Stochastic Wind Loads Research Articles

Global reliability assessment of coupled transmission tower-insulator-line systems considering soil-structure interaction subjected to multi-hazard of wind and ice

This study aims to assess the global reliability of coupled transmission tower-insulator-line systems considering soil-structure interaction (CTTILSs-SSI) subjected to multi-hazard of wind and ice. Firstly, two simplified models of CTTILSs-SSI under stochastic wind and ice loads are established, and their governing equations are derived through the Lagrange equation. On this basis, a global reliability assessment framework of CTTILSs-SSI is proposed based on the improved maximum entropy method, in which the global performance function of CTTILSs-SSI is defined via the state variable description method. Finally, a practical ultra-high voltage overhead transmission line located on the icing zone is chosen to illustrate the proposed framework. Moreover, to investigate the influence of soil-structure interaction (SSI) and soil types on the global reliability of transmission tower-insulator-line systems (TTILSs), the global reliability of CTTILSs-SSI with various soil types is compared with that of a fixed base system. The results indicate that under the in-plane wind and ice loads, the global failure probability of TTILSs is almost zero, and it is essentially not affected by the SSI effect and soil types. However, under the out-of-plane wind and ice loads, the global failure probability of CTTILSs-SSI is higher than that of the fixed base system, and the global failure probability of CTTILSs-SSI increases as the soil stiffness decreases. Accordingly, it may be more reasonable to consider the SSI effect into the global reliability analysis of TTILSs subjected to ice and out-of-plane wind loads, particularly when the soil is soft.

Active learning-based optimization of structures under stochastic excitations with first-passage probability constraints

In various efforts to manage the risk of structural failures caused by stochastic excitations such as wind and earthquake loads, the first-passage probability often needs to be calculated as a reliability constraint. Estimating the first-passage probability with low computational costs is essential, especially in structural optimization requiring iterative reliability calculations for design alternatives. This paper presents a new active learning-based framework for reliability-based design optimization (RBDO) of structures under stochastic excitations. A mixture-distribution-based formulation of the first-passage probability is utilized to handle the high-dimensional sequences of stochastic excitations during the optimization. The design parameter sensitivity of the first-passage probability is introduced to use a gradient-based optimizer in the RBDO iterations. These procedures employ heteroscedastic Gaussian process-based surrogates of the logarithmic responses. An active-learning scheme identifies the best training point to reduce the computational costs in the first-passage probability calculations and optimization. The numerical examples dealing with the optimal design of an eight-story building system and a tower structure subjected to stochastic wind loads demonstrate the accuracy and efficiency of the proposed method.

A new metamodel for predicting the nonlinear time-domain response of offshore structures subjected to stochastic wave current and wind loads

Offshore structures are subjected to stochastic loads from wave, current, and wind. A long-term response analysis is important for evaluating the structural safety; however, it is computationally demanding to perform the large number of nonlinear time-domain simulations. Metamodeling is an attractive prospect, but there are two existing obstacles to overcome. First, existing metamodels are mostly confined to a single sea state and are unable to predict the response for different wave directions. Second, for floating systems, the inputs are usually vessel loads/motions, which are a priori unknown. This paper develops a new metamodel framework for accurately predicting the time series response under short-term uncertainties from the stochastic process, and seven long-term variables, namely the significant wave height, spectral period, wave direction, and speeds and directions of current and wind. The exogenous input is based only on the environmental variables, which can be predefined. The proposed metamodel is implemented on a floating system and used to predict the time series of riser stress, the extreme stress response and fatigue damage. Four cases with increasing number of long-term variables are tested. Excellent agreement is found between the metamodel prediction and numerical simulation even for the most critical case with all variables included.

Safety evaluation of tubing and sucker rod vertically handling equipment under stochastic wind load

Workover operations are crucial for maintain the normal production of oil, gas and water wells and require significant manpower and material resources. In recent years, automation equipment has become more widely used in the operations of oilfield workover operations. The present paper established the finite element model of the newly developed tubing and sucker rod vertically handling equipment, and the deformation, equivalent stress and wind-resistant ability of the structure model under dead weight load and wind load are investigated. The wind load is equivalent to the wind pressure acting on the structural unit, and the transient wind field is composed through linear superposition of harmonic function with random amplitude and frequency. Results show that the maximum equivalent stress is much lower than the yield stress of the structural material under typical working conditions, the maximum displacement of the manipulator position meets the design requirements of positioning accuracy.

