Quantifying the Robustness of Complex Networks with Heterogeneous Nodes

The robustness of a complex network measures its ability to withstand random or targeted attacks. Most network robustness measures operate under the assumption that the nodes in a network are homogeneous and abstract. However, most real-world networks consist of nodes that are heterogeneous in nature. In this work, we propose a robustness measure called fitness-incorporated average network efficiency, that attempts to capture the heterogeneity of nodes using the `fitness’ of nodes in measuring the robustness of a network. Further, we adopt the same measure to compare the robustness of networks with heterogeneous nodes under varying topologies, such as the scale-free topology or the Erdős–Rényi random topology. We apply the proposed robustness measure using a wireless sensor network simulator to show that it can be effectively used to measure the robustness of a network using a topological approach. We also apply the proposed robustness measure to two real-world networks; namely the CO2 exchange network and an air traffic network. We conclude that with the proposed measure, not only the topological structure, but also the fitness function and the fitness distribution among nodes, should be considered in evaluating the robustness of a complex network.

Modified, Reliability-Based Robust Geotechnical Design Method, in Accordance with Eurocode 7

In this paper a modification of the reliability-based robust geotechnical design (RGD) method is proposed. The intention of the proposed modifications is to simplify the method, make it less computationally expensive, and harmonise of the results with Eurocode 7. The complexity of the RGD method mainly stems from the calculation of the design’s robustness measure, which is the feasibility robustness index (ββ). Due to this fact, the replacing of the existing robustness measure with a generalised reliability index (β) is considered. It was demonstrated that β fits into the robustness concept, and is traditionally used as a construction reliability measure, making it intuitive and “user friendly”. It is proposed to conduct a sensitivity analysis using Soboli indices, with the aim of freezing the variables whose contribution to the system response variance is negligible, which will further simplify the method. By changing the robustness measure, the number of the required reliability analyses is significantly decreased. Further reduction is achieved by conducting analyses only for the designs chosen in the scope of the genetic algorithm. The original RGD method is used as an extension of traditional reliability-based design. By applying the proposed modifications, the RGD method can be used as an alternative to the classic and reliability-based design method.

Measuring Instantaneous Resilience of a Highway Bridge Subjected to Earthquake Events

Bridges in a road network play a significant role in supporting the flows of people, goods, and freight during an earthquake event and are expected to maintain their functionality following the event. Thus, measuring the capability of a bridge immediately following an earthquake event is critical for understanding the post-earthquake functionalities of transportation networks and supply chain systems involving highway bridges. To this end, this paper proposes a new metric for measuring the resistant capacity of a highway immediately following an earthquake event, which is here called instantaneous resilience. The proposed metric first compares the reliability indices of a bridge before and following an earthquake event to measure the immediate earthquake impact. Although this comparison (i.e., robustness measure in this paper) indicates the remaining strength of the bridge subjected to a given earthquake event, it does not reflect collapse failure modes appropriately. Therefore, the proposed instantaneous-resilience metric combines the robustness measure with the structural redundancy measure to consider various scenarios of load path distribution. The proposed metric is computationally efficient because, in the process, it utilizes a generalized reliability-intensity (R-I) surface of a bridge which can be used to calculate the pre- and post-earthquake reliabilities of any bridge designed based on the American Association of State Highway and Transportation Officials (AASHTO) load and resistance factor design (LRFD). Without developing bridge-specific fragility curves and performing structural analysis of a bridge, the proposed measure enables engineers to make a preliminary assessment of the immediate impact of the earthquake on bridges on a quantitative basis. The step-by-step calculation process of the proposed instantaneous-resilience of a bridge is presented, and its potential use in highway network performance assessment is illustrated with a simple hypothetical network system.

A Construction Schedule Robustness Measure Based on Improved Prospect Theory and the Copula-CRITIC Method

A robustness measure is an effective tool to evaluate the anti-interference capacity of the construction schedule. However, most research focuses on solution robustness or quality robustness, and few consider a composite robustness criterion, neglecting the bounded rationality of subjective weights and inherent importance and nonlinear intercriteria correlations of objective weights. Therefore, a construction schedule robustness measure based on improved prospect theory and the Copula-criteria importance through intercriteria correlation (CRITIC) method is proposed. Firstly, a composite robustness criterion is established, including start time deviation rs and structural deviation rp for measuring solution robustness from project execution and completion probability rc for measuring quality robustness from the project result. Secondly, bounded rationality is considered, using prospect theory to calculate subjective weights, which is improved by the interval distance formula. Thirdly, the Copula-CRITIC method is proposed to determine objective weights incorporating both inherent importance and nonlinear intercriteria correlations. Finally, an information-entropy-based evidence reasoning method is applied to combine subjective and objective weights together while identifying their validity. An underground power station in China is used for a case study, whose robustness is measured using the proposed methods, single robustness criterion, and composite robustness criterion using traditional weighting methods. The comparison results verify the consistency, representativeness, and advantage of the proposed criterion and methods.