Robustness of Hopfield Neural Networks Described by Differential Algebraic Systems of Index-1 under the Conditions of Deviation Argument and Stochastic Disturbance

Robustness refers to the ability of a system to maintain its original state under a continuous disturbance conditions. The deviation argument (DA) and stochastic disturbances (SDs) are enough to disrupt a system and keep it off course. Therefore, it is of great significance to explore the interval length of the deviation function and the intensity of noise to make a system remain exponentially stable. In this paper, the robust stability of Hopfield neural network (VPHNN) models based on differential algebraic systems (DAS) is studied for the first time. By using integral inequalities, expectation inequalities, and the basic control theory method, the upper bound of the interval of the deviation function and the noise intensity are found, and the system is guaranteed to remain exponentially stable under these disturbances. It is shown that as long as the deviation and disturbance of a system are within a certain range, there will be no unstable consequences. Finally, several simulation examples are used to verify the effectiveness of the approach and are described below.

Multiple Attribute Decision-Making Model for Supplier Selection in Service-Oriented Manufacturing Paradigm

This paper proposes a multiattribute decision-making model for supplier selection under the service-oriented manufacturing, which can be used to effectively evaluate each candidate supplier. The supplier selection index system under the service-oriented manufacturing is proposed, and the interval evaluation matrix is established. In view of the mixed attribute of evaluation index, we construct a method that converts mixed attribute value to interval number. In order to avoid the subjectivity of the weight and make alternatives be provided with more discrimination, we use a combination model based on the deviation function model and the interval relative entropy ranking method to evaluate each candidate supplier. Finally, an application example is given to verify the correctness and practicability of the proposed decision-making model.

An assembly deviation calculation method based on surface deviation modeling for circumferential grinding plane

Performance of mechanical product is highly influenced by assembly deviation. Due to manufacturing errors, the real part surface is machined with morphology deviations, which would cause mating surface deviating from ideal position in assembly behavior, consequently leading to assembly deviation. Meanwhile, the random variation of relative position and orientation between two non-ideal parts also affects the assembly deviation. To efficiently obtain the maximum assembly deviation considering the comprehensive influence of two factors above for circumferential grinding plane, an assembly deviation calculation method based on surface deviation modeling is proposed in this paper. In this method, morphology deviations models of part surfaces are firstly established from the deviation function. The randomness of two factors are represented by a multivariate group with randomness containing deviation function coefficients and three deflected parameters. Then based on surface deviation modeling method, differential evolution algorithm is applied to search the maximum assembly deviation, which involves the construction of fitness function by implementing optimized progressive contact method and iterative operations of mutation, crossover and selection. Finally, the effectiveness of this method is illustrated by an assembly in the end.

A Photovoltaic Array Fault Diagnosis Method Considering the Photovoltaic Output Deviation Characteristics

There are a large number of photovoltaic (PV) arrays in large-scale PV power plants or regional distributed PV power plants, and the output of different arrays fluctuates with the external conditions. The deviation and evolution information of the array output are easily covered by the random fluctuations of the PV output, which makes the fault diagnosis of PV arrays difficult. In this paper, a fault diagnosis method based on the deviation characteristics of the PV array output is proposed. Based on the current of the PV array on the DC (direct current) side, the deviation characteristics of the PV array output under different arrays and time series are analyzed. Then, the deviation function is constructed to evaluate the output deviation of the PV array. Finally, the fault diagnosis of a PV array is realized by using the probabilistic neural network (PNN), and the effectiveness of the proposed method is verified. The main contributions of this paper are to propose the deviation function that can extract the fault characteristics of PV array and the fault diagnosis method just using the array current which can be easily applied in the PV plant.

Quantum spin probabilities at positive temperature are Hölder Gibbs probabilities

We consider the KMS state associated to the Hamiltonian [Formula: see text] over the quantum spin lattice [Formula: see text] For a fixed observable of the form [Formula: see text] where [Formula: see text] is self-adjoint, and for positive temperature [Formula: see text] one can get a naturally defined stationary probability [Formula: see text] on the Bernoulli space [Formula: see text]. The Jacobian of [Formula: see text] can be expressed via a certain continued fraction expansion. We will show that this probability is a Gibbs probability for a Hölder potential. Therefore, this probability is mixing for the shift map. For such probability [Formula: see text] we will show the explicit deviation function for a certain class of functions. When decreasing temperature we will be able to exhibit the explicit transition value [Formula: see text] where the set of values of the Jacobian of the Gibbs probability [Formula: see text] changes from being a Cantor set to being an interval. We also present some properties for quantum spin probabilities at zero temperature (for instance, the explicit value of the entropy).