Lognormal Function Research Articles

Some statistical remarks on GRBs jointly detected by Fermi and Swift satellites

ABSTRACT We made statistical analysis of the Fermi GBM and Swift BAT observational material, accumulated over 15 yr. We studied how GRB parameters (T90 duration, fluence, and peak flux) that were observed by only one satellite differ from those observed by both. In the latter case, it was possible to directly compare the values of the parameters that both satellites measured. The GRBs measured by both satellites were identified using the k-nearest neighbours algorithm in Euclidean distance. In the parameter space we determined the direction in which the jointly detected GRBs differ most from those detected by only one of the instruments using linear discriminant analyses. To get the strength of the relationship between the parameters obtained from the GBM and BAT, a canonical correlation was performed. The GBM and BAT T90 distributions were fitted with a linear combination of lognormal functions. The optimal number of such functions required for fit is two for GBM and three for BAT. Contrary to the widely accepted view, we found that the number of lognormal functions required for fitting the observed distribution of GRB durations does not allow us to deduce the number of central engine types responsible for GRBs.

EMPIRICAL VULNERABILITY ANALYSIS OF RAILWAY BRIDGE SEISMIC DAMAGE BASED ON 2022 MENYUAN EARTHQUAKE

A 6.9 magnitude earthquake at a depth of 10 km struck Menyuan County, Haibei Prefecture, Qinghai Province, China, on January 8, 2022. This earthquake damaged some railway bridges on the Lanzhou-Xinjiang Passenger Dedicated Line. This study combines relevant historical earthquake damage experience, considers the effects of earthquake intensity, site soil classification, superstructure type, foundation failure factor, number of spans, and total bridge length, and develops empirical formulas for seismic damage prediction of railway bridges using ordinal logistic regression model in SPSS software. The seismic damage matrix, as were the anticipated multi-intensity mean damage index and the empirical vulnerability curve based on the two-parameter lognormal distribution function, were generated on this basis. According to the conclusions, although the suggested particular equations and vulnerability curves do not apply to the remainder of the region owing to geographical uniqueness, the technical approach is valid. It may be used as a reference for seismic damage prediction and vulnerability evaluation in other regions. The empirical vulnerability analysis based on the earthquake damage prediction matrix derived from the regression analysis can provide reasonable and fast forecasts before the next earthquake.

Multi-objective optimal power flow of thermal-wind-solar power system using an adaptive geometry estimation based multi-objective differential evolution

Sustainable energy is a key component of sustainable development. The current grid can be supplied by fossil fuel generators and renewable energy sources (RESs)-based generators, such as solar photovoltaic (PV) and wind power generators. In an electrical network, power generation from several sources must be optimally coordinated to ensure efficient and economical operation. However, the intermittent and uncertain nature of RESs complicate the operation of power systems. In this study, an adaptive geometry estimation-based multi-objective differential evolution (AGE-MODE) method is proposed for multi-objective optimal power flow in a hybrid power system of thermal, wind, and solar energy sources (MOOPF-TWS). In the proposed approach, wind and solar PV power outputs are predicted based on Weibull and lognormal probability distribution functions, respectively. Therefore, the generation costs for solar and wind power can be divided into direct costs, penalty costs for underestimation, and reserve costs for overestimation. Furthermore, the emissions, voltage deviation, and real power loss are considered in particular cases. AGE-MODE is applied to modified IEEE 30-bus and 57-bus systems, where different case studies are simulated with combinations of two-, three-, and four-objective optimizations in MOOPF-TWS problems. Comparisons between AGE-MODE and other recently developed multi-objective methods demonstrate its effectiveness in resolving MOOPF-TWS problems, particularly for cases with more than two objectives.

Particle Size Distributions and Extinction Coefficients of Aerosol Particles in Land Battlefield Environments

