Prediction Of Dynamic Response Research Articles

Harmonic-modal hybrid frequency approach for parameterized non-linear dynamics

Structural dynamics systems are represented by discretized partial differential equations, whose solutions depend on various parameters. Developing high-fidelity numerical models for multi-dimensional systems or those with multiple parameters can be computationally expensive, particularly if the systems are non-linear. Consequently, the concept of a precalculated library of the system's response to a wide range of parameters is appealing. Thus, a global non-linear space-frequency solver is proposed that produces a low-rank representation of the solution using Modal Basis analysis known as the Harmonic Modal Hybrid Method. The DEIM is also used to accelerate its convergence by creating a reduced basis of the non-linear function(s) based on either calculated or experimental values. The optimized solver is then employed for rapid offline computations to construct surrogate models that can give real-time predictions of the parametrized dynamic response using the sPGD technique. These models serve as building blocks for virtual twins that necessitate near-instantaneous calculations when the system parameters and/or conditions are changed. A proof of concept is illustrated by using this technique to analyze a well-known non-linear system, the cantilevered beam with a non-linear cubic spring attached to its end. This method can be easily extended to solve other dynamical systems quickly and effectively.

Multiscale simulation and experimental studies on modal damping of ultra‐thick CFRP laminates

AbstractThe vibration characterization of ultra‐thick laminates widely used in aerospace and marine industries was different from that of thin laminates. However, modal testing and simulation methods were generally limited to relatively thin laminates. To explore the vibration behavior of ultra‐thick laminates, a novel multiscale simulation technology based on the representative volume modal strain energy (RVMSE) method is presented for predicting modal damping in this paper. The adaptive Greedy‐Based Generation (GBG) algorithm is used to create a 3D random distribution of fibers for composites. Modal shape information of the structure is obtained according to the Lanczos algorithm, which is used as an input parameter for the microscopic model. This is followed by homogenization based on the volumetric analysis performed on representative volume elements (RVEs) to determine the strain energy in six directions. The calculation of modal damping is performed by using the modal strain energy (MSE) method and the damping properties of the six directions. The fast rate of convergence and high accuracy of the method are demonstrated through different examples. The vibration response predictions produced by novel RVMSE methodology are shown to closely match experimental measurements, providing scope to expand the application of this approach to more complex, ultra‐thick laminate components.Highlights The RVMSE method uses a higher level of homogenization to overcome the limitations of the traditional MSE method for calculating the damping of ultra‐thick CFRP laminates. The modal parameter error is controlled to less than 10%, and the experimental results fill the gap of the damping data of ultra‐thick CFRP structure. The proposed RVMSE model improves the accuracy of dynamic response prediction for ultra‐thick laminates.

Finite element model updating and response prediction of a frame structure based on optimal sensor placement

This paper proposes an approach for finite element (FE) model updating and response prediction of frame structures based on optimal sensor placement (OSP), which integrates sensor placement optimization, mode expansion, and model updating techniques. Firstly, sensor optimization layout and modal testing analysis are conducted on a bolted laboratory frame structure. The covariance-driven stochastic subspace identification (SSI-COV) method identifies the real-world structure’s natural frequencies, modal damping, and mode shapes. Secondly, the complete mode shapes are expanded using the measured incomplete modal data from the limited number of sensors. Thirdly, a multi-objective function based on frequency and mode shapes is established to adjust the parameters of the FE model. This ensures that the updated model accurately represents the dynamic properties of the actual structure within a specific frequency range. Finally, the Rayleigh damping of the frame structure is estimated, and the damping matrix is assembled to enhance the accuracy of dynamic response prediction in the updated model. By comparing the response prediction results of the updated FE model with and without considering the updated damping effects to the measurement data of the real-world structure, it is demonstrated that the proposed method considering updated damping effects can more effectively predict the structural response.

