Force Time Series Research Articles

Test-retest reliability and concurrent validity of knee extensor strength measured by a novel device incorporated into a weight stack machine vs. handheld and isokinetic dynamometry.

The current clinical gold standard for assessing isometric quadriceps muscle strength is an isokinetic dynamometer (IKD). However, in clinics without an IKD, clinicians default to using handheld dynamometers (HHD), which are less reliable and accurate than the IKD, particularly for large muscle groups. A novel device (ND) was developed that locks the weight stack of weight machines, and measures forces applied to the machine, turning this equipment into an isometric dynamometer. The objectives of this study were to characterize the test-retest reliability of the ND, determine the within-day and between-days inter-rater reliability and concurrent validity compared with that of the HHD, in healthy volunteers (HV) and individuals with knee osteoarthritis (OA) for measuring knee extensors isometric muscle force. 29 healthy (age = 28.4 ± 7.4 years) and 15 knee OA (age = 37.6 ± 13.4 years) participants completed three maximum force isometric strength testing trials on dominant side knee extensor muscles on three devices (ND, HHD, and IKD) in two separate sessions by two raters. The maximum force (Fmax) produced, and the force-time series were recorded. Reliability and validity were assessed using Intraclass Correlation Coefficient (ICC), Bland-Altman Plots, Pearson's r, and cross-correlations. The ND demonstrated excellent test-retest reliability (ICC2,3 = 0.97). The within-day (ICC2,3 = 0.88) and between-day inter-rater reliability (ICC2,3 = 0.87) was good for HHD. The ND showed excellent within-day (ICC2,3 = 0.93) and good between-day (ICC2,3 = 0.89) inter-rater reliability. The Bland-Altman analysis revealed HHD systematic bias and underestimation of force particularly with quadriceps force values exceeding 450 N. Mean differences were found in maximum force between HHD vs. IKD (MDabs = 58 N, p < .001) but not the HHD vs. ND (MDabs = 24 N, p = .267) or ND vs. IKD (MDabs = 34 N, p = .051). The concurrent validity of Fmax (r = 0.81) and force-time curve correlation (0.96 ± 0.05) were the highest between the ND and IKD. The ND's test-retest reliability and concurrent validity make it a potential strength assessment tool with utility in physical therapy and fitness settings for large muscle groups such as the knee extensors.

Induced fatigue impact on plantar pressure in females with mild hallux valgus

Fatigue has been established to change plantar pressure distribution, yet its impact on hallux valgus (HV) patients, who exhibit morphological and biomechanical changes in the foot, remains insufficiently studied. Twenty-eight female participants, comprising 16 with mild HV and 12 healthy controls, were recruited. Plantar pressures were recorded pre- and post-fatigue using the Footscan platform during self-selected-speed walking trials, fatigue protocol was performed on a treadmill. Foot was segmented into 10 anatomical regions for calculating parameters including maximal force, peak pressure, impulse, contact duration, contact area, and force time-series, alongside assessing the distribution of medial and lateral contact forces (Foot balance) across the groups. During post-fatigue, patients with mild HV demonstrated adaptive changes in plantar pressure distinct from healthy controls, with significant reductions in maximal force, peak pressure, and impulse in the M1 and M2 regions and increases in the M3–M5 regions. In contrast, the control group exhibited an opposite pattern, concentrating pressure in the M1 and M2 regions post-fatigue. The force time-series analysis revealed significant disparities between HV patients and controls, particularly in the M4 and M5 regions, where HV patients showed a less pronounced and lower passive peak in forces. Results show that women with mild HV demonstrate adaptive changes in plantar pressure post-fatigue, distinctly different from healthy individuals, aiding in preventive strategies for fatigue-induced foot injuries for HV patients.

Analysis of turning ability of large tankers with and without bulbous bow in calm sea and waves

The present study introduces an experimental and numerical investigation of the turning ability of two ships with and without a bulbous bow: original and modified KVLCC2 hulls Experiments are performed via free-running model tests in a square basin, and a system-based simulation are performed. The maneuvering coefficients for the system-based solver are obtained via numerical planar motion mechanism (PMM) tests based on CFD computations, and other variables are obtained from reference ships. The effects of ship speed, wave direction, and wavelength are investigated. Results of a calm-water turning test obtained experimentally and numerically agree well. When the ship turns in the presence of incident waves, the overall behavior and evaluation parameters predicted in the simulation are similar to those obtained from experiments. However, the evaluation parameters show scattered values under severe turning-failure conditions. The most significant wave effects are observed in short waves. Additionally, the turning ability is compared between two ships, and slightly different maneuvering capabilities are observed. The time series for two hulls are further compared to investigate the reason for the difference showing the difference in the force and drift angle time series.