In land battlefield environments, aerosol particles can cause laser beams to undergo attenuation, thus deteriorating the operational performance of military laser devices. The particle size distribution (PSD) and extinction coefficient are key optical properties for assessing the attenuation characteristics of laser beams caused by aerosol particles. In this study, we employed the laser diffraction method to measure the PSDs of graphite smoke screen, copper powder smoke screen, iron powder smoke screen, ground dust, and soil explosion dust. We evaluated the goodness of fit of six common unimodal PSD functions and a bimodal lognormal PSD function employed for fitting these aerosol particles using the root mean square error (RMSE) and adjusted R2, and selected the optimal PSD function to evaluate their extinction coefficients in the laser wavelength range of 0.249~12 μm. The results showed that smoke screens, ground dust, and soil explosion dust exhibited particle size ranges of 0.7~50 µm, 1~400 µm, and 1.7~800 μm, respectively. The lognormal distribution had the best goodness of fit for fitting the PSDs of these aerosol particles in the six unimodal PSD functions, followed by the gamma and Rosin–Rammler distributions. For the bimodal aerosol particles with a lower span, the bimodal lognormal PSD functions exhibited the best goodness of fit. The graphite smoke screen exhibited the highest extinction coefficient, followed by the copper and iron powder smoke screens. In contrast, the ground dust and soil explosion dust exhibited the lowest extinction coefficients, reaching their minimum values at a wavelength of approximately 8.2 μm. This study provides a basis for analyzing and improving the detection and recognition performance of lasers in land battlefield environments.

Modeling of tsunami wave height distribution functions along the east coast of Sakhalin Island

The functions of the distribution of tsunami wave heights along the eastern coast of Sakhalin Island from sources located along the Kuril Islands are being studied. Known information about the tsunami on Sakhalin is given. Many of them were modeled numerically, which made it possible to assess the hazard of tsunami waves. The present work focuses on the functions of distributing the heights of tsunami waves, which were not previously calculated for this region at all. To this case, calculations were made of the propagation of tsunami waves from hypothetical strong earthquakes with M = 8.2 located in the regions of the Northern, Middle and Southern Kuril Islands. These calculations were carried out using the NAMI-DANCE computational code, which solves non-linear shallow water equations using nested grids with a minimum grid is about 9 m. Having no reliable coastal topography, the modeling was carried out to a depth of about 3 m. The results of the calculations confirmed that the calculated functions of the distribution of tsunami wave heights along the eastern coast of Sakhalin are well approximated by the lognormal function. The parameters of these distributions depend on the location of the source even with the same earthquake parameters, which once again emphasizes the significant role of seabed bathymetry on the characteristics of a tsunami on the shore.

Understanding the spatial statistical properties of a real estate listings point pattern in San José, Costa Rica

One should expect real estate sales, and properties listed as for sale, to be concentrated on market hotspots. Using data of real estate listings from San José, Costa Rica, this expected clustering is examined using point pattern processes of detached housing, apartments, and vacant lots. Non-stationary G and J functions describe the patterns and their interactions. Potential determinants of the point pattern were selected based on previous studies and theory. Their effect on the point pattern was estimated using an inhomogeneous Poisson model, with its intensity a lognormal function of the determinants. Results show detached houses, apartments, and lots are all clustered point patterns. The cross density (joint G function) of houses with apartments and with lots exhibits clustering, suggesting the patterns are related; however, the cross density of apartments and lots is no different from a Poisson distribution (they are not related). The inhomogeneous Poisson model with Euclidean distance to the central business district (CBD), nearest municipal center, and nearest main road, as well as elevation and slope, proved better than homogeneous Poisson models in explaining the point patterns of houses, apartments, and lots.

Fragility analysis of a multi-span continuous steel roadway bridge in Türkiye: A case study

One of the most widely utilized methods for determining seismic performance and allowing additional study is fragility analysis. The fragility curve, which is typically characterized by two-parameter log-normal distribution functions, depicts the probability of bridge components exceeding a certain damage limit. This study examines the fragility analysis of a multi-span continuous (MSC) steel roadway bridge in Türkiye. The probabilistic seismic demand model (PSDMs) is illustrated by conducting many time history analyses (THA). The nonlinear analyses are conducted for sixty earthquakes. Logarithmic regression analyses and fragility curves were derived for varying intensity measures (IM) in terms of efficiency. Monte Carlo analysis was used to derive the system fragility curve of the bridge. The PGA and ASI are the most proper intensity measure for the fragility curve of the bridge. Moreover, the slight damage can be visualized with a higher probability for the small intensity measure that even mild earthquake motion can cause some slight damage on the bridge but after slight damage bridge has further capacity until the collapse damage is visualized.

