Welded joints in stiffened structures exhibit complex dynamic behaviour that directly affects structural integrity and operational performance. Accurate estimation of stiffness and damping parameters is essential for reliable structural health monitoring and performance assessment. Traditional finite element model updating (FEMU) methods are computationally intensive, particularly when uncertainty quantification requires repeated simulations. This study presents a Gaussian Process Emulator (GPE) framework developed as a surrogate model to predict the dynamic characteristics of welded joints efficiently. The finite element model of a stiffened plate is used to generate Frequency Response Function (FRF) data, from which modal features such as natural frequencies and amplitude ratios are extracted. A dataset of 1000 realisations, generated using Latin Hypercube Sampling (LHS), is divided into training, validation, and test subsets to construct and evaluate the GPE models. The developed emulator achieves an RMSE of less than 2.5 % and anR2 exceeding 0.95 for stiffness and damping estimation, reducing computational time by nearly 80 % compared to the inverse eigen sensitivity method (IESM). Validation using simulated datasets confirms predictive robustness. The single-step GPE framework provides a reliable and computationally efficient approach for characterising welded joints, with potential applications in the design and monitoring of ship and offshore structures.

A stiffened structure is integral to complex structures such as ships. An advantage of the stiffened plate is that it has a greater load-carrying capacity. Therefore, structural health monitoring of stiffened structures is essential in a ship structure. The stiffened structure is modeled as a coupled system with a plate and stiffener forming the subsystems coupled with welded joints. The complex coupled system is modeled using finite element analysis. The coupling springs between a plate and beam could replicate the modal characteristics of welded joints in a stiffened structure. Since the welding characteristics could change depending on the operating conditions, the coupling spring was varied to account for the uncertainty in the weld strength. A hyperspace of coupling springs, one longitudinal and two torsional, was spanned using the Latin hypercube sampling technique following a uniform distribution. The eigenvalue problem for the stiffened structure was solved, and the modal characteristics of the system were determined. Dynamic features of the system, such as natural frequency, mode shape and frequency response function (FRF), were extracted. A metamodel for the system was developed using a Gaussian process emulator (GPE). The dataset was generated for a driving point response since this location's response magnitude was high. A validation study carried out on the metamodel indicated a good prediction of the weld strength. Future work would include a study to span more sensing locations and damping.

Agricultural disc mowers are used to cut crops in the field and are exposed to cyclic loading during their lifetime.A cutterbar is an essential part of a disc mower and consists of multiple parts welded together.This paper aims to develop a finite element model of a cutterbar, which can be used for fatigue assessments of the welded joints.A quasi-static experiment has been performed to validate the finite element model based on strain measurements.The finite element model has been updated using a parameter based method as several discrepancies were observed.The updated model reduces the mean absolute error of strain values from 7.5 % to 4.7 %.The hot spot approach has then been used to analyze three different weld locations on the cutterbar.The fatigue criterion by the International Institute of Welding has been used to determine the relative fatigue lives of the weld locations.The back weld is shown to be most exposed, which fits well with results from prior experiments.

Non-proportional stresses near welded joints are well known to cause increased fatigue damages as compared to proportional stresses. In this paper, a new method to remove noise from stress-time signals is developed and implemented in a principal component analysis-based approach for non-proportionality quantification. The noise removal method makes it possible to remove noise from stress-time signals causing low stress ranges, while still keeping the overall shape of the signal. When the signal shape is kept it is possible to accurately predict the levels of non-proportionality. The noise removal method is based on the standard rainflow counting method. By choosing a lower stress range limit, the stress ranges assumed to be caused by noise can be excluded and the original signal shape is kept by utilizing simple polynomial fitting. This makes the approach easy to implement and easy to control as it requires only two inputs. The noise removal method and non-proportionality quantification approach are then validated against simulated signals with noise and a simple experiment with proportional loading. The results show that the newly developed method for noise reduction accurately removes noise while keeping the signal shape.

