Shahram Sarkani

A network intrusion detection system based on a Hidden Naïve Bayes multiclass classifier

With increasing Internet connectivity and traffic volume, recent intrusion incidents have reemphasized the importance of network intrusion detection systems for combating increasingly sophisticated network attacks. Techniques such as pattern recognition and the data mining of network events are often used by intrusion detection systems to classify the network events as either normal events or attack events. Our research study claims that the Hidden Naive Bayes (HNB) model can be applied to intrusion detection problems that suffer from dimensionality, highly correlated features and high network data stream volumes. HNB is a data mining model that relaxes the Naive Bayes methods conditional independence assumption. Our experimental results show that the HNB model exhibits a superior overall performance in terms of accuracy, error rate and misclassification cost compared with the traditional Naive Bayes model, leading extended Naive Bayes models and the Knowledge Discovery and Data Mining (KDD) Cup 1999 winner. Our model performed better than other leading state-of-the art models, such as SVM, in predictive accuracy. The results also indicate that our model significantly improves the accuracy of detecting denial-of-services (DoS) attacks.

On applications of generalized functions to beam bending problems

Using a mathematical approach, this paper seeks an eAcient solution to the problem of beams bending under singular loading conditions and having various jump discontinuities. For two instances, the boundary-value problem that describes beam bending cannot be written in the space of classical functions. In the first instance, the beam is under singular loading conditions, such as point forces and moments, and in the second instance, the dependent variable(s) and its derivatives have jump discontinuities. In the most general case, we consider both instances. First, we study singular loading conditions and present a theorem by which the equivalent distributed force of a general class of singular loading conditions can be found. As a consequence of obtaining the equivalent distributed force of a distributed moment, we find a mathematical explanation for the corner condition in classical plate theory. While plate theory is not the focus of this paper, this explanation is interesting. Then beams with various jump discontinuities are considered. When beams have jump discontinuities the form of the governing diAerential equations changes. We find the governing diAerential equations in the space of generalized functions. It is shown that for Euler‐Bernoulli beams with jump discontinuities the operator of the diAerential equation remains unchanged, only the force term changes so that delta function and its distributional derivatives appear within it. But for Timoshenko beams with jump discontinuities, in addition to changes in the force terms, the operator of one of the governing diAerential equations changes. We then propose a new method for solving these equations. This method which we term the auxiliary beam method, is to solve the governing diAerential equations not in the space of generalized functions but rather to solve them by means of solving equivalent boundary-value problems in the space of classical functions. The auxiliary beam method reduces the number of diAerential equations and at the same time obviates the need to solve these diAerential equations in the space of generalized functions which can be more diAcult. 7 2000 Elsevier Science Ltd. All rights reserved.

An efficient approach for computing residual stresses in welded joints

Although the finite element method has emerged as one of the most attractive approaches for computing residual stresses in welded joints, its application to practical analysis and design problems has been hampered by computational difficulties. These difficulties do not arise in modeling the complex constitutive response of melting and solidifying metal; rather, they occur mostly because of the enormous computational size of any practical problem resulting primarily from the three-dimensional (3D) modeling of a welding process. Although two-dimensional (2D) modeling has been used widely in residual stress problems, current belief holds that 2D analysis cannot render accurate residual stresses that occur due to welding. This study investigates the residual stress fields in a welded T-joint, comparing those computed by 3D models with those computed by 2D models. The study shows that the temperature distribution in the central zone of the joint can be captured successfully by a 2D finite element model and a technique that takes into account the heat transfer balance and welding speed. The residual stresses in the plane of the 2D model computed by this method show fairly good agreement with those computed by the 3D model. More substantial differences are observed in the out-of-plane stresses, which are attributed primarily to the different mechanical boundary conditions in the out-of-plane direction of the 2D and the 3D models. All analyses in this investigation are performed with the finite element code ABAQUS.

On applications of generalized functions to the analysis of Euler–Bernoulli beam–columns with jump discontinuities

In this article some applications of the distribution theory of Schwarz to the analysis of beam–columns with various jump discontinuities are offered. The governing differential equation of an Euler–Bernoulli beam–column with jump discontinuities in flexural stiffness, displacement, and rotation, and under an axial force at the point of discontinuities, is obtained in the space of generalized functions. The auxiliary beam–column method is introduced. Using this method, instead of solving the differential equation of the beam–column in the space of generalized functions, another differential equation can be solved in the space of classical functions. Some examples of beam–columns and columns with various jump discontinuities are solved. Deflections of beam–columns and buckling loads for columns with jump discontinuities are calculated using the Laplace transform method in the space of generalized functions.

