Search Results (369)

The seismic fragility of reinforced concrete (RC) bridge piers is critical for urban rail transport systems, as severe pier damage may interrupt post-earthquake operation and threaten network safety. Compared with conventional highway bridge piers, urban rail transport RC solid piers usually have lower axial load ratios, larger cross-sections, and stricter serviceability requirements. However, the combined effects of geometric parameters, reinforcement detailing, and material strength on their cyclic behavior, dynamic response, and seismic fragility remain insufficiently understood. To address this issue, seven 1/4-scale RC solid pier specimens were tested under quasi-static cyclic loading to examine the effects of pier height, transverse reinforcement ratio, and longitudinal reinforcement ratio on damage evolution, hysteretic response, skeleton curves, and energy dissipation. A fiber-based OpenSees model considering bond-slip effects was then established, validated against the tests, and extended to a full-scale prototype pier for parametric analysis. The effects of aspect ratio, axial load ratio, longitudinal reinforcement ratio, stirrup ratio, steel yield strength, and concrete strength were evaluated under cyclic loading and nonlinear dynamic time-history excitations. An incremental dynamic analysis-based probabilistic seismic demand model was further developed using 30 near-fault ground motions, with peak ground acceleration as the intensity measure and displacement ductility as the engineering demand parameter. The results showed that increasing the aspect ratio changed the failure mode from flexure-shear-dominated to flexure-dominated behavior, increasing the ultimate displacement from 122 mm to 155 mm while reducing the peak lateral strength from 263 kN to 248 kN. Increasing the longitudinal reinforcement ratio improved both peak strength and ultimate displacement, from 226 kN to 262 kN and from 120 mm to 160 mm, respectively. The numerical results indicated that aspect ratio, axial load ratio, and longitudinal reinforcement ratio had more pronounced effects on seismic demand and fragility than stirrup ratio. Increasing steel yield strength generally reduced seismic fragility, whereas increasing concrete strength enhanced lateral resistance but did not necessarily improve fragility performance. These findings suggest that the seismic performance of urban rail transport RC solid piers should be evaluated by combining cyclic response, dynamic demand, and fragility-based performance, rather than by maximizing any single design parameter. Full article

Mesenchymal stromal cells (MSCs) are central to regenerative medicine and advanced therapies. However, the absence of consensus on reporting kinetic parameters, such as population doubling level (PDL), population doubling time (PDT), and the reliance on passage number alone obscures biological age and manufacturing history, and limits correlation of potency with expansion dynamics. Here, we clarify the distinctions among passages, PDL, PDT, and replication rate; we synthesize evidence that identical passage numbers can conceal multifold differences in cumulative doublings, with downstream effects on transcriptomic stability, and immunomodulatory performance. We further highlight culture determinants, oxygen tension, seeding density, media formulation, surface/bioreactor systems, and early niche mimetic stimuli, that shape proliferative kinetics and cellular aging trajectories in WJ-MSCs. Critically, we propose extracellular vesicles (EVs) as sensitive functional readouts of bioprocess stress and expansion history: EV quantity can increase while functional bioactivity declines, and EV miRNA cargo captures cell state programs not evident from minimal identity markers. To address these gaps, we recommend a reporting framework that incorporates: (1) culture conditions, (2) passage number and PDL at harvest, and (3) functional consequences of expansion. Adopting kinetic metrics beyond passage number will harmonize data capture and enable pooled analyses, accelerating clinical translation while safeguarding patient outcomes. Full article

