Robustness Coefficient Research Articles

Data-driven diagnosis of high temperature PEM fuel cells based on the electrochemical impedance spectroscopy: Robustness improvement and evaluation

Utilizing machine learning techniques for data-driven diagnosis of high temperature PEM fuel cells is beneficial and meaningful to the system durability. Nevertheless, ensuring the robustness of diagnosis remains a critical and challenging task in real application. To enhance the robustness of diagnosis and achieve a more thorough evaluation of diagnostic performance, a robust diagnostic procedure based on electrochemical impedance spectroscopy (EIS) and a new method for evaluation of the diagnosis robustness was proposed and investigated in this work. To improve the diagnosis robustness: (1) the degradation mechanism of different faults in the high temperature PEM fuel cell was first analyzed via the distribution of relaxation time of EIS to determine the equivalent circuit model (ECM) with better interpretability, simplicity and accuracy; (2) the feature extraction was implemented on the identified parameters of the ECM and extra attention was paid to distinguishing between the long-term normal degradation and other faults; (3) a Siamese Network was adopted to get features with higher robustness in a new embedding. The diagnosis was conducted using 6 classic classification algorithms—support vector machine (SVM), K-nearest neighbor (KNN), logistic regression (LR), decision tree (DT), random forest (RF), and Naive Bayes employing a dataset comprising a total of 1935 collected EIS. To evaluate the robustness of trained models: (1) different levels of errors were added to the features for performance evaluation; (2) a robustness coefficient (Roubust_C) was defined for a quantified and explicit evaluation of the diagnosis robustness. The diagnostic models employing the proposed feature extraction method can not only achieve the higher performance of around 100% but also higher robustness for diagnosis models. Despite the initial performance being similar, the KNN demonstrated a superior robustness after feature selection and re-embedding by triplet-loss method, which suggests the necessity of robustness evaluation for the machine learning models and the effectiveness of the defined robustness coefficient. This work hopes to give new insights to the robust diagnosis of high temperature PEM fuel cells and more comprehensive performance evaluation of the data-driven method for diagnostic application.

Optimizing the robustness of higher-low order coupled networks.

Enhancing the robustness of complex networks is of great practical significance as it ensures the stable operation of infrastructure systems. We measure its robustness by examining the size of the largest connected component of the network after initial attacks. However, traditional research on network robustness enhancement has mainly focused on low-order networks, with little attention given to higher-order networks, particularly higher-low order coupling networks(the largest connected component of the network must exist in both higher-order and low-order networks). To address this issue, this paper proposes robust optimization methods for higher-low order coupled networks based on the greedy algorithm and the simulated annealing algorithm. By comparison, we found that the simulated annealing algorithm performs better. The proposed method optimizes the topology of the low-order network and the higher-order network by randomly reconnecting the edges, thereby enhancing the robustness of the higher-order and low-order coupled network. The experiments were conducted on multiple real networks to evaluate the change in the robustness coefficient before and after network optimization. The results demonstrate that the proposed method can effectively improve the robustness of both low-order and higher-order networks, ultimately enhancing the robustness of higher-low order coupled networks.

Multi-Indicator Weighted Robustness Analysis of Planktonic Community Systems under Different Destructive Factors

Marine plankton communities play a vital role in global carbon and nutrient cycles. Ensuring the robustness of these intricate ecosystems is critical for sustainable environmental management. In this paper, we apply complex network analysis to assess plankton community resilience against disturbances. We construct ecological interaction networks and simulate disruptions using four attack strategies targeting vertices and edges. Our multi-indicator evaluation scheme provides a more nuanced measure of robustness compared to single metrics. Our experiments revealed varying vulnerabilities across networks. Targeted attacks caused abrupt collapse, while random failures led to gradual decline. Identifying critical species and linkages is key to guiding protection efforts. Overall, plankton networks proved fragile, especially against deliberate attacks on central hubs. In our simulations, betweenness-based attacks were the most destructive. The multi-indicator robustness coefficient achieved better performance than individual metrics, with under 3% variance. This network methodology reveals hidden topological vulnerabilities and complements traditional plankton research. The quantitative insights provided in this paper can support marine conservation and governance.

