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Based on the concept of blown‐ups of evolution, introduced by OuYang in 1995, for nonlinear models, the logistic model and its modification of population evolutions are analyzed analytically and numerically. Presents results that imply: (1) There does not exist successive whole evolution of time in both the logistic model and its modifications. (2) The increase or decrease of the population size, caused by unsuccessive evolution, is limited. (3) The discontinuity characteristic realizes the philosophy that “things will develop in the opposite direction when they have reached extremes”. (4) The exponential increase of the population size is a special case, where it is shown that the modified logistic model agrees more with the reality than the original model. At the end, it points out that it is necessary to reconsider the method of reducing the original model into an algebraic equation by changing Δt to a non‐dimensional nonvariable by using difference scheme.

The purpose of this paper is to solve difficult estimation problem on aircraft sudden fault by proposing a new pre-estimating method according to the energy evolution degree of the sensitive parameters to estimate the sudden fault. The sudden fault affects seriously the flight safety of aircraft.

It is based on the dissipative structure theory, and the evolution process of energy parameters is utilized. First, the evolution key points of sudden fault are determined by the time-varying entropy of sensitive parameters and the frequency band energy distribution. Then, we can obtain the evolution degree of sample while the evolution key points import the logistic regression (LR) model, and one can establish the pre-estimation model by means of relevance vector machine (RVM). While the evolution feature vector imports the RVM pre-estimation model, one can pre-estimate the sudden fault of aircraft.

The simulation results showed that this method can not only track the evolution process of aircraft sudden fault but also estimate its evolution degree, and it has a higher pre-estimating accuracy.

It provides a new way to forecast the sudden fault and increase the security of aircraft.

This paper proposes a pre-estimating method on aircraft sudden fault. It is based on the dissipative structure theory and the energy-sensitive parameters of the sudden faults are used. This method can enhance the security of aircraft and increase the protective ability of sudden fault on aircraft.

In this paper, some issues about model formulation and solving methods for the Lorenz’s model are discussed, which also deals with fundamental characteristics of non‐linear models. Mainly, there existed problems that Lorenz’s model was formulated based on the weak nonlinear, and spectral expansion which changed the fundamental properties of prototype of the N‐S equations. Furthermore, its solving methods, which are based on continuously smoothing schemes, not only distorted the fundamental characteristics of non‐linear models, but also led to misunderstanding of the concept of “schaos”, which has already caused confusion to people’s way of thinking. In essence, Lorenz’s chaos is an “error volute” which is trapped into “calculation of error values”. Whether it can be named “chaos” may need to be discussed with questions.

Relationship management evolves with dynamic and complex environments of megaprojects. However, studies on the longitudinal measurement of relationship management performance for each stakeholder in dynamic and complex project environments are lacking. The purpose of this research is to propose an NK-network evolution model to evaluate stakeholder performance on relationship management in the development of megaprojects.

The model input includes the stakeholder-associated issues and stakeholders' relational strategies, the co-effects of which determine the internal effects of relationship management in megaprojects. The model processing simulates the stakeholder performance of relationship management under the dynamic and complex nature of megaprojects. The NK model shows the dynamic stakeholder interactions on relationship management, whereas the network model presents the complex stakeholder structures of the relationships between stakeholders and relevant issues. The model output is the evolution graph to reveal the weak stakeholder performance on relationship management in the timeline of the project duration.

The research finding reveals that all stakeholders experience the plunge of stakeholder performance of relationship management at the decision-making moment of the planning stage. Construction, environmental and pressure groups may experience the hardship of relationship management at the start of the construction stage. The government is likely to suffer difficulties in relationship management in the late construction stage. Local industry groups would face challenges in relationship management in the middle of the construction stage and handover stage.

The research provides a useful approach to measuring weak moments of relationship management for each stakeholder in various project phases, considering the dynamic and complex environments of megaprojects. The proposed model extends the current knowledge body on how to make project stakeholder analysis by modelling dynamic and complex environments of megaprojects, with bridging the knowledge domains of evolution modeling techniques and network methods.

Mega construction projects (MCPs), which play an important role in the economy, society and environment of a country, have developed rapidly in recent years. However, due to frequent social conflicts caused by the negative social impact of MCPs, social risk control has become a major challenge. Exploring the relationship between social risk factors and social risk from the perspective of risk evolution and identifying key factors contribute to social risk control; but few studies have paid enough attention to this. Therefore, this study aims to systematically analyze the impact of social risk factors on social risk based on a social risk evolution path.

This study proposed a social risk evolution path for MCPs explaining how social risk occurs and develops with the impact of social risk factors. To further analyze the impact quantitatively, a social risk analysis model combining structural equation model (SEM) with Bayesian network (BN) was developed. SEM was used to verify the relationship in the social risk evolution path. BN was applied to identify key social risk factors and predict the probabilities of social risk, quantitatively. The feasibility of the proposed model was verified by the case of water conservancy projects.

The results show that negative impact on residents’ living standards, public opinion advantage and emergency management ability were key social risk factors through sensitivity analysis. Then, scenario analysis simulated the risk probability results with the impact of different states of these key factors to obtain management strategies.

This study creatively proposes a social risk evolution path describing the dynamic interaction of the social risk and first applies the hybrid SEM–BN method in the social risk analysis for MCPs to explore effective risk control strategies. This study can facilitate the understanding of social risk from the perspective of risk evolution and provide decision-making support for the government coping with social risk in the implementation of MCPs.