Uncertainty Quantification and Simulation of Wind-Tunnel-Informed Stochastic Wind Loads

The simulation of stochastic wind loads is necessary for many applications in wind engineering. The proper-orthogonal-decomposition-(POD)-based spectral representation method is a popular approach used for this purpose, due to its computational efficiency. For general wind directions and building configurations, the data-informed POD-based stochastic model is an alternative that uses wind-tunnel-smoothed auto- and cross-spectral density as input, to calibrate the eigenvalues and eigenvectors of the target load process. Even though this method is straightforward and presents advantages, compared to using empirical target auto- and cross-spectral density, the limitations and errors associated with this model have not been investigated. To this end, an extensive experimental study on a rectangular building model considering multiple wind directions and configurations was conducted, to allow the quantification of uncertainty related to the use of short-duration wind tunnel records for calibration and validation of the data-informed POD-based stochastic model. The results demonstrate that the data-informed model can efficiently simulate stochastic wind loads with negligible model errors, while the errors associated with calibration to short-duration wind tunnel data can be important.

Fragility Analysis of Transmission Towers Subjected to Downburst Winds

A downburst is a typical local highly intensive wind all over the world, which is attributed to be the main cause of wind damage to transmission lines in inland areas worldwide. The collapse accidents of transmission towers under the downburst still occur every year. Therefore, it is of great significance to assess the safety of the transmission towers under downbursts. The motivation of the present study is to propose a fragility assessment method for transmission towers under the action of a downburst considering the uncertainty of wind-resistance capacity and the stochastic wind load effect. First, the downburst wind field of the transmission tower with different wind attack angles and different radial distances is simulated according to the mixed stochastic model. Then, random material characteristic samples are generated by the Latin hypercube sampling technique and applied to establish uncertain finite element models for transmission towers. Next, the static nonlinear buckling analysis is carried out by numerical methods to determine the ultimate capacity under the downburst wind load. The parameter analysis of different wind attack angles and radial distances between the downburst and the tower is conducted to determine the most unfavorable location of the maximum response. The failure mode of the transmission tower and the probabilities of the initial failure main members are summarized. Finally, the fragility curves of the transmission tower under the downburst and the atmospheric boundary layer (ABL) wind are compared. The results show that the maximum response is located at R = 1.6D. Most of the initial buckling members are located close to the first section of the tower. The fragility curves of the tower under the downburst are more dangerous than the ABL wind with the attack angle increasing from 0° to 90°. Furthermore, considering the probability model of intensity and direction of the downburst and based on the previous fragility analysis, the collapse probability of the transmission tower caused by the downburst is obtained. By probability analysis of the parameters, including layout conditions, different directions, and different wind speeds, it is found that the most favorable arrangement is 157.5°, and the most unfavorable arrangement is 112.5°.

Numerical study of an ice-offshore wind turbine structure interaction with the pile-soil interaction under stochastic wind loads

In order to better understand the ice-induced collision/vibration mechanism of offshore wind turbines (OWTs) with ice-breaking cones, the Tsai-Wu yield criterion of ice for bending failure is coupled to the nonlinear collision simulation tool ANSYS/LS-DYNA in this paper, and a numerical approach is adopted to predict dynamic ice force. Through comparisons of ice force between simulations and physical tests, the accuracy of dynamic ice force simulated by the proposed approach is verified. Meanwhile, to consider the pile-soil interaction (PSI) effect, the Euler-Bernoulli Beam theory and the Timoshenko Beam theory are used, respectively, and the dynamic characteristics of the OWT are compared and analyzed. The discrepancies between the calculation results of the two methods and the influence of PSI on OWTs under combined wind-ice conditions are discovered. Further, the fully coupled interaction model between ice and flexible OWT with PSI under wind and ice loadings is established. Based on the full three-dimensional (3D) interaction model, the influence of the ice velocities, ice thicknesses, and cone angles on the dynamic ice force and structural response is investigated. The area damage rate and fatigue damage rate of the monopile foundation are proposed to further carry out damage and fatigue analyses under wind and ice loads. Higher fatigue damage is associated with smaller area damage rate. In addition, the ice thickness has a more significant effect on OWT damage and fatigue compared with the ice velocity.

Non-linear control design for optimized power regulations in spar wind turbines under wind and wave loads

Controlling motions for spar wind turbines (SWT) is necessary for reliable power production. In this paper, a control design is developed and its efficacy is demonstrated through the application to wind turbines installed on spar. SWT is expected to generate rated power under stochastic wind and wave loads. The controller design is derived from the quadratic regulator algorithm, which involves changing the dynamics of the system matrices (which are state dependent) of wind turbine. Three turbulent wind velocities are chosen at which the controller algorithm is working for turbines operational region. The ensemble average is used to eliminate statistical uncertainty, since the loads are stochastic. Illustrations through the generated power, torque and rotor speed show that the proposed controller (i.e., nonlinear quadratic one) works better than the existing baseline algorithm. More specifically, the achieved generated power through the proposed method is 29% higher than conventional one for 21 m/s stochastic wind field scenario. Along with controlling the desired variables, this algorithm also maintains the motions of platforms and forces at base of tower. Also, the ensemble means and the maxima of responses are closer to reference values with considerably lower standard-deviation.

