Stiffness Uncertainty Research Articles

Uncertainty-quantified parametrically upscaled continuum damage mechanics (UQ-PUCDM) model from microstructural characteristics induced uncertainties in unidirectional composites

This paper develops an uncertainty-quantified parametrically upscaled continuum damage mechanics (UQ-PUCDM) model for efficient multiscale analysis of unidirectional composite structures. Its constitutive parameters explicitly incorporate representative aggregated microstructural parameters (RAMPs), connecting structural response to the local microstructure. Uncertainty quantification accounts for microstructure characteristic model reduction error, neural network-based model reduction error, and aleatoric uncertainty due to inherent microstructural variability through uncertainty propagation. Development of the UQ-PUCDM framework involves machine learning tools operating on datasets generated by micromechanical simulations. The model quantifies uncertainty in RAMPs due to dimensionality reduction and quantifies the uncertainty in the upscaled elastic stiffness and damage coefficients propagated through ANN. A Bayesian principal component analysis (BPCA) derives probabilistic microstructure-dependent constitutive parameters in the PUCDM model. A Taylor expansion-based uncertainty propagation method enables computationally efficient, time-integration of the stochastic material response with consideration of uncertainty in the RAMPs. Validation studies are conducted with homogenized micromechanical solutions of SERVEs, with Monte Carlo analysis, and limited experimental results with satisfactory agreement. Finally, a single-edge notched beam (SENB) simulation is conducted to explore multiscale damage evolution problems in a structure with uncertainty propagation.

A lever-enhanced tuned inerter damper for controlling vibrations due to rotary unbalance and bounded parametric uncertainty: Classic and robust equal-peak optimization

This study proposes a lever-enhanced tuned inerter damper (LTID) for controlling the excessive vibrations induced by rotary unbalance within the primary system, whose stiffness is further considered a bounded uncertain parameter. Classic and robust equal-peak optimal design of the proposed LTID are carried out according to the methodologies stemming from the fixed-points phenomenon. Closed-form solutions to the H∞ optimization problem are analytically derived, whose accuracy is validated by comparing with either the long-established results in the literature or exact solutions numerically obtained in this study. Numerical results clearly suggest that in contrast to the classic one, robust equal-peak optimization can always produce the same and minimized vibration amplitude at the leftmost and rightmost peaks, regardless of the stiffness uncertainty magnitude. Compared to the classic LTID, the improvement made by the robust LTID in terms of minimizing and equalizing worst-case vibration amplitudes becomes more evident as the stiffness uncertainty magnitude increases. Meanwhile, the effectiveness of LTID is controlled by the amount of inertance and the lever amplification ratio simultaneously. Finally, the proposed LTID is exempt from the need for a large oscillating mass and is appropriate for lightweight applications of vibration control, as also inferred from the fact that the inerter device could generate an inertance far greater than its physical mass and the amplification ratio of a lever could be easily adjusted by changing the location of its fulcrum.

Trajectory tracking multi-constraint model predictive control of unmanned vehicles based on sideslip stiffness estimation with XGBoost algorithm

When the vehicle is driving at high speed on a slippery road, the sideslip stiffness of the tire which is closely related to the lateral force of the tire, will vary with the change of road conditions, tire inflation pressure, vertical load, and other factors. If the tire sideslip stiffness is set to a fixed value in the control system based on the model design, the uncertainty of the sideslip stiffness will cause a large error with the actual application. Therefore, in order to improve the trajectory tracking accuracy of the vehicle on the slippery road surface under the premise of ensuring the stability of the vehicle, an intelligent vehicle trajectory tracking control strategy considering the influence of sideslip stiffness is designed in this paper. In order to solve the multiple constraints of the vehicle driving on the low-adhesion road surface, a trajectory tracking controller based on the multi-constraint model predictive control algorithm is designed, and then the tire sideslip stiffness estimation strategy is designed based on the XGBoost algorithm, and the estimated sideslip deviation stiffness is added to the trajectory tracking control model. Carsim and MATLAB/Simulink are used to perform co-simulation to verify the accuracy of the proposed tire sideslip stiffness estimation and the tracking performance of the trajectory tracking controller. In order to further verify the reliability of the research content, the relevant working condition tests are carried out on the hardware-in-the-loop platform based on Carsim and LabVIEW, and the effectiveness of the trajectory tracking controller considering the influence of sideslip stiffness is verified.

