An enlarged polygon method without binary variables for obstacle avoidance trajectory optimization

In this article,an Enlarged Polygon/Polyhedron(ELP)method without binary variables is proposed to represent the Convex Polygonal/Polyhedral Obstacle Avoidance(CPOA)constraints in trajectory optimization.First,the equivalent condition of a point outside the convex set is given and proved rigorously.Then,the ELP condition describing the CPOA constraints equivalently is given without introducing binary variables,and its geometric meaning is explained.Finally,the ELP method is used to transform the CPOA trajectory optimization problem into an optimal control problem without binary variables.The effectiveness and validity of ELP method are demonstrated through simulations with both simple linear dynamic model(unmanned aerial vehicle)and complex nonlinear dynamic model(hypersonic glide vehicle).Comparison indicates the computational time of ELP method is only 1%-20%of that of the traditional Mixed-Integer Programming(MIP)method.

Development of a Bayesian inference model for assessing ventilation condition based on CO_(2)meters in primary schools

Outdoor fresh air ventilation plays a significant role in reducing airborne transmission of diseases in indoor spaces.School classrooms are considerably challenged during the COVID-19 pandemic because of the increasing need for in-person education,untimely and incompleted vaccinations,high occupancy density,and uncertain ventilation conditions.Many schools started to use CO_(2)meters to indicate air quality,but how to interpret the data remains unclear.Many uncertainties are also involved,including manual readings,student numbers and schedules,uncertain CO_(2)generation rates,and variable indoor and ambient conditions.This study proposed a Bayesian inference approach with sensitivity analysis to understand CO_(2)readings in four primary schools by identifying uncertainties and calibrating key parameters.The outdoor ventilation rate,CO_(2)generation rate,and occupancy level were identified as the top sensitive parameters for indoor CO_(2)levels.The occupancy schedule becomes critical when the CO_(2)data are limited,whereas a 15-min measurement interval could capture dynamic CO_(2)profiles well even without the occupancy information.Hourly CO_(2)recording should be avoided because it failed to capture peak values and overestimated the ventilation rates.For the four primary school rooms,the calibrated ventilation rate with a 95%confidence level for fall condition is 1.96±0.31 ACH for Room#1(165 m^(3)and 20 occupancies)with mechanical ventilation,and for the rest of the naturally ventilated rooms,it is 0.40±0.08 ACH for Room#2(236 m^(3)and 21 occupancies),0.30±0.04 or 0.79±0.06 ACH depending on occupancy schedules for Room#3(236 m^(3)and 19 occupancies),0.40±0.32,0.48±0.37,0.72±0.39 ACH for Room#4(231 m^(3)and 8–9 occupancies)for three consecutive days.