Spectral characteristics of nonstationary random processes — a critical review

Abstract This article analyzes the approaches to defining “spectral characteristics” derived from the spectral functions of nonstationary random processes. The processes considered are those for which an evolutionary power spectrum as designated by Priestley can be defined. Two basic approaches to defining spectral characteristics are reviewed. The first, characterized as geometric, leads to Vanmarkes spectral moments, which have proven to be very useful characteristics for stationary processes. However, these moments may be infinite for nonstationary processes, which creates problems for applications. The second approach, viewed as nongeometric, is based on Di Paolas pre-envelope covariances. The advantages and deficiencies of both approaches are discussed. It is also shown that the nongeometric spectral characteristics can be directly defined from the frequency domain as integrals of the one-sided auto- and cross-spectra of the evolutionary process and its derivatives. These nongeometric spectral characteristics are then used in defining parameters that characterize the central frequency and the bandwidth of evolutionary processes. To this end, the probability distributions of the process envelope are analyzed. It is demonstrated that suitable central frequencies and bandwidth factors can be defined from the probability density functions of the derivatives of the envelope and the phase.

The mechanics of self-similar and self-affine fractal cracks

In this paper we study the mechanical attributes of the fractal nature of fracture surfaces. The structure of stress and strain singularity at the tip of a fractal crack, which can be self-similar or self-affine, is studied. The three classical modes of fracture and the fourth mode of fracture are discussed for fractal cracks in two-dimensional and three- dimensional solid bodies. It is discovered that there are six modes of fracture in fractal fracture mechanics. The J-integral is shown to be path-dependent. It is explained that the proposed modified J-integrals in the literature that are argued to be path-independent are only locally path-independent and have no physical meaning. It is conjectured that a fractal J-integral should be the rate of potential energy release per unit of a fractal measure of crack growth. The powers of stress and strain singularities at the tip of a fractal crack in a strain-hardening material are calculated. It is shown that stresses and strains have weaker singularities at the tip of a fractal crack than they do at the tip of a smooth crack.

On nonuniform Euler–Bernoulli and Timoshenko beams with jump discontinuities: application of distribution theory

In this article, bending of nonuniform Euler–Bernoulli and Timoshenko beams with jump discontinuities in the slope, deflection and mechanical properties are studied. The governing equations are obtained in the space of generalized functions, and the expression of its governing differential equations in terms of a single displacement function and a single rotation function is shown always to be possible. In contrast, for a nonuniform Euler–Bernoulli beam with jump discontinuities in slope and deflection and abrupt changes in flexural stiffness, the governing equation can be written in terms of a single displacement function only under certain conditions. It is observed that for most discontinuous nonuniform Euler–Bernoulli beams we cannot write the governing differential equation in terms of a single displacement function: usually, if there are n discontinuity points on a nonuniform Euler–Bernoulli beam, n+1 displacement functions appear in the governing equilibrium equation.

A response spectrum approach for seismic analysis of nonclassically damped structures

Abstract A response spectrum approach for the analysis of nonclassically damped structural systems is presented. In this approach, which is similar to the response spectrum procedure for the analysis of classically damped systems, the only required information regarding the ground motion input is its response spectrum. The procedure takes into account the effect of cross-correlation between modes with closely spaced frequencies, and it is simple for practical application. The proposed method is used to approximate the maximum response of several nonclassically damped structural systems. Emphasis is placed on nonclassically damped primary-secondary systems in which the effect of nonclassical damping is known to be significant. Numerical results indicate that the maximum structural responses predicted by the proposed response spectrum approach are generally closer to the exact solutions than those obtained using the approximate classically damped procedure.

Stochastic fatigue damage accumulation under broadband loadings

Abstract Fatigue tests were conducted on 72 high-strength welded steel cruciform-shaped specimens subjected to stochastic loadings. Results of these tests are used to investigate experimentally the effects of loading non-normality and frequency bandwidth and truncation on the rate of fatigue damage accumulation. Test results are compared with predictions made using Rayleigh approximation and rainflow analysis in terms of cycles and time to failure. Results indicate that non-normality can significantly increase the rate of fatigue damage accumulation, and can result in non-conservative fatigue life estimates if its effect is not accounted for, regardless of frequency content. Likewise, frequency content was also found to influence the rate of fatigue damage accumulation, but to a lesser extent than non-normality. When higher-frequency components were included, shorter fatigue lives were observed. Fatigue life predictions using rainflow analysis produced good agreement with experimental results; predictions made using Rayleigh approximation produced non-conservative fatigue life estimates.

Mean stress effects in fatigue of welded steel joints

Mean stress effects in steel weldments were examined under both constant and random narrowband amplitude fatigue loadings. The purpose of these tests was to provide experimental data with which to substantiate the use of analytical expressions to account for mean stress effects. Fatigue tests were performed under both tensile and compressive mean stress levels. Test results indicate agreement with the modified Goodman equation to be favorable in accounting for the effect of tensile mean stresses on fatigue life. However, test results from high fatigue loadings (maximum stresses nominally above half ultimate) were found to possess better agreement with the Gerber formulation than with the modified Goodman one. Behavior under compressive mean stresses indicated a linear correction relationship was required, which was less conservative than any of the relationships considered. Test results obtained under random amplitude fatigue loadings exhibited trends similar to those observed under constant amplitude loadings. This finding, along with supporting analysis, indicates that the same correction relationship can be used in the same manner for both constant amplitude and random (narrowband) amplitude loadings.