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• Average convergence rate measures the convergence speed of evolutionary algorithms by the geometric average of the reduction rate of the approximation error over consecutive generations. • Evolutionary programming with landscape-invariant or zero landscape-adaptive mutation converges slowly, while that with positive landscape-adaptive mutation converges fast. • Average convergence rate are classified into two types: polynomial or exponential as a function of the decision space dimension. The average convergence rate (ACR) measures how fast the approximation error of an evolutionary algorithm converges to zero per generation. It is defined as the geometric average of the reduction rate of the approximation error over consecutive generations. This paper makes a theoretical analysis of the ACR in continuous optimization. The obtained results are summarized as follows. According to the limit property, the ACR is classified into two categories: (1) linear ACR whose limit inferior value is larger than a positive and (2) sublinear ACR whose value converges to zero. Then, it is proven that the ACR is linear for evolutionary programming using positive landscape-adaptive mutation, but sublinear for that using landscape-invariant or zero landscape-adaptive mutation. The relationship between the ACR and the decision space dimension is also classified into two categories: (1) polynomial ACR whose value is larger than the reciprocal of a polynomial function of the dimension for any generation, and (2) exponential ACR whose value is less than the reciprocal of an exponential function of the dimension for an exponential long period. It is proven that for easy problems such as linear functions, the ACR of the (1 + 1) adaptive random univariate search is polynomial. But for hard functions such as the deceptive function, the ACR of both the (1 + 1) adaptive random univariate search and evolutionary programming is exponential. [ABSTRACT FROM AUTHOR]

Modelling heat conduction is of significant importance for evaluating temperature effects of granular materials. Since the randomness of the grain structure and the heat resistance characteristics of grain interfaces, to realistically modelling the heat conduction of granular materials, the heat interactive among these random-shaped grains should be correctly reflected. In this study, the numerical manifold method (NMM) is extended to model the transient heat conduction of granular materials. The random-shaped grain structure of granular materials is represented with Voronoi polygons. The heat interactive among grains is realistically simulated by inserting heat conductive cohesive elements between grain boundaries. Besides, an interfacial heat conductivity is defined for the cohesive element to better represent the heat conduct capacity of grain interfaces. As a result, the temperature jumps at grain interfaces are naturally captured due to the dual cover systems of the NMM, while the heat fluxes across the interfaces are assumed to be continuous. To validate the developed numerical method, a benchmark test is carried out. At last, effects of the grain characteristics and interfacial heat resistance on the temperature field as well as the effective heat conductivity (EHC) of a plane consists of granular material are investigated by the developed NMM. [ABSTRACT FROM AUTHOR]

In order to gain an insight into creep induced cracking in viscoelastic materials, the creep crack phenomenon in viscoelastic materials are numerically investigated in this paper based on the numerical manifold method (NMM). To more realistically capture the mechanical behaviour in the vicinity of crack tips, the local displacements around crack tips are enriched with the viscoelastic crack-tip asymptotic displacement field. To better represent the viscoelastic materials, an incremental viscoelastic constitutive law based on the generalized Kelvin-Voigt model is incorporated into the NMM. To achieve these treatments in the NMM, an incremental viscoelastic NMM formulation is derived. In addition, an incremental formulation of the mixed mode viscoelastic energy release rate (ERR), which can be tackled in the same process with the incremental viscoelastic constitutive law, is derived and incorporated into the NMM for investigating the variations of the ERR in viscoelastic materials. Based on the developed method, three creep crack problems with different loading conditions and pre-existing crack configurations are simulated, and the crack opening and sliding displacements as well as corresponding mixed mode ERR are analysed. Simulation results show good agreement with the theoretical solutions, which indicate that the proposed NMM is suitable for complex creep crack problems. [ABSTRACT FROM AUTHOR]