Canopy gaps and associated losses of biomass – combining UAV imagery and field data in a central Amazon forest

Abstract. Understanding mechanisms of tree mortality and the dynamics of associated canopy gaps is relevant for robust estimates of carbon balance in forests. We combined monthly RGB images acquired from an unoccupied aerial vehicle with field surveys to identify gaps in an 18 ha plot installed in an old-growth central Amazon forest. We measured the size and shape of gaps and analyzed their temporal variation and correlation with rainfall over a period of 28 months. We further described associated modes of tree mortality (i.e., snapping, uprooting and standing dead) and branch fall and quantified associated losses of biomass. In total, we detected 32 gaps either in the images or field ranging in area from 9 to 835 m2. Relatively small gaps (< 39 m2) opened by branch fall were the most frequent (11 gaps). Out of 18 gaps for which both field and image data were available, three could not be detected remotely. Gaps observed in the field but not captured on the imagery were relatively small and mainly formed by the fall of branches from live and standing dead trees. Our data show that ∼ 17 % of the tree-mortality and branch-fall events only affected the lower canopy and the understory of the forest and are likely neglected by top-of-the-canopy assessments. Regardless of the detection method, the size distribution was best described by a lognormal function for gaps starting from the smallest detected size (9 and 10 m2 for field and imagery data, respectively), and the Weibull and Power functions for gaps larger than 25 m2. Properly assessing associated confidence intervals requires larger sample sizes. Repeated field measurements reveal that gap area does not differ significantly among modes of tree mortality or branch fall in central Amazon forests, with the last contributing the least to biomass loss. Predicting mechanisms of gap formation based on associated area and biomass loss remains challenging, which highlights the need for larger datasets. The rate of gap area formation was positively correlated with the frequency of extreme rainfall events, which may be related to a higher frequency of storms propagating extreme rain and wind gusts. While remote sensing has proven to be an accurate and precise method for mapping gaps compared to field data (i.e., ground truth), it is important to note that our sample size was relatively small. Therefore, the extrapolation of these results beyond our study region and landscape shall be made cautiously. Apart from improving landscape assessments of carbon balance, regional information on gap dynamics and associated mechanisms of formation are fundamental to address forest responses to altered disturbance regimes resulting from climate change.

The cluster initial mass function of the M82 disc super star clusters

ABSTRACT The presence of a population of a large number (∼400) of almost coeval (100–300 Myr) super star clusters (SSCs) in the disc of M82 offers an opportunity to construct the Cluster Initial Mass Function (CIMF) from the observed present-day Cluster Mass Function (CMF). We carry out the dynamical and photometric evolution of the CMF assuming that the clusters move in circular orbits under the gravitational potential of the host galaxy using the semi-analytical simulation code Evolve Me a Cluster of StarS. We explore power-law and lognormal functions for the CIMFs, and populate the clusters in the disc assuming uniform, power-law, and exponential radial distribution functions. We find that the observed CMF is best produced by a CIMF that is power law in form with an index of 1.8, for a power-law radial distribution function. More importantly, we establish that the observed turn-over in the present-day CMF is the result of observational incompleteness rather than due to dynamically induced effects, or an intrinsically lognormal CIMF, as was proposed for the fossil starburst region B of this galaxy. Our simulations naturally reproduce the mass–radius relation observed for a sub-sample of M82 SSCs.

On a Data-Driven Optimization Approach to the PID-Based Algorithmic Trading

This paper proposes an optimal trading algorithm based on a novel application of conventional control engineering (CE). We consider a fundamental CE concept, namely, the feedback control, and apply it to algorithmic trading (AT). The concrete feedback control strategy is designed in a form of the celebrated proportional–integral–derivative (PID) model. The highly fluctuating nature of the modern financial markets has led to the adoption of a model-free realization of the generic PID framework. The control theoretical methodology we propose is combined with the advanced statistics for the historical market data. We obtain a specific log-normal probability distribution function (pdf) associated with the specific quantities associated with the available stock data. The empirical log-normal pdf mentioned above enables the necessary PID gains optimization. For this aim, we apply the data-driven optimization approaches and consider the corresponding Monte Carlo solution procedure. The optimized PID trading algorithm we propose is also studied in the Fourier analysis framework. This equivalent frequency domain representation involves a new concept in financial engineering, namely, the “stock market energy” concept. For the evaluation, we implement the proposed PID optimal trading algorithm and develop a Python-based prototype software. We finally apply the corresponding prototype software to a data set from the Binance BTC/USDT (Bitcoin/Tether) stock market. The experimental result illustrates the implementability of the proposed optimal PID trading scheme and also shows the effectiveness of the proposed CE methods in the modern AT.