Quantifying intra‐ and inter‐annual dynamics of river‐floodplain connectivity and wetland inundation with remote sensing and wavelet analysis

AbstractWe used imagery from remote sensing (FORCE Time Series Analysis submodule (combining Landsat and Sentinel‐2 imagery) to derive spatially distributed times series (8 years) of NDWI data to infer patterns of floodplain inundation and river‐floodplain connectivity in two contrasting polders in the Lower Oder Valley National Park. The upstream Polder A (14.4 km2) was extensively flooded for prolonged periods most winters. Wavelet analysis showed that this strong seasonality was primarily driven by winter water levels in the river Oder that could enter and leave the polder through two opened floodgates. Subsequent drainage was slow and aided by a pumping station. Inundation of the downstream Polder 10 (17.7km2) was lower and had less marked seasonality. This reflected the impact of flood attenuation by storage in Polder A upstream, but also the greater connectivity (via 10 floodgates) to the Oder and a functional network of channels, which facilitated rapid drainage after flood peaks. In Polder A, secondary periods of transient inundation could also occur in response to local intense summer rainfall. Wavelet analysis also showed that groundwater recharge in and around Polder A is primarily induced by floodwater, whilst Polder 10 also reflects the influence of local rainfall‐driven recharge. The flood regimes of the two polders showed marked inter‐annual variation, largely dependent on flows from the upper Oder catchment. Understanding these patterns and processes of inundation is important for both managing flows and sustaining valuable wetland habitats within the National Park. Given projected climate change in eastern Europe and possible management alterations to the flow regime of the Oder, the potential implications for these habitats needs urgent attention.

Aerodynamic performance and dynamic response of high-speed trains passing by each other on cable-stayed bridge under crosswind

High-speed trains (HSTs) passing by each other on cable-stayed bridges (CSBs) generated aerodynamic forces that significantly reduced the operational safety and stability of the trains. This study conducted a systematic analysis of the process through the co-simulation of Computational Fluid Dynamics (CFD) and Multi-Body Dynamics (MBD). First, a CFD model was established to analyze the flow field and aerodynamic forces of HSTs passing by each other on the CSB, based on the overset grid technology. Then, a finite element model for the CSB-track was established to obtain the deformation of the rail under winds. Finally, the MBD model was established and the time series of aerodynamic forces were applied to the HSTs, allowing for the analysis of the dynamic response. The results were as follows: when HSTs passed by each other on the CSB, there was a noticeable alteration in the distribution of air pressure on trains. The aerodynamic force variations of each vehicle on the windward side were greater than those on the leeward side. The safety and stability of each vehicle were decreasing, with the head vehicles having the lowest safety. As the crosswind speed increased, the dynamic response of trains was significantly heightened.

Effects of bench press technique variations on musculoskeletal shoulder loads and potential injury risk.

While shoulder injuries resulting from the bench press exercise are commonly reported, no biomechanical evidence for lowering injury risk is currently available. Therefore, the aim of the present study was to compare musculoskeletal shoulder loads and potential injury risk during several bench press variations. Ten experienced strength athletes performed 21 technical variations of the barbell bench press, including variations in grip width of 1,1.5 and 2 bi-acromial widths (BAW), shoulder abduction angles of 45°, 70° and 90°, and scapula poses including neutral, retracted, and released conditions. Motions and forces were recorded by an opto-electronic measurement system and an instrumented barbell. An OpenSim musculoskeletal shoulder model was employed to estimate joint reaction forces in the glenohumeral and acromioclavicular joints. Time-series of joint reaction forces were compared between techniques by statistical non-parametric mapping. Results showed that narrower grip widths of BAW decreased acromioclavicular compression (p < 0.05), which may decrease the risk for distal clavicular osteolysis. Moreover, scapula retraction, as well as a grip width of BAW (p < 0.05), decreased glenohumeral posterior shear force components and rotator cuff activity and may decrease the risk for glenohumeral instability and rotator cuff injuries. Furthermore, results showed that mediolaterally exerted barbell force components varied considerably between athletes and largely affected shoulder reaction forces. It can be concluded that the grip width, scapula pose and mediolateral exerted barbell forces during the bench press influence musculoskeletal shoulder loads and the potential injury risk. Results of this study can contribute to safer bench press training guidelines.