Probabilistic analysis of resistance for RC columns with wind-dominated combination considering random biaxial eccentricity

For reinforced concrete (RC) column with biaxial eccentricity, the conventional design methods usually use the fixed eccentricity criterion to check its resistance, which may underestimate the variations of column resistance. Based on the load statistics compatible with the codes, the random properties of biaxial eccentricity are analyzed with Monte Carlo simulation (MCS) for representative columns in regular frame structures under both vertical load and wind load. Then, the tested capacity results of 103 relevant column specimen are collected from literatures. The uncertainty of the resistance model is analyzed for the reciprocal load method in code ACI 318-14. Based on the criterion of both random eccentricity and fixed eccentricity, the probability regarding load bearing capacity exceedance is analyzed for columns by MCS with different design parameters (e.g. axial compression ratio, etc.). The results indicate that based on the prescribed load statistics, the random properties of eccentricities along two principal directions are mainly controlled by the stochastic wind load, leading to that the eccentricities along two principal directions show an approximate perfect correlation; the random biaxial eccentricity has a significant influence on resistance variations and the maximum coefficient of variation is as large as 0.73.

Reliability-Based Collapse Assessment of Wind-Excited Steel Structures within Performance-Based Wind Engineering

As inelastic design for wind is embraced by the engineering community, there is an increasing demand for computational tools that enable the investigation of the nonlinear behavior of wind-excited structures and subsequent development of performance criteria. To address this need, a probabilistic collapse assessment framework for steel structures is proposed in this paper. The framework is based on the integration of a high-fidelity fiber-based nonlinear structural modeling environment with a wind-tunnel-informed stochastic wind load model to perform nonlinear time history analysis. General uncertainty is propagated using a stratified sampling scheme enabling the efficient estimation of reliabilities associated with rare events. The adopted models for simulating high-fidelity nonlinear structural behavior were found, in general, to be adequate for capturing phenomena, including progressive yielding, buckling, and low-cycle fatigue, that are essential for wind induced collapse analysis. In particular, the adopted fatigue model was found to be capable of predicting damage and potential fiber/section fracture associated with non–fully reversing stress-strain cycles that are characteristic of wind loading. Through illustration on a 45-story archetype steel building, critical discussions on the types of observed collapse mechanisms, the difference between along-wind and across-wind nonlinear behavior, reliabilities associated with first yield, and collapse are presented. A probabilistic description of the residual and peak story drifts is also provided through development of fragility functions.

Predicting dynamic responses of frame structures subjected to stochastic wind loads using temporal surrogate model

Determining structures' dynamic response is a challenging and time-consuming problem because it requires iteratively solving the governing equation of motion with a significantly small time step to ensure convergent results. This study proposes an alternative approach based on the deep learning paradigm working in a complementary way with conventional methods such as the finite element method for quickly forecasting the responses of structures under random wind loads with reasonable accuracy. The approach works in a sequence-to-sequence fashion, providing a good trade-off between the prediction performance and required computation resources. Sequences of known wind loads plus time history response of the structure are aggregated into a 3D tensor input before going through a deep learning model, which includes a long short-term memory layer and a time distributed layer. The output of the model is a sequence of structures' future responses, which will subsequently be used as input for computing structure' next response. The credibility of the proposed approach is demonstrated via an example of a two-dimensional three-bay nine-story reinforced concrete frame structure.

Wind load estimation and virtual sensing in long-span suspension bridges using physics-informed Gaussian process latent force models

Wind loading is an essential aspect in the design and assessment of long-span bridges, but it is often not well-known and cannot be measured directly. Most structural health monitoring systems can easily measure structural responses at discrete locations using accelerometers. This data can be combined with reduced-order modal models in Kalman filter-based algorithms for an inverse estimation of wind loads and system states. As a further development, this work investigates the incorporation of Gaussian process latent force models (GP-LFMs), which can characterize the evolution of the wind loading. The Hardanger Bridge, a 1310 m long suspension bridge instrumented with a monitoring system for wind and vibrations, is used as a case study. It is shown how the LFMs can be enriched with physical information about the stochastic wind loads using monitoring anemometer data and aerodynamic coefficients from wind tunnel tests. It is found that the estimates of the modal wind loads and modal states obtained from a Kalman filter and Rauch–Tung–Striebel smoother are stable for acceleration output only, thus avoiding the accumulation of errors. The proposed approach demonstrates how physical or environmental data can be injected as valuable information for global monitoring strategies and virtual sensing in bridges.