Prediction model of sintering bed temperature based on lognormal distribution function: construction and application

The monitoring of sintering bed temperature is crucial for controlling physical and chemical reactions during the sintering process and achieving low carbonization trends. However, accurately monitoring this temperature is challenging due to the "black box" nature of the sintering bed, which includes the sintering trolley and cup. As a result, a theoretical model needs to be developed urgently to predict the sintering bed's temperature profile. In this investigation, we propose a mathematical model that utilizes the characteristic value of the lognormal distribution to estimate indirectly the temperature of the sintering bed based on the measured temperature of the sintering exhaust gas. The sintering exhaust gas temperature and sintering bed temperature conform to the function: T=T0+A2πw⋅te−(ln(t−tc))2w22. To further enhance the accuracy of the sintering bed temperature prediction, the longitudinal positions of the sintering bed were expanded from three points to multiple points, enabling the construction of a temperature prediction function for the entire sinter bed and obtaining a cloud map of the sintering bed temperature. By determining the sintering terminal point and controlling the sintering machine's speed according to the location of the high-temperature region on the cloud map, the performance of the temperature prediction model was optimized. Through an analysis of the mathematical model and construction of the sintering temperature profile, a predictive route of exhaust gas temperature → three-point sintering bed → total sintering bed was established. This predictive method can significantly enhance the understanding of the sintering process and can be employed in industrial plants.

Grain coarsening during liquid phase sintering of zircon–glass composites

This study examined zircon grain growth during isothermal sintering of a zircon–glass composite with a zircon volume fraction of 0.525 zircon volume/solids volume, at a temperature of 1200°C, with different residence times, ranging from 5min to 1500min. Scanning electron microscopy and image analysis were used to determine zircon grain size and number in the fired test specimens. The residual glass composition was determined by energy dispersive X-ray spectroscopy. For each firing condition, the grain size number distribution was fitted to a lognormal function and to a Weibull function. In every case, the lognormal distribution described the results better. Grain size grew and distribution width decreased with sintering time in accordance with non-steady-state grain growth models. At high sintering times, the variation of average grain diameter and grain number density per unit solids cross-section fitted well to steady-state growth models. Moreover, when grain size distribution was scaled by the average size, it was practically time independent. In contrast, scaled grain distribution width was much wider than that predicted by these models. A model was developed that satisfactorily predicts zircon grain evanescence throughout the sintering process.

A Quasi-periodic Oscillation of ∼4.6 yr in the Radio Light Curves of Blazar PKS 0607-157

We present periodicity search analyses on long-term radio light curves at 4.8, 8, and 14.5 GHz of blazar PKS 0607–157 observed by the University of Michigan Radio Astronomical Observatory telescope. The highly variable radio emissions are approximately distributed as a log-normal probability distribution function. The Power Spectral Density for the radio light curves can be well characterized by a power-law model. Using the Weighted Wavelet Z-transform and Lomb-Scargle periodogram methods, significant Quasi-periodic Oscillation (QPO) of ∼4.6 yr in the radio light curve has been observed above the 3σ confidence level, which presents an interesting case among blazar QPO phenomena. We explore three plausible physical models to explain the observed QPOs: a supermassive binary black hole system, Lense-Thirring precession of the disk, and helical motion of plasma blobs within the jet.

IDA-Based Collapse Safety Assessment of Torsional-Irregular Buildings, Considering Ductility and Damage