Mathematical Complexities in Modelling Damage in Spur Gears

Analytical modelling is an effective approach to obtaining a gear dynamic response or vibration pattern for health monitoring and useful life prediction. Many researchers have modelled this response with various fault conditions commonly observed in gears. The outcome of such models provides a good idea about the changes in the dynamic response available between different gear health states. Hence, a catalogue of the responses is currently available, which ought to aid predictions of the health of actual gears by their vibration patterns. However, these analytical models are limited in providing solutions to useful life prediction. This may be because a majority of these models used single fault conditions for modelling and are not valid to predict the remaining life of gears undergoing more than one fault condition. Existing reviews related to gear faults and dynamic modelling can provide an overview of fault modes, methods for modelling and health prediction. However, these reviews are unable to provide the critical similarities and differences in the single-fault dynamic models to ascertain the possibility of developing models under combined fault modes. In this paper, existing analytical models of spur gears are reviewed with their associated challenges to predict the gear health state. Recommendations for establishing more realistic models are made especially in the context of modelling combined faults and their possible impact on gear dynamic response and health prediction.

Model-Free Dynamic Response Prediction at Unmeasured Locations for Three-Dimensional Structures Based on Polynomial Shape Functions

Model-Free Dynamic Response Prediction at Unmeasured Locations for Three-Dimensional Structures Based on Polynomial Shape Functions

Investigating Tailless UAV Flight Dynamics through Modeling, Simulation, and Flight Testing

Tailless Unmanned Aerial Vehicles (UAVs) offer several advantages over their conventional counterparts, including enhanced maneuverability, higher durability, and better stealth. However, they are challenging in their stability and control due to the absence of stabilizing and control surfaces that typically exist in conventional empennage. A crucial process for analyzing the tailless UAVs’ stability/performance characteristics and determining/validating their flight control parameters is done via the modeling and simulation of flight dynamics. This paper presents a comprehensive and systematic procedure for investigating the flight dynamics of a tailless UAV, including modeling, simulation, analytical verification, and flight testing, while also explaining the interconnections among these elements. It also addresses the common challenge of limited accessibility of UAV essential data through using diverse analytical, empirical, and experimental methods. First, a rapid and effective first-principles modeling approach is introduced to simulate the nonlinear six-degree-of-freedom flight dynamics of a small tailless UAV case study. The modeling process follows a modular framework where well-defined experiments and commercial of-the-shelf software, tools, and sensors are employed to build the necessary sub-models, including geometric, mass–inertia, aerodynamic, propulsion, and actuator models. Then, all sub-models are integrated into a simulation environment to allow the prediction of the UAV dynamic response obtained from the given control inputs. The developed flight dynamic model is subjected to a thorough verification process to ensure its integrity and proper functionality by comparing the simulated trim and natural flight modes with the calculated analytical results. Finally, a set of specific flight tests are performed to validate the developed simulation model and verify relevant performance characteristics for the case-study UAV. The results show that the proposed approach provides a systematic and straightforward method for examining the flight dynamics of small tailless UAVs with reasonable accuracy.

Multi-source uncertainty propagation and sensitivity analysis of turbine blades with underplatform dampers

Underplatform dampers (UPDs) mitigate turbine blade vibrations in aeroengines through friction dissipation generated by the contact interface. However, in UPD design, uncertainties are often overlooked, including manufacturing discrepancies, excitation forces, and wear factors, leading to suboptimal predictions of structural dynamic responses. This study presents a dynamic model for the blade-UPD system with cyclic symmetric attributes, which simulates uncertainties using statistical methods. An efficient algorithm using adaptive techniques is proposed to construct polynomial chaos expansions (PCE) for precise and efficient uncertainty quantification (UQ) in turbine blades with UPDs. Further, the influence of single/multiple parameter uncertainties on the dynamic characteristics of the blade-UPD is explored. Sobol' indices are then employed to assess the sensitivity of uncertain factors to the vibration reduction properties of UPDs. The findings suggest that the new approach, which offers precise UQ at minimal computational cost, outperforms traditional methods like Ordinary Least Squares (OLS) and Sparse Least Angle Regression (LARS). Observations reveal a significant impact of parameter uncertainties on blade-UPD dynamic responses, which manifest as "resonance bands" and "frequency shifts" in some cases. Sensitivity analysis indicates noticeable variations in Sobol' indices for each uncertainty parameter as the excitation frequency changes. Specifically, the uncertainty in the friction coefficient demonstrates pronounced sensitivity to amplitude when slip occurs at the contact interface. Furthermore, the observed "drop" phenomenon in Sobol' indices is explained.