Authority Allocation Approach for the Human-Machine Co-Driving System in Crosswinds

To improve driving safety and the stability of human-machine co-driving vehicles in crosswinds, a human-machine co-driving system to address the impact of crosswinds is developed. To reveal the relationship between crosswinds and tire cornering stiffness, the effect of tire load on cornering stiffness is analyzed based on the Magic Formula tire model. On this basis, the correction function of tire cornering stiffness is obtained. A human-machine co-driving system framework is introduced, which includes the driver model, controller, and authority allocation strategy. The controller is used to guarantee the stability of the system, which can remain robust to the uncertainty of tire cornering stiffness and vehicle velocity. The authority allocation strategy can adjust the authority level of the driver and controller according to the crosswind speed, working states of the vehicle, and driving feeling of drivers. The effectiveness of the proposed system is verified by simulation. The results show that the proposed system can improve the vehicle’s lane-keeping and obstacle-avoidance abilities in crosswinds. Further, the system can be compatible with drivers with different driving characteristics and achieve greater versatility. In addition, the impact of crosswinds on the trajectory tracking performance and driving stability of the vehicle, at different speeds and different tire cornering stiffnesses, can be weakened and the reliability of the system improved significantly.

System Identification and Dynamic Analysis of the Propulsion Shaft Systems Using Response Surface Optimization Technique

Marine vessels rely heavily on propeller shaft systems to adjust the engine torque and propeller thrust. However, these systems are subjected to various dynamic excitations during operation, such as transverse, longitudinal, and torsional excitations. These excitations can arise from factors like non-uniform stern flow fields, misaligned components, and the whirling motion of the shafts, which can affect the integrity and reliability of the vehicle. To analyze the dynamic response of the propulsion shaft system and ensure its reliability, numerical/analytical models are currently in practice. The finite element method (FEM) is a popular choice, but uncertainties in bearings and connectors stiffness lead to inaccuracies in the Finite Element model, resulting in significant differences between the experimental and theoretical models. This paper proposes the response surface optimization (RSO) technique to estimate unknown bearing stiffness in the propulsion shaft system. The experimental model of the propeller shaft system is constructed using steady-state response with step sine excitation. The RSO technique is then used to update the natural frequencies and vibration amplitude of the FE (Finite Element) model. The updated model shows less than a 10% difference in natural frequencies and vibration amplitude compared to the experimental model, demonstrating that the proposed technique is an efficient tool for marine shaft dynamic analysis.

Seismic design and performance evaluation of steel braced frames with post-tensioned and disc-spring-based self-centering buckling-restrained braces

In this study, we focus on two types of self-centering buckling-restrained braces (SC-BRBs), which are post-tensioned (PT) SC-BRB and disc-spring-based SC-BRB, and develop a seismic design method for steel braced frames with these braces according to the displacement-based design theory. The whole independent parameters that describe the hysteretic behavior of the SC-BRBs are first determined. Then nonlinear time history analysis (NLTHA) is conducted to explore the effects of these hysteretic parameters on the ductility demands of the nonlinear single-degree-of-freedom (SDOF) system. Based on the analysis results, a ductility demand spectral model is developed, followed by a nonlinear displacement ratio spectral model. Subsequently, the seismic design procedure for SC-BRB frames is proposed based on the two spectral models. Finally, a total of 24 six-story steel frames with the two types of SC-BRBs, two target inter-story drifts, and different parameter combinations are designed at the maximum considered earthquake (MCE) level. The pushover analysis and NLTHA results indicate that a smaller strength ratio β and a larger initial stiffness ratio αs are beneficial for reducing the base shear and obtain an economical design when the designed frames achieve the same target inter-story drift. Considering the initial stiffness of the SC-BRBs is highly sensitive to machining errors, it is recommended that the value of β be taken within 0.25 to reduce the influence of the initial stiffness uncertainty of the braces on seismic design results. Moreover, controlling β within 0.25 also helps to reduce the higher-mode effect and peak floor acceleration responses of the designed structures effectively.