Background/Objectives: Obstructive sleep apnea (OSA) and related sleep disorders affect a substantial proportion of hospitalized patients, with an estimated 48% pooled prevalence of undiagnosed OSA in cardiac inpatients and up to 80% of moderate-to-severe community OSA cases carrying no formal diagnosis at the time of hospital admission. In parallel, frailty—a state of heightened physiological vulnerability arising from cumulative multi-system biological decline—is present in 40–80% of inpatients and shares deep, bidirectional neurobiological pathways with sleep-disordered breathing through circadian dysregulation, intermittent hypoxia, hypothalamic–pituitary–adrenal axis activation, and chronic low-grade inflammation. Despite this convergence, no prior study has integrated validated, administratively computable frailty phenotyping with a machine learning framework specifically designed to predict inpatient sleep disorder diagnosis—and OSA in particular—at the point of hospital admission. The present study addresses this gap by developing an admission-time, explainable machine learning framework for the prediction of inpatient sleep disorder diagnoses (ICD-10 G47.x, encompassing OSA G47.3, insomnia G47.0, hypersomnia, and circadian rhythm disorders) and of insomnia specifically (ICD-10 G47.00). Methods: We developed and evaluated a suite of five binary classification models—XGBoost, Random Forest, LightGBM, CatBoost, and Decision Tree—using 9682 balanced hospitalization episodes from the MIMIC-IV (version 2.2) database. The predictor set comprised 23 admission-time structured features across three domains: (i) frailty and comorbidity burden, including the Hospital Frailty Risk Score (HFRS) derived from ICD-10 codes, the Elixhauser comorbidity index, prior admission history, and six binary disease flags (obesity, hypertension, type 2 diabetes, heart failure, COPD, and depression/anxiety); (ii) physiological and laboratory biomarkers from the first 24 h of care, including minimum SpO₂, heart rate variability, hemoglobin, creatinine, albumin, and arterial blood gas parameters; and (iii) sociodemographic and administrative variables encompassing age, sex, ethnicity, insurance type, and admission acuity. Model performance was assessed through five-fold stratified cross-validation and bootstrap confidence intervals (n = 1000 iterations), with predictor importance quantified using SHapley Additive exPlanations (SHAP). Results: XGBoost achieved the strongest aggregate performance across all evaluation metrics, attaining an area under the receiver operating characteristic curve (AUC) of 0.871 (95% CI: 0.856–0.887), accuracy of 79.6%, F1-score of 0.820, and sensitivity of 94.9%, correctly identifying 903 of 952 true positive cases in the held-out test set; all gradient boosting frameworks substantially outperformed the Decision Tree baseline (AUC 0.836). SHAP analysis identified the HFRS and Elixhauser index as the two dominant predictors, followed by depression/anxiety, obesity, hypertension, and minimum SpO₂—a hierarchy that recapitulates the canonical clinical phenotype of obstructive sleep apnea in frail inpatients rather than that of primary insomnia, indicating that the model is preferentially capturing the OSA–frailty axis within the broader G47.x outcome. The predicted probability outputs were well-calibrated across all risk deciles. Conclusions: Frailty-derived features, in combination with admission-time clinical and physiological data, can predict inpatient sleep disorder diagnoses—predominantly OSA—with high sensitivity and well-calibrated risk estimates. The deployable, interpretable nature of the XGBoost model makes it directly suitable for integration into clinical decision support systems, offering a screening tool that requires no dedicated instrumentation beyond routine admission data. By flagging high-risk patients at the moment of admission, the framework provides a concrete mechanism for accelerating referral for definitive diagnostic confirmation (overnight oximetry, polysomnography) and earlier initiation of CPAP and related therapies, with direct implications for reducing the persistent diagnostic gap, perioperative risk, and preventable adverse outcomes in frail hospitalized populations. Full article

We develop a fast Chebyshev spectral collocation method for a coupled system of nonlinear Klein–Gordon equations augmented by Caputo-type fractional memory integrals. The governing equations retain the classical second-order time derivative as the leading operator and incorporate weakly singular convolution integrals modelling viscoelastic memory damping. The spatial discretisation employs Chebyshev–Gauss–Lobatto collocation, while the temporal integration uses a Newmark scheme (${\beta }_{\mathrm{NM}}=1/4$) combined with an implicit–explicit linearisation in which the linear spatial operator is treated implicitly and the nonlinear terms are treated explicitly through a second-order extrapolation. This linearisation eliminates the need for Newton–Raphson iterations at each time step. To overcome the dense memory bottleneck arising from two distinct fractional orders $\alpha \ne \beta$, the convolution memory kernels are compressed by independent sum-of-exponentials approximations obtained from a double-exponential quadrature of the kernel’s integral representation, which significantly reduces the computational complexity of the history term. A rigorous stability estimate and a global convergence bound are established using a discrete Grönwall inequality. Numerical experiments confirm the theoretical temporal and spatial convergence rates and demonstrate the practical speed-up afforded by the sum-of-exponentials acceleration. A solitary wave collision scenario illustrates the method’s capability to capture asymmetric dispersive wakes generated by the fractional memory. Full article