Forecasting Pitch Response of Floating Offshore Wind Turbines with a Deep Learning Model

The design and optimization of floating offshore wind turbines (FOWTs) pose significant challenges, stemming from the complex interplay among aerodynamics, hydrodynamics, structural dynamics, and control systems. In this context, this study introduces an innovative method for forecasting the dynamic behavior of FOWTs under various conditions by merging Convolutional Neural Network (CNN) with a Gated Recurrent Unit (GRU) network. This model outperforms traditional numerical models by delivering precise and efficient predictions of dynamic FOWT responses. It adeptly handles computational complexities and reduces processing duration, while maintaining flexibility and effectively managing nonlinear dynamics. The model’s prowess is showcased through an analysis of a spar-type FOWT in a multivariate parallel time series dataset using the CNN–GRU structure. The outcomes are notably promising, underscoring the model’s proficiency in accurately forecasting the performance of FOWTs.

Dynamic response prediction of high-speed train on cable-stayed bridge based on genetic algorithm and fused neural networks

To predict the dynamic response of high-speed trains (HSTs) passing through cable-stayed bridges (CSBs), this paper proposed a prediction framework based on the genetic algorithm (GA) and the neural network. Firstly, an HST-CSB coupled dynamic model was established using the rigid-flexible coupling method. Subsequently, a fused Temporal Convolutional Network and Long Short-Term Memory (TCN-LSTM) neural network model was developed, and its hyperparameters were optimized using the GA. The dataset was created based on the HST-CSB coupled dynamic model for training and testing the model. Additionally, the generalization capability of the model after adopting different track deformations was discussed. The main results were as follows: Comparative analysis with various neural network models revealed that the GA-TCN-LSTM model exhibited the most accurate prediction results across different train speeds. The significant temperature fluctuations of the bridge led to a drastic deterioration of the track smoothness, resulting in decreased predictive performance of the neural network models. The GA-TCN-LSTM model could optimize the hyperparameters, demonstrating good robustness and generalization capabilities. The predictive performance of the model improved when using the German low-interference spectrum, attributed to the greater irregularities in the German low-interference spectrum, resulting in larger train dynamic responses and stronger feature characteristics in the training data for the neural network. Different neural network models exhibited varying adaptability to track irregularities, with the GA-TCN-LSTM model demonstrating high accuracy in predicting dynamic responses under different train speeds.

Numerical derivation of homogenised constitutional relation of mortar-less interlocking brick wall for dynamic response prediction

This paper introduces a homogenisation technique for dry-stacking interlocking masonry structures to improve the modelling and computational efficiency when such interlocking brick walls are subjected to blast loading. Based on periodic construction pattern, a representative volume element (RVE) is derived, whose equivalent material properties are determined through numerical modelling under different stress states. Nonlinear material properties and strain rate effects are both considered in the numerical simulations of the RVE. The hardening and softening behaviour of the RVE are analysed using compressive and tensile damage scalars based on the theory of continuum damage mechanics. To verify the suitability and accuracy of the obtained equivalent material properties, interlocking brick walls subjected to TNT blast loading, gas explosion loading and impact loading are modelled using the homogenised material properties. The results are compared with those obtained from detailed numerical models of the interlocking brick wall and the test data for the impact loading case. It is found that the developed homogenisation approach could significantly reduce computational resource.

Data-driven analysis and prediction of dynamic postprandial metabolic response to multiple dietary challenges using dynamic mode decomposition.

In the field of precision nutrition, predicting metabolic response to diet and identifying groups of differential responders are two highly desirable steps toward developing tailored dietary strategies. However, data analysis tools are currently lacking, especially for complex settings such as crossover studies with repeated measures.Current methods of analysis often rely on matrix or tensor decompositions, which are well suited for identifying differential responders but lacking in predictive power, or on dynamical systems modeling, which may be used for prediction but typically requires detailed mechanistic knowledge of the system under study. To remedy these shortcomings, we explored dynamic mode decomposition (DMD), which is a recent, data-driven method for deriving low-rank linear dynamical systems from high dimensional data.Combining the two recent developments "parametric DMD" (pDMD) and "DMD with control" (DMDc) enabled us to (i) integrate multiple dietary challenges, (ii) predict the dynamic response in all measured metabolites to new diets from only the metabolite baseline and dietary input, and (iii) identify inter-individual metabolic differences, i.e., metabotypes. To our knowledge, this is the first time DMD has been applied to analyze time-resolved metabolomics data. We demonstrate the potential of pDMDc in a crossover study setting. We could predict the metabolite response to unseen dietary exposures on both measured (R2 = 0.40) and simulated data of increasing size (= 0.65), as well as recover clusters of dynamic metabolite responses. We conclude that this method has potential for applications in personalized nutrition and could be useful in guiding metabolite response to target levels. The measured data analyzed in this study can be provided upon reasonable request. The simulated data along with a MATLAB implementation of pDMDc is available at https://github.com/FraunhoferChalmersCentre/pDMDc.

