Modeling fire detector signals by means of system identification techniques

The design of fire detection algorithms is an iterative process that requires a continual performance estimation. The performance can be evaluated using statistical values, e.g., mean fire detection times, fire detection probabilities, and false alarm rates. The determination of these parameters requires many test data measured by defined test fires and disturbing events. In order to reduce the test and design costs, it is advantageous to model sensor responses by test experiments. The modeling process requires the definition of ancillary conditions for the validation of the models. They include experimental (EN54) and mathematical (nonlinearity) conditions. In this paper, we investigated selected modeling techniques including ARX models and weighting functions. Hereby, relative mass losses of used fuels are introduced as inputs and sensor responses as outputs. Although the measured sensor responses are different for experiments with the same test fire, models have been identified using one experiment for each considered test fire only. The generation of the artificial sensor responses is performed by modifying analytical functions that describe the burning process (relative mass loss) and then subjecting them to the investigated models. The evaluation of the selected model has been performed with regard to the capability to reproduce measured data as well as to the independence of inputs from the residuals. The simulator was able to generate a valid variety of sensor response shapes by changing defined characteristics of the fire progresses that are described by relative mass losses.