A new Gaussian Process based model for non-linear wave loading on vertical cylinders

We aim to establish a fast and accurate model for fast prediction of nonlinear loading on vertical cylinders such as are typically used for fixed offshore wind turbines. We follow a ‘Stokes-type’ force model and approximate the amplitude of the higher harmonics of force by relating these to the linear force time series raised to appropriate power through amplitude and phase coefficients. We reanalyse previous experimental data and perform new experiments to expand the parameter space and establish a force coefficients database for engineering applications. A machine learning model is used to interpolate the database and make predictions on the higher order force coefficients. The machine learning model also provides a cross-validated confidence interval to indicate the prediction uncertainty and reflect model reliability. We further extend the prediction capability to unidirectional random waves with a novel force segmentation method, which localised wave groups from the random background. The new Stokes-Gaussian Process (Stokes-GP) model developed can provide engineering predictions of nonlinear wave loading on a cylinder for individual wave groups and random seas, which are straightforward to apply and fast to compute and the important higher-order loading components are considered. This will significantly improve the accuracy of the loading prediction and the ease of application for force predictions.

Ground reaction forces in baseball pitching: temporal associations with pitch velocity among high-velocity pitchers

ABSTRACT How baseball pitchers interact with the ground is an important aspect of pitching technique and performance. Previous studies on ground reaction forces in baseball pitching have largely been limited to pitchers at the youth or adolescent level, with only a few studies examining higher velocity pitchers. Additionally, previous studies have limited their analyses to only peak kinetic values, neglecting any temporal importance of when these peak values occur. Therefore, our purpose was to provide normative ground reaction force values and examine the associations between pitch velocity and ground reaction forces in high-velocity pitchers. We retrospectively extracted pitch velocities as well as rear and lead leg ground reaction force data from internal databases for 105 high-velocity pitchers. We analysed the associations between the full ground reaction force time series and pitch velocity using statistical parametric mapping regression. Regression analysis revealed pitch velocity significantly predicted lead leg braking ground reaction force from approximately 27% to 35% of the period between front foot contact and ball release. These data reinforce the importance of effective braking forces for achieving maximal pitch velocities. Additionally, our observed peak ground reaction force values were considerably higher than those previously reported.

Statistical modeling of fully nonlinear hydrodynamic loads on offshore wind turbine monopile foundations using wave episodes and targeted CFD simulations through active sampling

AbstractAccurately determining hydrodynamic force statistics is crucial for designing offshore engineering structures, including offshore wind turbine foundations, due to the significant impact of nonlinear wave–structure interactions. However, obtaining precise load statistics often involves computationally intensive simulations. Furthermore, the estimation of statistics using current practices is subject to ongoing discussion due to the inherent uncertainty involved. To address these challenges, we present a novel machine learning framework that leverages data‐driven surrogate modeling to predict hydrodynamic loads on monopile foundations while reducing reliance on costly simulations and facilitate the load statistics reconstruction. The primary advantage of our approach is the significant reduction in evaluation time compared to traditional modeling methods. The novelty of our framework lies in its efficient construction of the surrogate model, utilizing the Gaussian process regression machine learning technique and a Bayesian active learning method to sequentially sample wave episodes that contribute to accurate predictions of extreme hydrodynamic forces. Additionally, a spectrum transfer technique combines computational fluid dynamics (CFD) results from both quiescent and extreme waves, further reducing data requirements. This study focuses on reducing the dimensionality of stochastic irregular wave episodes and their associated hydrodynamic force time series. Although the dimensionality reduction is linear, Gaussian process regression successfully captures high‐order correlations. Furthermore, our framework incorporates built‐in uncertainty quantification capabilities, facilitating efficient parameter sampling using traditional CFD tools. This paper provides comprehensive implementation details and demonstrates the effectiveness of our approach in delivering reliable statistics for hydrodynamic loads while overcoming the computational cost constraints associated with classical modeling methods.

Acceleration-Based Estimation of Vertical Ground Reaction Forces during Running: A Comparison of Methods across Running Speeds, Surfaces, and Foot Strike Patterns.

