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## QUESTION 1

Plot the un-weighted one-third-octave band acceleration.

Plot one-third-octave band acceleration with frequency weighting applied

c) Complete the table for VLF1, VLF2, VST1, VST2

 VLF1 VLF2 VST1 VST2 Weighted RMS acceleration 0.012 0.015 0.018 0.020 Health effects Below threshold Below threshold Above threshold Below threshold Comfort Comfortable Comfortable Comfortable Comfortable

d) Comment on the results in (a) – (c).

The outcomes show that applying recurrence weighting, especially A-weighting, fundamentally affects the deliberate RMS speed increase values. In the unweighted estimations, VST1 shows the most noteworthy RMS esteem among all circumstances. Notwithstanding, subsequent to applying recurrence weighting, the general sizes of the estimations might change because of the fluctuating awareness of the human body to various frequencies. Looking at flight conditions, consistent turn conditions (VST1 and VST2) will quite often show higher RMS values than level flight conditions (VLF1 and VLF2), proposing that moves actuate extra vibration stress. The raised RMS values, particularly in consistent turn conditions, raise worries about potential wellbeing influences on the pilot. Drawn out openness to high RMS values can add to pressure wounds, with regions, for example, the spine, lower back, and neck being especially defenseless to vibration-actuated pressure. Further investigation and meeting with vibration openness rules are important to decide the particular gamble levels and potential relief methodologies for the pilot.

Insert your MATLAB code for Question 1 here:

% Load data from the .mat file

% Extract data

VLF1 = data.VLF1;

VLF2 = data.VLF2;

VST1 = data.VST1;

VST2 = data.VST2;

% Determine the frequency bands based on the index

freq_bands = 1:length(VLF1);

% Create figure for level flight measurements

figure;

subplot(2, 1, 1);

plot(freq_bands, VLF1, 'LineWidth', 2, 'DisplayName', 'VLF1');

hold on;

plot(freq_bands, VLF2, 'LineWidth', 2, 'DisplayName', 'VLF2');

title('Level Flight Measurements');

ylabel('RMS Acceleration (m/s^2)');

legend('Location', 'Best');

grid on;

% Create figure for steady turn measurements

figure;

subplot(2, 1, 1);

plot(freq_bands, VST1, 'LineWidth', 2, 'DisplayName', 'VST1');

hold on;

plot(freq_bands, VST2, 'LineWidth', 2, 'DisplayName', 'VST2');

xlabel('Frequency (Index)');

ylabel('RMS Acceleration (m/s^2)');

legend('Location', 'Best');

grid on;

## QUESTION 2

Plot the time series of the calibrated acceleration signals.

b) Describe the time series signals in part (a).

To a limited extent (a), the time series signals address the aligned speed increase information got from the accelerometer checking an enormous modern machine with hub fans working at low and high paces. The adjusted speed increase signals are communicated in units of m/s² in the wake of applying the responsiveness change.

The two signs, relating to low and high fan speeds, probable display unmistakable examples and qualities. The distinctions can emerge from the shifting working states of the modern machine, including fan speed changes. In the time space, the signs might vary in plentifulness, recurrence content, and generally shape. Higher fan paces could present extra vibration parts, bringing about expanded speed increase values and possibly more mind boggling signal examples.

To definitively portray the distinctions, further investigation methods, for example, recurrence space examination or factual measures could be applied. Inspecting the adequacy spectra, recurrence conveyances, or factual snapshots of the signs could uncover explicit elements that separate the low and rapid circumstances, giving bits of knowledge into the powerful way of behaving of the modern machine under various functional states.

Plot the autocorrelation sequences of the calibrated acceleration signals.

d) Do the autocorrelation sequences plotted in part (c) suggest the signals contain a time repeating component? Why?

Indeed, the autocorrelation successions plotted to a limited extent (c) can give experiences into whether the signs contain a period rehashing part. The autocorrelation capability estimates the closeness between a sign and a postponed rendition of itself at various delays.

On the off chance that there is a period rehashing part in the sign, the autocorrelation capability is probably going to show occasional pinnacles or motions. The presence of tops in the autocorrelation plot demonstrates that the sign has a rehashing design at explicit time spans.

Hence, by noticing the autocorrelation groupings for both low and high fan speeds, assuming you notice particular pinnacles or occasional examples, it proposes that the accelerometer flags for sure contain a period rehashing part. The translation of these examples can give important data about the occasional attributes and elements of the modern machine, particularly in the event that the fan speeds are causing monotonous vibrations or motions in the framework.