Practical Approach to Digitally Simulate Nonsynoptic Wind Velocity Profiles and Its Implications on the Response of Monopole Towers

AbstractIn the numerical simulation of stochastic nonstationary wind loads, rapidly varying wind speed fluctuations about a deterministic mean value typically represent the sole source of random va...

Reliability analysis of a large curved-roof structure considering wind and snow coupled effects

Ensuring the safety of large curved-roof structures subjected to blizzards in cold regions remains challenging. This paper assesses the reliability of a large curved-roof structure considering the coupled effects of wind and snow. To this end, a two-way coupled simulation considering the interaction between snow particles and turbulent wind is first carried out using a computational fluid dynamics scheme and a spectral representation method based on the wavenumber-frequency joint power spectrum and stochastic harmonic function; thereby, the uneven snow distribution and stochastic wind field on a large curved roof are revealed. The probability density evolution method is then adopted to conduct a stochastic response and reliability analysis of the structure. The simulation results reveal that a credible uneven distribution of snow on the large curved roof can be obtained using the suggested snowdrift simulation scheme, and the refined spectral representation method can efficiently and accurately simulate the two-dimensional fluctuating wind field of the large curved-roof structure. It is shown that under stochastic wind, snow and self-weight loads for a 100-year return period, the large curved-roof structure has a higher risk of member yielding than of node deflection. Meanwhile, the axial stress acting on the structural member is far less than the maximum allowable stress and the structure is thus deemed to be sufficiently safe.

Modeling of soil-pile-structure interaction for dynamic response of standalone wind turbines

The accurate prediction of the dynamic behavior of the offshore wind turbine plays a significant role in its safe and efficient operation, where special importance should be attached to the foundation modeling of soil-pile-structure interaction. The present study aims to compare the three foundation modeling approaches with special attention to their displacement, acceleration, and internal force response subject to the combined stochastic wind and wave loading. In addition, parametric studies have been conducted on the foundation modeling approaches with the focus on their sensitivity to the variation of the foundation stiffness, pile diameter, thickness, and pile embedded depth. Using the high-fidelity FE model of the soil-pile system as the benchmark, the apparent fixity model underestimates the foundation stiffness remarkably, while the distributed spring model can give a relatively accurate prediction of the foundation stiffness. Furthermore, the FE model of the soil-pile system is more sensitive to the soil densification and the pile embedded depth, while the apparent fixity model exhibits higher sensitivity to the pile diameter and thickness. Compared with the benchmark FE model, the study provides guidance for the applicability of the simplified foundation modeling approaches, the apparent fixity model and distributed spring model, to different foundation stiffness in engineering practice.

Performance-based Bi-objective optimization of structural systems subject to stochastic wind excitation

This paper outlines the development of a stochastic simulation-based design optimization approach for dynamic wind excited structures in which correlations between component damages and losses are explicitly treated. The proposed approach integrates a bi-objective design optimization scheme with a probabilistic performance-based wind engineering methodology which systematically accounts for the various sources of uncertainties involved in system loss estimation. Through the ∊-constraint technique, the bi-objective optimization problem is transformed into a series of single-objective stochastic optimization problems. To solve each ∊-constraint optimization problem, a pseudo-simulation scheme is proposed that allows for the formulation of an approximate sub-problem that can be solved sequentially to identify solutions that define a set of Pareto optimal designs. In the proposed scheme, samples of engineering demands are approximated in terms of auxiliary variable vectors, which are by-products of an augmented simulation carried out in a fixed design point. Analytical expressions are derived that relate the engineering demand samples to the second-order statistics of wind-induced losses based on the concept of fragility. Potential correlations between the component capacities and component losses are explicitly treated. The effectiveness of the proposed approach and its scalability to high-dimensional problems are illustrated through optimal designs of moment-resisting frames subject to stochastic wind loads.