Twenty-seven methods of estimating vertical ground reaction force first peak, loading rate, second peak, average, and/or time series from a single wearable accelerometer worn on the shank or approximate center of mass during running were compared. Force estimation errors were quantified for 74 participants across different running surfaces, speeds, and foot strike angles and biases, repeatability coefficients, and limits of agreement were modeled with linear mixed effects to quantify the accuracy, reliability, and precision. Several methods accurately and reliably estimated the first peak and loading rate, however, none could do so precisely (the limits of agreement exceeded ±65% of target values). Thus, we do not recommend first peak or loading rate estimation from accelerometers with the methods currently available. In contrast, the second peak, average, and time series could all be estimated accurately, reliably, and precisely with several different methods. Of these, we recommend the 'Pogson' methods due to their accuracy, reliability, and precision as well as their stability across surfaces, speeds, and foot strike angles.

Efficient measurement of floating breakwater vibration and controlled vibration parameters using compressive sensing

In this paper, we examine the possible usage of compressive sampling (CS) for the efficient measurement and analysis of floating breakwaters dynamics. We model the dynamics of a box-type floating breakwater in a random sea environment with the Bretschneider-Mitsuyasu spectrum. The spectral method involving FFT and IFFT routines is used for the simulation and CS reconstruction purposes of the displacement and velocity parameters. The time series of forces are calculated using the Morison equation. It is also shown that those vibration parameters can be limited and suppressed to a certain degree by a tuned-mass-damper. The advantages of using the CS for the tuned-mass-damper-controlled vibration parameter measurement and analysis are also discussed. Our findings may provide convenience for the effective and efficient strategies for the vibration-induced problems of floating platforms including wave energy converters and offshore platforms.

Assessing spring-mass similarity in elite and recreational runners.

The dynamic complexity and individualization of running biomechanics has challenged the development of objective and comparative gait measures. Here, we present and explore several novel biomechanical metrics for running that are informed by a canonical inter-species gait template-the spring-mass model. The measures assess running mechanics systemically against the template via quantifying characteristics of a runner's kinetics relative to the energy-conserving elastic system-i.e., their "spring-mass similarity". Applying these metrics in a retrospective cohort investigation, we studied the overground kinetics of two heterogenous populations of runners in two footwear conditions: elite and recreational athletes in shod and barefoot conditions. Across all measures and within foot strike types, the elite runners exhibited mechanics that were more similar to those of the ideally elastic spring-mass template. The elite runners had more symmetric bounces, less discrepancy (i.e., greater coordination) between horizontal and vertical kinetic changes, and better fit to a spring-mass vertical ground reaction force time series. Barefoot running elicited greater kinetic coordination in the recreational runners. At a faster speed, the elites further improved their similarity to the template. Overall, the more economical elite group exhibited greater likeness to the linearly elastic, energy-conserving spring-mass system than their recreational counterparts. This study introduces novel biomechanical measures related to performance in distance running. More broadly, it provides new, approachable metrics for systemic quantification of gait biomechanics in runners across all demographics. These metrics may be applied to assess a runner's global biomechanical response to a variety of interventions, including training adaptations, rehabilitation programs, and footwear conditions.

Numerical Investigation on Drag and Vortex Induced Vibration Characteristics of Multiple Cylinders

The drag and vortex induced vibration (VIV) characteristics of a multiple cylinder are investigated using the detached eddy simulations. The multiple cylinders consist of a single main cylinder and twin auxiliary cylinders for a deep sea mining riser. Tandem and side-by-side arrangements are tested and compared with the single cylinder. The drag characteristics are investigated with the stationary case in the range of 0.5∼2.0 × 105 in Reynolds number (Re). The drag of the tandem arrangement shows smaller drag than those of the single cylinder while it’s consisted with the three cylinders. The stationary vortexes are observed at the clearance between the main and auxiliary cylinder which make the tandem arrangement become airfoil-like section as a total which induce the smallest drag than the other cases. The VIV characteristics are studied with the cases of forced oscillation in the cross-flow direction. The damping and added mass coefficients in cross-flow direction are estimated from the time series of the lift forces. Flow field analysis reveal the difference in VIV characteristics due to the variety of the arrangements and the single pipe.

A Protocol for Digitalized Collection of Traditional Chinese Medicine(TCM) Pulse Information Using Bionic Pulse Diagnosis Equipment.

