As the largest contributor of carbon emissions in China, the building sector currently relies mostly on enterprises’ own efforts to report carbon emissions, which usually results in challenges related to information transparency and workload for regulatory bodies, who play an otherwise vital role in controlling the building sector’s carbon footprint. In this study, we established a novel regulatory model known as QCEPM (Quantitative Carbon Emission Prediction Model) by conducting multiple linear regression analysis using the quantities of concrete, rebar, and masonry structures as independent variables and the embodied carbon emissions of a building as the dependent variable. We processed the data in the detailed quantity list of 20 multi-story frame structure buildings and fed them to the QCEPM for the solution. Comparison of the QCEPM-calculated results against the time-consuming and error-prone manual calculation results suggested a mean absolute percentage error (MAPE) of 2.36%. Using this simplified model, regulatory bodies can efficiently supervise the embodied carbon emissions in multi-story frame structures by setting up a carbon quota for a project in its approval stage, allowing the construction enterprise to carry out dynamic control over the three most important audited building materials throughout a project’s planning and implementation phase.

In prescriptive fire protection designs of buildings, exit location is generally designed with the constraint of the maximum travel distance. And the optimal exit location has not been given enough attention to in performance-based fire protection designs of buildings. However, in order to improve the reliability of successful evacuation, the optimal exit location for minimizing evacuation time should be studied with consideration of the uncertainty of initial occupant density. Due to the expensive computational cost, the surrogate-based optimization is proposed to search the optimal exit location, which combines the polynomial chaos expansion and genetic algorithm. The polynomial chaos expansion is used to construct the surrogate model of evacuation time and then genetic algorithm is applied to the polynomial chaos expansion of evacuation time to search the optimal exit location. In order to demonstrate the proposed method, a fire compartment of commercial buildings with two exits is presented. The results of this case study suggest that the optimal layout of two exits with the same size should be distributed symmetrically and the optimal exit location is different for different probability levels. When the probability level of successful evacuation is low with two narrow exits, the better method is merging two exits into be one exit around the center of the wall, which is also consistent with that determined by minimizing the maximum travel distance. However, when the probability level of successful evacuation is high with two narrow exits, the optimal location of two exits should be around two corners of the wall in this case. This proposed method can be used to find the suitable exit location under uncertain initial occupant density, which provides a reference for the performance-based design of building exits.

Let A be a nonnegative matrix of order n and $f(A)$ denote the number of positive entries in A. We prove that if $f(A)\leq3$ or $f(A)\geq n^{2}-2n+2$ , then the sequence $\{f(A^{k})\}_{k=1}^{\infty}$ is monotonic for positive integers k.

The eigenvalues and the spectral radius of nonnegative tensors have been extensively studied in recent years. In this paper, we investigate the analytic properties of nonnegative tensors and give some inequalities on the spectral radius.