NGM (1,1,k) model is built accordingly. The parameter characteristics of the two models under multiple transformations and its effect of the simulation value and forecasting value are analyzed by studying the properties of multiple transformation of the two models.

The research finding shows that the modeling accuracies of the NGM (1,1,k) model and the optimized NGM (1,1,k) model are all in no relation to multiple transformations.

The above results imply that the data level can be reduced; the process of building the NGM (1,1,k) model and the optimized NGM (1,1,k) model can be simplified; but the simulative and predictive accuracy of the two models remain unchanged.

The paper succeeds in realising the properties of NGM (1,1,k) model and the optimized NGM (1,1,k) model by using the method of multiplication transformation, which is helpful for understanding the modeling mechanism and expanding the application range of the NGM (1,1,k) model.

The purpose of this paper is to study the properties of derived grey verhulst prediction model with multiplication transformation and reduce its modeling complexity.

The paper discussed the parameter characteristics of grey derived verhulst model under multiple transformation, and demonstrated its effect on its simulative value and predictive value by investigating the multiple transformation acting on the raw data sequence of this grey model. The parameter characteristics of this model under multiple transformations and its effect of the simulation value and forecasting value are analyzed by studying the properties of multiply transformation of this model.

The research finding shows that the modeling accuracy of derived grey verhulst model is in no relation to multiple transformations.

The above results imply that the data level can be reduced; the process of building derived grey verhulst model can be simplified; but the simulative and predictive accuracy of this model remain unchanged.

The paper succeeds in realising the properties of derived grey verhulst model by using the method of multiplication transformation, which is helpful to understand the modeling mechanism and expand the application range of derived grey verhulst model.

The purpose of this paper is to summarize the progress in grey system research during 2000-2015, so as to present some important new concepts, models, methods and a new framework of grey system theory.

The new thinking, new models and new methods of grey system theory and their applications are presented in this paper. It includes algorithm rules of grey numbers based on the “kernel” and the degree of greyness of grey numbers, the concept of general grey numbers, the synthesis axiom of degree of greyness of grey numbers and their operations; the general form of buffer operators of grey sequence operators; the four basic models of grey model GM(1,1), such as even GM, original difference GM, even difference GM, discrete GM and the suitable sequence type of each basic model, and suitable range of most used grey forecasting models; the similarity degree of grey incidences, the closeness degree of grey incidences and the three-dimensional absolute degree of grey incidence of grey incidence analysis models; the grey cluster model based on center-point and end-point mixed triangular whitenization functions; the multi-attribute intelligent grey target decision model, the two stages decision model with grey synthetic measure of grey decision models; grey game models, grey input-output models of grey combined models; and the problems of robust stability for grey stochastic time-delay systems of neutral type, distributed-delay type and neutral distributed-delay type of grey control, etc. And the new framework of grey system theory is given as well.

The problems which remain for further studying are discussed at the end of each section. The reader could know the general picture of research and developing trend of grey system theory from this paper.

A lot of successful practical applications of the new models to solve various problems have been found in many different areas of natural science, social science and engineering, including spaceflight, civil aviation, information, metallurgy, machinery, petroleum, chemical industry, electrical power, electronics, light industries, energy resources, transportation, medicine, health, agriculture, forestry, geography, hydrology, seismology, meteorology, environment protection, architecture, behavioral science, management science, law, education, military science, etc. These practical applications have brought forward definite and noticeable social and economic benefits. It demonstrates a wide range of applicability of grey system theory, especially in the situation where the available information is incomplete and the collected data are inaccurate.

The reader is given a general picture of grey systems theory as a new model system and a new framework for studying problems where partial information is known; especially for uncertain systems with few data points and poor information. The problems remaining for further studying are identified at the end of each section.

The purpose of this paper is to introduce the special issue on innovation and education towards innovation in China.

The Guest Editors discuss the impetus behind the special issue and describe the papers published in it.

It is evident in the papers presented in this special issue that China is on its way towards becoming world‐class in a number of technological areas.

The paper introduces the special issue on innovation and education towards innovation in China, as well as an agenda for future research in the area.

The purpose of this paper is to review systematically the research of grey relation analysis (GRA) models.

Three different approaches, the springboard to build a GRA model, the angle of view in modelling, and the dimension of objects, are analysed, respectively.

The GRA models developed from the models based on relation coefficients of each point in the sequences in early days to the generalized GRA models based on integral or overall perspective. It evolved from the GRA models which measure similarity based on nearness, into the models which consider similarity and nearness, respectively. The objects of the research advanced from the analysis of relationship among curves to that among curved surfaces, and further to the analysis of relationship in three‐dimensional space and even the relationship among super surfaces in n‐dimensional space.

The further research on GRA models is proposed. One is about the property of GRA model. An in‐depth knowledge about the properties of GRA model will help people to understand its function, applicable area and requirements for modelling. The other one is about the extension of research object system. The object to be analysed should be extended from the common sequence of real numbers to grey numbers, vectors, matrices, and even multi‐dimensional matrices, etc.