To ensure a reliable electrical isolation point in power systems, the seismic performance assessment of disconnect switches is of critical importance for maintaining operational continuity under earthquake excitations. In this study, a hybrid method combining a convolutional neural network (CNN) and a long short-term memory (LSTM) network is proposed for the seismic intelligent classification and response prediction of disconnect switches. Unlike conventional approaches that rely on finite element simulations or shake table tests with high computational costs, the proposed method learns directly from raw ground motion records. The CNN component is designed to capture local frequency characteristics of input ground motions, enabling automatic classification into low-, medium-, or high-frequency categories. Subsequently, category-specific LSTM models are established to map the ground motion time series to multi-dimensional performance indicators of the disconnect switch. These indicators include top absolute accelerations, bottom shear forces, and relative deformations of porcelain posts. A training set comprising 102 ground motion records is constructed based on numerical simulations of a validated simplified model, while another testing set comparing 21 ground motion records are employed to validate the performance of predicted models. Training and validation results demonstrate that the CNN achieves a great classification accuracy. The LSTM predictions show good agreement with the computed time-history responses, with errors of root-mean-square responses generally within 10%. The proposed method provides a rapid, data-driven alternative to traditional seismic analysis, significantly reducing computational time while preserving prediction fidelity. It also enables the parallel prediction of multiple coupled performance indicators, which is not readily achievable by existing single-output surrogate models. Full article

The piping systems are critical non-structural elements (NSEs) whose seismic performance directly affects the post-earthquake functionality of essential facilities. However, current seismic design provisions for such systems remain largely empirical, and behavioural factors are rarely calibrated using performance-based methods. This study implements an FEMA P695-inspired framework to calibrate the behaviour factor $\left(q_a\right)$for the installation of sway-braced suspended piping restraint systems in following the force-based requirements specified in Eurocode 8. The representative piping archetypes were developed and analysed using non-linear time history analyses under multiple seismic intensity levels derived from the floor response spectra (FRS) of prototype-reinforced concrete buildings. Fragility curves for two limit states were derived with displacement ductility adopted as the engineering demand parameter (EDP) and peak floor acceleration (PFA) used as the intensity measure (IM). The results show that increasing $\left(q_a\right)$ systematically shifts the fragility curves towards lower median PFA values, indicating higher seismic vulnerability at larger behaviour factor values. The effect of piping layout configuration was of secondary importance compared to the applied reduction factor. The implemented approach provides a rational basis for selecting behavior factors consistent with explicit performance objectives and supports further development of performance-oriented seismic design procedures for non-structural systems. The results show that increasing the behaviour factor $\left(q_a\right)$ leads to a systematic shift in the fragility curves towards lower median PFA values and a noticeable increase in the dispersion of the response. A quantitative analysis shows that increasing the behaviour factor $\left(q_a\right)$ from 1 to 4 results in a reduction of up to approximately 60% in median PFA, highlighting a significant increase in seismic vulnerability at higher behaviour factor values. Full article

Top-heavy industrial towers, which carry large, concentrated masses of equipment at upper levels and feature open lower stories, are vertically irregular by design and tend to amplify seismic displacement and acceleration demands near the tower top. Although tuned mass dampers (TMDs) have been studied extensively for buildings, bridges and chimneys, their application to this particular class of slender industrial towers—where production-equipment vibration tolerance, retrofit accessibility and limited downtime drive the design—has received little dedicated attention. This paper reports a focused numerical investigation of seismic response mitigation for a 101.2 m molten-asphalt granulation tower retrofitted with a single pendulum-type TMD. A three-dimensional coupled finite element (FE) model was constructed in ABAQUS using C3D8R solid elements for the reinforced-concrete shaft and T3D2 truss elements for the embedded reinforcement; modal analysis returned a fundamental frequency of 0.912 Hz and a torsional-to-translational period ratio of 0.65, indicating a translational-mode-dominated response. Elastic time-history analyses under the El Centro and Taft records together with a code-spectrum-compatible synthetic accelerogram show that a pendulum TMD with mass ratio μ = 2.5%, tuning frequency offset Δf = 5% and damping ratio ξ = 10%—installed at the uppermost equipment level guided by the modal-displacement criterion—reduces the peak top displacement, peak top acceleration and peak base shear by roughly 23%, 23% and 22%, respectively, in both principal directions. The controlled top acceleration falls comfortably below the 2.94 m/s² operational tolerance of the on-tower melting equipment. To address the rationality of the chosen TMD parameters, a single-variable parametric sensitivity study spanning μ ∈ [1%, 5%], ξ ∈ [5%, 15%] and Δf ∈ [0%, 10%] is performed on an equivalent reduced model that captures the qualitative parameter-response trends; the chosen baseline values lie inside a stable performance plateau and are shown to be a balanced compromise among the three response measures. The principal contribution of the work is, therefore, (i) a complete TMD retrofit framework—modal-based placement, parameter design, coupled FE assembly and multi-record verification—adapted to top-heavy industrial towers, and (ii) qualitative evidence, supported by a sensitivity scan, with a robust proposed parameter set for small-to-moderate detuning. The study is restricted to elastic time-history analyses under frequent-earthquake-level excitation, three ground-motion records and a fixed-base assumption; nonlinear response, larger record sets and soil–structure interaction effects are explicitly identified as scope limitations and are left for follow-up work. Full article