The complexity in nonlinear behavior of torsional-irregular buildings in combination with uncertainty due to the natural randomness of earthquake records has been always a main challenge for buildings’ seismic design. To find a solution to this challenge, three reinforced concrete (RC) building archetypes were designed and next developed into their nonlinear models. Nonlinear static (pushover) analyses were performed to calculate the capacity of the archetype models in all principal and non-principal directions while incremental dynamic analyses (IDAs) were conducted by applying 30 accelerograms from both near-field and far-field earthquakes. The IDA capacity curves, collapse fragility curves and log-normal cumulative distribution functions (CDFs) were established by including both the aleatory randomness and epistemic uncertainty. Despite previous studies wherein fragility curves were given by evaluating structures’ collapse along structural reference axes or simply on [Formula: see text], [Formula: see text]-axes, in this paper, possible building collapse on a critical non-principal direction (where maximum seismic response was observed) was simulated and its probability was accounted for developing IDA curves and log-normal CDFs. Accordingly, this issue was mirrored in computing available/acceptable collapse margin ratios (CMRs). In addition to the well-known outline used for calculating CMRs in the literature (that is based on estimation of collapse capacity in terms of earthquake intensity measure (IM)), the framework proposed here includes a new method for calculating the CMRs in terms of displacement-based drift, ductility, and damage. The superiority of the proposed method over the former is consistent with the buildings’ design procedure that is governed by storey drift control rather than base-shear strength. Refined statistics of CMRs given by taking into account displacement-based responses illustrate the available CMRs exceed the acceptable CMRs, meaning that a satisfactory safety margin against collapse will be anticipated in the targeted building class if a suitable yielding mechanism with sufficient ductility is provided for seismic force-resisting system by applying seismic design provisions of the current codes.

Quasi-periodic variability in the γ-Ray blazar PKS 0426–380

The identification of quasi-periodic oscillations (QPOs) inactive galactic nuclei (AGN) light curvescan shed light on supermassive black holes (SMBHs) and their surrounding central engines. They could signal the existence of SMBH binaries and reflect theirpreponderance through cosmic evolution. The Flat Spectrum Radio Quasar (FSRQ) at intermediate redshift (z=1.1) PKS 0426–380 was reported to possibly exhibit a quasi-periodic signal. Using the Fermi-LAT Pass 8 data, we generate an updated γ-ray light curve (LC) time series of this object from 2008 August to 2020 November. Aperture photometry γ-ray LCs were extracted at three energy ranges (E1: 200 MeV–1 GeV, E2: 1 GeV–10 GeV, and E3: 10 GeV–500 GeV). The cross-correlation function was applied to examine the variability properties within these bands. The source showed an E1-E2 high degree of correlation. Its flux distribution was noted to be closer a log-normal probability density function than a Gaussian. A search for QPOs in 100 MeV–500 GeV γ-ray LC was carried out using Lomb–Scargle periodogram, as well as the weighted wavelet Z-transform. Monte Carlo simulations were used to test the significance of the results. Furthermore, the REDFIT tool was used to precisely evaluate the power spectrum signal against the red-noise background. The results confirm the existence of QPO for the PKS 0426–380 blazar at high energy γ-rays, lasting for at least 12.2 yr with a period 3.65±0.45 yr at significance ∼3σ. They are consistent with this distant blazar being a binary system of SMBH with separation R∼0.0029pc, total mass M∼3×108M⊙, and timescale for SMBHs merging TGW∼6.9×104yr.

Pulse wave signal modelling and feature extraction based on Lognormal function from photoplethysmography in wireless body area networks

Among the various physiological signals of the human body, the pulse wave signal from photoplethysmography is widely used for commercial products in Wireless Body Area Networks. The comfortable wearing of a product and the richness of physiological information are two advantages of Wireless Body Area Networks. To address the shortcomings of the existing modelling pulse wave signal in lacking characteristics that are consistent with a human physiological mechanism in medicine, we proposed a Lognormal function model of the pulse wave signal and a novel model to extract physiological parameters. The proposed Lognormal function model consists of four successively spaced single-peaked pulses with long trailing features. To define the parameters in the proposed Lognormal function model, we proposed a method that took advantage of the positivity and negativity of the first-order derivatives and the trans-zero point of the second-order derivatives. Based on the determined parameters, we introduced a four-shot staged curve fitting approach that can displace the sum of the four fits at iterative and different time scales. Finally, a parameter vector with 12 elements, which is known as a physiological feature to determine the health status of the human body in Wireless Body Area Networks. Experimental results show that the proposed Lognormal function model is superior to the conventional Gaussian function model in terms of physiological importance and waveform fitting accuracy.

