The Savitzky–Golay filter (SGF) is a time-domain technique that determines a trend line for a signal. The direct application of SGF for damage localization and quantification is investigated in this paper. Therefore, a single-stage trend line-based damage detection method employing SGF is proposed in which the damage is located and quantified at the bridge under moving load. A simply supported beam under moving sprung mass is numerically simulated to verify the proposed method. Four different velocities and five different single- and multi-damage scenarios are considered. The acceleration data along the beam are obtained, manually polluted with noise and their trend lines are then determined using SGF. The results show that the proposed method can accurately locate and quantify the damage using these trend lines. It is proved that the proposed method is insensitive to the noise and velocity variation in which having a constant velocity is a hard task before and after damage. Additionally, defining a normalization factor and fitting a Gaussian curve to this factor provide an estimation for the baseline and therefore, it categorizes the proposed method as baseline-free method.

In this paper, a two-stage time-domain output-only damage detection method is proposed with a new energy-based damage index. In the first stage, the random decrement technique (RDT) is employed to calculate the random decrement signatures (RDSs) from the acceleration responses of a simply supported beam subjected to a moving load. The RDSs are then filtered using the Savitzky–Golay filter (SGF) in the second stage. Next, the filtered RDSs are processed by the proposed energy-based damage index to locate and quantify the intensity of the possible damage. Finally, by fitting a Gaussian curve to the damage index resulted from the non-damage conditions, the whole process is systematically implemented as a baseline-free method. The proposed method is numerically verified using a simply supported beam under moving sprung mass with different velocities and damage scenarios. The results show that the proposed method can accurately estimate the damage location/quantification from the acceleration data without any prior knowledge of either input load or damage characteristics. Additionally, the proposed method is neither sensitive to noise nor velocity variation, which makes it ideal when obtaining a constant velocity is difficult.

Predicting the way diseases spread in different societies has been thus far documented as one of the most important tools for control strategies and policy-making during a pandemic. This study is to propose a network autoregressive (NAR) model to forecast the number of total currently infected cases with coronavirus disease 2019 (COVID-19) in Iran until the end of December 2021 in view of the disease interactions within the neighboring countries in the region. For this purpose, the COVID-19 data were initially collected for seven regional nations, including Iran, Turkey, Iraq, Azerbaijan, Armenia, Afghanistan, and Pakistan. Thenceforth, a network was established over these countries, and the correlation of the disease data was calculated. Upon introducing the main structure of the NAR model, a mathematical platform was subsequently provided to further incorporate the correlation matrix into the prediction process. In addition, the maximum likelihood estimation (MLE) was utilized to determine the model parameters and optimize the forecasting accuracy. Thereafter, the number of infected cases up to December 2021 in Iran was predicted by importing the correlation matrix into the NAR model formed to observe the impact of the disease interactions in the neighboring countries. In addition, the autoregressive integrated moving average (ARIMA) was used as a benchmark to compare and validate the NAR model outcomes. The results reveal that COVID-19 data in Iran have passed the fifth peak and continue on a downward trend to bring the number of total currently infected cases below 480,000 by the end of 2021. Additionally, 20%, 50%, 80% and 95% quantiles are provided along with the point estimation to model the uncertainty in the forecast.

This paper employs the random decrement technique as an output-only method to detect damage from the acceleration signals under a moving load. The random decrement technique is an especial averaging method that produces Random Decrement Signatures (RDS). For this purpose, Arias Intensity (AI) was employed to calculate the energy content of each RDS and substitute each acceleration signal by a scalar invariant value. Normalizing AIs, all RDSs were then updated so as to show a unique energy along the undamaged structure. Once the normalizing factor was computed for the intact structure, the damage was determined by the absolute difference of normalized AIs obtained from each individual RDS along the structure simultaneously. To verify the proposed method, two experimental models of a simply supported beam and a scaled arch bridge were developed under a moving load (vehicle simulation), and acceleration data were recorded. The results of laboratory models proved that the RDSs can accurately detect the damage location using the normalized AI without applying any further frequency filtering. This method needs neither the damage location nor modal parameters in advance, and could properly work in a noisy environment as well.

This paper presents a review of the existing models for the estimation of explosion-induced crushed and cracked zones. The control of these zones is of utmost importance in the rock explosion design, since it aims at optimizing the fragmentation and, as a result, minimizing the fine grain production and recovery cycle. Moreover, this optimization can reduce the damage beyond the set border and align the excavation plan with the geometric design. The models are categorized into three groups based on the approach, i.e., analytical, numerical, and experimental approaches, and for each group, the relevant studies are classified and presented in a comprehensive manner. More specifically, in the analytical methods, the assumptions and results are described and discussed in order to provide a useful reference to judge the applicability of each model. Considering the numerical models, all commonly-used algorithms along with the simulation details and the influential parameters are reported and discussed. Finally, considering the experimental models, the emphasis is given here on presenting the most practical and widely employed laboratory models. The empirical equations derived from the models and their applications are examined in detail. In the Discussion section, the most common methods are selected and used to estimate the damage size of 13 case study problems. The results are then utilized to compare the accuracy and applicability of each selected method. Furthermore, the probabilistic analysis of the explosion-induced failure is reviewed using several structural reliability models. The selection, classification, and discussion of the models presented in this paper can be used as a reference in real engineering projects.