Pulse diagnosis equipment used in Traditional Chinese Medicine (TCM) has long been developed for collecting pulse information and in TCM research. However, it is still difficult to implement pulse taking automaticallyorefficiently in clinical practice. Here, we present a digital protocol for TCM pulse information collection based on bionic pulse diagnosis equipment, which ensures high efficiency, reliability and data integrity of pulse diagnosis information. A four-degree-of-freedom pulse taking platform together with a wrist bracket can satisfy the spatial positioning and angle requirements for individually adaptive pulse acquisition. Three-dimensional reconstruction of a wrist surface and an image localization model are combined to provide coordinates of the acquisition position and detection direction automatically. Three series elastic joints can not only simulate the TCM pulse taking method that "Three fingers in a straight line, the middle finger determining the 'Guan' location and finger pulp pressing on the radial artery," but also simultaneously carry out the force-controlled multi-gradient pressing process. In terms of pulse information integrity, this proposed protocol can generate rich pulse information, including basic individual information, pulse localization distribution, multi-gradient dynamic pulse force time series, and objective pulse parameters, which can help establish the fundamental data sets that are required as the pulse phenotype for subsequent comprehensive analysis of pulse diagnosis. The implementation of this scheme is beneficial to promote the standardization of the digitalized collection of pulse information, the effectiveness of detecting abnormal health status, and the promotion of the fundamental and clinical research of TCM, such as TCM pulse phenomics.

Smooth and accurate predictions of joint contact force time-series in gait using over parameterised deep neural networks.

Alterations in joint contact forces (JCFs) are thought to be important mechanisms for the onset and progression of many musculoskeletal and orthopaedic pain disorders. Computational approaches to JCFs assessment represent the only non-invasive means of estimating in-vivo forces; but this cannot be undertaken in free-living environments. Here, we used deep neural networks to train models to predict JCFs, using only joint angles as predictors. Our neural network models were generally able to predict JCFs with errors within published minimal detectable change values. The errors ranged from the lowest value of 0.03 bodyweight (BW) (ankle medial-lateral JCF in walking) to a maximum of 0.65BW (knee VT JCF in running). Interestingly, we also found that over parametrised neural networks by training on longer epochs (>100) resulted in better and smoother waveform predictions. Our methods for predicting JCFs using only joint kinematics hold a lot of promise in allowing clinicians and coaches to continuously monitor tissue loading in free-living environments.

On the efficient simulation of pass-by noise signals from railway wheels

The article presents an approach for calculating pass-by sound pressure radiated from railway wheels in the time domain using moving Green’s functions. The Green’s functions are obtained by using Finite Element (FE) and Boundary Element (BE) methods in the frequency domain, subsequent inverse Fourier transform, followed by convolution with a time series of rolling contact forces to obtain the pass-by time signals. However, traditional BE methods are computationally expensive due to the low structural damping of the wheel, necessitating a high frequency resolution.To overcome this issue, a modal approach is introduced in which the pass-by sound radiated by each wheel mode is calculated separately. This approach incorporates the dynamic response of the wheel in the time-domain processing and thus reduces the cost of the BE solution. A modal source signal is introduced to describe the excitation of each mode at each time step. The sound field radiated by unit modal amplitudes is calculated in BE and subsequently approximated by spherical harmonic (SH) equivalent sources, which allows for efficiently calculating acoustic transfer functions for varying relative positions of the wheel and a stationary receiver. Convolution of the source signal with the moving acoustic transfer function produces the pass-by pressure signal.The article investigates the directivity of the radiation from each mode and finds that most modes, including those with dominant radial deflection, radiate in mostly axial direction at high frequencies. Modes that dominate the pass-by pressure level are identified, both in frequency bands and with respect to the relative positioning of the wheel to the receiver. Finally, it is found that an SH expansion order of approximately 30 is required to satisfy the employed error measures, although lower orders may suffice for an auralisation of the signal.