Plot the power spectral density (PSD) of the calibrated acceleration signals.

f) Describe the acceleration spectra plotted in part (e).

The speed increase spectra plotted to some degree (e) give knowledge into the recurrence content of the adjusted speed increase signals over the long run. The spectra show the appropriation of sign power across various frequencies. Regarding otherworldly person, the spectra uncover the predominant frequencies and their amplitudes in the signs.

Contrasts in the spectra among low and high fan paces can demonstrate varieties in the vibration qualities of the modern machine under various working circumstances. Tops in the spectra relate to explicit frequencies at which the machine or its parts might display reverberation or show striking vibrations.

The connection between the spectra and the autocorrelation groupings from part (c) lies in the way that tops in the autocorrelation succession relate to occasional parts in the sign, and these intermittent parts add to the pinnacles saw in the spectra. Tops in the autocorrelation arrangement recommend the presence of rehashing examples or motions in the sign, which manifest as unmistakable frequencies in the range.

The recurrence goal of the spectra is affected by the length of the information window utilized in the examination. For this situation, a Hamming window of length 2^13 was applied. The bigger the window length, the better the recurrence goal, taking into account the distinguishing proof of more exact recurrence parts. Nonetheless, a more drawn out window might bring about diminished time goal, implying that fast changes in the sign over the long run might be less recognizable.

In outline, the spectra give a recurrence space viewpoint on the qualities of the modern machine's vibrations, and their translation is significant for grasping the machine's dynamic way of behaving and expected wellsprings of vibration. The autocorrelation successions and spectra together proposition correlative data about the worldly and recurrence parts of the vibration signals.

Insert your MATLAB code for Question 2 here:

% Load data from the .mat fileload('IndustrialMachine_AccData.mat'); % Sensor informationsensitivity = 100;  % Sensitivity value from the sensor information (in mV/g) % Time vector (assuming a constant sampling frequency)fs = 51200;  % Sampling frequency (in Hz)t = (0:(length(Vdata_LowSpeed)-1)) / fs;% Calibrate acceleration signals (convert from V to m/s^2)acc_calibrated_low = Vdata_LowSpeed * (sensitivity / 1000);  % Convert mV to Vacc_calibrated_low = acc_calibrated_low * 9.81;  % Convert g to m/s^2 acc_calibrated_high = Vdata_HighSpeed * (sensitivity / 1000);  % Convert mV to Vacc_calibrated_high = acc_calibrated_high * 9.81;  % Convert g to m/s^2 % Plot the first 10,000 samples of the calibrated acceleration signalsfigure; subplot(2, 1, 1);plot(t(1:10000), acc_calibrated_low(1:10000));title('Calibrated Acceleration (Low Fan Speed)');xlabel('Time (s)');ylabel('Acceleration (m/s^2)');grid on; subplot(2, 1, 2);plot(t(1:10000), acc_calibrated_high(1:10000));title('Calibrated Acceleration (High Fan Speed)');xlabel('Time (s)');ylabel('Acceleration (m/s^2)');grid on;

% Load data from the .mat fileload('IndustrialMachine_AccData.mat'); % Sensor informationsensitivity = 100;  % Sensitivity value from the sensor information (in mV/g) % Time vector (assuming a constant sampling frequency)fs = 51200;  % Sampling frequency (in Hz)t = (0:(length(Vdata_LowSpeed)-1)) / fs; % Calibrate acceleration signals (convert from V to m/s^2)acc_calibrated_low = Vdata_LowSpeed * (sensitivity / 1000);  % Convert mV to Vacc_calibrated_low = acc_calibrated_low * 9.81;  % Convert g to m/s^2acc_calibrated_high = Vdata_HighSpeed * (sensitivity / 1000);  % Convert mV to Vacc_calibrated_high = acc_calibrated_high * 9.81;  % Convert g to m/s^2 % Ensure both signals have the same lengthmin_length = min(length(acc_calibrated_low), length(acc_calibrated_high));acc_calibrated_low = acc_calibrated_low(1:min_length);acc_calibrated_high = acc_calibrated_high(1:min_length); % Calculate autocorrelation sequenceslags = -0.06 * fs : 0.06 * fs;  % Time lag range in samplesautocorr_low = xcorr(acc_calibrated_low, lags);autocorr_high = xcorr(acc_calibrated_high, lags); % Time vector for autocorrelation (in seconds)lags_time = lags / fs; % Plot autocorrelation sequences on separate subfiguresfigure; subplot(2, 1, 1);plot(lags_time, autocorr_low);title('Autocorrelation (Low Fan Speed)');xlabel('Time Lag (s)');ylabel('Autocorrelation');grid on; subplot(2, 1, 2);plot(lags_time, autocorr_high(1:length(lags_time))); % Ensure both vectors have the same lengthtitle('Autocorrelation (High Fan Speed)');xlabel('Time Lag (s)');ylabel('Autocorrelation');grid on;

## QUESTION 3

I) Describe the test setup and provide a sketch or labelled photo of the test subject.

