Karen C. Chou

Simulation of hourly wind speed and array wind power

Abstract Statistical summaries of wind speed are sufficient to compute many characteristics of turbine-generated power, such as the mean, variance and reliability of various power levels. However, a wind speed time series is necessary to produce a sequence of power values as used for investigating load matching and storage requirements. Since a long historical record of wind speed may not be available at a wind turbine candidate site, it is desirable to be able to generate a simulated numerical sequence of hourly wind speed values. Two such approximate procedures are developed in this paper. One procedure generates sequential wind speed values at a site based on the Weibull parameters of hourly wind speed and the lag-one autocorrelation of hourly wind speed values. Comparison with historical data at a site is made. The second procedure generates sequential hourly wind power values for a regional array of wind turbines. It utilizes the typical site wind characteristics, the spatial and lag-one cross correlation and autocorrelation of hourly wind speed values and an equivalent linearized relationship between array average wind speed and array power. Comparison with results for six different wind turbines in three different regional arrays indicates good agreement for wind power histograms, autocorrelation function and mean persistence.

Safety assessment of existing structures using a filtered fuzzy relation

Abstract Most constructed systems, as well as our infrastructure system, require regular inspection and reassessment so that proper actions can be taken to maintain their current usefulness. Although the quantitative information obtained from these inspections can be analyzed systematically and consistently using probability theory, a parallel analysis is not yet developed for the qualitative information obtained. A filtered fuzzy relation algorithm which utilizes the fuzzy set theory is developed to analyze the qualitative data methodologically. The analysis yields a safety function which shows the degree of belonging for each level of safety reduction from the original design reliability. A sensitivity analysis on the membership functions associated with the input data to the resulting safety function is also performed. The results indicate that, in general, the preciseness of these membership functions has little or no influence on the safety functions. Thus the filtered fuzzy relation algorithm has practical application in assessing existing membership functions.

Limit analysis of 2-d tunnel keyblocks

Abstract The mechanical response of rock blocks adjacent to tunnels depends on joint orientations and joint shear strength, on the in situ stresses and on the size, shape, depth and orientation of the tunnel. The stability of rock blocks can be usefully studied by means of block theory, which is based on the application of kinematics and statics principles to a jointed rock mass. When in situ stresses are considered together with self-weight, the system of forces governing block stability becomes statically indeterminate. The standard block theory stability analysis treats blocks as rigid bodies subject to self weights or other applied loads. This approach is generally conservative, but limits the applicability of the method to design. This paper describes a limit analysis of block stability which yields bounds on the ranges of stability and instability and their region of overlap, potential instability. The mathematical problem of finding these limits is carried out by linear programming. A measure of keyblock stability is mapped onto a gray scale and plotted on a grid representing all possible keyblocks around a tunnel, giving a measure of the overall stability of the rock mass. A parametric study of the effects of joint orientation and initial stress ratio on block stability is presented.

Uncertainty analysis of tunnel roof stability

Fractures, joints, and other discontinuities significantly influence the stability of excavations in rock. Unstable blocks of rock in the roofs of tunnels can have a significant effect on the safety and economic feasibility of highways and railroads. The stability of tunnel roof keyblocks subject to self-weight and surface forces is examined using linear programming methods. An instability measure based on the concept of fuzzy sets is used to characterize the level of instability. On the basis of analysis of the instability measure, the support pressure required to stabilize the tunnel roof can be estimated. A probabilistic analysis based on the expectation of the instability measure is used to examine the effect of the uncertainties caused by the variability of rock material properties.

