Using Fuzzy Logic to Evaluate the Seismic Preparedness of New Mexico Emergency Response Buildings Elliot Esquivel eesquive@nmt.edu New Mexico Institute of Mining and Technology Socorro, NM Advised by Dr. Claudia Wilson cwilson@nmt.edu New Mexico Institute of Mining and Technology Socorro, NM ABSTRACT This paper will discuss the application of fuzzy logic to prioritize buildings potentially susceptible to earthquake loads, which was developed by the author and a colleague. Although a prioritization method had already been developed in 2014 by students at New Mexico Tech, it was challenging to be used by the general public without training. For this reason, the method was modified with the use of fuzzy logic to be more functional for emergency management officials by providing a descriptive score output along with a ranking of each building s importance. This method was applied to 58 essential buildings that had been considered potentially seismically hazardous by the Rapid Visual Screening (RVS) method in New Mexico, which was developed by the Federal Emergency Management Agency (FEMA). INTRODUCTION Even though earthquakes are some of the most damaging natural disasters, seismic preparedness has not been a priority in the state of New Mexico. While this might seem reasonable because most of the state is in a low seismicity region (FEMA, 2002), Socorro county is a moderately active seismic region because of an underground magma chamber ten miles beneath the surface in the center of the county. This is why, in 2010, Dr. Claudia Wilson at the New Mexico Institute of Mining and Technology was contacted by the Department of Homeland Security and Emergency Management to help them improve the state s earthquake preparedness.
BACKGROUND The RVS method, which was developed by FEMA, does a good job of determining whether or not a building needs to be evaluated by a structural engineer (scores lower than 2), but this method was not particularly useful in New Mexico. This is because 58 of the 72 buildings that were evaluated using RVS (Brewster, et. al., 2012) received a score of zero. While this is useful because it allows the government to focus their efforts on buildings that need to be reviewed, there are simply too many buildings to feasibly review. Because there is a limited budget to hire a professional engineer to review each of these buildings, a prioritization method was needed to determine which buildings would need to be reviewed first. FUZZY LOGIC PRIORITIZATION Fuzzy logic is a subset of logic that is intrinsically different from Boolean logic. Where Boolean logic can return true or false results, fuzzy logic is able to give results such as partially true, or mostly false (MathWorks, 2015). In this case, it allows for a more complete analysis of the parameters considered for each building, rather than ranking buildings with one structural irregularity the same as buildings with several of these same irregularities, like the RVS approach. To implement fuzzy logic, MATLAB was used with the Fuzzy Logic Toolbox to allow for visual editing of fuzzy inference systems (FIS) and fuzzy rules. A diagram of the entire system can be seen in Figure 1. Figure 1. Overview of inputs, FIS, and output generation.
FUZZY INFERENCE SYSTEMS Fuzzy inference systems are where the computations are housed. The system is comprised of inputs, rules, membership functions, and outputs. An example of a FIS can be seen in Figure 2. This FIS uses a defined set of rules to generate an output (score for the falling hazards category) based on structural characteristics input into the system. In the Falling Hazard FIS pictured in Figure 1, the inputs are whether or not the building has exterior cladding, parapets or protrusions, or structural features that could potentially become a falling hazard in an earthquake. The central box is the brains of the FIS. This is where the inputs are evaluated using their membership functions, then assigned an output value (score for the falling hazards category) using a defined set of rules. A detail of the degrees of membership can be found in Figure 3. There are FIS for the following categories of risks: plan irregularities, vertical irregularities, and falling hazards. Each of these systems have unique inputs, membership functions, rules, and outputs. Figure 2. Fuzzy Inference System for Falling Hazards FUZZY MEMBERSHIP FUNCTIONS Membership functions change numerical values into degrees of membership to fuzzy sets which are described linguistically. For this application, these fuzzy sets are either Yes or No, as is the case with presence of cladding, or Few, Some, or Many, as is the case for both number of aesthetic and structural falling hazards. A visual representation of the membership function for aesthetic falling hazards can be found in Figure 3. If, for example, a structure was observed to have six aesthetic falling hazards, according to the membership functions, it would belong to Few approximately 50% and to Some approximately 50%. A structure with eight aesthetic falling hazards, however, would belong 100% to the Some fuzzy set. These degrees of membership are then used in conjunction with the rules to generate an output value.