Structural performance of detachable precast concrete column-column joint

A novel type of detachable precast concrete column-column joint (DPC) is proposed in this study to solve the problems in current column-column dry connections including complex load path, uncertainty of structural stiffness of beam-column joints and inconvenience for disassembly. The dry connection technology is applied by composing of steel plate and concrete. Finite element models of DPC were created to study its structural performance including hysteresis curve, skeleton curve, ductility, and energy dissipation capacity. The benchmark models are firstly established and validated against the test data and after that a small-scale parametric study is prepared. The effect of axial pressure ratio and eccentricity distance size on the seismic performance of DPC was studied. Results indict that the optimal value of axial pressure ratio ranges from 0.5 to 0.7. With increase of the axial pressure ratio, the ductility coefficient shows a decreasing trend in general. The eccentricity has little effect on the energy dissipation capacity of the joint.

Harmonic-wavelet approach for response spectrum estimation of vehicle and bridge systems with uncertain parameters subjected to stochastic excitation

Vehicle and bridge systems (VBSs) are subjected to stochastic excitations. Significant research effort has been devoted to the stochastic response analysis of VBSs. In most previous studies, VBSs have been treated as deterministic systems with certain parameters. However, the real VBSs always have uncertain parameters, such as the mass and spring stiffness of the vehicles and elastic modulus of the bridge material, which significantly affect the response power spectrum (RPS) estimation. Moreover, the equations of motion of the VBSs are essentially second-order differential equations with time-dependent and random coefficient matrices, and the excitation-response spectral relation cannot be directly described using the frequency response functions. These properties render the available methods unsuitable for the RPS estimation of the VBSs when both structural uncertainty and stochastic excitations are considered. In the present study, a harmonic-wavelet approach is proposed to estimate the time-varying RPSs of the VBSs with random parameters. The second-order differential equations of motion of VBSs with random parameters are first transformed into linear algebraic equations with random coefficient matrices using a harmonic-wavelet analysis technique; then, the excitation-response spectral relation of VBSs is derived based on these linear algebraic equations. Finally, the RPSs of VBSs with uncertain parameters are solved using the perturbation technique. The accuracy of the proposed method was verified by comparing it with the Monte Carlo method using a numerical example of railway VBS. The numerical simulation results show that the parameter uncertainties significantly affect the RPSs of the VBSs and increase the amplitude of the time-varying RPSs. The uncertainty of vehicle stiffness was the most sensitive factor for vehicle RPSs, and the bridge elastic modulus was the most sensitive factor for the bridge RPSs.

Analisis Tidak Langsung Pada Desain Terhadap Stabilitas Struktur Gedung Baja

There are three methods of design for stability defined in AISC 360-16 Specification for Structural Steel Buildings, namely Direct Analysis Method (DAM), Effective-Length Method (ELM), and First-Order Analysis Method (FOM). DAM is the method that is featured by AISC. Based on DAM, Rafael Sabelli proposed another method called Indirect Analysis Method (IAM). IAM is a new method that has not generally been used, and also has not been included in the AISC Specification. This research is conducted in order to study IAM and compares the analysis results of IAM with those of DAM. Using a nonlinear structural analysis software, design and analysis were conducted for stability design of an eight-story building loaded with dead load, live load, and wind load. IAM provides a simple amplifier approach which is called B3 to address the member inelasticity, member imperfections, and uncertainty in member stiffness. From the study that has been conducted, the analysis results using IAM show close values with those of DAM, in terms of demand-to-capacity ratios, with IAM is more conservative than DAM. The use of IAM simplifies the design process without affecting the economy of the design.

Neural network-based variable stiffness impedance control for internal/external forces tracking of dual-arm manipulators under uncertainties

The desired interaction between manipulators, objects, and environments has resulted in the internal/external force control for dual-arm manipulators being in increasing demand. Consequently, this study focused on the internal/external force tracking for dual-arm manipulator systems under external disturbances, geometries, and stiffness uncertainties which continuously lead to unsatisfactory internal force tracking. The proposed scheme is based on a two-level adaptive impedance control scheme, where the stiffness coefficient is adjusted to adapt to uncalibrated objects. An object-level hybrid impedance controller was used to regulate the external disturbance to produce a compliant response. A manipulator-level neural network-based variable stiffness impedance controller (NNVSIC) was proposed to regulate the internal force under various uncertainties. Additionally, an adaptive wavelet neural network was designed to compensate for the geometric estimation errors of the object. The variable stiffness coefficient could automatically adapt to an unknown object during the cooperation process. One advantage of the proposed method is that no prior knowledge was required. The same controller parameters could be adapted to various objects. The asymptotic stability of the proposed NNVSIC was proven via Lyapunov stability analysis. A series of experiments were conducted using two self-developed nine-degrees-of-freedom redundant manipulators. Furthermore, hard and soft objects of various geometries and stiffnesses were used to verify the effectiveness of the algorithm. The experimental results demonstrated the efficiency and superiority of the proposed controller through performance comparison with various algorithms.