Stochastic Multi-Objective Optimal Reactive Power Dispatch with the Integration of Wind and Solar Generation

The exponential growth of unpredictable renewable power production sources in the power grid results in difficult-to-regulate reactive power. The ultimate goal of optimal reactive power dispatch (ORPD) is to find the optimal voltage level of all the generators, the transformer tap ratio, and the MVAR injection of shunt VAR compensators (SVC). More realistically, the ORPD problem is a nonlinear multi-objective optimization problem. Therefore, in this paper, the multi-objective ORPD problem is formulated and solved considering the simultaneous minimization of the active power loss, voltage deviation, emission, and the operating cost of renewable and thermal generators. Usually, renewable power generators such as wind and solar are uncertain; therefore, Weibull and lognormal probability distribution functions are considered to model wind and solar power, respectively. Due to the unavailability and uncertainty of wind and solar power, appropriate PDFs have been used to generate 1000 scenarios with the help of Monte Carlo simulation techniques. Practically, it is not possible to solve the problem considering all the scenarios. Therefore, the scenario reduction technique based on the distance metric is applied to select the 24 representative scenarios to reduce the size of the problem. Moreover, the efficient non-dominated sorting genetic algorithm II-based bidirectional co-evolutionary algorithm (BiCo), along with the constraint domination principle, is adopted to solve the multi-objective ORPD problem. Furthermore, a modified IEEE standard 30-bus system is employed to show the performance and superiority of the proposed algorithm. Simulation results indicate that the proposed algorithm finds uniformly distributed and near-global final non-dominated solutions compared to the recently available state-of-the-art multi-objective algorithms in the literature.

Multi-wavelength method based on global optimization for particle size distribution

The particle size distribution (PSD) of particle medium plays an important role in the field of particle science, so the inversion of PSD is of great significance. To study spherical particle PSD, a multi-wavelength detection model based on a global optimization algorithm called OptQuest nonlinear programming (OQNLP) is established in this paper and an experiment to verify the reliability of the system is designed. The numerical results show that the selection of detection wavelength has great influence on the results of PSD inversion. The relative error of PSD parameters is minimized by choosing the wavelength at the peak of extinction coefficient curve of appropriate particle size. Both simulation and experimental results indicate that the five-wavelength method has the highest testing accuracy. When high accuracy is not required, choosing the four-wavelength method is the most suitable testing method. Furthermore, the universality of the model is also confirmed for the Rosin-Rammer (R-R) function, normal (N-N) function, and lognormal (L-N) function.

Dynamical behavior and density function of a stochastic model of HPV infection and cervical cancer with a case study for Xinjiang, China

In this article, combining the transmission features of HPV infection and secondary cervical cancer in Xinjiang, China, a stochastic dynamical model for the HPV infection and secondary cervical cancer with environmental white noise is proposed. Firstly, the stochastic extinction of disease is investigated. A sufficient criterion for the asymptotic behavior of any positive solution of stochastic model revolving around the disease-free equilibrium of corresponding deterministic model is established. Secondly, a threshold criterion for the existence of unique ergodic stationary distribution is obtained by means of the auxiliary function. Furthermore, a new technique of partitioned matrix for the calculation of probability density function is proposed, the expression of a log-normal density function around the quasi-endemic equilibrium of stochastic model is calculated. Lastly, the best-fit parameter values in our model are identified by the MCMC algorithm on the basis of the cervical cancer data in Xinjiang province, China. The basic reproduction number is estimated as 1.3496 (95% CnI: (1.3458, 1.3716)). Then, to determine the key parameters of the model, the sensitivity analysis is explored. Some possible interventions and control measures are provided to reduce the HPV infection spread and cervical cancer in Xinjiang of China.

Seismic Resilience Assessment of Curved Reinforced Concrete Bridge Piers through Seismic Fragility Curves Considering Short- and Long-Period Earthquakes

Curved bridges are commonly used for logistics and emergencies in urban areas such as highway interchange bridges. These types of bridges have complicated dynamic behaviors and also are vulnerable to earthquakes, so their functionality is a critical parameter for decision makers. For this purpose, this study aims to evaluate the bridge seismic resilience under the effects of changes in deck radius (50, 100, 150 m, and infinity), pier height irregularity (Regular and Irregular), and incident seismic wave angle (0°, 45°, and 90°) under short- and long-period records. In the first step, fragility curves are calculated based on the incremental dynamic analysis and probabilistic seismic demand models. Finally, seismic resilience curves/surfaces are constructed and their interpolated values of the log-normal distribution function presented for assessing system resilience. It is found that when long-period records are applied in one given direction, the angle of incidence has the most significant effect on seismic resilience, and bridges are most vulnerable when the angle of incidence tends to 0°. The effect of deck radius on seismic resilience became more remarkable as the angle of incidence increased. Additionally, results indicate that the bridge vulnerability in long-period records is more significant than that under short-period records.