Introduction

This screen shows the parameters of the measurement quality as well of the comfort ones associated to the selected signal.

With in the same screen, two analyses are done.

• Original signal: All the parameters that don't require a constant time interval are obtained on the original signal.
• Interpolated signal: the original signal is interpolated to a time constant series with a frequency sampling given by the floor rounded of the mean frequency in steps of 10 Hz.

In the interplated signal, the same analysis than in the Original signal is done in this series, and therefore similar values should be obtained.

The difference can be used as an estimation of the error due to the interpolation.

Aditionally, the Fast Fourier Transform (FFT) is also given which helps to identify the resonant frequencies.

Series information

This information is very usefull to analyze the quality of the recorded signal. The results are very conditionated by the mobile phone performance. In fact, the most important parameters to consider are:

• $(F_{med})$ Sampling frequency: Average sampling frequency in Hz of the whole measure. This value is very dependent on the mobile used, and must be high enough to assure a the identification of the maximum desired frequency. A minimum of 2.5 times will be recomended.

• $(dt_{max})$ Maximum time increment between consecutive records: Maximum time in miliseconds between 2 consecutive records in the serie. If this value is high it means that the quality of the recording is very poor.

• $(dt_{min})$ Minimum time increment between consecutive records: This value is important when compared to the previous one. Ideally it should be the same. That would mean a regular time interval along the serie. A big difference means bad quality of the recording.

Other parameters are:

• $(Dur)$ Duration:

• $(N_{rec})$ Number of records:

• $(N_{rms})$ Number of records in 1 second:

• $(dt_{med})$ Average time increment: Average time increment in milisecods between records in the serie. It must be between the minimum and maximum time increments. It is also related to the mean frequency as:

$$dt_{med} = \frac{1}{F_{med}}$$

• $(\sigma_{dt})$ Standard deviation: Standard deviation of the time increments in the serie with respect to the mean value

Detrend values

Detrend mean values are essential to know which is the base acceleration value that the Mems is measuring.

The Mean detrended values, are an indicator of the inclination of the mobile phone. In this sense, the mean detrended value in X and Y axis should be 0 and the mean value in Z axis should be the gravity acceleration. Mean detrend values can be used to fix the error provided by the inclination of an accelerometers when it is not exatcly horizontal.

Detrended values have to be removed from the temporal serie when performing the FFT. If they are not removed, the FFT shows at frequency equal to 0 Hz, reflecting that a constant energy is being introduced into the system.

• $(X_{med})$ Weighted arithmetic mean of the acceleration in the X axis
• $(Y_{med})$ Weighted arithmetic mean of the acceleration in the Y axis
• $(Z_{med})$ Weighted arithmetic mean of the acceleration in the Z axis

$$X_{med} = \frac{\sum (x_i \cdot w_i)}{\sum w_i} = \frac{\sum (x_i \cdot dt_i)}{T}$$

Time history parameters

This is a really usefull information to assess the vibration serviceability of the measured structure. These values are different indicators, which provide different points of view of the recorded information.

Within the following formulas, the value T will indicate the duration of the whole measurement.

Mean Acceleration

• $(X_{|Med|})$ Mean acceleration of the whole measurement: mean value of the excitation in the X axis
• $(Y_{|Med|})$ Mean acceleration of the whole measurement: mean value of the excitation in the Y axis
• $(Z_{|Med|})$ Mean acceleration of the whole measurement: mean value of the excitation in the Z axis

$$a_{|Med|} = \frac{1}{T} \int_{0}^{T} \!|a|dt$$

Peak Acceleration

Maximum absolute value of acceleration (+ or -) over the entire time history of interest. This can be calculated for the ‘raw’ time history or following frequency weighting. DynApp does not perform frequency weighting as a function of the human sensitiity according to ISO 2631.

• $(X_{Peak})$ Peak acceleration of the whole measurement in the X axis
• $(Y_{Peak})$ Peak acceleration of the whole measurement in the Y axis
• $(Z_{Peak})$ Peak acceleration of the whole measurement in the Z axis

$$a_{Peak} = max ({|a_i|})$$

Root Mean Square (RMS) Acceleration of the whole test with duration T

• $(X_{RMS})$ RMS acceleration of the whole measurement in the X axis
• $(Y_{RMS})$ RMS acceleration of the whole measurement in the Y axis
• $(Z_{RMS})$ RMS acceleration of the whole measurement in the Z axis

$$a_{RMS} = \sqrt{\frac{1}{T} \int_{0}^{T} \!a^2dt}$$

Crest Factor

It is defined as the modulus of the ratio of the maximum instantaneous peak value of the frequency-weighted acceleration signal to its RMS value. DynApp uses the values without performing frequency weighting. Future versions of the application contemplate this option.

It is used to decide the serviceability analysis method:

• a) Basic evaluation weighted RMS acceleration when the crest factor is small. That indicates that the pak acceleration is similar to the RMS of the whole measurement

• b) Additional evaluation: running RMS and VDV (Vibration Dose Value) when the Crest factor is high. That indicates that the peak value is considerably higher than the mean acceleration, and so, further analysis is required.

DynApp calculate the following values

• $(Crest_{X})$ Crest factor in the X axis
• $(Crest_{Y})$ Crest factor in the Y axis
• $(Crest_{Z})$ Crest factor in the Z axis

$$Crest_{a} = \frac{a_{Peak}}{a_{RMS}}$$

Maximum Transient Vibration Value (MTVV)

Peak of the running RMS with 1 s integration time.

The running RMS is a curve which relates each value of time, with the RMS value of a certain integration time before that value of time.

$$a_{rms,\tau}(t) = \sqrt{\frac{1}{\tau} \int_{t-\tau}^{t} \!a(t)^2dt}$$

The MTVV is the maximum point of that function when the integration time is equal to 1 second

$$MTVV_{a} = max (a_{rms,\tau}(t))$$

• $(MTVV_{X})$ MTVV in the X axis
• $(MTVV_{Y})$ MTVV in the Y axis
• $(MTVV_{Z})$ MTVV in the Z axis