Figure 3. Aesthetic Falling Hazard Membership Functions RULE LISTS The rule list is the governing set of logic rules that the FIS references when assigning the final output value for the system. An example of the rule list for the falling hazard FIS can be found in Figure 4. The rule list allows the user to combine the different inputs and assign higher importance to one input over another. In this case, more weight is given to the structural falling hazards than the aesthetic ones because falling structural features can potentially lead to structural failure, while falling aesthetic features would only lead to cosmetic damages. An example of how this appears in the rule list can be seen by comparing lines one, two, and four from Figure 4. Figure 4. Falling Hazard FIS Rule List
The first line states that if there is no cladding, few aesthetic features are present, and few structural features, the output will be low hazard for this structure. Line two states that if cladding is still not present and the number of aesthetic features is still few, but if there are some structural features, the output would now be moderate hazard. Finally, line four shows that if there is no cladding and the number of structural features is few, while there are some aesthetic features, the output would still be given as a low hazard, which tells the system that aesthetic hazards are less of a priority than structural ones. OUTPUT The output of the FIS is a number obtained based on the degree of membership in each fuzzy set for each input and the rules developed. In the case of the Falling Hazard FIS, this number ranges from one to ten. Membership functions describing the output are then used to linguistically describe this result, as seen in Figure 5. This output is then sent back to the original MATLAB code, where it is added to the outputs from the vertical and plan irregularity membership functions and the historical significance score. After these values are added together, they are weighted according to their ASCE 7-10 Risk Category (ASCE, 2010). The more vital a building is to preserving human lives and/or providing services essential to the community during and after a disaster or an emergency, the higher it is ranked. A hospital, for example, would receive a final weighted score of 2.5 times the final score, whereas the score for a warehouse would be 1 times the final score. Figure 5. Falling Hazard FIS Output Membership Function
APPLICATION OF THE PRIORITIZATION METHOD As mentioned previously, the RVS method is effective in determining whether a structure needs to be evaluated by a structural engineer. However, it assigns similar scores to structures with different levels of irregularities, leading to several structures receiving identical scores and leaving the emergency manager with no guidance regarding which structure should be evaluated first. The objective of the fuzzy logic prioritization method is to differentiate between buildings that received identical failing scores. A comparison of the RVS score and the new score assigned can be found in Table 1. As shown, the proposed method was able to successfully prioritize the structures: the higher the Fuzzy Score is, the more pertinent it is that the building be evaluated. Table 1. RVS Score vs. Fuzzy Score Building RVS Score Fuzzy Score NM State Hospital 0 18.57 Holy Cross Hospital 0 34.38 Santa Fe Fire Station 8 0 24.68 San Miguel Wastewater Treatment Plant Building 4 0 9.51 FUTURE WORK: IMPROVING USABILITY OF CODE While it is very convenient for individuals with MATLAB installed on their computer to run this code, it is very doubtful that emergency response managers will have this program available. This problem brought forth the next phase of developing the code: adding Microsoft Excel functionality. Thus far, the code will read in lines of building characteristics, output a value that reflects the buildings importance, and then rank all buildings based on priority. This step is essential as it allows for more than a single building to be analyzed at one time. It also saves time for the emergency response managers because they will be able to input an excel sheet of data and evaluate as many buildings at a time as they need, instead of entering the data and manually recording the results. This still requires running the code in MATLAB, therefore, the next and final phase of development will be writing a script or graphic user interface (GUI) that can be used without the MATLAB program being installed on the user s computer. A GUI version of the program would likely have an option for downloading a template of the required Excel file, which the user would then populate with data, and then choosing that template to access the data directly from the GUI. CONCLUSIONS Fuzzy logic was successfully implemented to give a more diverse range of outputs and rank the buildings that need to be evaluated by a professional engineer. The method was successfully applied to several buildings that received failing RVS scores in New Mexico. In the future, Excel and GUI implementation will be finalized and a program will be published that will allow emergency response managers throughout the nation to evaluate buildings in their respective counties. It is important that this program be accessible for use on any computer.
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