Topology optimization of buildings subjected to stochastic wind loads

Traditionally, the main structural system of tall buildings is designed iteratively to resist extreme wind loads, which provides safe, but typically suboptimal building systems. Topology optimization provides a general approach to obtain optimal material layout to carry the required load within specified design constraints. The wind loading on a structure is typically modeled as an equivalent static load or as a spatio-temporal stochastic field. While a few models for stochastic wind excitation are available, these approaches are focused on obtaining samples for time history analyses. In this study the stochastic wind excitation is modeled as a filtered vector white noise; the state space representation of the filter is obtained by solving a regularized optimization problem from known stationary wind power spectral densities. An augmented state space representation is formed by combining the equation of motion for the structure with the excitation filter. The stationary covariances of the structural responses of interest are then obtained by solving the associated Lyapunov equation. Dynamic condensation of the equations of motion is employed to increase the efficiency of the proposed approach. Objective functions for the optimization scheme are defined in terms of the stationary covariance of the response; various objectives are considered corresponding to typical design considerations. An equivalent smooth formulation is employed to solve the non-smooth min–max problem. A gradient-based method is used to update the design variables, while the sensitivities are computed from the solution of an adjoint Lyapunov equation. The proposed topology optimization scheme is illustrated for a tall building subjected to along-wind and across-wind loads. The results presented herein demonstrate the efficacy of the proposed approach for efficient topology optimization of buildings subjected to stochastic wind excitation.

A Response Spectrum Analysis of Wind Deflection in Railway Overhead Contact Lines Using Pseudo-Excitation Method

The wind deflection of overhead contact lines (OCLs) challenges the stable and safe operation of electrified railways. The steady wind causes the static deflection of the contact line, while the fluctuating wind leads to the OCL buffeting. This paper performs a response spectrum analysis of the wind deflection caused by the combined effects of steady and fluctuating winds. Considering the initial configuration of OCL, an absolute nodal coordinate formulation method is employed to model the OCL. A spatial wind field including the fluctuating wind in three directions is constructed and the aerodynamic forces on the OCL are derived. A nonlinear solution procedure is proposed to include the geometrical nonlinearity and dropper slackness in the evaluation of static wind deflection. The pseudo-excitation method is utilised to evaluate the buffeting response of the OCL with stochastic wind load. The analysis results indicate that the dropper slackness has a significant effect on the vertical static deflection. Under an extreme wind speed of 40 m/s, the contact line is always within the safe working range of pantograph head when only the steady wind load is considered. However, the stochastic wind load causes non-negligible fluctuation of OCL, and the contact line may be outside of the pantograph working range under the same wind speed. Sensitivity analyses on the effects of some key parameters to the OCL buffeting suggest that the increases of damping ratio and the tension class are effective measures to improve the wind-resistance capability of OCL.

Reliability model for wind turbine blade composites under alternate action of normal and extreme wind loads

Wind turbine blade is the key component to capture wind power, and it is mainly composed of glass fiber reinforced polymer (GFRP). Due to the randomness and volatility of wind speed in nature, wind turbine blade is usually subjected to the alternate action of normal and extreme wind loads during its long-term service. In this study, a reliability model that considering the stochastic wind loads and strength degradation of GFRP is proposed. Firstly, a residual strength model is developed based on the Palmgren-Miner (P-M) damage theory and the same damage state (SDS) principle, which is capable of characterizing the strength degradation law of GFRP under the normal wind load. Then, the alternate actions of normal and extreme wind loads are considered, and a dynamic reliability model is presented based on Poisson process and mathematical derivation. Finally, the traditional discrete stress-strength interference (DSSI) model is extended to calculate the dynamic reliability when probability distributions of stochastic wind loads and residual strength of GFRP are unknown. The wind load data and GFRP test data are utilized to demonstrate the effectiveness of the proposed model. The result shows that the reliability of GFRP keeps at a high level in the early stage, then it rapidly decreases due to the accumulation of fatigue damage.

Gaussian process regression for fatigue reliability analysis of offshore wind turbines

The fatigue limit state (FLS) often drives the design of offshore wind turbine (OWT) substructures in European waters. Assessing fatigue damage over the intended design life of an OWT is computationally expensive, primarily as dynamic structural analyses have to be run for a large number of stochastic wind and wave loading conditions. This makes structural reliability assessment for the FLS a challenging task. In addition to evaluating load-induced fatigue damage, simulation-based structural reliability analysis also requires sampling of random variables that model uncertainties in the capacity of OWT structural components. To this aim, we develop and validate a computational framework for OWT fatigue reliability analysis that relies on Gaussian process (GP) regression to build surrogate models of load-induced fatigue damage. We demonstrate that the proposed approach can reduce the computational effort required to evaluate FLS reliability with high accuracy through application to three plausible offshore wind farm sites in Europe. The sensitivity of various goodness-of-fit metrics to different model assumptions is investigated to further reduce the computational effort required to perform GP regression/predictions. The results from this study can provide guidance for practical applications of the proposed framework in OWT projects.