Theoretical prediction of classical evolutionary games shows that public goods is contributed either by strong players in asymmetric games or by all of the involved players in symmetric games. However, it is inconsistency with experimental observations that weak players could also contribute to public goods in real cooperation systems. To reconciling these conflicts, we here study an evolutionary volunteer's dilemma game by assuming different roles can be interchangeable. In this model, not only the existence of multiple equilibria is possible but also the evolutionary result of the system depends on initial conditions, which can be interpreted as the production modes of public goods under different circumstances. Specifically, we found that the survival of strong individuals with mixed strategies is associated with two different outcomes: one is similar to Selten's model, that is, public goods are produced by strong players if the defectors are weak players and strong defectors are scarce in the initial condition; and the other is that the weak individuals with mixed strategies produce public goods if the defectors are strong individuals, where the strong cooperators are absent in the initial condition. Moreover, the weak individuals with mixed strategies produce public goods while strong individuals mainly display defection if the cooperation of strong players is absent in the initial condition. Our main results may help to explain the emergence of diverse forms of cooperation in asymmetric evolutionary games. • The results of both symmetric and asymmetric game models are combined. • An asymmetric volunteer's dilemma game with four strategy types is developed. • Theoretical explanations for strategy diversification of the reality of cooperation systems are provided. [ABSTRACT FROM AUTHOR]

In the classical numerical manifold method (NMM), contact conditions are enforced by applying or releasing contact springs repeatedly. Penalty spring stiffness is constant during the calculation process. In this study, a modified contact model describing joint mechanical behavior is proposed using the NMM. Two rock joint constitutive models, namely the BB model and hyperbolic model, are used to modify normal and shear stiffness, respectively. In the modified contact model, stiffness varies with normal and shear inter-penetration distance in each iteration step. Therefore, stiffness varies for different contact points. With increasing inter-penetration distance, the normal stiffness increases and shear stiffness decreases. As a result, the force needed for trigger sliding along the joint increased. Finally, three example simulations are conducted to validate the effectiveness of the modified contact model. [ABSTRACT FROM AUTHOR]

As is well known, the vortex beams have significant potential applications in both quantum and classical communication systems. In this paper, we study the existence and robustness to propagation of families of multi-vortex waveforms, namely multi-vortex optical beams in nonlinear self-focusing cubic (Kerr) media with harmonic potential wells. The intensity patterns, phase structures, transverse energy flow, and gradient forces (upon micro-particles) of those multi-vortex beams are presented and we found that they are all different from those of the ordinary vortex beams. The evolution during propagation of the intensities and widths of the multi-vortex beams is investigated in detail. The obtained results show that the one-vortex beams have asymmetric patterns and spiral propagation trajectories, depending on the off-axis parameter of the vortices. The two-vortex beams and the higher than two-vortex waveforms have symmetric patterns, which rotate during propagation, and the rotation direction can be controlled by the sign of the topological charge. [ABSTRACT FROM AUTHOR]

Multi-label learning deals with the problem that each instance is associated with multiple labels simultaneously. Most of the existing approaches aim to improve the performance of multi-label learning by exploiting label correlations. Although the data augmentation technique is widely used in many machine learning tasks, it is still unclear whether data augmentation is helpful to multi-label learning. In this article, we propose to leverage the data augmentation technique to improve the performance of multi-label learning. Specifically, we first propose a novel data augmentation approach that performs clustering on the real examples and treats the cluster centers as virtual examples, and these virtual examples naturally embody the local label correlations and label importances. Then, motivated by the cluster assumption that examples in the same cluster should have the same label, we propose a novel regularization term to bridge the gap between the real examples and virtual examples, which can promote the local smoothness of the learning function. Extensive experimental results on a number of real-world multi-label datasets clearly demonstrate that our proposed approach outperforms the state-of-the-art counterparts. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is to assess the water resources vulnerability (WRV) rationally in Haihe River Basin (HRB) using set pair analysis (SPA) theory. Design/methodology/approach – An improved intelligent set pair analysis (IISPA) model is established, in which intelligent SPA theory is introduced and the weights are determined by use of the maximum entropy principle and the improved analytic hierarchy process method. The index systems and criteria of WRV assessment in terms of water cycle, socio-economy, and ecological environment are established based on the analysis of sensibility and adaptability. Findings – The authors apply IISPA to the WRV assessment of seven administrative divisions in HRB. Results show IISPA can fully take advantage of certain and uncertain information compared with fuzzy assessment and topsis assessment models. For present situation, Shanxi, Shandong, Tianjing, Inner Mongolia, Hebei are higher, Henan and Beijing are the middle vulnerability. But Henan will become worse under climate change scenario II and IV. Research limitations/implications – The analysis results may be affected by the limited climate change data. Practical implications – It is helpful for further research to the complexity analysis of water resources system. Social implications – This paper will have an important impact on water resources sustainable utilization. Originality/value – This is the first time to utilize IISPA method to analyze the WRV of seven administrative divisions in HRB. This paper provides an important theoretical support for water resources management. [ABSTRACT FROM AUTHOR]

