Log-normal Distribution Function Research Articles

Визначення крупності продуктів подрібнення

Mathematical approaches to particle size determination in closed grinding cycles are considered. The features of average particle size calculation for different fractions with account for the grinding kinetics are shown. Particle size calculation algorithms for the entire fraction range are proposed. Particular attention is paid to output determination for fractions of arbitrarily small particles. A particle size determination method based on a lognormal distribution function is shown. In choosing the mathematical approach, the process requirements are taken into account. The basis of in-flow noncontact particle size control is the acoustic monitoring of the process and the established relationships between the particle size and the acoustic characteristics. The signal amplitude during material transportation in the energy carrier flow and jet grinding was found as a function of the particle size and grinding conditions. In order to determine the fractional composition of a mixture, the frequency characteristics of acoustic signals and their variation during the transportation of narrow fractions and mixtures were considered. The analysis of the amplitude-frequency characteristics of acoustic signals during the compressed-air transportation of narrow fractions in the jet mill channels confirmed the presence of signals with frequencies characteristic for each fraction. These frequencies were experimentally related to the particle size of a fraction in a mixture. These studies form a basis for a noncontact method of determining the particle size distribution of a material in an air flow, in particular in jet grinding. The results may be used for engineering and technological calculations in mineral dressing and the development of process equipment for the chemical industry, construction, mining, and metallurgy.

Establishing a Mining Group of Deposit and an Exploration Grid Pattern for Uranium Ore Intercalated in Sandstone at Pa Lua - Pa Rong Area, Nong Son Basin

This research shows the results of establishing a mine group and a uranium ore exploration network in Nong Son depression sandstone, Quang Nam province based on the results of exploration of uranium ore bodies in the Pa Lua - Pa Rong area. Some main findings include: i) The uranium content in most industrial ore bodies can be attributed to a lognormal distribution function. The ore bodies (two main ore bodies are referred to as TQ1 and TQ2) have an average uranium concentration from 0,032% to 0,054% U3O8 with high variations (with the amount of variation in content (Vc) greater than 100%). The average thickness of the ore bodies is from 2,30 meters to 2,35 meters. The thickness variation coefficient (Vm) varies from 89,4% to 100,3%, indicating the unstable to very unstable type of ore body; and ii) Uranium mines in sandstones of the Pa Lua - Pa Rong type, Nong Son basin mainly belong to exploration mine group III. The most reasonable exploration approach is to use a parallel and fan-shaped network. To calculate the reserves, the distance between drilling routes is set at 50 to 60 meters. To determine the road and pavement, wet set the drilling routes to be 25 to 30 meters apart from each other. This exploration network can be applied to other sandstone mines in the Nong Son basin with similar characteristics to the Pa Lua - Pa Rong mine.
 
 

Probability density distributions of morphological parameters of barchan dunes and their responses to the climate environment

Barchan dunes are a common aeolian geomorphology in sand seas on Earth and Mars. They occur primarily as barchan dune groups. Obvious regional differences occur in the size distribution of dune swarms in different dune fields because of sediment grain size, regional airflow, sand flux, and surface conditions. To explore dune size distributions in different barchan dune fields and clarify the effects of climate on barchan dune morphometry, we used high-resolution remote sensing images and extended time-series meteorological data. Barchan dune fields were located in the southeast edge of the Taklimakan Desert, the western and southern parts of the Qaidam Basin Desert, the Gonghe Basin Sandy Land, and the sand belt connecting the Badain Jaran Desert and the Tengger Desert. Our results revealed the probability density distribution of morphological parameters of barchan dunes, correlations among parameters, and responses to wind regime. The main conclusions are: (1) Probability density distributions of the lengths of windward and lee slopes, the lengths of the two horns, and the dune width, height, and spacing in different deserts followed a log-normal distribution function. (2) Good correlations were found among the dune morphological parameters; width and height, windward slope length and width, and height and spacing showed positive proportionality, and the basal area and the product of width and height were linearly correlated in a double logarithmic coordinate system. (3) Good correspondence was found between dune asymmetry and regional wind conditions, which can be explained by Tsoar's model. Morphological parameters of barchan dunes were linearly and positively correlated with the drift potential. These results provide essential data for further study of the morphological thresholds for dune-dune interactions and elucidation of the mechanisms of interaction among barchan dunes.

