Determination of Thermal Properties for Structural Fire Modeling Using a Genetic Algorithm, 01-R8103
J. Marshall Sharp
Inclusive Dates: 09/28/09 – 04/01/11
Background — In all fields of engineering, substantial efforts have been put forth to develop models or other systems to predict performance in response to an external input. As technology advances, these models have grown in size and complexity. However, in all cases, the accuracy of the models is limited by the quality of the input data and the underlying assumptions. Structural fire modeling is no different. In the past decade, significant efforts have been placed on measuring fire events in order to improve fire models for predicting both structural and thermal response of a structure exposed to the fire. One area that has not received a lot of attention in recent years is the characterization of thermophysical properties of materials. These properties are inherently difficult to measure due to the temperature-dependent nature of the properties. Other significant factors are: 1) the broad range of values that can be expected for fire-resistant materials (i.e., materials with very low thermal conductivity are difficult to accurately measure) and 2) the dynamic nature of the combustion event and the potential for reactions to occur as the materials are heated by the fire (in some cases, materials may ignite and contribute to the fire or facilitate moisture migration away from the heat source).
Approach — In this project, SwRI personnel investigated a technique to determine these thermophysical properties by analyzing bench-scale fire test data using a parameter estimation technique known as genetic algorithm optimization. Through this technique a full set of thermophysical properties (density, specific heat capacity, and thermal conductivity) is compiled as a function of temperature. The approach will be compared to model predictions of full-scale fire resistance test performance of assemblies comprising the materials. Additionally, a second technique called genetic programming will be evaluated to determine its effectiveness on predicting the response of materials exposed to fires.
Accomplishments — Small-scale testing was conducted on several materials. Testing included thermo-gravimetric analysis (TGA), differential scanning calorimetry (DSC), modified cone calorimetry, and micro-flow combustion calorimetry. Furnace testing was conducted to compare the thermal model with actual experimental results. During this period of performance, successful fits of mass and mass loss rate were achieved using a model based on the Arrhenius function. The kinetic parameters associated with the Arrhenius function were optimized using a genetic algorithm to create the mass loss rate model. The mass curve was then reconstructed by integrating the mass loss rate with respect to time. The predicted and calculated mass loss rate and mass of type "X" gypsum wallboard are shown in Figure 1. One set of Arrhenius parameters was able to accurately predict mass and mass loss rate curves from TGA data at three different heating rates (5, 10, and 20 °C/min). The mass curves were then used to calculate density as a function of temperature. Next, the DSC data was used to estimate the apparent specific heat capacity of the material. Given the specific heat capacity and density, the final parameter, thermal conductivity, can be estimated using heat transfer data from a bench scale fire test such as the cone calorimeter test method.
A genetic algorithm was used to optimize a linear piecewise fit of thermal conductivity as a function of temperature. The predicted and calculated temperature response of Type "X" gypsum wallboard is shown in Figure 2. The transient 1-D heat transfer equation was used to model heat transfer through a slab of material. The midpoint temperature was compared and used as part of the fitness calculation for the genetic algorithm during thermal conductivity optimization.