Umberto Alibrandi

Seismic metamaterials based on isochronous mechanical oscillators

This Letter introduces a seismic metamaterial (SM) composed by a chain of mass-in-mass system able to filter the S-waves of an earthquake. We included the effect of the SM into the mono dimensional model for the soil response analysis. The SM modifies the soil behavior and in presence of an internal damping the amplitude of the soil amplification function is reduced also in a region near the resonance frequency. This SM can be realized by a continuous structure with inside a 3d-matrix of isochronous oscillators based on a sphere rolling over a cycloidal trajectory.

A response surface method for stochastic dynamic analysis

Abstract A Response Surface (RS) strategy is presented for the evaluation of the response statistics of dynamic systems subjected to stochastic excitation. The proposed approach adopts a strategy based on the High Dimensional Model Representation (HDMR), which gives a Gaussian Model (GM) of the response. The GM requires only a reduced number of analyses which can be adopted for all the degrees of freedom of a MDOF dynamic system and it can be successfully adopted for weakly nonlinear dynamic systems. For more strongly nonlinear systems a Non-Gaussian approximation may be necessary for the highest response thresholds. In this paper this issue is accomplished through the FORM solution, and the design point is obtained by using a response surface method recently proposed by the author and Der Kiureghian to this aim. The latter response surface is based on a variant of the Model Correction Factor Method (MCFM), which is here applied by using as a starting model the GM itself. In many applications of engineering interest, both the input and the response processes are stationary, so that the stochastic excitation through the Fourier series can be modeled in terms of the underlying Power Spectral Density (PSD). In these cases, it is seen that the dynamic computations required by the proposed approach can decrease significantly. The application to SDOF and MDOF hysteretic systems shows the effectiveness of the presented method.

First-Order Reliability Method for Structural Reliability Analysis in the Presence of Random and Interval Variables

This paper presents a novel procedure based on first-order reliability method (FORM) for structural reliability analysis in the presence of random parameters and interval uncertain parameters. In the proposed formulation, the hybrid problem is reduced to standard reliability problems, where the limit state functions are defined only in terms of the random variables. Monte Carlo simulation (MCS) for hybrid reliability analysis (HRA) is presented, and it is shown that it requires a tremendous computational effort; FORM for HRA is more efficient but still demanding. The computational cost is significantly reduced through a simplified procedure, which gives good approximations of the design points, by requiring only three classical FORMs and one interval analysis (IA), developed herein through an optimization procedure. FORM for HRA and its simplified formulation achieve a much improved efficiency than MCS by several orders of magnitude, and it can thus be applied to real-world engineering problems. Represent...

Implications of High-Dimensional Geometry for Structural Reliability Analysis and a Novel Linear Response Surface Method Based on SVM

The geometry of high-dimensional spaces is very different from low dimensional spaces and possesses some counter-intuitive features. It is shown that, for high dimensions, the sampling points fall far away from the origin and concentrate within an intersection between a very thin shell and a suitable equatorial slab. The well-known First-Order Reliability Method (FORM), originally formulated for low dimensions, may work well in many engineering problems of high dimension. But it is not able to reveal the level of achieved accuracy. Considering the features of high-dimensional geometry, a novel linear response surface based on Support Vector Method (SVM) is proposed for structural reliability problems of high dimension. The method is shown to outperform FORM for structural reliability problems of high dimension in terms of robustness and accuracy.

TAIL EQUIVALENT LINEARIZATION METHODS FOR SEISMIC RESPONSE SPECTRUM ANALYSIS

This paper aims to conduct seismic reliability analysis of systems using stochastic ground motion model coherent with the codes. This is achieved by developing a Power Spectral Density (PSD) which is compatible with the response spectrum, for assigned valued of seismic zone, soil category and limit state. The seismic reliability analysis is developed inside the most general framework of Performance Based Earthquake Engineering (PBEE) and adopts the tools of the Stochastic Dynamic Analysis. It has been adopted the FORM approximation because of its computational simplicity and effectiveness. FORM allows also to define the Tail Equivalent Linearization System (TELS), which is an equivalent linear system having for each threshold the same design point of the original nonlinear system. The application of the linear theory of the random vibrations to the TELS allows to determine the first-passage probability of the seismic demand, without requiring no further dynamic computations with respect to FORM.

The Tail Equivalent Linearization Method for Nonlinear Stochastic Processes, Genesis and Developments

This chapter aims to provide a general prospective of the Tail Equivalent Linearization Method, TELM, by offering a review that starts with the original idea and covers a broad array of developments, including a selection of the most recent developments. The TELM is a linearization method that uses the first-order reliability method (FORM) to define a tail-equivalent linear system (TELS) and estimate the tail of the response distribution for nonlinear systems under stochastic inputs. In comparison with conventional linearization methods, TELM has a superior accuracy in estimating the response distribution in the tail regions; therefore, it is suitable for high reliability problems. Moreover, TELM is a non-parametric method and it does not require the Gaussian assumption of the response. The TELS is numerically defined by a discretized impulse-response function (IRF) or frequency-response function (FRF), thus allowing higher flexibility in linearizing nonlinear structural systems. The first part of the chapter focuses on the original idea inspiring TELM. The second part offers fourth developments of the method, which were studied by the authors of this chapter. These developments include: TELM in frequency domain, TELM with sinc expansion formula, TELM for multi-supported structures, and the secant hyperplane method giving rise to an improved TELM.

