Grey Box System Identification of Bus Mass Darren Achtymichuk M. Sc. Student University of Alberta Department of Mechanical Engineering
Project Background When analyzing vehicle dynamics, the mass of the vehicle is usually known, either through published specifications from the manufacturer or by putting the vehicle on a scale. The mass of a transit bus, however, changes with time as passengers get on and off. The purpose of this project is to develop a technique to determine the mass of a transit bus as a function of time as it travels along a route using parameters that can easily be logged from the bus computer. If successful, this technique will be used to improve the accuracy of future analyses on data from transit buses by taking into account changing passenger mass. Available Data The data was recorded using a data logger connected to the bus computer through the CAN-bus. A GPS receiver was also mounted on the bus and connected to the data logger. While the bus was in operation, vehicle speed, engine speed, fuel flow rate, coolant temperature, latitude, longitude, and altitude were logged every second. The data was saved in coma separated variable format, as shown in Figure 1. Figure 1 - Sample data
System Identification Process To model the motion of the bus the governing equation, shown in Figure 2, is used. The frontal area and coefficients of aerodynamic drag and rolling resistance are known for the bus being studied, the tractive power is computed based on the measured fuel flow rate, and the slope of the road is computed based on the measured altitude. m& x = u motor ρc D x& A mc 2 R g mg sin( β ) where: x is the position of the bus m is the mass of the bus u motor is the tractive power delivered by the motor ρ is the density of air C D is the coefficient of drag A is the frontal area of the bus C R is the coefficient of rolling resistance g is acceleration due to gravity β is the slope of the road Figure 2 - Governing equation of bus motion Matlab code is used to identify the intervals between bus stops along a route. Grey box system identification techniques are then applied in each of these intervals to determine the mass of the bus. The number of passengers on the bus is determined by subtracting the empty mass of the bus from the calculated mass and dividing the result by an average passenger mass. The Matlab code generates a KML file to allow the results to be viewed in Google Earth. Advantages of Using Google Earth The major advantage of displaying the results in Google Earth is that it allows one to make a connection between the results and where they are occurring spatially. Figures 3 and 4 show the same set of results displayed in Matlab and Google Earth respectively. Other than noting that most of the data falls within the expected range of zero to 82 passengers (the rated capacity of the bus) and that the sudden jump to 92 passengers in the middle of the plot seems suspect, simply looking at the Matlab plot does not enable one to make any sort of judgment on whether or not the results seem reasonable. Observing the same results in Google Earth enables one to apply engineering
judgment to the results. In Figure 4, the position of the line represents the route the bus has driven on, the height of the line represents the velocity of the bus, the width of the line represents the rate of fuel consumption, and the color of the line represents the calculated number of passengers on the bus. The red section of line corresponds to the jump to 92 passengers seen in Figure 3. By noting that this increase in passengers occurs at a major transit center (the loop off the main road), the large increase in passengers doesn t seem unreasonable; however, it seems unlikely that over 70 passengers would get off the bus less than a block later, as indicated by the results, suggesting that additional fine tuning of the system identification process is required. Along with observing where passengers get on and off the bus, viewing the data in Google Earth enables one to compare fuel consumption rates at different positions along the route, to observe sections of the route where velocity was slower than expected indicating that congestion may have been an issue, and to observe how closely the bus was able to follow its schedule.
100 Number of Passengers versus Time (70 kg per passenger) 90 80 70 # of Passengers 60 50 40 30 20 10 0 7.5 7.6 7.7 7.8 7.9 8 8.1 Time (hrs) Figure 3 - Sample results in Matlab
Figure 4 - Sample results in Google Earth