An inverse solution for reconstruction of the area-moment-of-inertia of a beam using deflection data

The main purpose of this study was to develop a mathematical model that could be used to determine the changes in the structural characteristics – such as changes that could occur due to corrosion in the cross-sectional area-moment-of-inertia of a bridge – from the knowledge of its loading and deflection. Reconstruction of the cross-sectional area-moment-of-inertia of a bridge from the knowledge of its loading and deflection is an inverse problem. In this investigation, the cross-sectional area-moment-of-inertias of a scaled model of simply supported steel bridge (with simulated corrosion) are reconstructed using the deflection and load data. The deflection data used in this inverse problem were numerically generated using the finite element method and the ANSYS software. The deflection data for each model were then used in the inverse problem to reconstruct the cross-sectional area-moment-of-inertias for the model. To solve the inverse problem, the solution domain was discretized into finite number of elements and nodes. The nodal deflections and slopes were represented by Hermite shape functions. For each element, the strain energy and the work done by the external forces were formulated. The minimum total potential energy principle was then used to create the stiffness matrices and reconstruct the area-moment-of-inertia for each element. The inverse model creates a set of linear equations that must be solved simultaneously. Moreover, since the formulation led to more equations than unknowns, the least squared method was used to minimize the errors associated with the solutions, and to match the number of equations with unknowns. Comparison of the inverse solutions with the direct solutions confirms that the variations in the area-moment-of-inertia for a bridge cross-section can be reconstructed, with good accuracy, from the knowledge of its loading and deflection.

Teaching of uncertainty analysis and risk assessment in civil engineering

There have been many research results related to uncertainty analysis and risk assessment during the past several decades. However, practical applications of these results remain scarce. The slow growth in interest, both in academic and among practicing engineers, in rigorous risk assessment and uncertainty analysis signals a need to reexamine our current means and practice of delivering the risk assessment education to our students. In this paper, a discussion on various techniques in teaching uncertainty analysis and its applications to engineering decision-making are presented. In addition, steps are recommended to develop a decision making framework for the environmental and infrastructure systems.

Probabilistic analysis of nonlinear response to sustained load processes

Abstract Reliability study of structural members subjected to a stochastic load process has been extended to include material nonlinearity. Tractable expressions for the first moment statistics of the number of load exceedances and damage duration were derived previously, primarily for a Poisson square wave process and for material with a bilinear force-deformation relationship. A probability distribution for the number of load exceedances is derived herein. It is found that the derived distribution, when approximated by a Taylor series, is in good agreement with that obtained from the simulated sustained load processes if the coefficient of variation of load exceedances is under 50%. In addition, the relationship between linear load effect and non-linear structural response is examined for different elastic limits both in load exceedances and in damage duration. It appears that for high threshold levels, nonlinear response may not be as critical as linear response.

Infrastructure assessment: fuzzy regression with neural networks

In modeling a problem where the information is dependent on subjective estimations the fuzzy structure of the problem must be included. One approach in formulating the fuzzy structure is fuzzy regression with neural network analysis. The procedure is to use a neural network model that provides both upper and lower bounds to the data. These bounds define an interval model from which a fuzzy model can be developed. Such an approach has been demonstrated on the problem of quality evaluation of injection mouldings. We propose that fuzzy regression with neural networks would prove most beneficial for the implementations of bridge and pavement management systems. The neural network analysis is more computational intense with six input variables. The development of a fuzzy regression model from the upper and lower bounds neural network models becomes more complex.<<ETX>>

Nonlinear load exceedance model for cyclic load processes : Development

Studies of structural response due to stochastic load processes have been extended to include nonlinear material response. The studies on the Poisson processes with rectangular pulses were for positive pulse intensity such as gravity load. The reliability analysis developed was not applicable for processes with reversible cyclic load pulses such as earthquake, thermal or wind loads. Since these reversible loads are critical to the safety of a structure, it is vital that a rigorous analysis be developed to perform the safety assessment. In this paper, the development of a probability model for nonlinear load exceedances subjected to a stochastic process with reversible cyclic load pulses is presented. A probability mass function for the nonlinear load exceedances was developed based on the Markov process. The load deformation relationship used in the study was assumed to be bilinear with the unloading parallel to the initial loading path and the compressive properties being the same as tensile. Good agreements were found between the probability model developed and the histograms computed based on simulated load processes.