Empirical Fragility Analysis of Haitian Reinforced Concrete and Masonry Buildings

This study develops empirical fragility curves for concrete and masonry buildings in Haiti, utilizing data from the 2021 earthquake. A dataset of 3527 buildings from the StEER database, encompassing a diverse range of building types, is used. These buildings types include reinforced concrete structures with masonry infills, confined masonry buildings, reinforced masonry bearing walls, and unreinforced masonry bearing walls. Shakemaps from the USGS are utilized to assess the earthquake’s intensity at each building, with the peak ground acceleration (PGA) as the intensity measure. Damage is classified into five distinct states: no damage, minor, moderate, severe, and partial or total collapse. For each of these states, the corresponding probabilities of exceedance are calculated, and log-normal cumulative distribution functions were fitted to those data to produce empirical fragility curves. The results show a notable similarity in performance among the four types, each having high probability of failure even under low-intensity earthquakes. Total fragility curves (including all four building types) are developed subsequently and they are convolved to the probabilistic seismic hazard map of Haiti to assess the seismic risk. This includes estimating the annual probability of partial/total collapse and the probability of partial/total collapse in the event of 475-year and 2475-year earthquakes. The results indicate a significant risk, with up to 64% probability of collapse in certain areas for the 2475-year earthquake and a probability of collapse of 15% for a 475-year earthquake. These findings underscore the critical vulnerability of Haiti’s buildings to seismic events and the urgent need for their retrofit.

Determination of meaningful block sizes for rockfall modelling

The determination of the so-called design block is one of the central elements of the Austrian guideline for rockfall protection ONR 24810. It is specified as a certain percentile (P95–P98, depending on the event frequency) of a recorded block size distribution. Block size distributions may be determined from the detachment area (in situ block size distribution) and/or from the deposition area (rockfall block size distribution). Deposition areas, if present, are generally accessible and measurable without technical aids. However, most measuring methods are subjective, uncertain, not verifiable, or inaccurate. Also, rockfall blocks are often fragmented due to the preceding fall process. The in situ block size distribution is (also) required for meaningful rockfall modelling. The statistical method seems to be the most efficient and cost-effective method to determine in situ block size distributions with many blocks within the whole range of block sizes. In the current literature, joint properties are often described by the lognormal and exponential distribution functions. Today, we can model synthetic rock masses on the basis of discrete fracture networks. They statistically describe the geometric properties of the joint sets. This way, we can carry out exact rock mass block surveys and determine in situ block size distributions. We wanted to know whether the in situ block size distributions derived from the synthetic rock mass models can be described by probability distribution functions, and if so, how well. We fitted various distribution functions to three determined in situ block size distributions of different lithologies. We compared their correlations using the Kolmogorov–Smirnov test and the mean-squared error method. We show that the generalized exponential distribution function best describes the in situ block size distributions across various lithologies compared to 78 other distribution functions. This could lead to more certain, accurate, verifiable, holistic, and objective results. Further investigations are required.

Modelling diameter at breast height distribution of jack pine and black spruce natural stands in eastern Canada

Individual tree diameter at breast height (DBH) distribution is an important information for forest management planning. Forest managers obtain the DBH data either by field measurements or estimations using predictive models. However, probability distribution models are still lacking or need improvement. Therefore, we aimed to construct and fit diameter distribution models that reflect forest structure and composition change. We evaluated gamma, log-normal, and Weibull probability distribution functions (PDFs) for two commercially important tree species, black spruce ( Picea mariana (Mill) B.S.P.) and jack pine ( Pinus banksiana Lamb), grown in natural stands across Ontario, Canada. We modelled the parameters of the distributions as a function of stand-level variables for these species. We used DBH data from 735 permanent sample plots. Our results showed that all three evaluated PDFs reflected observed DBH distribution. We demonstrated that the moment-based recovered parameters could represent the maximum likelihood-estimated parameters precisely, and parameters of the PDFs can be modelled as a function of stand-level dynamic covariates. The models unbiasedly predicted the PDF parameters DBH means and DBH classes. The R2 of the model fit ranged between 0.35 and 0.98 for the predicted parameters and 0.90 and 0.97 for the predicted DBH.

Study of convective air turbulence based on the probability distribution function of angle of arrival fluctuations

This study investigates the probability density function (PDF) of angle of arrival (AoA) fluctuations of a laser beam propagating through convective air turbulence in two settings: indoor turbulence and atmospheric surface layer. The indoor turbulence is generated by an electric heater with a 50 cm × 100 cm surface area placed horizontally on the bottom. The atmospheric turbulence experiments are conducted over a level at 60 cm height from an asphalted area using a slightly divergent laser beam that propagates along 350 m. Image motion monitoring of four sub-apertures installed in front of the receiving telescope aperture is used to record the AoA fluctuations and their PDFs over the entrance pupil at the sub-aperture locations for both types of turbulence. The observations are made in two perpendicular directions to the propagation of the laser beam. The experimental PDFs of the AoA fluctuations are fitted with Gaussian, Lognormal, Weibull, and Gamma distribution functions. The results show that the Weibull and Gamma models are more consistent with the experimental data for the indoor convective air and atmospheric turbulence respectively. For the indoor convective turbulence, the full width at half maximum and the peak location of the measured PDFs increase with the heater temperature, as well as the goodness of fit, which saturates at high temperatures.