A Bi-level optimization model of integrated energy system considering wind power uncertainty

To cope with the volatility of renewable energy and improve the efficiency of energy storage investment, a bi-level (B-L) optimization model of an integrated energy system (IES) with multiple types of energy storage is established by considering the uncertainty of wind power. The upper-level optimization model considers the lowest configuration cost of energy storage as the objective function and satisfies the constraints of the energy storage configuration. The lower-level optimization model considers the lowest operation cost of the IES as the objective function and satisfies the constraints of the system operation. Second, to overcome the fluctuation problem of wind power output, a robust optimization theory is introduced to describe the uncertainty. Robust coefficients are set to reflect different risk attitudes, which improves the adaptability of the system to uncertainty. Third, the B-L optimization model is solved using the Karush–Kuhn Tucker condition. Finally, a new park is used to implement the simulation. The conclusions are as follows: (1) The economic configuration strategy and optimal operation scheme can be obtained by applying the B-L optimization model, and the upper- and lower-levels interact with each other. The optimal targets of the upper- and lower-level models are −115,848 ¥ and 57,131,102 ¥, respectively. (2) The robust optimization theory improves the ability of a system to deal with risks. Robust optimization theory improves the ability of a system to deal with risks. With an increase in the robustness coefficient, the profit space of the upper-level model increases; however, the operation cost of the lower-level model increases.

Robust Operating Room Scheduling Model with Violation Probability Consideration under Uncertain Surgery Duration.

This paper proposes an operating room (OR) scheduling model to assign a group of next-day patients to ORs while adhering to OR availability, priorities, and OR overtime constraints. Existing studies usually consider OR scheduling problems by ignoring the influence of uncertainties in surgery durations on the OR assignment. In this paper, we address this issue by formulating accurate patient waiting times as the cumulative sum of uncertain surgery durations from the robust discrete approach point of view. Specifically, by considering the patients’ uncertain surgery duration, we formulate the robust OR scheduling model to minimize the sum of the fixed OR opening cost, the patient waiting penalty cost, and the OR overtime cost. Then, we adopt the box uncertainty set to specify the uncertain surgery duration, and a robustness coefficient is introduced to control the robustness of the model. This resulting robust model is essentially intractable in its original form because there are uncertain variables in both the objective function and constraint. To make this model solvable, we then transform it into a Mixed Integer Linear Programming (MILP) model by employing the robust discrete optimization theory and the strong dual theory. Moreover, to evaluate the reliability of the robust OR scheduling model under different robustness coefficients, we theoretically analyze the constraint violation probability associated with overtime constraints. Finally, an in-depth numerical analysis is conducted to verify the proposed model’s effectiveness and to evaluate the robustness coefficient’s impact on the model performance. Our analytical results indicate the following: (1) With the robustness coefficient, we obtain the tradeoff relationship between the total management cost and the constraint violation probability, i.e., a smaller robustness coefficient yields remarkably lower total management cost at the expense of a noticeably higher constraint violation probability and vice versa. (2) The obtained total management cost is sensitive to small robustness coefficient values, but it hardly changes as the robustness coefficient increases to a specific value. (3) The obtained total management cost becomes increasingly sensitive to the perturbation factor with the decrease in constraint violation probability.

Rational evaluation of various epidemic models based on the COVID-19 data of China

In this paper, based on the Akaike information criterion, root mean square error and robustness coefficient, a rational evaluation of various epidemic models/methods, including seven empirical functions, four statistical inference methods and five dynamical models, on their forecasting abilities is carried out. With respect to the outbreak data of COVID-19 epidemics in China, we find that before the inflection point, all models fail to make a reliable prediction. The Logistic function consistently underestimates the final epidemic size, while the Gompertz’s function makes an overestimation in all cases. Towards statistical inference methods, the methods of sequential Bayesian and time-dependent reproduction number are more accurate at the late stage of an epidemic. And the transition-like behavior of exponential growth method from underestimation to overestimation with respect to the inflection point might be useful for constructing a more reliable forecast. Compared to ODE-based SIR, SEIR and SEIR-AHQ models, the SEIR-QD and SEIR-PO models generally show a better performance on studying the COVID-19 epidemics, whose success we believe could be attributed to a proper trade-off between model complexity and fitting accuracy. Our findings not only are crucial for the forecast of COVID-19 epidemics, but also may apply to other infectious diseases.