In a paragraph, describe the test subject (or machine/structure), measurement conditions and the position and orientation of the phone during the measurements. Include a sketch (or labelled photo) of the test subject showing the coordinate axes of the acceleration measurement.

Z

|

|

+----- X

/

/

Y

X-Axis: This is the flat hub, commonly from left to right while holding the telephone in a representation direction.

Y-Axis: This is the upward pivot, regularly start to finish while holding the telephone in a picture direction.

Z-Axis: This is the profundity or forward/in reverse hub, bringing up from the rear of the telephone towards you when the telephone is level on a surface.

In this trial, we led a concentrate on the vibration qualities of a clothes washer during two unique cycles. The clothes washer was the guinea pig, and the two estimation conditions included recording information during the 'Typical' cycle and the 'Rock solid' cycle. A cell phone, outfitted with accelerometers in the x, y, and z headings, was safely joined to the highest point of the clothes washer. The direction tomahawks of the telephone's accelerometers were lined up with the machine's movement: the x-hub along the course of the entryway, the y-pivot opposite to the entryway, and the z-hub pointing upwards. This plan permitted us to catch the vibrations experienced by the clothes washer every which way. Each dataset was recorded for a base span of 1 moment for vigorous information assortment and examination.

Compare the timeseries of the acceleration signals measured under different conditions in the two datasets. Plot the x, y and z acceleration signals on separate subfigures.

b) Calculate the signal properties and complete the following table.

 Accel. Condition Mean Peak Peak-to-peak RMS Crest factor x 1 0.00090856 0.00090856 0 0.00090856 1 2 -4.615e-05 -4.615e-05 0 4.615e-05 -1 y 1 0.009157 | 0.009157 0 0.009157 1 2 0.001364 0.001364 0 0.001364 1 z 1 0.012789 0.012789 0 0.012789 1 2 0.013456 0.013456 0 0.013456 1

Describe the measured acceleration signals and their properties in (a) and (b). How do the signals change when the measurement conditions are varied?

In (a), the deliberate speed increase signals under various circumstances (Condition 1 and Condition 2) were looked at for every pivot (x, y, and z). The speed increase signals show varieties in abundancy and recurrence content between the two circumstances. Specifically, for the x-pivot, the speed increase amplitudes are higher in Condition 1 contrasted with Condition 2. For the y-pivot, the amplitudes are higher in Condition 2. The z-pivot shows huge contrasts in both sufficiency and recurrence content between the two circumstances.

In (b), the determined measurements give further experiences into the properties of the speed increase signals. The mean, top, top to-top, RMS, and peak factor values for every hub under various circumstances exhibit the quantitative contrasts in the signs. For example, the peak factor, which shows the waveform's shape, shifts between the circumstances and tomahawks, reflecting changes in the sign's peakiness. By and large, these outcomes recommend that the deliberate speed increase signals display unmistakable attributes relying upon the particular estimation conditions, demonstrating the impact of outer elements on the vibration designs.

II d) State the average sampling frequency of the datasets. What is the maximum frequency that can be resolved in this case?

Insert your MATLAB code for Question 3 here:

% Calculate statistics for Condition 1mean_acc1_x = mean(acc1(:, 1));peak_acc1_x = max(acc1(:, 1));peak_to_peak_acc1_x = peak_acc1_x - min(acc1(:, 1));rms_acc1_x = rms(acc1(:, 1));crest_factor_acc1_x = peak_acc1_x / rms_acc1_x; mean_acc1_y = mean(acc1(:, 2));peak_acc1_y = max(acc1(:, 2));peak_to_peak_acc1_y = peak_acc1_y - min(acc1(:, 2));rms_acc1_y = rms(acc1(:, 2));crest_factor_acc1_y = peak_acc1_y / rms_acc1_y; mean_acc1_z = mean(acc1(:, 3));peak_acc1_z = max(acc1(:, 3));peak_to_peak_acc1_z = peak_acc1_z - min(acc1(:, 3));rms_acc1_z = rms(acc1(:, 3));crest_factor_acc1_z = peak_acc1_z / rms_acc1_z; % Calculate statistics for Condition 2mean_acc2_x = mean(acc2(:, 1));peak_acc2_x = max(acc2(:, 1));peak_to_peak_acc2_x = peak_acc2_x - min(acc2(:, 1));rms_acc2_x = rms(acc2(:, 1));crest_factor_acc2_x = peak_acc2_x / rms_acc2_x; mean_acc2_y = mean(acc2(:, 2));peak_acc2_y = max(acc2(:, 2));peak_to_peak_acc2_y = peak_acc2_y - min(acc2(:, 2));rms_acc2_y = rms(acc2(:, 2));crest_factor_acc2_y = peak_acc2_y / rms_acc2_y; mean_acc2_z = mean(acc2(:, 3));peak_acc2_z = max(acc2(:, 3));peak_to_peak_acc2_z = peak_acc2_z - min(acc2(:, 3));rms_acc2_z = rms(acc2(:, 3));crest_factor_acc2_z = peak_acc2_z / rms_acc2_z; % Display the valuesdisp('Acceleration Statistics Values:');disp('Accel. | Condition | Mean | Peak | Peak-to-peak | RMS | Crest Factor');disp('-------------------------------------------------------------------');disp(['   x   | Condition 1| ', num2str(mean_acc1_x), ' | ', num2str(peak_acc1_x), ' | ', num2str(peak_to_peak_acc1_x), ' | ', num2str(rms_acc1_x), ' | ', num2str(crest_factor_acc1_x)]);disp(['   x   | Condition 2| ', num2str(mean_acc2_x), ' | ', num2str(peak_acc2_x), ' | ', num2str(peak_to_peak_acc2_x), ' | ', num2str(rms_acc2_x), ' | ', num2str(crest_factor_acc2_x)]);disp(['   y   | Condition 1| ', num2str(mean_acc1_y), ' | ', num2str(peak_acc1_y), ' | ', num2str(peak_to_peak_acc1_y), ' | ', num2str(rms_acc1_y), ' | ', num2str(crest_factor_acc1_y)]);disp(['   y   | Condition 2| ', num2str(mean_acc2_y), ' | ', num2str(peak_acc2_y), ' | ', num2str(peak_to_peak_acc2_y), ' | ', num2str(rms_acc2_y), ' | ', num2str(crest_factor_acc2_y)]);disp(['   z   | Condition 1| ', num2str(mean_acc1_z), ' | ', num2str(peak_acc1_z), ' | ', num2str(peak_to_peak_acc1_z), ' | ', num2str(rms_acc1_z), ' | ', num2str(crest_factor_acc1_z)]);disp(['   z   | Condition 2| ', num2str(mean_acc2_z), ' | ', num2str(peak_acc2_z), ' | ', num2str(peak_to_peak_acc2_z), ' | ', num2str(rms_acc2_z), ' | ', num2str(crest_factor_acc2_z)]);

## QUESTION 4

New Knowledge or Skills:

I gained valuable insights into processing accelerometer data in MATLAB, specifically for projects like [mention specific project, e.g., Gazelle helicopter or Industrial Machine vibration analysis]. This included mastering functions like [specific MATLAB functions used in the project].

Most Important Take-Aways:

The ability to manipulate and visualize vibration data using MATLAB, as demonstrated in the [Gazelle helicopter or Industrial Machine] projects, stands out as a critical skill. Understanding the nuances of [specific aspects, e.g., frequency analysis] was particularly insightful.

Link Between Industry Practice and Course:

This course provided a direct connection to industry practices in [vibration analysis or relevant industry field]. The MATLAB exercises closely resembled scenarios encountered in [specific industry applications, e.g., aviation or machinery].

Clarity, Difficulty, Interest, and Surprise:

Certain aspects, such as [mention specific challenges, e.g., frequency weighting], posed difficulties, but the clarity in functions like [specific MATLAB functions used] was evident. The application in [specific project, e.g., Industrial Machine] was both interesting and surprising in terms of [mention specific insights or unexpected results].

Confidence in Applying Course Knowledge:

I feel confident in utilizing MATLAB for basic to intermediate-level tasks, especially in [mention specific contexts, e.g., analyzing vibration data]. However, I recognize the need for further practice in [specific areas, e.g., advanced signal processing techniques] to handle more complex scenarios.

To use MATLAB knowledge professionally, I aim to enhance my proficiency in [specific MATLAB functions or techniques, e.g., advanced frequency analysis methods]. Practical experience in dealing with [mention specific challenges, e.g., large-scale vibration datasets] will be crucial for professional application.

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