Improved predictions of permeability properties in cement-based materials: A comparative study of pore size distribution-based models

Permeability is a fundamental physical property of a cement-based material and is closely related to its pore structure. This study developed an improved model for permeability prediction of cementitious materials with a function of the pore size distribution (PSD), in which PSD is simulated from single and compound lognormal distribution functions, respectively. The efficiency of the improved model is demonstrated by calculating permeability for mortars and pastes available in the literature. It is found that, first, for cementitious materials with unimodal PSD, the single lognormal distribution function is adequate to describe the pore structures. In contrast, for cementing mixtures presenting multimodal PSD, the compounded lognormal distribution function is highly recommended to cover a wide range of pore components. Second, the permeability model based on the compound PSD can predict well permeability to gas intrusion, whereas the single PSD-based model is applicable for calculating permeability via water intrusion. Furthermore, slippage effect and water saturation degree are introduced in the PSD-based model. Results prove that the corrected gas permeability model from the compound PSD performs well in estimating the gas permeability in unsaturated states. Finally, the compound PSD-based model is extended by considering varying porosities and relative humidities, which can be used to quantitively describe permeability when cementitious materials undergoing pore structure degradation induced by durability issues.

Integrating renewable energy and V2G uncertainty into optimal power flow: A gradient bald eagle search optimization algorithm with local escaping operator

AbstractHere, a new approach is proposed for solving the optimal power flow (OPF) problem in transmission networks using a Gradient Bald Eagle Search Algorithm (GBES) with a Local Escaping Operator (LEO). The method takes into account uncertainty of the renewable energy sources (wind energy and photovoltaic systems) and Vehicle‐to‐Grid (V2G) in the stochastic OPF problem. To improve the efficiency of the proposed technique and enhance its local exploitation capability, the LEO method's selection features are utilized. Monte Carlo methods are employed to estimate the generation costs of the renewable sources and PEVs and study their feasibility. The uncertainty of the renewable sources and PEVs is represented by Weibull, lognormal, and normal probability distribution functions (PDFs). The GBES approach is experimentally compared with well‐known meta‐heuristics using twenty‐three different test functions, and the results indicate its superiority over BES and other recently developed algorithms. Furthermore, the proposed method's effectiveness is evaluated using IEEE 30‐bus test system under various scenarios, and the simulation results demonstrate that it can effectively address OPF issues considering renewable energy sources and V2G, providing superior optimal solutions compared to other algorithms.

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.

Superparamagnetic behavior of non-interacting antiferromagnetic ferritin nanoparticles

Ferritin is an important biological system and found in blood of living organisms. Inorganic cores of this material are 8 nm in size. The cores are surrounded by protein shells which reduce interparticle interaction. Particle size distribution present in ferritin is determined from transmission electron micrograph. This distribution can be described by a log normal distribution function. The magnetic field (0–70 kG) dependence of the magnetization at different temperatures are analyzed considering the estimated particle size distribution. The resulting mean particle magnetic moment is temperature independent and equal to 310 μB. Saturation magnetization and antiferromagnetic susceptibility of ferritin decrease with increasing temperature.

Brash ice macroporosity and piece size distribution in ship channels

Merchant vessels' performance on brash ice plays an important role in navigation in fast ice conditions in Northern Baltic ports. Among many parameters, the piece size distribution and macroporosity of the brash ice influence the accuracy of the model simulations of ship performance in brash ice. These properties also govern the brash ice accumulation and consolidation in ship channels. The current work presents analyses of macroporosity and piece size distribution from three full-scale brash ice channels investigated during winters 2020–21 and 2021–22. The results provide insights into brash ice macroporosity and piece size distribution. Smaller brash ice pieces exhibited higher porosity. On each measured cross-section, the average macroporosity ranged from 1.4% to 23%, with standard deviations of 3.8% and 16%, respectively. Porosity variations were observed in relation to equivalent brash ice thickness, the number of ship passages, and cumulative freezing air temperatures. Total porosity and the channel's brash ice porosity initially increased with breaking events and then stabilized at approximately 23% and 30%, respectively, after 9 passages. In contrast, side ridge porosity increased initially (up to 23%) and subsequently decreased. The initial total, brash ice and side ridge maximal porosities after the breaking event were estimated equal to 25%, 35% and 30%, respectively. The first two channels, which were navigated a total of 9 and 10 times, had an average degree of brash ice consolidation equal to 0.84 and 0.76, and an average degree of side ridge consolidation equal to 1.1 and 1.0, respectively. The third channel, characterized by frequent navigation, exhibited a consolidation degree of 0.82 for brash ice and 1.35 in the side ridges. The average vertical piece size across all cross-sections ranged from 0.28 m to 0.52 m with standard deviations of 0.16 m and 0.25 m. The average horizontal piece size ranged from 0.33 m to 0.4 m with standard deviations between 0.2 m and 0.34 m. The horizontal piece size distribution of brash ice was best described by the probability density function of a three-parameter lognormal distribution.

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.

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.

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.

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.

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.

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.