Liquefaction-induced damages related to excess pore water pressure generation in soils and stiffness degradation significantly influence infrastructure and seismic ground response, requiring reliable experimental testing setups and validated numerical models for accurate assessment. This study investigates the free-field liquefaction behavior of saturated sands using the newly proposed ETILam (Enhanced Transparent Impermeable Laminar) soil container under 1 g shaking table conditions. Specimens composed of loose and dense saturated sands overlain by a dry sand layer were prepared and tested under two harmonic motions (0.1 g–2 Hz and 0.2 g–2 Hz), the second motion being two consecutive 6 s excitations. Dynamic response was evaluated through acceleration time histories, shear strains obtained through displacement measurements, excess pore water ratio (r_u), response spectra, transfer functions, and Fourier amplitude computations. Fully coupled effective stress analyses were performed in 2D and 3D using calibrated PM4Sand and P2PSand constitutive models. Experimental results showed limited liquefaction for the lower-amplitude motion, whereas the higher-amplitude motion triggered significant shear strains (up to 10%) and r_u values approaching 0.8, with depth-dependent dissipation patterns between sequential shakings. Numerical simulations reproduced acceleration amplitudes and general pore-pressure trends, with the 2D model providing closer agreement in both generation and dissipation behavior. The findings validate the ETILam container’s capability to simulate free-field liquefaction response and demonstrate that a well-calibrated 2D approach can reliably capture the essential features of the observed behavior. Full article

Based on the fractional entropy originating from fractional quantum mechanics, the fractional holographic dark energy (FHDE) model has been proposed. In this paper, we consider an interaction between the pressureless matter and FHDE and analyze three different interacting FHDE models. Combining the latest observational data including SNIa, OHD, BAO, and CMB, we estimate the model parameters and find that the interaction forms $Q=\gamma H{\rho }_{de}$ and $Q=\beta H{\rho }_m+\gamma H{\rho }_{de}$ show some preference from the observational data. Using phase space analysis, we further find that only interacting FHDE model with $Q=\beta H{\rho }_m+\gamma H{\rho }_{de}$ can describe the full evolutionary history of the universe. The statefinder diagnostic pair reveals that this model deviates from the $\mathsf{\Lambda }$CDM model but converges to the $\mathsf{\Lambda }$CDM fixed point and the de Sitter expansion fixed point in the future. Finally, we analyze the evolution of cosmological parameters and demonstrate that this model can drive the late time acceleration of the universe. Full article

Damping modeling significantly influences the numerical seismic response of buildings, something that, despite being repeatedly emphasized in earthquake engineering research, is still overlooked even by seismic codes. It is a fact that, for simplification and ease of application, modern seismic design provisions assume damping for buildings entirely composed of a single material, e.g., reinforced concrete or structural steel. The current codes offer no guidance on damping assumptions for so-called mixed buildings comprising a lower part (stories) of reinforced concrete and an upper part (stories) of structural steel. Despite the growing use of mixed reinforced concrete-structural steel buildings, damping modeling of their seismic response remains almost unexplored. This study aims to contribute to this field by investigating the effect of different damping models on the elastic and inelastic seismic response of realistic three-dimensional mixed buildings. Modal response spectrum and time-history analyses served for this purpose. Key seismic response parameters, including interstory drift ratios, floor accelerations, and base shear demands, are extracted and systematically compared for the examined damping models. The results highlight the sensitivity of computed seismic demands to the assumed damping model. Guidance on selecting a damping model for the seismic analysis of mixed reinforced concrete-structural steel buildings is provided. Full article