Welded structures are integral to complex bodies such as ships and offshore rigs. Welded joints are frequently used in connecting various plates and substructures, making their assessment pivotal. The numerical model used here consists of plates coupled using springs and dashpots. The coupling models the welded joint and exemplifies the uncertainties in the welding process. The joint identification algorithm systematically defines the coupling in two steps: first, by updating the model for spring stiffness and later, by identifying the dashpot coefficients. The dynamic characteristic is determined using a frequency response function (FRF). After model updating and damping identification, a comparison between the updated FRF and that obtained from the experimental modal test is carried out to ascertain the efficiency of the algorithm. Further, the test structure is subjected to experimental testing to correlate the results from the model updating with material properties. The experimental study includes tensile testing of the weld joints and microstructural analysis. The characterisation is carried out by partitioning the welded joint. The joint stiffness and damping are correlated to the stress-strain response and crystallographic texture of the welded plate.

Fatigue is often driving the design of agricultural mowers as they are exposed to highly dynamic loading. The fatigue life of welded joints is well known to be reduced when exposed to non-proportional stresses. Thus, it is of great interest to quantify the levels of non-proportionality in agricultural mowers. In this paper, an experimental setup of a lifting arm in a mower structure has been developed in order to obtain experimental strain measurements. Based on the experimental setup, a digital twin is developed using the finite element method and the model is validated and updated against the experimental data. Using the digital twin in combination with a non-proportionality quantification approach, the levels of non-proportionality at four different locations of the lifting arm are predicted. The results show that geometry and loading influence the level of non-proportionality to a high degree.

Axial piston pumps (APP) are energy efficient while operating, but they are prone to catastrophic failures by virtue of their construction and tight tolerances. Reliability can be improved either by (i) increasing the robustness of each component used in the APPs or (ii) predicting their health status by using different techniques, so that failures can be prevented. To predict the characteristics of APPs, the underlying model and physics of the pump operation need to be studied before deploying any of the condition monitoring algorithms. Although studies indicate that deploying a machine learning (ML) algorithm can be helpful, it requires a considerable amount of failure data. The typical nature of failure in APPs is quite catastrophic, and it develops very fast and, consequently, the time to react is very limited. The goal of this work is to achieve a validated FE model of the APP that can subsequently be used for creating simulated failure data. This, in turn, can be used as training data for developing an ML-based failure detection system, where specific features can be tailored to the respective simulated failures. In this paper, model updating techniques are used to validate the FE model against experimental data, which have been obtained from modal testing of an APP and its parts. A simplified APP consisting of a swashplate, housing, end cover, and port flange are considered for the initial experimental testing. Here, the APP is subjected to impact testing, where the structural response is measured using accelerometers. The accelerometer signals are then analyzed using MATLAB to derive the first few modal frequencies.

Complex engineering systems are generally manufactured using joints. This paper proposes a methodology for accurately identifying the stiffness and damping properties of welded stiffened plates. The results of the substructure based finite element models are compared with the actual experimental data. Discrepancies have been observed between the finite element and experimental results. Eigensensitivity studies have been carried out to select the updating parameters. The stiffness and viscous damping properties of the stiffened plate are identified using model updating. The accuracy of the proposed methodology has been validated by matching the predicted finite element FRF with the experimental FRF.

The finite element method (FEM) is often used in the analysis of welded tubular joints. In 2019, DNV stated that non-proportional stress states must be taken into account in the fatigue life assessment. In this paper, three fatigue experiments of T-nodes representing a chord and brace connection in a jacket structure have been performed with various phase shifts between the normal and shear stresses. The accuracy of the FE has been validated using strain measurements on the T-nodes. The FE models are developed based on the recommendations from both the IIW and DNV. The validation of the FE models shows that the strain predictions are very close to the measured strain readings indicating accurate FE modelling. Furthermore, the phase shifts between the normal and shear stresses in the experiments vary with less than 6 % from the expected phase shifts.

