Determine OWA operator weights using kernel density estimation

Some subjective methods should divide input values into local clusters before determining the ordered weighted averaging (OWA) operator weights based on the data distribution characteristics of input values. However, the process of clustering input values is complex. In this paper, a novel probability density based OWA (PDOWA) operator is put forward based on the data distribution characteristics of input values. To capture the local cluster structures of input values, the kernel density estimation (KDE) is used to estimate the probability density function (PDF), which fits to the input values. The derived PDF contains the density information of input values, which reflects the importance of input values. Therefore, the input values with high probability densities (PDs) should be assigned with large weights, while the ones with low PDs should be assigned with small weights. Afterwards, the desirable properties of the proposed PDOWA operator are investigated. Finally, the proposed PDOWA operator is applied to handle the multicriteria decision making problem concerning the evaluation of smart phones and it is compared with some existing OWA operators. The comparative analysis shows that the proposed PDOWA operator is simpler and more efficient than the existing OWA operator

Estimator-based adaptive neural network control of leader-follower high-order nonlinear multiagent systems with actuator faults

The problem of distributed cooperative control for networked multiagent systems is investigated in this paper. Each agent is modeled as an uncertain nonlinear high-order system incorporating with model uncertainty, unknown external disturbance, and actuator fault. The communication network between followers can be an undirected or a directed graph, and only some of the follower agents can obtain the commands from the leader. To develop the distributed cooperative control algorithm, a prefilter is designed, which can derive the state-space representation to a newly constructed plant. Then, a set of distributed adaptive neural network controllers are designed by making certain modifications on traditional backstepping techniques with the aid of adaptive control, neural network control, and a second-order sliding mode estimator. Rigorous proving procedures are provided,which show that uniform ultimate boundedness of all the tracking errors can be achieved in a networked multiagent system. Finally, a numerical simulation is carried out to evaluate the theoretical results

Biaxial creep test study on the influence of structural anisotropy on rheological behaviour of hard rock

Rheological characteristics are one of most important properties needed to be considered for the designing and construction for the long term stability and serviceability of underground structures in the rock mass. Up to date, although extensive studies on the rheological properties of rocks are available in the literature, most of existing studies reported the strain-time data for the axial deformation through compression rheological method and did not mention the lateral deformation, and mainly focused on the soft rocks at shallow depth. Thus, very limited attention has been paid to the rheological properties of deep and hard rock, neglecting the effects of structural anisotropy on the rheological properties. This paper presents a comprehensive in-depth study on the rheological behaviours of super-deep hard rock considering the effects of structural anisotropy by using the uniaxial and biaxial creep tests. The results revealed that significant creep behaviour can be observed in the hard rock specimens under high stress in the in-situ conditions, and the strain-time behaviour of hard rock exhibited brittle failure. The strain-time curves of hard rock exhibited two obvious phases of instantaneous creep and steady state creep without the phase of accelerated creep. Moreover, it was observed that the rheological behaviours, including the instantaneous modulus, transient creep duration, axial and lateral creep deformations, steady state creep rate, volumetric strain and contraction ratio are strongly affected by the structural anisotropy. Based on the experimental data, empirical models of the parameters governing creep behaviour have been established