Coordinated control of AFS and DYC for electric vehicles with mechanical elastic electric wheels considering the roll effects and uncertain parameters

In order to improve the lateral stability of in-wheel motors electric vehicles (IMEV) equipped with mechanical elastic electric wheels (MEEW) under extreme conditions, this paper proposes an integral sliding mode control (ISMC) algorithm based on the coordination of active front steering (AFS) and direct yaw moment control (DYC) considering the roll effects and the uncertainty of tire cornering stiffness. Firstly, the AFS control algorithm based on adaptive integral terminal sliding mode is proposed, which uses radial-basis-function neural network (RBFNN) to adaptively approximate the integrated nonlinear unknown disturbance. Secondly, considering the roll effects and uncertain cornering stiffness, a mismatched uncertain system for integrated control of AFS and DYC is established. An integral sliding mode control algorithm based on linear matrix inequality (LMI) is designed, and the asymptotic stability of sliding mode dynamics is proved. Further, a constraint optimization algorithm is used to distribute the additional yaw moment. Then, a coordinated control strategy based on the elliptical stable region of the phase plane and the rollover index is designed to activate the integrated controller of AFS and DYC at the right time. Finally, the effectiveness of the control algorithm is verified by high-fidelity CarSim-Matlab simulations. The results show that the proposed controller can effectively and robustly ensure the vehicle lateral stability under extreme conditions.

New error estimators, based on the Neumann-Monte Carlo methodology for quantification of the uncertainty of the problem of stochastic bending of Levinson-Bickford beam

This paper proposes to apply the Neumann – Monte Carlo method to obtain the estimates of the statistical moments of the solution for stochastic bending problem of Levinson-Bickford beams, with uncertainty in beam stiffness. The approximate solutions represent the stochastic displacement processes. For uncertainty modeling, parameterized stochastic processes will be used. The methodology proposed in this work differs from the usual one, as it is developed from theoretical results of existence and uniqueness of the realizations. The consistency of the approximate solutions will be based on studies on the existence and uniqueness of the theoretical solutions to this problem. In addition, error estimates are presented for the statistical moments of the beam response. The uncertainty will be quantified by estimating the statistical moments of the stochastic transverse displacement processes. The Monte Carlo simulation method is used to evaluate the performance of the proposed methodology.

Uncertainty Quantification of the ONERA 7A Rotor Performance and Loads Using Comprehensive Analysis

Quantification of blade stiffness uncertainties and sensitivities on rotor power and structural loads for the ONERA 7A rotor is established using the U.S. Army and ONERA rotorcraft comprehensive analysis tools. A stochastic-based approach is implemented to generate probabilistic bounds of the response outputs, including rotor performance and loads due to uncertainties in blade stiffness using 1) a Monte Carlo approach coupled directly with U.S. Army’s rotorcraft comprehensive toolset, and 2) a surrogate of ONERA’s rotorcraft comprehensive analysis solver using polynomial chaos expansions to efficiently predict the response outputs. The analysis showed that uncertainties in blade torsion, flap, and lag stiffnesses impact the predicted rotor power by a quantifiable amount. Significant uncertainties in peak torsion, flap, and chord bending moments are also confirmed. The sensitivities of the stiffness properties on response outputs using Sobol indices are also studied. The results show that total required power is exclusively sensitive to variability in torsion stiffness with no interaction effects with flap and lag stiffnesses. Sensitivities due to independent parameter effects and by combining with other parameters on peak structural loads are also examined. The analysis demonstrates the merits of integrating a stochastic, data-driven approach for uncertainty and sensitivity analyses in rotorcraft aeromechanics predictions.