Research on dynamic response prediction of semi-submersible wind turbine platform in real sea test model based on machine learning

The motion response of floating offshore wind turbine (FOWT) platform is closely related to its safety, and model test is the most direct method to fully study its dynamic characteristic behavior. In this paper the dynamic response of intermediate-scale physical semi-submersible FOWT model test under real sea environmental loads is studied and compared with the numerical model dynamic response, demonstrating that some limitations of small-scale physical model tests can be overcome, such as the catenary effect of mooring lines. It is found that the nonlinear dynamic characteristics of the physical model under actual marine environmental loads can be captured by the numerical model, which can improve the fidelity of model test data for semi-submersible FOWT structures in the existing literature. The dynamic response database of semi-submersible FOWT under complex wind, wave and current loads was established by using a numerical model with high accuracy, and was used in the prediction research of different machine learning algorithm models such as Genetic Algorithm optimization Back Propagation neural network (GA-BP), Support Vector Machine (SVM) and Gaussian Process (GP). The research shows that the relationship between the environmental load and the dynamic response of FOWT can be established by using the machine learning model, in which the number of samples has a significant impact on the prediction of the mooring line tension, and the research on the three algorithm models shows that GP performs significantly better than GA-BP and SVM in predicting the mean value of surge, pitch and mooring line force. For the dynamic response prediction of mooring line tension, GP model can get better results. In the future, this method will become an important method to predict and monitor the dynamic response of FOWT.

Dynamic mechanical response prediction model of honeycomb structure based on machine learning method and finite element method

In this study, a novel framework was presented for accelerating the prediction of the mechanical response of honeycomb structures under dynamic crushing, using 2D cells to surrogate 3D honeycomb structures by machine learning (ML). The sizes of different honeycomb structures were designed and the necessary training data obtained through finite element (FE) simulations, but without using any explicit design parameters of the honeycomb cells in the ML model. A pixelization method of FE model was proposed to separate the complete cell structure from the honeycomb FE grid data and convert it into a matching pixel map. FE data was structuralized while reducing the large amount of computational power consumed in identifying complex array structures. Unsupervised automatic extraction of low-dimensional features of pixel maps was performed using a convolutional denoising autoencoder (CDAE). The crushing velocity and the extracted latent features were used as the input of the long-short term memory (LSTM) network to predict the crushing deformation and stress-strain curve of the honeycomb structure under different dynamic loading. Results showed that the constructed ML model could describe the dynamic crushing response behavior. Compared with the traditional FE method, the prediction model was 4.45 × 103 and 1.05 × 103 times faster in predicting the stress-strain and structural deformation response, respectively. The mechanical response prediction model provided a method for rapidly evaluating the dynamic mechanical response behavior of similar periodic array structures using FE model data, which could be beneficial for the design and development of equipment based on bionic structures.

Form Shear Stress Correction in Bulk Flow Analysis of Grooved Seals Based on Effective Film Thickness