All structures exhibit some form of damping, but the characterization of damping is not well-understood, and there is no universal damping model for the dynamic systems. Recently, model updating methods have been used to update or identify the damping matrix in dynamic systems. Most of the finite element updating methods assume viscous and proportional damping models for updating or identifying of damping matrix. In this paper, a new finite element model updating method is proposed in which the damping model is assumed as non-viscous and non-proportional. A parametric exponential non-viscous damping model has been used to model the damping in the dynamic system. The proposed method is the frequency response function (FRF)-based updating model, which updates the non-viscous and non-proportional damping matrix in the dynamic system. The effectiveness of the proposed damped finite element updating method is demonstrated by a numerical example and actual laboratory experiments. First, a numerical study is performed on a cantilever beam structure with non-viscous and non-proportional damping. The numerical study is followed by cases involving actual measured data. Joints and boundary conditions are assumed as a major source of damping, therefore joints and boundary conditions are modelled using relaxation functions and damping coefficients. The updated results have shown that the proposed damped element model updating method can be used to derive accurate models for the non-viscous and non-proportional damped systems. This is illustrated by matching complex FRFs obtained from the updated model with from the experimental data.

The levels of non-proportionality in fatigue stress-time series are difficult to determine. Approaches from literature are not easy to interpret and predicts different levels for variable and constant amplitude stresses. In this paper, an extension to the PCA-based method is proposed in which variable amplitude stresses are transformed into equivalent constant amplitude stresses by scaling the stress reversal points. This ensures robust and easily interpretable results. The proposed method is compared with other approaches given in literature using published experiments and a designed offshore jacket structure. The results show that the proposed method can predict the levels of non-proportionality accurately.

This paper evaluates three critical plane criteria, namely the Findley, Matake and modified Wöhler curve method and compares them to the IIW's implementation of the Gough–Pollard criteria. Assessment is conducted on a large set of fatigue data of thin-walled tube–tube laser beam welded specimens made of magnesium and aluminum alloys that were tested under proportional/non-proportional and constant/variable amplitude loading. Each criterion is evaluated based on their assessment reliability using both design and experimental S-N curves. The critical plane approaches show encouraging results for weld fatigue assessment but lead to non-conservative fatigue assessment in comparison to the IIW's Gough–Pollard criteria.

Offshore structures are exposed to cyclic loading and thereby at risk of fatigue failure, especially at the welded joints between trusses in offshore jacket foundations. In this paper, an optimization framework for welded joints considering fatigue damages is presented. The framework can be used to optimize the orientation and location of welds connecting the joint in a welded K-node in offshore jacket structures considering fatigue damage. It is known that longer welds are at higher risk of fatigue failure compared to shorter welds. To account for this, the statistical size effect is modelled using the Karhunen-Loéve expansion which can be used to take into account the effect of longer welds in the damage assessment. The approach is included in the optimization framework and it is shown that using this method it is possible to simulate the effect of having a good welding quality and a poor welding quality using the correlation length and coefficient of variation. The proposed optimization framework is validated on a simple plate structure and the effect of the statistical input parameters in the statistical size effect is examined. The results show that the proposed optimization approach is robust in predicting the expected tendencies for a simple plate structure. Furthermore, a full-scale welded K-node in an offshore jacket structure manufactured using cast steel is optimized with respect to mass. The optimization is performed considering a good quality weld and a poor-quality weld by including the statistical size effect. The results show that using high quality welds will result in lower mass of the K-node.

Two-color emissive 0D–2D quantum-dot quantum-well (QD-QW) heteronanocrystals has created profound research activities. First multicolor emission in the visible region has been reported by Peng and co-workers in CdSe(core)–ZnS(barrier)-CdSe(shell) (core-barrier-shell) based heteronanostructures where the both CdSe phases (core and the shell) are emissive and tuneable as well. Owing to this enhanced and tuneable functionality, the QD-QW systems colloidal nanocrystals has fuelled their optical and imaging applications. Single particle spectroscopy has taken a giant step toward unravelling the features of individual particles and thus to provide direct information on their heterogeneity. To elucidate the dual emission characteristic of individual nanocrystals we performed energy mapped photoluminescence imaging. Surprisingly, the pseudo color PL intensity image shows that not all single particles are dual emissive in nature, few are either green emitting or red emitting. Photoluminescence spectrum of individual nanocrystals further confirms that individual nanocrystals can be dual emissive in nature. However, single color emissive dots are also present indicating the ensemble heterogeneity at single particle levels. The temporal evolution PL spectra of a single quantum shows spectral diffusion. The single dot experiments on the dual emissive QD-QW system unravels hidden photophysics which are otherwise not observed by ensemble spectroscopy.