Robust global reverse logistics network redesign for high-grade plastic wastes recycling

The circular economy represents an alternative closed-loop production and consumption patterns instead of traditional linear take-make-waste approaches. It presents a new vision with global sustainability where plastic waste is viewed as a material that can be reused, to avoid depleting natural resources. In this context, it is essential to redesign the global reverse logistics network (GRLN) by incorporating the existing facilities across national boundaries into the integrated global recycling system. A mean-variance robust model with quadratic functions is developed to address the time-ambiguous currency exchange rate, the ocean freight rate, and the carbon prices. To the best of our knowledge, this is one of the first efforts to evaluate the effects of the multiplicative relationships between the uncertain elements, e.g. currency exchange rate and carbon trading prices. In the proposed model, the economic and the environmental performances of a GRLN are evaluated by the robustness coefficient. The application of the model is demonstrated in a sample case of the PWR between China and Belgium. The analysis shows that a lower robustness coefficient leads to a higher cost of the GRLN, but lower emissions. It is worthy to note that considering the maritime emission is not definite to guarantee global net sustainability. Moreover, a social GRLN network leads to a more cost-efficient system compared to developing two recycling networks individually in the importing and the exporting countries.

AdvAndMal: Adversarial Training for Android Malware Detection and Family Classification

In recent years, Android malware has continued to evolve against detection technologies, becoming more concealed and harmful, making it difficult for existing models to resist adversarial sample attacks. At the current stage, the detection result is no longer the only criterion for evaluating the pros and cons of the model with its algorithms, it is also vital to take the model’s defensive ability against adversarial samples into consideration. In this study, we propose a general framework named AdvAndMal, which consists of a two-layer network for adversarial training to generate adversarial samples and improve the effectiveness of the classifiers in Android malware detection and family classification. The adversarial sample generation layer is composed of a conditional generative adversarial network called pix2pix, which can generate malware variants to extend the classifiers’ training set, and the malware classification layer is trained by RGB image visualized from the sequence of system calls. To evaluate the adversarial training effect of the framework, we propose the robustness coefficient, a symmetric interval i = [−1, 1], and conduct controlled experiments on the dataset to measure the robustness of the overall framework for the adversarial training. Experimental results on 12 families with the largest number of samples in the Drebin dataset show that the accuracy of the overall framework is increased from 0.976 to 0.989, and its robustness coefficient is increased from 0.857 to 0.917, which proves the effectiveness of the adversarial training method.

Simple and scalable synthesis of super-repellent multilayer nanocomposite coating on Mg alloy with mechanochemical robustness, high-temperature endurance and electric protection

Multi-functionalization is the future development direction for protective coatings on metal surface, but has not yet been explored a lot. The effective integration of multiple functions into one material remains a huge challenge. Herein, a superhydrophobic multilayer coating integrated with multidimensional organic-inorganic components is designed on magnesium alloy via one-step plasma-induced thermal field assisted crosslinking deposition (PTCD) processing followed by after-thermal modification. Hard porous MgO ceramic layer and polytetrafluoroethylene (PTFE) nano-particles work as the bottom layer skeleton and filler components separately, forming an organic-inorganic multilayer structure, in which organic nano-particles can be crosslinked and cured to form a compact polymer-like outer layer with hierarchical surface textures. Remarkably, the chemical robustness after prolonged exposure to aqua regia, strong base and simulated seawater solution profits from polymer-like nanocomposite layer uniformly and compactly across the film bulk. Moreover, the self-similar multilayer structure coating endows it attractive functions of strong mechanical robustness (>100th cyclic rotary abrasion), stable and ultra-low friction coefficient (about 0.084), high-temperature endurance, and robust self-cleaning. The organic-inorganic multilayer coating also exhibits high insulating property with breakdown voltage of 1351.8 ± 42.4 V, dielectric strength of 21.4 ± 0.7 V/µm and resistivity of 3.2 × 1010 Ω·cm. The excellent multifunction benefits from ceramic bottom skeleton, the assembly and deposition of multidimensional nano-particles, and the synergistic effect of organic inorganic components. This study paves the way for designing next generation protective coating on magnesium alloy with great potential for multifunctional applications.

