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.
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, because it adopts a kernel density 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: (1) applicable to distributions with any kind of support, (2) computational efficiency because the ME solution is simply obtained as a set of systems of linear equations, (3) good tradeoff between bias and variance, and (4) good estimates of the tails of the distribution, in the presence of samples of small size. Moreover, the joint application of generalized kernel density maximum entropy 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. /journal/nme other quantities derived from the data. The first general representations for a PDF have adopted Hermite polynomials, eg, A-type and C-type Gram Charlier series and the Edgeworth series expansion. 3,4 An improvement is represented by the model proposed by Winterstein, 5 and it is largely applied in engineering.The choice of the distribution type is an open issue, from a conceptual and practical point of view. In the presence of limited information (sample of small size and/or lower-order moments), in the most general case, there is no theoretical justification to prefer one distribution over another. In such case, an attractive technique is based on the principle of maximum entropy (ME). [6][7][8] The ME distribution represents the least biased distribution given the available information. However, the application of the ME principle, as typically adopted in literature, has some practical and theoretical limitations.If the power moments represent the available information, then the ME PDF f ME (x) may require a large number M of moments (M ≥ 4) to accurately describe the tails of the distribution. However, the moment problem is an ill-posed problem. 9 Thus, for large M, the entropy maximization algorithm experiences numerical instability. Moreover, at the tails, the ME distribution oscillates because of the nonmonotonic nature of the polynomial embedded in the f ME (x). Thus, only the lower-order moments are typically considered, but in such case, f ME (x) hardly models tails fatter than the Gaussian. Therefore, the tails of many distributions cannot be well fitted by the ME distribution with M ≤ 4. 10 Furthermore, from a practical point of view, we do not have the true moments, but samples of data, f...
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 multiattribute 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.1 2 expressed in terms of the direct interest of various stakeholders to define the global performance of the system. Together with the performances, the decision maker explores several design alternatives and/or actions through the building lifecycle. Subsequently, making use of the decision making system, the optimal alternative may be determined with general consensus from the stakeholders. The optimal choice takes into account multiple conflicting criteria by making use of the multi-attribute utility theory (MAUT) [5]. An important challenge of MAUT for sustainable design stems from the different sources of uncertainty, giving rise to a problem of decision under uncertainty or under risk. Thus, the objective of this paper is to
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