A Decision Support Tool for Sustainable and Resilient Building Design

In this chapter, an integrated approach for a holistic (involving notions of safety, resiliency and sustainability) building design is presented to select the optimal design alternative based on multiple conflicting criteria under uncertainty. A probabilistic framework of the Multi-Attribute Utility Theory (MAUT) is adopted, where MAUT is developed in conjunction with Performance-Based Engineering (PBE) approach, giving rise to a general framework, namely the PBE-MAUT. In PBE-MAUT different design alternatives may be ranked based on the expected utility. The discrepancies from the expected utility theory may be modelled through a risk-averse modelling of the utility functions based on the individual perceptions, or a more detailed description of the consequences valuable to the decision makers. Moreover, a risk-averse decision-maker towards extreme events can consider suitable quantiles or superquantiles. The distribution of the utility function is obtained from the First Order Reliability Method (FORM) which, through the design point, gives also the most critical realizations of the consequences for different degrees of risk aversion. The decision-making process is dynamic, in the sense that the optimal decision changes accordingly when new information is available. Such dynamic behavior is effectively represented using the Bayesian analysis, here modeled by combining PBE-MAUT with the Bayesian Network (BN). In this manner, the proposed framework represents a powerful Decision Support Tool (DST) for holistic building design. The BN, in conjunction with an array of sensors, can also be effectively used to determine the multi-criteria optimal decision considering the building lifecycle for a sustainable and resilient building design. The key features of the DST are demonstrated by an application to an office located on the Create Building, in Singapore.

Prediction of Response of a SCR Using the Multi-Gaussian Maximum Entropy Method

The dynamic analysis of deepwater floating production systems has many complexities, such as the dynamic coupling between the vessel and the lines, the coupling between the first-order and second-order wave forces, several sources of nonlinearities. These complexities can be captured by fully coupled time domain analyses. However they require an enormous computational cost, especially for the evaluation of tails of the distributions of the extreme responses, which are of great interest for practical reliability design purposes. In this paper the non-Gaussian probability density functions of the responses are evaluated through a novel moment-based approach, based on the Maximum Entropy principle, called Multi-Gaussian Maximum Entropy Method (MGMEM). The application to a Steel Catenary Riser (SCR) shows the accuracy and effectiveness of the presented procedure.Copyright

Stochastic dynamic analysis of a marine riser using the First-Order Reliability Method

The dynamic analysis of a deepwater floating production systems has many complexities, such as the dynamic coupling between the vessel and the riser, the coupling between the first-order and second-order wave forces, several sources of nonlinearities. These complexities can be captured by fully coupled time domain analyses. Moreover, the sea state is random, hence the need of stochastic dynamic analysis. In this paper the non-Gaussian responses of the system are obtained through the well-known First-Order Reliability Method (FORM) of the structural reliability analysis. The application to a simplified 2 degrees-of-freedom model shows the accuracy and effectiveness of the presented procedure.

The method of the independent components for sustainable building design

The probabilistic framework of the Multi-Attribute Utility Theory (MAUT) is a powerful tool to determine the optimal decision under uncertainty. In this case, the goal of the decision problem is to find the probability that an option is better than another. The authors have previously developed MAUT in conjunction with the Performance-Based Engineering (PBE) approach, giving rise to the extended framework PBE-MAUT. It has been previously applied for sustainable building design, where analyses involving energy expenditures and sustainability are considered in addition to safety of the building. The main challenge of PBE-MAUT is the evaluation of the distribution of the uncertain parameters; these typically are not independent, and do not follow known parametric distributions. In this paper, we present a novel method for the evaluation of the joint distributions of the uncertain random variables, starting from their sample data. The proposed approach is based on the Independent Components Analysis and the Maximum Entropy (MaxEnt) principle, giving rise to the Independent Component Maximum Entropy Method (IC-MEM). In IC-MEM, at first the method of the Independent Component (IC) is applied to sample data. In this way, a coordinate transformation from the original space toward the space of the ICs is developed. Second, the Probability Density Function (PDF) of the ICs are determined through the Multi Gaussian Maximum Entropy Method (MGMEM), which is a method based on the MaxEnt principle. The knowledge of the PDF of the ICs allows their simulation. Through the inverse coordinate transformation, from space of the ICs toward the original space, samples of the joint random variables are determined. As a result, PBE-MAUT can be effectively adopted as a powerful Decision Support Tool (DST) for the decision-maker.