# PUBLICATIONS

Selected Recent Publications

## DISTRIBUTION WITH INDEPENDENT COMPONENTS FOR UNCERTAINTY QUANTIFICATION AND STRUCTURAL RELIABILITY ANALYSIS

U. Alibrandi & K.M. Mosalam. 2019, ICASP13

This paper presents a novel method based on the Information Theory, Machine Learning and Independent Component analysis for Uncertainty Quantification and Structural Reliability Analysis. At first, it is shown that the optimal probabilistic model may be determined through minimum relative entropy and the theory of statistical learning. It is also discussed that methods based on the maximum entropy may perform well for the evaluation of the marginal distributions, including the tails. To determine the joint distribution of the basic random variables it is introduced the multivariate probabilistic model of Distributions with Independent Components (DIC). It has same computational simplicity of Nataf, but it is more accurate, since it does not pursue any assumption about the tail dependency. The proposed framework is applied to determine the joint distribution of wave height and period of wave data. Its extension for high dimensional reliability analysis of complex structural systems is straightforward.

## PERFORMANCE BASED ENGINEERING AND MULTI CRITERIA DECISION ANALYSIS FOR SUSTAINABLE AND RESILIENT BUILDING DESIGN

K. Mosalam, U. Alibrandi, H. Lee & J. Armengou , 2018, Structural Safety, 74: 1-13

In this paper, an integrated approach for a holistic (involving notions of resiliency and sustainability) building design is presented to select the optimal design alternative based on multiple conflicting criteria using the multi-attribute utility theory (MAUT). A probabilistic formulation of MAUT is proposed, where the distributions of the uncertain parameters are determined by a performance-based engineering (PBE) approach. Here PBE is used to evaluate the building energy efficiency and sustainability in addition to structural safety. In the proposed framework, different design alternatives of a building are ranked based on the generalized expected utility, which is able to include the most adopted probabilistic decision models, like the expected utility and the cumulative prospect theory. The distributions of the utilities are obtained from the first-order reliability method to provide (i) good tradeoff between accuracy and efficiency, and (ii) rational decision making by evaluating the most critical realizations of the consequences of each alternative through the design point. The application of the proposed approach to a building shows that design for resilience may imply design for sustainability and that green buildings (alone) may be not resilient in the face of extreme events.

## CODE-CONFORMING PEER PERFORMANCE BASED EARTHQUAKE ENGINEERING USING STOCHASTIC DYNAMIC ANALYSIS AND INFORMATION THEORY

U. Alibrandi & K.M. Mosalam 2018, KSCE Journal of Civil Engineering, 22(3): 1002-1015

In this paper, the tools of the stochastic dynamic analysis are adopted for Performance-Based Earthquake Engineering (PBEE). The seismic excitation is defined through a evolutionary Power Spectral Density compatible with the response spectrum given by mandatory codes. In this way, the performance-based design is applied considering the excitation coherent with the codes. Inside the framework, the seismic fragility curves are determined through the Kernel Density Maximum Entropy Method (KDMEM), recently proposed by the authors. It is a novel statistical method capable to reconstruct the seismic fragility curves, including the tails, from a small number of code-conforming artificial ground motions. Moreover, KDMEM is based on the Maximum Entropy (ME) principle and it provides the least biased probability distribution given the available information. Comparison between stationary and nonstationary artificial accelerograms is analyzed, and the corresponding model uncertainty discussed. KDMEM provides also credible bounds of the uncertain performances, which is beneficial for risk-informed decisions. The proposed formulation does not require the selection of a suitable set of ground motions. Accordingly, it can be adopted for optimal design in current engineering practice. Therefore, it fills the gap between the classical code-conforming designs and the enhanced performance-based designs.

## KERNEL DENSITY MAXIMUM ENTROPY METHOD WITH GENERALIZED MOMENTS FOR EVALUATING PROBABILITY DISTRIBUTIONS, INCLUDING TAILS, FROM A SMALL SAMPLE OF DATA

U. Alibrandi & K.M. Mosalam 2017, International Journal for Numerical Methods in Engineering, 113(13): 1904-28

In this paper, a novel method to determine the distribution of a random variable from a sample of data is presented. The approach is called Generalized Kernel Density Maximum Entropy Method (GKDMEM), because it adopts a Kernel Density (KD) representation of the target distribution, while its free parameters are determined through the principle of Maximum Entropy (ME). Here, the ME solution is determined by assuming that the available information is represented from generalized moments, which include as their subsets the power and the fractional ones. The proposed method has several important features: (i) applicable to distributions with any kind of support, (ii) computational efficiency because the ME solution is simply obtained as a set of systems of linear equations, (iii) good trade-off between bias and variance, and (iv) good estimates of the tails of the distribution, in presence of samples of small size. Moreover, the joint application of GKDME with a bootstrap resampling allows to define credible bounds of the target distribution. The method is first benchmarked through an example of stochastic dynamic analysis. Subsequently, it is used to evaluate the seismic fragility functions of a reinforced concrete frame, from the knowledge of a small set of available ground motions.

## EQUIVALENT LINEARIZATION METHODS FOR NONLINEAR STOCHASTIC DYNAMIC ANALYSIS USING LINEAR RESPONSE SURFACES

U. Alibrandi & K.M Mosalam. 2017, Journal of Engineering Mechanics.

Three methods of stochastic equivalent linearizations defined in the broad framework of structural reliability analysis are presented. These methods are (1) the Gaussian equivalent linearization method (GELM), here defined for the first time as a linear response surface in terms of normal standard random variables; (2) the tail equivalent linearization method (TELM), here reinterpreted as a stochastic critical excitation method; and (3) a novel equivalent linearization called the tail probability equivalent linearization method (TPELM). The Gaussian equivalent linear system (GELS) is the equivalent linear system (ELS) obtained by minimizing the difference between the variance

of the GELS and the original nonlinear system. The tail equivalent linear system (TELS) is the ELS having the same critical excitation as the original system. The tail probability equivalent linear system (TPELS) is the ELS obtained by minimizing the difference between the tail probability of the equivalent system and the original nonlinear system. The knowledge of the ELS allows the evaluation of engineering quantities of interest—e.g., first-passage probabilities—through the application of the random vibration analysis to these systems. Shortcomings and advantages of the three methods are presented and illustrated through applications to selected representative nonlinear oscillators. Finally, the methods are applied to an inelastic multi-degree-of-freedom (MDOF) system, showing their scalability to systems of higher complexity