To investigate the influence of ambient temperature variations on the natural vibration characteristics and seismic responses of suspen-dome structures, a 1:20 geometric similarity dynamic scale model was designed using the symmetric suspen-dome roof of the Lanzhou Olympic Sports Center Gymnasium as the prototype. First, white noise excitation tests and seismic simulation tests were performed on the model, and the indoor ambient temperature was measured simultaneously. Subsequently, a corresponding numerical scaled model was developed using the ABAQUS 2024 finite element software, and its temperature was set according to the shaking table test measurements. Modal analysis and seismic time–history analysis were then performed, and the model’s natural frequencies and seismic responses (such as acceleration, displacement, and internal force) were compared with the shaking table test results, thereby validating the accuracy of the numerical model and confirming that the modeling approach reliably reproduces the natural frequencies and seismic responses measured in the tests. Finally, the ambient temperature of the numerical model was set according to the historical temperature data for Lanzhou. A comparative analysis was performed to examine the variations in the natural vibration characteristics and seismic responses of the suspen-dome structure under different temperature conditions. The result shows that, as the ambient temperature increases from −30 °C to 60 °C, the natural frequencies of the suspen-dome structure decrease by up to 21.8% (e.g., the third-order frequency drops from 9.423 Hz to 7.734 Hz), with low-order natural frequencies being the most significantly affected. Furthermore, under both unidirectional and three-dimensional earthquake excitations, the peak seismic responses increase markedly: acceleration increases by up to 35.5%, displacement increases by up to 88.3%, and internal force in critical members increases by up to 68.9%. Notably, structural members experiencing higher internal force responses demonstrate greater sensitivity to ambient temperature changes. These findings indicate that ambient temperature variation significantly reduces structural stiffness and amplifies seismic responses, providing a valuable reference for the seismic performance evaluation and safety design of suspen-dome structures in regions with large annual temperature fluctuations. Full article

The prediction of drying kinetics in hygroscopic biological materials remains challenging due to the strong coupling between internal moisture diffusion, evolving surface wettability, material deformation and thermolabile bioactive compounds degradation. In this context, periodic temperature variations are inherent to many industrial and solar drying systems, yet most experimental and modeling studies evaluate product quality under constant-temperature conditions. This work provides a demonstration that periodic drying can alter quality degradation pathways in ways that may not be captured by constant-temperature experiments. A coupled non-isothermal lattice Boltzmann method (LBM) model for heat and moisture transport was integrated with a Weibull kinetic formulation to describe the degradation of total carotenoids, total polyphenols, and antioxidant activity in carrot slices. Validation against experimental data across 50–70 °C demonstrates excellent agreement (R² > 0.96 for moisture ratio; quality retention within ±2% of the literature values). Seven drying scenarios were systematically evaluated: constant temperature (60 °C), fast and slow periodic oscillations, high-amplitude cycles, a mixed strategy combining constant initial drying with subsequent oscillations, and two intermittent ON/OFF profiles. Results reveal that while total polyphenol degradation within the present model is constrained to ~13.3% retention under the adopted kinetic parameters, carotenoid and antioxidant retention are highly sensitive to temperature history. The mixed strategy (60 °C for 2 h followed by 50–60 °C oscillations) achieves the highest quality retention (TC: 51.6%, AA: 34.4%) while requiring the lowest energy input (0.512 kJ), outperforming constant drying (TC: 48.8%, AA: 32.9%, 0.563 kJ). Conversely, high-amplitude intermittent drying (70/25 °C) accelerates carotenoid degradation (TC: 46.7%) despite shorter drying time (8.81 h), and low-amplitude intermittent cycling (65/55 °C) yields the poorest mean quality (31.4%) with the highest energy consumption (0.583 kJ). The framework reveals that oscillation frequency critically determines quality outcomes: slow cycles (8 h period) marginally improve retention, while fast cycles (2 h) offer no benefit over constant drying. These findings provide quantitative insights toward the design of drying strategies, demonstrating that optimal strategies must account for the coupling between temperature history and moisture-dependent vulnerability, with the mixed strategy emerging as the best-performing strategy among the tested scenarios. Full article