Design of Vehicle Stability Controller Based on Fuzzy Radial Basis Neural Network Sliding Mode Theory with Sideslip Angle Estimation

This study is targeted at the key state parameters of vehicle stability controllers, the controlled vehicle model, and the nonlinearity and uncertainty of external disturbance. An adaptive double-layer unscented Kalman filter (ADUKF) is used to compute the sideslip angle, and a vehicle stability control algorithm adaptive fuzzy radial basis function neural network sliding mode control (AFRBF-SMC) is proposed. Since the sideslip angle cannot be directly determined, a 7-degrees-of-freedom (DOF) nonlinear vehicle dynamic model is established and combined with ADUKF to estimate the sideslip angle. After that, a vehicle stability sliding mode controller is designed and used to trace the ideal values of the vehicle stability parameters. To handle the severe system vibration due to the large robustness coefficient in the sliding mode controller, we use a fuzzy radial basis function neural network (FRBFNN) algorithm to approximate the uncertain disturbance of the system. Then the adaptive rate of the system is solved using the Lyapunov algorithm, and the systemic stability and convergence of this algorithm are validated. Finally, the controlling algorithm is verified through joint simulation on MATLAB/Simulink-Carsim. ADUKF can estimate the sideslip angle with high precision. The AFRBF-SMC vehicle stability controller performs well with high precision and low vibration and can ensure the driving stability of vehicles.

Analysis of collapse resistance of offshore rigid frame - Continuous girder bridge based on time-varying fragility

In service period, the key to ensure the service performance of bridge is to control its material durability damage and continuous collapse better. Nowadays, most anti - collapse analysis under earthquake is for the frame structure, the theory and method of anti - collapse analysis of bridge is not systematically summarized. Taking a 4 - span rigid frame - continuous girder bridge in offshore seismic prone region as an example, a new quantitative criterion for collapse resistance was proposed based on theoretical fragility, reliability theory and concept removal method of components, which is suitable for the example bridge. The results show that the time-varying durability damage and time-varying bond - slip effect on mechanical properties of materials can't be ignored in service period; the fragility and importance coefficient increase with service life, while the robustness coefficient decreases with service life, the different optimization algorithms all improve their corresponding parameters; when the bridge reaches its designed service life, its robustness coefficient is about 25% of that of the new, when the bridge exceeds the designed service life, its robustness coefficient decay rate is low, and the residual robustness coefficient is about 18%, the bridge still has certain anti - collapse performance.

Robustness analysis of vertical resistance to progressive collapse of diagrid structures in tall buildings

SummaryIn order to investigate the vertical resistance to progressive collapse and the evolution of its robustness in the process of loading, a quantitative method of the robustness index of diagrid structure is established based on the mechanical properties of the components and the vertical bearing capacity of the structure. A scale experiment model of diagrid tube structure is established in laboratory which verified the availability of the proposed robustness quantification method. Results demonstrated that, the axial force of inclined column is pressure, and the axial force of ring beam is tension under vertical load. The ring beam is the main restraint to the side bulge of the diagrid structure. The welded strength of the inclined column have great influence on the vertical bearing capacity, so it is necessary to consider the reduction of the strength of welded joint. The influence of the welding line of the joint can lead to the plastic stage of the local components of the structure, which makes the structural robustness worse. In addition, the experimental study and numerical simulation results verify that the proposed method of robustness coefficient quantification for diagrid tube structure can accurately and reasonably evaluate the resistance of vertical progressive collapse performance.

Multi-criteria comprehensive study on predictive algorithm of heating energy consumption of district heating station based on timeseries processing

Refined control of district heating station relies on reasonable and accurate prediction of heating energy consumption. Due to the influence of building thermal inertia and time-delay of the district heating system, certain research work is necessary to thoroughly illustrate and analyze the impact of data timeseries processing on various prediction models. Four kinds of prediction algorithms were investigated and compared in this paper. Results showed that all of three timeseries processing methods, namely time feature construction, sliding window and building thermal inertia coefficient (CBTI), can improve the prediction accuracy of all four models and CBTI had the greatest impact on model accuracy improvement. Moreover, timeseries processing method has no limitation on the types of prediction model and it is a general method to improve the model accuracy. Time feature construction and sliding window had greater influence on the non-neural network models while CBTI was the opposite. In terms of model robustness, the robustness had been significantly improved after introducing timeseries processing except random forest, and the comprehensive robustness coefficient for the other three models had been reduced by about 95%. Recurrent neural network had extremely excellent robustness under different temporal granularity.

