Comparison of sensitivity matrix method, power function-based response surface method, and artificial neural network in the analysis of building fire egress performance

Abstract

Unlike the areas of building energy and structural health, performance monitoring tools are currently absent in the area of building fire protection. Computational Fluid Dynamics (CFD) models like Fire Dynamics Simulator (FDS) are widely applied in building fire performance design, which can be equally used to predict changes of building fire performance. However, due to its time-consuming nature, it is not realistic to apply FDS frequently. The sensitivity matrix method (SMM) has been discussed as a quick method to predict changes of building fire egress performance. However, this approach can have significant uncertainties when being applied to datasets with many input parameters due to its inherent incapability of predicting accurately system responses if input data are considerably far away from the baseline points around which a SMM is developed. Response surface methods (RSM) are commonly used to characterize the relationships between input variables and output quantities for complicated problems. Different from conventional RSMs, a novel two phase power function fitting process is proposed to develop substitute algebraic models of the available safe egress time (ASET) from FDS numerical experiments based on a theorem which states that an output variable is proportional to the product of input parameters to their respective powers if the output variable is proportional to each input parameter to some power and the input parameters are independent of each other. An artificial neural network (ANN) is a universal method to approximate any arbitrary complicated, nonlinear system response with limited number of discontinuities without deep understanding of how the system works. This paper employs MATLAB's feedforward neural networks with error backpropagating algorithm to approximate the FDS response. Applicability in terms of uncertainties including system bias and relative standard deviation (RSD) or percentage of predictions falling in a preset acceptable error range are compared among RSMs developed from various datasets, ANNs with various hidden layer sizes and dataset sizes, and SMMs which use the same fire scenarios in a small three-story apartment building. The result shows that it is possible for ANNs to have lowest model uncertainties and highest percentage of predictions within the preset 20% error scope as far as the specific fire egress safety problem discussed in this paper is concerned, but the cost of developing a SMM, namely the number of data cases, is the lowest. Due to the different aspects of RSMs, ANNs, and SMMs, to better understand the building fire performance gap continuously, a hybrid strategy of starting with SMMs followed by RSMs and/or ANNs is recommended in a fire performance monitoring tool. • A novel Response Surface Method is proposed based on two-phase power function fitting. • MATLAB's feedforward NN with error backpropagating algorithm is employed to approximate the FDS simulation results. • The applicability of Sensitivity Matrix Method, Response Surface Method, and Artificial Neural Network is compared. • A hybrid strategy of starting with SMM followed by RSM and/or ANN is recommended in a fire performance monitoring tool.