Seismic structural control using magneto-rheological dampers: A decentralized interval type-2 fractional-order fuzzy PID controller optimized based on energy concepts

In this paper, a combination of the interval type-2 fuzzy logic controller (IT2FLC) with the fractional-order proportional–integral–derivative (FOPID) controller, namely optimal interval type-2 fractional-order fuzzy proportional–integral–derivative controller (OIT2FOFPIDC), is developed for enhancing the seismic performance and robustness in seismic structural control applications. Based on the energy concepts, a decentralized framework of the OIT2FOFPIDC is proposed for easy and simple implementation in structures during earthquakes. For this purpose, a coot optimization algorithm (COA), as a powerful optimization algorithm, is also applied to adjust the membership functions (MFs), scaling factors, and the main controller parameters. Three controllers, namely optimal type-1 fuzzy proportional–integral–derivative controller (OT1FPIDC), optimal interval type-2 fuzzy proportional–integral–derivative controller (OIT2FPIDC), and optimal proportional–integral–derivative controller (OPIDC), are also proposed for comparison purposes. The seismic performances of the suggested controllers are examined with the evaluation of nine seismic performance indices and different ground accelerations in a 6-story smart structure equipped with two dampers. The robustness of the four controllers in the presence of the stiffness uncertainties is also compared in this study. On average, a reduction of 25.0%, 18.8%, and 18.5% in peak displacement, inter-story drift, and acceleration of stories is obtained for the OIT2FOFPIDC over the OT1FPIDC, respectively. Similarly, these reductions in comparison with the OIT2FPIDC are 16.3%, 13.3%, and 12.0%. Also, these reductions, in comparison with the OPIDC, are 33.3%, 27.8%, and 25.8%. Furthermore, simulation results show that the OIT2FOFPIDC is more robust than the other proposed controllers against uncertainties due to structural stiffness.

Identification of a cantilever beam’s spatially uncertain stiffness

This study identifies non-homogeneous stiffnesses in a non-destructive manner from simulated noisy measurements of a structural response. The finite element method serves as a discretization for the respective cantilever beam example problems: static loading and modal analysis. Karhunen–Loève expansions represent the stiffness random fields. We solve the inverse problems using Bayesian inference on the Karhunen–Loève coefficients, hereby introducing a novel resonance frequency method. The flexible descriptions of both the structural stiffness uncertainty and the measurement noise characteristics allow for straightforward adoption to measurement setups and a range of non-homogeneous materials. Evaluating the inversion performance for varying stiffness covariance functions shows that the static analysis procedure outperforms the modal analysis procedure in a mean sense. However, the solution quality depends on the position within the beam for the static analysis approach, while the confidence interval height remains constant along the beam for the modal analysis. An investigation of the effect of the signal-to-noise ratio reveals that the static loading procedure yields lower errors than the dynamic procedure for the chosen configuration with ideal boundary conditions.

Robust path following control of 4WID autonomous vehicle with driving condition adaptive mechanism

This paper proposes a novel integrated path following control scheme for a 4-Wheel Independent Drive (4WID) autonomous vehicle that can adaptively change its mechanism according to the driving conditions. The proposed integrated system handles the lateral steering controller, longitudinal speed, and yaw moment controls considering tire force capacity of each corner. For the lateral controller, the cornering stiffness uncertainties and the transient performance are considered and combined into an H∞ robust controller based on linear matrix inequality (LMI) theory. A super-twisting sliding mode controller (STSMC) based longitudinal controller is designed to deal with disturbances and suppress chattering. When encountering extreme conditions, the active yaw moment controller with hierarchical structure is adaptively activated to prevent large deviation from the reference path and maintain the stability of vehicle. For the tire force allocation, an optimization algorithm is proposed, which has flexible equality constraints to coordinate the longitudinal and lateral motions according to the driving conditions. Simulations based on Carsim-Simulink co-simulation platform show that the proposed method is effective and has excellent performance in both normal and extreme driving conditions.

