Static Frame Model Validation with Small Samples Solution Using Improved Kernel Density Estimation and Confidence Level Method

An improved method using kernel density estimation （KDE） and confidence level is presented for model validation with small samples. Decision making is a challenging problem because of input uncertainty and only small samples can be used due to the high costs of experimental measurements. However, model validation provides more confidence for decision makers when improving prediction accuracy at the same time. The confidence level method is introduced and the optimum sample variance is determined using a new method in kernel density estimation to increase the credibility of model validation. As a numerical example, the static frame model validation challenge problem presented by Sandia National Laboratories has been chosen. The optimum bandwidth is selected in kernel density estimation in order to build the probability model based on the calibration data. The model assessment is achieved using validation and accreditation experimental data respectively based on the probability model. Finally, the target structure prediction is performed using validated model, which are consistent with the results obtained by other researchers. The results demonstrate that the method using the improved confidence level and kernel density estimation is an effective approach to solve the model validation problem with small samples.

Gravimetric analysis for PM_(2.5) mass concentration based on year-round monitoring at an urban site in Beijing

Daily PM_（2.5）（particulate matter with an aerodynamic diameter of below 2.5 μm） mass concentrations were measured by gravimetric analysis in Chinese Research Academy of Environmental Sciences（CRAES）, in the northern part of the Beijing urban area, from December 2013 to April 2015. Two pairs of Teflon（T1/T2） and Quartz（Q1/Q2） samples were obtained, for a total number of 1352 valid filters. Results showed elevated pollution in Beijing,with an annual mean PM_（2.5）mass concentration of 102 μg/m^3. According to the calculated PM_（2.5）mass concentration, 50% of our sampling days were acceptable（PM_（2.5）〈 75 μg/m^3）, 30% had slight/medium pollution（75–150 μg/m^3）, and 7% had severe pollution（〉 250 μg/m^3）. Sampling interruption occurred frequently for the Teflon filter group（75%） in severe pollution periods,resulting in important data being missing. Further analysis showed that high PM_（2.5）combined with high relative humidity（RH） gave rise to the interruptions. The seasonal variation of PM_（2.5）was presented, with higher monthly average mass concentrations in winter（peak value in February, 422 μg/m^3）, and lower in summer（7 μg/m^3 in June）. From May to August, the typical summer period, least severe pollution events were observed, with high precipitation levels accelerating the process of wet deposition to remove PM_（2.5）. The case of February presented the most serious pollution, with monthly averaged PM_（2.5）of 181 μg/m^3 and 32% of days with severe pollution. The abundance of PM_（2.5）in winter could be related to increased coal consumption for heating needs.