Ensuring the crashworthiness of heavy-duty truck cabs is essential for reducing occupant fatalities and improving passive safety in commercial vehicles. Regulatory frameworks such as UNECE Regulation No. 29 (R29) define structural integrity requirements through full-scale destructive impact tests, which are costly and limit iterative design. In this study, an integrated experimental–numerical methodology is presented for the impact assessment of a real Iveco Eurocargo 120E18 truck cab reconstructed using high-resolution 3D scanning. The scanned geometry was used to generate a dimensionally accurate CAD model of the load-bearing cab structure, which was analysed using explicit finite element simulations in ANSYS Academic Mechanical and CFD Teaching package under impact conditions compliant with UNECE R29 and implemented according to the Swedish regulation VVFS 2003:29. In parallel, a full-scale physical pendulum impact test was performed on the same cab using a cylindrical impactor with a diameter of 580 mm, a length of 1800 mm, and a mass of approximately 1000 kg, impacting the upper region of the A-pillar. The experimental setup was instrumented using high-speed optical measurements and an accelerometer to capture impact kinematics and structural response. The numerical predictions showed good agreement with experimental results in terms of acceleration–time histories, absorbed energy evolution, and structural deformation, with differences generally below 6%. Critical regions susceptible to local buckling and plastic collapse were consistently identified in both approaches, while preservation of the driver survival space was confirmed. The results demonstrate that scan-based finite element models, when properly calibrated and validated, can reliably reproduce certification-level impact behaviour. The proposed workflow provides a robust and cost-effective framework for regulatory pre-validation, structural optimisation, and digitalisation of crashworthiness assessment for heavy-duty truck cabs. Full article

On 6 February 2023, two major earthquakes occurred approximately nine hours apart in the Pazarcık (M_w = 7.7) and Elbistan (M_w = 7.6) districts of Kahramanmaraş, Türkiye. These devastating earthquakes caused extensive damage in many cities in the region. Kahramanmaraş and Malatya were among the cities most severely affected. Therefore, Kahramanmaraş and Malatya were chosen for this study. The aim was to investigate the effects of the earthquakes on the city centers of the selected cities. Reinforced concrete buildings of four, six, eight, and 10 floors were designed in accordance with Türkiye seismic codes. Linear response spectrum analysis (LRSA) was applied to these buildings according to the Türkiye Earthquake Code 2018 (TEC-2018), the Türkiye Earthquake Code 2007 (TEC-2007), and the Eurocode 8 (EC8). In addition, acceleration records of the 2023 Kahramanmaraş earthquakes were obtained from accelerometer stations near the city centers of the aforementioned cities. Nonlinear time history analysis (NTHA) was performed on sample buildings using these acceleration records. As a result of these analyses, base shear forces and roof displacements were obtained. Design acceleration spectra were obtained according to the Türkiye earthquake codes and the Eurocode 8. Acceleration spectra of the earthquakes were also obtained based on the acceleration records of the earthquakes. A comparison was made between TEC-2007, TEC-2018, and EC8 based on the LRSA calculation results. The calculations show that TEC-2018 is more detailed and realistic than TEC-2007. Furthermore, it was determined that the values obtained according to EC8 were greater than the values obtained according to TEC-2007 and TEC-2018. The results obtained from LRSA and NTHA were compared. It was determined that the results obtained from NTHA were much larger than those obtained from LRSA. Full article

To evaluate the seismic performance of single-degree-of-freedom (SDOF) systems under mainshock–aftershock (MS–AS) seismic excitation, nonlinear time-history analyses were conducted on SDOF systems with various parameter combinations, using 50 sets of real MS–AS sequences and 150 sets of artificial sequences generated by repetition, random, and attenuation methods. The results indicate that the ground motion characteristics of MS–AS sequences generated by the repetition, random, and attenuation methods differ from those of real MS–AS sequences, with the repetition and random methods tending to overestimate the peak ground motion parameters and acceleration response spectra of MS–AS sequences, and the attenuation method potentially underestimating them, while all three methods for generating MS–AS sequences are prone to overestimating the ground motion duration of MS–AS sequences. Residual deformation is influenced by relative yield strength coefficient (η), aftershock relative intensity (χ), post-yield stiffness ratio (r), natural vibration period (T) and the hysteresis model under MS–AS seismic excitation, and residual deformation exhibits a positive dependence on aftershock intensity (χ) and a negative dependence on post-yield stiffness ratio (r), while the relationship between residual deformation and relative yield strength coefficient (η) is influenced by the natural vibration period (T), showing a positive correlation in the short-period range and a negative correlation in the mid-to-long period range. A log-normal distribution can be adopted to describe the probability distribution of the ratio of residual deformation to peak elastic-plastic deformation subjected to MS–AS seismic excitation with different parameters. Finally, a probabilistic prediction model for residual deformation under MS–AS seismic excitation was proposed which can effectively predict residual deformation under MS–AS seismic excitation. Full article