Deep CNNs as universal predictors of elasticity tensors in homogenization

In the present work, 3D convolutional neural networks (CNNs) are trained to link random heterogeneous, multiphase materials to their elastic macroscale stiffness thus replacing explicit homogenization simulations. The proposed CNN model is universal in that it accounts for various types of microstructures, for arbitrary phase fractions, non-constant and thereby very large ranges of Young’s moduli of the constituent phases (from 1 to 1000 GPa) and of their Poisson’s ratios (from 0 to 0.4). Moreover, the CNN predicts the stiffness for periodic boundary conditions (BCs) along with its upper bound through kinematically uniform BCs and its lower bound through stress uniform BCs. The triple of BCs reduces the stiffness uncertainty due to the embedding of the material volume into arbitrary adjacent host materials. Beyond, the stiffness bounds provide an indicator for the proper size of a representative volume element. The proposed universal CNN model achieves high accuracy in its predictions. The reasons for the rare outliers with larger errors are rigorously analyzed. For a real, two-phase diamond–SiC coating material the universal CNN is almost as accurate as a CNN exclusively trained for fixed elastic phase properties of that material. The speedup compared to finite element computations for homogenization is above factor 20500. The proposed CNN model hence enables fast and accurate stiffness predictions in universal analyses of heterogeneous materials in their linear elastic regime.

Adaptive control of dual-motor autonomous steering system for intelligent vehicles via Bi-LSTM and fuzzy methods

In order to achieve better trajectory tracking of intelligent vehicle on different road surfaces, which include underling the weather of rain and snow, an adaptive tire cornering stiffness strategy (ACS) and a trajectory tracking autonomous steering control strategy were proposed in this paper. Firstly, the tire–road friction coefficient estimator was designed to obtain the tire–road friction coefficient based on Bi-LSTM neural network, then combining the tire cornering stiffness coefficient by fuzzy controller to obtain the online tire cornering stiffness. Secondly, considering the uncertainty of tire cornering stiffness, a trajectory tracking upper-level controller based on model predictive control (MPC) algorithm was proposed to calculate the optimal front wheel angle. Thirdly, in order to better adapt to various road conditions, a dynamic equivalent stiffness model is proposed to replace the self-aligning torque model during vehicle steering, and a lower-level controller for pinion gear target position tracking was designed based on the sliding mode control (SMC) algorithm. In addition, this paper also designed a dual-motor control strategy, which cooperates with the pinion gear target position tracking lower-level controller to quickly and accurately achieve the target front wheel angle. Finally, the simulation and HiL test results show that the proposed control algorithm greatly improves the trajectory tracking accuracy and stability of the intelligent vehicle on roads with different tire–road friction coefficients.

Influence of uncertainty in geosynthetic stiffness on deterministic and probabilistic analyses using analytical solutions for three reinforced soil problems

The paper examines the quantitative influence of uncertainty in the estimate of geosynthetic reinforcement stiffness on numerical outcomes using analytical solutions for a) the maximum outward facing deformation in mechanically stabilized earth (MSE) walls, b) maximum reinforcement tensile loads and strain in MSE walls under operational conditions, and c) the mobilized reinforcement stiffness in a geosynthetic layer used to reinforce a fill over a void. The stiffness of the reinforcement is modelled using an isochronous two-parameter hyperbolic load-strain model. A linear relationship between isochronous stiffness and the ultimate tensile strength of the reinforcement is used to estimate reinforcement stiffness when product-specific creep data are not available at time of design. Solution outcomes are presented deterministically and probabilistically. The quantitative link between nominal factor of safety used in deterministic working stress design practice and reliability index is provided. The latter is preferred in modern performance-based design to quantify margins of safety within a probabilistic framework. Finally, the paper highlights the practical benefit of using product-specific isochronous secant stiffness data when available, rather than estimates of isochronous stiffness values based on reinforcement type or pooled data.

Pore–microcrack interaction governs failure in bioconsolidated space bricks

Understanding the mechanical response and failure of consolidated extra-terrestrial soils requires analyses of the interactions between propagating cracks and the material’s inherent pore structure. In this work, we investigate the fracture behaviour of lunar soil simulant consolidated using microbially induced calcite precipitation (MICP). We develop a numerical lattice network model using local beam elements to simulate the nucleation, propagation, branching, and merging of multiple cracks within a space brick subject to uniaxial compression. Our simulations capture the effects of local pores on crack paths as well as provide a means to predict the behaviour of samples with varying global porosity and/or uncertainties in local material stiffness. We identify multiple statistical lattice parameters that encode signatures of single or multiple crack growth events. Our results reveal the complexities involved in the fracture process with porous brittle solids and may easily be adapted to understand failure mechanisms and micro/macro crack evolution in other consolidated structures.