Analysis and Design of Seismic Robustness of FRP-Reinforced Frame based on Interlayer Displacement

For a structure, robustness is a high-level performance index since it takes account of the effects of impact, explosion, earthquake and other instantaneous dynamic actions on the structure safety. In this work, layer is taken as the tie between the column and the frame. Two concepts, namely, “layer importance coefficient” of the column and “layer vulnerability coefficient” of the frame, are introduced. Based on these, the method for calculating the seismic robustness is proposed and analyzes the seismic robustness of three FRP-reinforced frame models. The results show that: The robustness of the frame with the 1st layer column reinforced with two layer CFRP (carbon fiber reinforced polymer) (F20RC) and the 1st and 2nd layer column reinforced with one layer CFRP (F11RC), respectively are better than that of the 1st layer column reinforced with one layer CFRP (F10RC). As the intensity of earthquake action increases, the seismic robustness index decreases. When UBC97’s acceleration-related parameter Ca = 0.36 and velocity-related parameter Cv = 0.36, the robustness coefficient of the three models F20RC, F11RC, F10RC are 36.5, 37.2, 34.1, respectively. When Ca = 0.6, Cv = 0.6, that of F20RC, F11RC, F10RC are 24.2, 20.4, 19.5, respectively. Finally, the procedure for designing the FRP-reinforced frame based on the seismic robustness is presented and demonstrated.

A sustainable water-food-energy plan to confront climatic and socioeconomic changes using simulation-optimization approach

The provision of reliable water resources, safe grain production, and sustainable energy supply can be deemed as key guarantees for economic growth and human living improvement, but which have been challenged by imbalance relationship between increasing demand and limited supply capacity. In this study, a sustainable water-food-energy plan has been developed to conduct an optimal framework into a multiple water-reservoir system for confronting regional natural and artificial damages such as water deficit, food crisis and electric insufficient contemporarily. A simulation-optimization approach has been proposed to handle multiple uncertainties due to climatic and socioeconomic changes. The proposed approach has advantages of reflecting the climatic change in a lumped and conceptual way; meanwhile, it is effective to deal with socioeconomic uncertainties regarded as probability and possibility distributions, reducing the risk of decision-making with Green criterions. The developed water-food-energy plan with simulation-optimization approach can be applied to a real case study of Jing River, China. The obtained results of water-food-energy shortage, optimal water allocation-food production-energy generation, flood control, and system benefit under various policy-scenarios can be identify comprehensive water-food-energy alternatives in a multi-reservoir optimization system. Meanwhile, the results associated with credibility confidence, risk-averse attitude parameter and robustness coefficient can support the generation of a water-food-energy plan with a robust manner. It can support the improvement of water supply, irrigative production, energy generation, industrial pattern adjustment, flood risk control, supply capacity at a regional view, with aim to achieve sustainability of human activities and resource-energy conservation.

Optimized Diffusion-Weighting Gradient Waveform Design (ODGD) formulation for motion compensation and concomitant gradient nulling.

To present a novel Optimized Diffusion-weighting Gradient waveform Design (ODGD) method for the design of minimum echo time (TE), bulk motion-compensated, and concomitant gradient (CG)-nulling waveforms for diffusion MRI. ODGD motion-compensated waveforms were designed for various moment-nullings Mn (n=0,1,2), for a range of b-values, and spatial resolutions, both without (ODGD-Mn ) and with CG-nulling (ODGD-Mn -CG). Phantom and in-vivo (brain and liver) experiments were conducted with various ODGD waveforms to compare motion robustness, signal-to-noise ratio (SNR), and apparent diffusion coefficient (ADC) maps with state-of-the-art waveforms. ODGD-Mn and ODGD-Mn -CG waveforms reduced the TE of state-of-the-art waveforms. This TE reduction resulted in significantly higher SNR (P< 0.05) in both phantom and in-vivo experiments. ODGD-M1 improved the SNR of BIPOLAR (42.8±5.3 vs. 32.9±3.3) in the brain, and ODGD-M2 the SNR of motion-compensated (MOCO) and Convex Optimized Diffusion Encoding-M2 (CODE-M2 ) (12.3±3.6 vs. 9.7±2.9 and 10.2±3.4, respectively) in the liver. Further, ODGD-M2 also showed excellent motion robustness in the liver. ODGD-Mn -CG waveforms reduced the CG-related dephasing effects of non CG-nulling waveforms in phantom and in-vivo experiments, resulting in accurate ADC maps. ODGD waveforms enable motion-robust diffusion MRI with reduced TEs, increased SNR, and reduced ADC bias compared to state-of-the-art waveforms in theoretical results, simulations, phantoms and in-vivo experiments.