Most of the rainflow counting methods are developed for uniaxial stress states. In this paper, a new method for rainflow counting of multiaxial stress states has been proposed. The proposed method is a two-step procedure based on a modified three-point ASTM uniaxial rainflow counting algorithm where normal stress ranges are identified along with start and end indexes of each range. For each identified cycle, shear stress ranges are evaluated based on cycle start and end points using the minimum circumscribed circle method. The proposed algorithm is compared to two commonly applied multiaxial cycle counting methods on simulated and experimental data.

Non-proportional multiaxial stresses in welded structures cause higher fatigue damage than proportional stresses. In this paper, a new approach based on principal component analysis for quantifying the level of non proportionality in stress signals is developed. The quantifier is developed for large-scale structures (civil and offshore structures), where the influence of mean stresses is negligible. The proposed quantifier is compared and validated with other approaches from literature with the relevant fatigue criteria and experimental data. The results show that the proposed principal component-based quantifier can capture the level of non-proportionality accurately, which can be used for accurate fatigue life estimations.

Dynamically loaded structures are generally in risk of fatigue damage. The fatigue lives of such structures can be improved using traditional methods like producing a better weld or using post-weld treatment. Another method is to improve the overall design of the structure by using the finite element method in combination with shape optimization. In this paper, a framework for finite element shape optimization has been developed, considering the fatigue life of welded joints. Simplicity and the possibility of including different fatigue estimation methods have been in focus for the framework. The framework has been used on a simple plate structure, where the weld orientation has been optimized based on four different fatigue criteria. The results show that the criteria from governing guidelines predict the same optimized weld orientation. However, the critical plane approaches cannot produce optimized weld orientations, when using the nominal stress approach as it does not account for increased stresses from the weld.

Fatigue assessment of welded joints is vital for accurately designing and predicting lifetime of many engineering structures. Assessing weld fatigue is challenging due to the high variability in weld quality and geometry because of the volatile nature of the joining method and further challenges arise when assessing multiaxial fatigue. In this paper, two approaches, the Findley criterion and Modified Wöhler Curve Method, on several multiaxial experimental data sets of welded joints are compared to predict the fatigue life of the welded joints. Six experimental sets from literature are tested under a proportional torsion/bending multiaxial load. The notch stress method is used for calculating stresses at the toes of a weld.

Stiffened structures form an integral part of the ship structure. The fatigue life and the load carrying capacity of the ship structure are dependent on the stiffened panels. Stiffened structures are formed by welding beam stiffeners on bare plates. The current study proposes a methodology to accommodate the welding uncertainties in the theoretical model. The uncertainties in the strength and damping of the weld line are incorporated, using coupling spring and dampers. The coupling elements couples the beam and plate subsystems of the stiffened structure assembly. A representative model of a stiffened structures is developed. Model updating on the representative model is carried out based on simulated experimental data using the inverse eigensensitivity method. The coupling spring stiffnesses were identified using model updating. The algorithm was verified for the ability to capture the variability of strength along the weld line. The variation in damping due to welding was determined on the updated model using a damping identification technique, which requires prior knowledge of accurate stiffnesses of the weld. Studies were carried out to investigate the robustness of the proposed algorithm by inducing random noise in the modal parameters. The generated Frequency Response Function (FRF) was verified to be sufficiently stable against the random perturbations of the modal parameters. It can be concluded from the numerical studies that the proposed algorithm can be used for the identification of dynamic characteristics of the welded stiffened plates with confidence.

The stochastic behaviour of materials and loading is of great importance for buckling and analysis of prestressed beam and frame structures. In this paper, the stochastic stiffness and stress stiffness matrices are developed for stochastic analysis and buckling analysis. The bending rigidity and the buckling load are modelled as stochastic fields. The spectral decomposition known as the Karhunen–Loéve expansion has been used to expand the random fields. Using the Karhunen–Loéve expansion, the stiffness and stress stiffness closed-form matrices are formulated in terms of discrete parameters. The matrices are developed considering both classical Euler–Bernoulli theory and Timoshenko beam theory. Two case studies involving a pinned-pinned column and a frame structure is used to demonstrate the effectiveness of the proposed methods.