Matiiematical equations and system identification models for a portable pneumatic bladder system designed to reduce human exposure to whole body shock and vibration

A mathematical representation is sought to model the behavior of a portable pneumatic foam bladder designed to mitigate the effects of human exposure to shock and whole body random vibration. Fluid Dynamics principles are used to derive the analytic differential equations used for the physical equations Model. Additionally, combination of Wiener and Hammerstein block oriented representation techniques have been selected to create system identification (SID) block oriented models. A number of algorithms have been iterated to obtain numerical solutions for the system of equations which was found to be coupled and non-linear, with no analytic closed form solution. The purpose is to be able to predict the response of such system due to random vibrations and shock within reasonable margin of error. The constructed models were found to be accurate within accepted confidence level. Beside the analytic set of physical equations model representation, a linear SID model was selected to take advantage of the available vast amount of mathematical tools available to further analyze and redesign the bladder as a dynamic system. Measured field-test and lab test data have been collected from several helicopter and land terrain vehicle experiments. Numerous excitation and response acceleration measurement records were collected and used to prove the agreement with predictions. The estimation of two selected models were later applied to standard metrics in the frequency domain realization and compared with measurement responses. The collected test records are obtained from measured data at the US Army fields and facilities and at UNLV-CMEST environmental lab. The emerged models have been validated for conformity with actual accelerometer measurement responses and found within accepted error tolerance that is in both time and frequency domains. Further, standard metrics have been used to further confirm the confidence in the validation results. When comparing model prediction with the already proven pneumatic bladder system effectiveness both equally proves that bladder performance exceeds metrics standard to reduce human exposure to shock and random vibrations.