Abstract Bulk flow models for grooved annular seals provide computationally efficient static and dynamic response predictions, though heavy reliance on empirical relationships often leads to undesirable levels of uncertainty. The flow complexity caused by the grooves adds difficulty to shear stress modeling for these seals. This study seeks to improve shear stress modeling for grooved seals through the identification and quantification of the additional bulk flow shear stress contributions within the groove region. Through single groove computational fluid dynamics (CFD) simulations and an effective film thickness analysis framework, the additional groove shear stress component is identified as a form shear stress (FSS) due to its clear relationship to the effective film thickness behavior. The FSS is quantified as a correction to traditional shear stress definitions. Predictive models for the FSS are developed as functions of the ratio of circumferential to axial Reynolds number and the total resultant Reynolds number. Implementation of the FSS models into a simplified bulk flow method delivers leakage predictions for three seal cases within 10% of the experimental results and qualitative agreement in predicted circumferential velocity profiles while eliminating the need for an assumed groove loss coefficient. This is the first paper to utilize an effective film thickness-based procedure to quantify and model the FSS component in grooved seal bulk flow analysis. The demonstrated predictive capability and widespread applicability of the models and approach presented in this paper provide an avenue for significant improvements in grooved seal bulk flow prediction accuracy through improved shear stress modeling.

Machine learning prediction of structural dynamic responses using graph neural networks

Prediction of structural responses is essential for the analysis of structural behaviour subjected to dynamic loads. Existing approaches are limited in different ways. Experimental tests are expensive due to the requirement of intensive labour hours and specialised equipment. Numerical models can provide high-fidelity and labour-effective simulation of impact tests after proper validation, but it comes with high computational costs, which prohibit the usage of numerical methods for intensive and large-scale simulations in a design office. Data-driven machine learning approaches are also applied to structural response predictions, but they often exploit direct input–output mapping schemes that predict static field variables without capturing the dynamic response process. To close these gaps, we propose a novel machine learning approach based on graph neural networks (GNN) for full-field structural dynamics prediction. Our approach adopts a discretised representation of structures with an iterative rollout prediction scheme, and therefore it can simulate comprehensive spatiotemporal structural dynamics, providing the full potential for structural dynamics analysis. With several benchmark tests, it is demonstrated that our approach can generate accurate predictions of related field variables, e.g., displacement, strain, and stress, for different structures with a wide range of input parameters, such as structure geometry, impact speed and location. Additional interpolation and extrapolation tests are also conducted to show that our approach enjoys inherent generalisability and can produce satisfactory prediction even when all inputs are sampled outside of the training distribution. Our approach is also efficient and runs an order of magnitude faster than the commonly used numerical competitors. As the first attempt of using GNN for structural dynamics prediction and the result is promising, it is believed that GNN is well-suited for effective and efficient prediction of dynamic structural responses.

Squeak and rattle noise prediction in vehicle acoustics

AbstractSqueak and rattle belong to unintended noise audible by occupants of a vehicle. This noise negatively affects the perceived built quality, leading to nonbuying decisions, high warranty costs, and poor brand reputation. Therefore, vehicle manufacturers seek to prevent the emergence of such noise, preferably in the early development phase and during production at the latest. This causes substantial monetary and temporal expenditure, which must be minimized. Rattle is defined as repeated impact. The underlying physical phenomenon is impulsive short‐duration contact normal to the surface. Squeak, in contrast, originates from an in‐contact motion in the tangential direction and is a friction‐induced stick‐slip phenomenon. State‐of‐the‐art numerical squeak and rattle prediction is based on linear analysis resulting in an empirical noise risk index. However, quantification of noise and assessment of audibility is not possible. The reason is the nonlinearity of the contact forces. Hence, the actual system response is not calculable with a linear approach. Mathematically, the nature of both excitation events is nonlinear due to frictional contact and nonsmooth due to short impulsive behavior in time. This makes linear simplification and a solution process in the time domain challenging. Both events appear periodically, leading to an oscillation characterized by fundamental and higher harmonics. Due to this periodic character, squeak and rattle phenomena fulfill the prerequisite for applying the harmonic balance method (HBM) to solve the governing nonlinear equation of motion. The more harmonics considered, the more precise the modeling and the dynamic response prediction. In addition, the alternating frequency/time domain method (AFT) allows for switching between the frequency and the time domain during the iterative solution process. Thus, the nonlinear contact forces can be evaluated in the time domain. The equation‐solving process results in the calculation of surface velocities. This gives way to determining a proxy for the emitted sound power of the oscillatory system. The simulation method based on combining HBM and AFT was validated on test rigs for squeak and rattle noise. The industrial applicability of this simulation approach was demonstrated numerically and experimentally on an actual vehicle part showing promising results. Thereby, important steps in nonlinear structural dynamics and vehicle acoustics were made toward a calm, smooth, and enjoyable ride for vehicle occupants.