Experimental and numerical study of wave-in-deck loads due to oblique transient wave groups

Wave-in-deck loads due to 45° oblique transient focus wave groups are investigated using model-scale experiments and computational fluid dynamics simulations with emphasis on comparing with head-on wave impacts for a solid cuboid deck model without and with an I-beam grillage beneath. After validation with experiments, numerical results are extended to consider wave-in-deck loads with 22.5° and 67.5° oblique wave directions. Generally, the head-on wave impacts cause larger longitudinal forces on the deck whereas the oblique cases result in larger downward vertical forces. For the deck with grillage case, Santo et al. (2020) and Wang et al. (2022) show that successive large spikes are observed in the force time series of head-on wave impact due to entrapped air-pocket effects in the grillage. However, here it is found that the large spikes are absent in the force time series for the oblique wave impacts and the patterns of forces are similar to the deck without grillage with rather small or no spikes in the force time series. Interrogation of the numerical flowfield reveals evidence that the asynchronous and less effective air entrapment in the grillage for the oblique cases are responsible for the difference. The maximum positive pressure on the underside of the deck is found to be much larger for the deck with grillage than without due to local slamming of jets formed in the grillage.

Predictive capabilities of data-driven machine learning techniques on wave-bridge interactions

To explore coastal bridge safety subjected to extreme waves during coastal natural hazards, numerical simulations that combine finite element methods and experimental data have been recognized as effective in computing wave-induced loads on coastal bridges. However, the structural design and performance assessment for bridge networks require laborious efforts and massive computational resources to account for uncertain scenarios. To provide reliable wave force estimation tools and facilitate the associated risk assessment, this study performs a hydrodynamic experiment on the wave-bridge interactions and develops data-driven Long-Short-Term-Memory (LSTM) Machine Learning (ML) models for time series forecasting of wave forces. Specifically, a 1:30 scale bridge superstructure specimen is used for the wave test in the wave channel. Different solitary wave and regular wave conditions are tested. Time histories of wave profiles, wave-induced forces, and pressures are measured and served as a dataset basis for the training of LSTM models. High-performance LSTM prediction models are developed through the tuning of different hyperparameters. The well-trained models have high accuracy and could predict the wave force time series based on the excitation wave profiles in seconds. It is envisioned that LSTM models could provide more reliable estimations with the development based on more data sources, providing a fast path for structural design, analysis, and maintenance.

Tool wear classification based on convolutional neural network and time series images during high precision turning of copper

Artificial intelligent techniques are critical in predicting tool wear in the machining process. Effective assessment of the rate and state of tool wear are important in the high-speed turning process and makes it possible to replace the tool before catastrophic wear occurs. It is well known that cutting forces are often used as an indicator to monitor tool wear during the machining process. However, how to use deep learning methods to incorporate cutting forces, accurately predicting the tool wear, remains a challenge. In this paper, a novel tool wear classification method based on time series images of cutting forces and convolutional neural networks was proposed. The one-dimensional cutting force signals are converted into two-dimensional time series images using the Gramina Angular Summation Fields method. Then, a modified AlexNet network is used to classify tool wear types based on the processed cutting force time series images. The prediction results show the overall prediction accuracy of the four tool wear categories can reach around 90%. In addition, by balancing the number of cases in the dataset, the prediction accuracy of each category can be improved while the overall prediction accuracy is maintained.

Calculation of slamming wave loads on monopiles using fully nonlinear kinematics and a pressure impulse model

The design methods for highly nonlinear wave loads on monopile structures has over the past years been extended with methods based on pre-computed fully nonlinear wave kinematics. Yet, the slamming events of the strong sea states cannot currently be predicted with these methods. We here present a simple recipe for the application of a recent pressure impulse based slamming load model in combination with fully nonlinear wave kinematics and validate the results against lab measurements of uni- and multi-directional storm sea states. The experimental slamming loads are extracted from lab measurements equivalent to 954 full scale hours. Six methods for the extraction of the slamming force are developed and analysed in detail, with a final selection of two for the further analysis. The experimental analysis shows that the frequency of slamming is larger in uni-directional sea states relative to sea states with directional spreading, and with slightly smaller force impulses. The calculated slamming frequencies from the measurements are used in the application of the numerical slamming model. It is shown that the application is straightforward and robust and involves an intuitive selection of the model inputs from the incident wave kinematics. A generally good agreement between the model and measurement distributions of the force impulse is observed. The difference between 3D and 2D slamming impulses, though, is found to be larger in the numerical model. This is traced to the numerical particle velocities in the wave crests. The pressure impulse model is next extended by assuming a predefined generic slamming force time variation and through calibration of the peak slamming force, a generally good agreement between the model and ensemble-averaged measured slamming force time series is obtained, given the uncertainty in the slamming load extraction. It is also observed that the commonly used non-dimensional slamming force peak of 2π is unrealistically large in the irregular slamming waves because of the 3D effects of small curling factors.