The product family assembly line (PFAL) is a mixed model-assembly line, which is widely used in mass customization and intelligent manufacturing. The purpose of this paper is to study the problem of PFAL, a flexible (evolution) planning method to respond to product evolution for PFAL, to focus on product data analysis and evolution planning method.

The evolution balancing model for PFAL is established and an improved NSGA_II (INSGA_II) is proposed. From the perspective of data analysis, dynamic characteristics of PFAL are researched and analyzed. Especially the tasks, which stability is considered, can be divided into a platform and individual task. In INSGA_II algorithm, a new density selection and a decoding method based on sorting algorithms are proposed to compensate for the lack of traditional algorithms.

The effectiveness and feasibility of the method are validated by an example of PFAL evolution planning for a family of similar mechanical products. The optimized efficiency is significantly improved using INSGA_II proposed in this paper and the evolution planning model proposed has a stronger ability to respond to product evolution, which maximizes business performance over an effective period of time.

The assembly line designers and managers in discrete manufacturing companies can obtain an optimal solution for PFAL planning through the evolution planning model and INSGA-II proposed in this paper. Then, this planning model and optimization method have been successfully applied in the production of small wheel loaders.

In this “Info-plosion” era, recommendation systems (or recommenders) play a significant role in finding interesting items in the surge of online digital activity and e-commerce. The purpose of this paper is to model users' preference evolution to recommend potential items which users may be interested in.

A novel recommendation system, namely evolution-learning recommendation (ELR), is developed to precisely predict user interest for making recommendations. Differing from prior related methods, the authors integrate the matrix factorization (MF) and recurrent neural network (RNN) to effectively describe the variation of user preferences over time.

A novel cumulative factorization technique is proposed to efficiently decompose a rating matrix for discovering latent user preferences. Compared to traditional MF-based methods, the cumulative MF could reduce the utilization of computation resources. Furthermore, the authors depict the significance of long- and short-term effects in the memory cell of RNN for evolution patterns. With the context awareness, a learning model, V-LSTM, is developed to dynamically capture the evolution pattern of user interests. By using a well-trained learning model, the authors predict future user preferences and recommend related items.

Based on the relations among users and items for recommendation, the authors introduce a novel concept, virtual communication, to effectively learn and estimate the correlation among users and items. By incorporating the discovered latent features of users and items in an evolved manner, the proposed ELR model could promote “right” things to “right” users at the “right” time. In addition, several extensive experiments are performed on real datasets and are discussed. Empirical results show that ELR significantly outperforms the prior recommendation models. The proposed ELR exhibits great generalization and robustness in real datasets, including e-commerce, industrial retail and streaming service, with all discussed metrics.

While still arguing whether a quasi‐linear equation has a “stability” problem in integration, comparative analyses are made by numerical experimentations using conservation with smoothing and non‐conservation schemes as well as a time‐moving treatment scheme proposed by the first author respectively. The results show that the solution seeking method of the quasi‐linear model should not be considered as a “stability” problem. The traditional well‐posed computational model needs to be improved. The Lorenz’s “butterfly effect” should be in nature a Richardson’s explosive increase in time evolution of moving fluid.

The numerical simulation of dispersed-phase evolution in injection molding process of polymer blends is of great significance in both adjusting material microstructure and improving performances of the final products. This paper aims to present a numerical strategy for the simulation of dispersed-phase evolution for immiscible polymer blends in injection molding.

First, the dispersed-phase modeling is discussed in detail. Then the Maffettone–Minale model, affine deformation model, breakup model and coalescence statistical model are chosen for the dispersed-phase evolution. A general coupled model of microscopic morphological evolution and macroscopic flow field is constructed. Besides, a stable finite element simulation strategy based on pressure-stabilizing/Petrov–Galerkin/streamline-upwind/Petrov–Galerkin method is adopted for both scales.

Finally, the simulation results are compared and evaluated with the experimental data, suggesting the reliability of the presented numerical strategy.

The coupled modeling of dispersed-phase and complex flow field during injection molding and the tracing and simulation of droplet evolution during the whole process can be achieved.

The purpose of this paper is to build a symbiotic evolution model to analyze the symbiotic modes and dynamic equilibrium of mobile internet platform innovation ecosystem (MIPIE) in order to explore its evolutionary path.

From a symbiosis theory perspective, the authors studied the dynamic evolution stages and symbiotic mode of MIPIE. By adopting logistic model, the symbiotic evolution model of MIPIE is established. After calculating the steady conditions and equilibrium point of this model, numerical simulation was done with MATLAB software to illustrate the impact of symbiotic parameters on evolution path in this ecosystem.

The symbiotic evolution mode of MIPIE experienced parasitism, commensalism to asymmetric mutualism, and symmetry mutualism or independence. In given conditions, the dynamic evolution of MIPIE eventually tends to a steady equilibrium point. The evolutionary consequence of innovative subjects is not only determined by the natural growth rate, but symbiotic modes can also affect the evolutionary path. Different symbiotic modes result in different evolutionary paths.

Improved understanding of symbiosis in MIPIE could help policy makers to promote value co-creation and dynamic interests balance while facilitating the cooperation of others for successful platform ecosystem management.

The logistic model introduced here bridge theory and practice while establishing a stronger link between symbiosis theory and platform ecosystem management.