Optimization Design of Lubrication Performance of Planetary Gear Transmission

Due to the need to clarify the interaction between tooth surface lubrication characteristics and dynamic behavior, it is necessary to consider the influence of time-varying characteristics of lubrication contact on dynamic behavior and the effect of dynamic gear tooth force on lubrication characteristics, establish a friction dynamics coupling analysis model for spur gears, and achieve accurate prediction of dynamic response and lubrication characteristics. In this paper, the planetary gear transmission system model is built, the planetary gear transmission system model is solved, and the lubrication performance of planetary gear transmission is analyzed.

Damping Identification From Subsea Logger Axial Riser Response Data

Summary For decades, it has been known that, as drilling riser deployment depths increase, the potential for excessive hookload response will also increase. Using data collected from a drilling riser deployed to a record-setting water depth, nearly 12,000 ft, this paper provides insight that significantly reduces uncertainty about the severity of this resonant response. The typical drilling riser and blowout preventer (BOP) stack, disconnected from the wellhead, has its first axial resonant period at approximately 1 second for every 2,000 ft of deployed length, thus 5 seconds for 10,000 ft, 6 seconds for 12,000 ft, and so on. Therefore, vessel heave response can incite a significant, adverse axial resonant condition in very deep water. Damping reduces resonant response. Historically, the true amount of damping has been uncertain, and damping has been applied in the form of hydrodynamic drag. This typically produces a predicted response with total damping that is well under 1% of critical. This can lead to the prediction of a large dynamic hookload that can produce significant restrictions on riser configuration (running weight) and seastate for BOP stack deployment as well as storm hang-off of the riser and lower marine riser package (LMRP). A recent drilling riser deployment to the record-setting water depth of 11,903 ft produced a unique opportunity to collect high-quality data that reduces damping uncertainty. This paper describes damping ratio and natural frequency identification for the first few axial riser modes for this deployment. The data were collected during deployment and retrieval using subsea vibration data loggers (SVDLs) installed on the BOP stack, drillship, and riser. These measurements reveal damping that is between 2% and 3% of critical. This result can be used to provide more accurate predictions of dynamic hookload response.

Effect of floater flexibility on global dynamic responses of a 15-MW semi-submersible floating wind turbine

Floater structural flexibility plays a significant role in accurate predictions of global dynamic responses of floating wind turbines (FWTs), especially for ultra-large wind turbines with increasing size and cost-effective floater design. The conventional analysis of FWTs often considers the floater as one rigid body, which cannot capture the correct resonant responses of the floater (especially the column that supports the tower). In this paper, a new approach where the floater is divided into multiple rigid bodies connected by flexible beams is developed for advanced modelling of flexible floaters in combination with coupled time-domain simulations. The hydrostatic and hydrodynmaic loads on each body from a one-body hydrodynamic analysis, together with gravitational loads and inertial loads, are implemented in the beam-based finite element model of the floater to carry out a time-domain analysis. The proposed approach is used to compare the responses of a 15-MW semi-submersible FWT considering a rigid and a flexible floater. The inclusion of floater flexibility reduces the tower natural frequency. It leads to larger bending moment amplitudes at the tower base close to the tower bending natural frequency, particularly in only-wind, irregular wave and wind-wave conditions, but smaller dynamic responses in regular wave conditions.

Research on sparse identification method for aeroelastic dynamic response prediction

Nonlinear aeroelastic system has the characteristics of complex structure, difficult modeling and difficult calculation of dynamic response. For the analysis of nonlinear aeroelastic systems, model identification is a very attractive method. However, the models identified by traditional methods are often relatively complex and limited in scope of use, so it is necessary to develop an interpretable equivalent reduced model. In this paper, sparse regression method and sequential threshold least squares technique are used to establish sparse identification method for complex aeroelastic systems. This method has the ability to identify reduced models containing only required nonlinear terms through measurement data. Then, the sparse identification method is used to identify the binary wing with dead zone nonlinearity and cubic stiffness nonlinearity. The obtained model can provide rapid and accurate prediction of the response of the system according to the sensor measurement, and can also be used as an explicit surrogate model for aeroelastic optimization design, thus verifying the superiority of the proposed method.