Online Piecewise Convex-Optimization Interpretable Weight Learning for Machine Life Cycle Performance Assessment.

Machine life cycle performance assessment is of great significance to use a health index to inform the time of incipient fault initiation in a normal stage and realize fault identification and fault trending in a performance degradation stage. However, most existing works consider using unexplainable model parameters and historical data to build models and infer their off-line parameters for machine life cycle performance assessment. To overcome these limitations, an online piecewise convex-optimization interpretable weight learning framework without needing any historical abnormal and faulty data is proposed in this article to generate a piecewise health index to practically implement machine life cycle performance assessment. Firstly, based on a separation criterion, the first submodel in the proposed framework is built to detect the time of incipient fault initiation. Here, the piecewise health index generated by the first submodel is continuously updated by on-line monitoring data to timely detect the occurrence of any abnormal health conditions. Secondly, once the time of incipient fault initiation is informed, online updated model weights are highly correlated with fault characteristic frequencies and informative frequency bands for immediate fault identification. Simultaneously, the second submodel integrated with monotonicity and fitness properties in the proposed framework is triggered to generate the piecewise health index to realize overall monotonic fault trending. The significance of this article is that only online monitoring data are used to continuously update interpretable model weights as fault frequencies and informative frequency bands to generate the proposed piecewise health index so as to practically realize machine life cycle performance assessment. Two run-to-failure cases are studied to show the effectiveness and superiority of the proposed framework.

A Novel Analytical Modeling Approach for Quality Propagation of Transient Analysis of Serial Production Systems.

Production system modeling (PSM) for quality propagation involves mapping the principles between components and systems. While most existing studies focus on the steady-state analysis, the transient quality analysis remains largely unexplored. It is of significance to fully understand quality propagation, especially during transients, to shorten product changeover time, decrease quality loss, and improve quality. In this paper, a novel analytical PSM approach is established based on the Markov model, to explore product quality propagation for transient analysis of serial multi-stage production systems. The cascade property for quality propagation among correlated sequential stages was investigated, taking into account both the status of the current stage and the quality of the outputs from upstream stages. Closed-form formulae to evaluate transient quality performances of multi-stage systems were formulated, including the dynamics of system quality, settling time, and quality loss. An iterative procedure utilizing the aggregation technique is presented to approximate transient quality performance with computational efficiency and high accuracy. Moreover, system theoretic properties of quality measures were analyzed and the quality bottleneck identification method was investigated. In the case study, the modeling error was 0.36% and the calculation could clearly track system dynamics; quality bottleneck was identified to decrease the quality loss and facilitate continuous improvement. The experimental results illustrate the applicability of the proposed PSM approach.

Retraction Note: Modified box dimension and average weighted receiving time on the weighted fractal networks.

This paper has been retracted.

On the Fractality of Complex Networks: Covering Problem, Algorithms and Ahlfors Regularity.

In this paper, we revisit the fractality of complex network by investigating three dimensions with respect to minimum box-covering, minimum ball-covering and average volume of balls. The first two dimensions are calculated through the minimum box-covering problem and minimum ball-covering problem. For minimum ball-covering problem, we prove its NP-completeness and propose several heuristic algorithms on its feasible solution, and we also compare the performance of these algorithms. For the third dimension, we introduce the random ball-volume algorithm. We introduce the notion of Ahlfors regularity of networks and prove that above three dimensions are the same if networks are Ahlfors regular. We also provide a class of networks satisfying Ahlfors regularity.

The entire mean weighted first-passage time on a family of weighted treelike networks.

In this paper, we consider the entire mean weighted first-passage time (EMWFPT) with random walks on a family of weighted treelike networks. The EMWFPT on weighted networks is proposed for the first time in the literatures. The dominating terms of the EMWFPT obtained by the following two methods are coincident. On the one hand, using the construction algorithm, we calculate the receiving and sending times for the central node to obtain the asymptotic behavior of the EMWFPT. On the other hand, applying the relationship equation between the EMWFPT and the average weighted shortest path, we also obtain the asymptotic behavior of the EMWFPT. The obtained results show that the effective resistance is equal to the weighted shortest path between two nodes. And the dominating term of the EMWFPT scales linearly with network size in large network.

Modified box dimension and average weighted receiving time on the weighted fractal networks.

In this paper a family of weighted fractal networks, in which the weights of edges have been assigned to different values with certain scale, are studied. For the case of the weighted fractal networks the definition of modified box dimension is introduced, and a rigorous proof for its existence is given. Then, the modified box dimension depending on the weighted factor and the number of copies is deduced. Assuming that the walker, at each step, starting from its current node, moves uniformly to any of its nearest neighbors. The weighted time for two adjacency nodes is the weight connecting the two nodes. Then the average weighted receiving time (AWRT) is a corresponding definition. The obtained remarkable result displays that in the large network, when the weight factor is larger than the number of copies, the AWRT grows as a power law function of the network order with the exponent, being the reciprocal of modified box dimension. This result shows that the efficiency of the trapping process depends on the modified box dimension: the larger the value of modified box dimension, the more efficient the trapping process is.

A class of scale-free networks with fractal structure based on subshift of finite type.

In this paper, given a time series generated by a certain dynamical system, we construct a new class of scale-free networks with fractal structure based on the subshift of finite type and base graphs. To simplify our model, we suppose the base graphs are bipartite graphs and the subshift has the special form. When embedding our growing network into the plane, we find its image is a graph-directed self-affine fractal, whose Hausdorff dimension is related to the power law exponent of cumulative degree distribution. It is known that a large spectral gap in terms of normalized Laplacian is usually associated with small mixing time, which makes facilitated synchronization and rapid convergence possible. Through an elaborate analysis of our network, we can estimate its Cheeger constant, which controls the spectral gap by Cheeger inequality. As a result of this estimation, when the bipartite base graph is complete, we give a sharp condition to ensure that our networks are well-connected with rapid mixing property.

Random walks on non-homogenous weighted Koch networks.

In this paper, we introduce new models of non-homogenous weighted Koch networks on real traffic systems depending on the three scaling factors r1,r2,r3∈(0,1). Inspired by the definition of the average weighted shortest path (AWSP), we define the average weighted receiving time (AWRT). Assuming that the walker, at each step, starting from its current node, moves uniformly to any of its neighbors, we show that in large network, the AWRT grows as power-law function of the network order with the exponent, represented by θ(r1,r2,r3)=log4(1+r1+r2+r3). Moreover, the AWSP, in the infinite network order limit, only depends on the sum of scaling factors r1,r2,r3.