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Introduction : ENGG1811 22T3 Processing vibration & signals
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Data has been collected based on experiments performed on a bridge to test the response of the bridge to vibrations caused. Hammers hit the bridge and the vibrations were caused due to the hammer strikes studied in the experiment. The data is loaded into a python program and the data is analyzed using python code. The shaking motion of a structure causes vibrations when a force affects it and the structure settles down as the vibration reduces with time. The dataset formed from the experiment conducted to record the vibration of a beam caused by hammer strikes. Consists of the time_listvariable which stores the time instances when the bridge is hit by the beam and the resp_list which stores the time points at which the reaction of the bridge on being hit by the hammer is recorded. One of the parameters, which have used for the analysis of the data using python, is trough_amp_upper_bound.
Identifying the troughs
The amplitudes of the troughs are determined through the above step in the algorithm for the python program. The response of the bridge when the hammer hits it is considered and a particular value for the response of the bridge takes to be -0.5. The values of the response, which are greater than the response value -0.5 and form a peak, are considered troughs. For this assignment, only the troughs whose amplitude is lower than the level of the trough_amp_upper_bound are used. The value of the initial four troughs is lower than trough_amp_upper_bound and they have been accepted. The next trough has amplitude of -0.46 is greater than trough_amp_upper_bound and this trough has been rejected for the study. The reason for using trough_amp_upper_bound is to isolate those troughs, which might have been affected by noise.
The amplitudes of the troughs that have been accepted for the study are -1.03,-0.85,-0.69, and -0.57 and the times of these troughs are 3.0, 7.0, 11.0, and 15.0, and these two sets of values are stored in the variables trough_time_list and trough_amp_list respectively (Stan?in and Jovi?, 2019).
Determining the usability of the data
The least number of accepted troughs is determined initially and it needs to be determined that there are four or more acceptable troughs present in the data collected from the experiment. The variables called trough_time_list and trough_amp_listare used for this stage of the assignment. After this test, a second hammer is struck on the bridge and the observations are recorded.
The occurrence of a second hammer hot can be affirmed if the troughs are spaced at regular distances concerning the time plotted along the x-axis. The differences of successive values of trough_time_list are calculated and the maximum and minimum values are found. The ratio of the maximum to the minimum is determined (Lee et al. 2019).
Function for Checking Second Hammer Hit
The ratio between the maximum and the minimum has been obtained as 1.0 and it can be found from the ratio that which of the troughs are not regularly spaces concerning the time plotted along the x-axis. Python code has been written to perform these checks and to calculate the ratio between maximum and minimum.
Calculation of the Geometric mean and damping ratio
The geometric mean is calculated on the assumption that the trough_amp_ratio_list has already been determined. The expected value of the geometric mean of the values in trough_amp_ratio_listis 0.8210.
Checking the validity
While performing the analysis of data using python the data has to check and it has to be ensured the data is valid because data that is not valid produces poor results on being analyzed. The value of the trough_amp_upper_boundis considered valid if it is of the type int or float and the values should be lower than zero (Davidson-Pilon, 2019).
Six functions are implemented using thepython programing language and all these six functions form the vibration signal-processing algorithm. The function named find_trough_time_amp has been defined and the parameter list of the function includes time_list, resp_list, trough_amp_upper_bound. This function ascertains the trough_time_list and trough_amp_list from the parameters and the output variables of the function are trough_time_list and trough_amp_list. The validity_time_list_andresp_listfunction defined and the parameters passed are time_list and resp_list.
On running the function, the above result is clear from the figure given above and it is suggestive that the function runs properly without any errors or bugs (Holmgren et al. 2018).
The purpose of finding the usability of the data is to check whether a second hammer hit struck the bridge. Along with the check for the second hammer hit, it needs to be determined that there are acceptable troughs present in the data collected regarding the amplitudes of the responses to the hammer hit.