Grouting is a typical HM (hydro-mechanical) coupling process between slurry and rock and widely used in underground engineering to reinforce the strength of fractured rock mass. In present work, based on numerical manifold method (NMM), an NMM-HM grouting model is proposed to investigate slurry flowing and analyze grouting efficiency. In this NMM-HM grouting model, the slurry flows in fractures and grouting pressure can cause fracture aperture variation and fracture propagation. Then, two numerical examples for central embedded crack and hydraulic fracturing are adopted to validate the presented model. Furthermore, grouting simulations are conducted on a multi-crack and a roadway with fracture networks. Results show that Grouting pressure in fractures can increase fracture aperture, which is beneficial for grouting efficiency. However, fluid pressure could also cause closure of neighboring fractures or even fracture propagation and failure of rock mass, which will weaken grouting effectiveness. Therefore, the coupled HM impacts on grouting efficiency and grouting pressure should be seriously considered and optimized to achieve the expected grouting performance in practice. [ABSTRACT FROM AUTHOR]

Grouting is a commonly used technique in rock engineering to enhance the joint strength and improve the stability of surrounding rock. Grout penetration characteristic is controlled by grouting parameters and has a significant role on practice. In the study, a numerical manifold method (NMM) for grout penetration process simulation in fractured rock mass is firstly proposed. The fluid flow behaviour of the grout is assumed to be a Bingham fluid and control equations are established using discrete fracture network model. The global discretization equation, element sub-matrixes and NMM simulation algorithm for grouting are presented. Then, numerical tests for grouting process in a single fracture and a regular fracture network are conducted firstly to verify the proposed NMM grouting model by comparing with analytical solutions and experimental results. Furthermore, the effects of mesh size, fracture and slurry parameters on the grouting performance are systematically investigated using a random fracture network example. The numerical results indicate that the grouted zone and propagation depth decrease as the mesh size of numerical model and yield strength increases, while it increases as initial fracture aperture and grouting pressure increases. [ABSTRACT FROM AUTHOR]

Abstract The geothermal production from enhance geothermal system (EGS) involves complex thermal–hydraulic (TH) coupling process, which may affect the production efficiency and performance of EGS reservoir. In the study, a numerical manifold method (NMM) for TH coupling in fractured EGS is proposed. The EGS reservoir is considered to be formed from intact rock matrix blocks and discrete fractures networks. TH coupling control equations are firstly established using discrete fracture networks model. Then, the weight residual method was used to establish the discretized governing equation for transient heat conduction. Furthermore, the element sub-matrixes for heat conduction were presented. NMM approach simulating the fluid flow, heat conduction in fracture and rock matrix and TH coupling process was established. Finally, a single fracture heat extraction example was used to validate the effectiveness of the proposed method for solving a simplified TH coupling problem. Furthermore, a 2D fracture networks case was conducted to predict the performance of an EGS reservoir. The results in here validate the capability and accuracy of the proposed method and extend the application of NMM. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is to simulate and analyze accurately the multi-scale characteristics, variation periods and trends of the annual streamflow series in the Haihe River Basin (HRB) using the Hilbert-Huang Transform (HHT). Design/methodology/approach – The Empirical Mode Decomposition (EMD) approach is adopted to decompose the original signal into intrinsic mode functions (IMFs) in multi-scales. The Hilbert spectrum is applied to each IMF component and the localized time-frequency-energy distribution. The monotonic residues obtained by EMD can be treated as the trend of the original sequence. Findings – The authors apply HHT to 14 hydrological stations in the HRB. The annual streamflow series are decomposed into four IMFs and a residual component, which exhibits the multi-scale characteristics. After the Hilbert transform, the instantaneous frequency, center frequency and mean period of the IMFs are obtained. Common multi-scale periods of the 14 series exist, e.g. 3.3a, 4∼7a, 8∼10a, 11-14a, 24∼25a and 43∼45a. The residues indicate that the annual streamflow series has exhibited a decreasing trend over the past 50 years. Research limitations/implications – The HHT method is still in its early stages of application in hydrology and needs to be further tested. Practical implications – It is helpful for the study of the complex features of streamflow. Social implications – This paper will contribute to the sustainable utilization of water resources. Originality/value – This study represents the first use of the HHT method to analyze the multi-scale characteristics of the streamflow series in the HRB. This paper provides an important theoretical support for water resources management. [ABSTRACT FROM AUTHOR]