Development of a fuzzy-stochastic programming with Green Z-score criterion method for planning water resources systems with a trading mechanism.

This study developed a fuzzy-stochastic programming with Green Z-score criterion (FSGZ) method for water resources allocation and water quality management with a trading-mechanism (WAQT) under uncertainties. FSGZ can handle uncertainties expressed as probability distributions, and it can also quantify objective/subjective fuzziness in the decision-making process. Risk-averse attitudes and robustness coefficient are joined to express the relationship between the expected target and outcome under various risk preferences of decision makers and systemic robustness. The developed method is applied to a real-world case of WAQT in the Kaidu-Kongque River Basin in northwest China, where an effective mechanism (e.g., market trading) to simultaneously confront severely diminished water availability and degraded water quality is required. Results of water transaction amounts, water allocation patterns, pollution mitigation schemes, and system benefits under various scenarios are analyzed, which indicate that a trading-mechanism is a more sustainable method to manage water-environment crisis in the study region. Additionally, consideration of anthropogenic (e.g., a risk-averse attitude) and systemic factors (e.g., the robustness coefficient) can support the generation of a robust plan associated with risk control for WAQT when uncertainty is present. These findings assist local policy and decision makers to gain insights into water-environment capacity planning to balance the basin's social and economic growth with protecting the region's ecosystems.

A Comparison of Network-Based Metrics of Behavioral Degradation in Complex Engineered Systems

It has been assumed, but not yet tested, that the topological disintegration of networks is relatable to degradations in complex engineered system behavior and that extant network metrics are capable of capturing these degradations. This paper tests three commonly used network metrics used to quantify the topological robustness of networks for their ability to characterize the degree of failure in engineered systems: average shortest path length, network diameter, and a robustness coefficient. A behavioral network of a complex engineered system is subjected to “attack” to simulate potential failures to the system. Average shortest path length and the robustness coefficient showed topological disintegration patterns which differed between nominal and failed cases, regardless of failure implementation location. The network diameter metric is not sufficiently dependent on local cluster topology to show changes in topology with edge removal failure strategies. The results show that topological metrics from the field of complex networks are applicable to complex engineered systems when they account for both local and global topological changes.

A Novel Data-Driven Fast Capacity Estimation of Spent Electric Vehicle Lithium-ion Batteries

Fast capacity estimation is a key enabling technique for second-life of lithium-ion batteries due to the hard work involved in determining the capacity of a large number of used electric vehicle (EV) batteries. This paper tries to make three contributions to the existing literature through a robust and advanced algorithm: (1) a three layer back propagation artificial neural network (BP ANN) model is developed to estimate the battery capacity. The model employs internal resistance expressing the battery’s kinetics as the model input, which can realize fast capacity estimation; (2) an estimation error model is established to investigate the relationship between the robustness coefficient and regression coefficient. It is revealed that commonly used ANN capacity estimation algorithm is flawed in providing robustness of parameter measurement uncertainties; (3) the law of large numbers is used as the basis for a proposed robust estimation approach, which optimally balances the relationship between estimation accuracy and disturbance rejection. An optimal range of the threshold for robustness coefficient is also discussed and proposed. Experimental results demonstrate the efficacy and the robustness of the BP ANN model together with the proposed identification approach, which can provide an important basis for large scale applications of second-life of batteries.

Quantifying topological robustness of networks under sustained targeted attacks

In this paper, we introduce a measure to analyse the structural robustness of complex networks, which is specifically applicable in scenarios of targeted, sustained attacks. The measure is based on the changing size of the largest component as the network goes through disintegration. We argue that the measure can be used to quantify and compare the effectiveness of various attack strategies. Applying this measure, we confirm the result that scale-free networks are comparatively less vulnerable to random attacks and more vulnerable to targeted attacks. Then we analyse the robustness of a range of real world networks, and show that most real world networks are least robust to attacks based on betweenness of nodes. We also show that the robustness values of some networks are more sensitive to the attack strategy as compared to others. Furthermore, robustness coefficient computed using two centrality measures may be similar, even when the computational complexities of calculating these centrality measures may be different. Given this disparity, the robustness coefficient introduced potentially plays a key role in choosing attack and defence strategies for real world networks. While the measure is applicable to all types of complex networks, we clearly demonstrate its relevance to social network analysis.