# Measuring functions

program Formula

Measuring functions are intended for measurements of signals’ various parameters. Just like as for other functions of Formula program, the arguments can be set as equations.

*Mean( , t)* – allows to find average value by the channel for a particular time period t (in seconds).

*Gradient ( , t) *– allows to define the slope of a straight line using the least square method.

*Min( , t)* – allows to find the minimum value by the channel for a particular time period t (in seconds).

*Max( , t)* – allows to find the maximum value by the channel for a particular time period t (in seconds).

In fact, these functions can be described as filters with AFR similar to the function sin(x)/x, where x is a reciprocal value of the set time interval. In the case, if this interval duration is more than 0,1 s, the values will be rounded with a precision of 0,1 s to the next larger value in order to accelerate operation and save program memory.

The Figure below shows the calculation of minimal, maximal and average values of the channel. As a signal for analysis, we use a signal of triangular shape. Calculation results are displayed at the oscillograph in the compatibility mode:

*StdDev( , t)* –allows to find a standard deviation from the expected mean (square root from the dispersion) by the channel for a particular time period t. For periodical signals, it operated like a DC voltmeter.

*RMS( , t)* – RMS signal level for time period t.

The figure below shows the result of functions *StdDev *and *RMS *operation, in which as an argument there is used a signal of the same amplitude, but with a different constant component level.

*CrestFactor( , t)* – crest factor is used for calculation of signal peak value ratio to RMS with averaging by t (previous time period, seconds).

The figure below shows an example of *CrestFactor *function operation. A sinusoidal signal is used as an argument. Its parameters (RMS and peak value) are measured by DC voltmeter. Operation results of *CrestFactor* function are displayed by DC voltmeter.

*VDV(, t)* – vibration dose for time t.

*MSDV(, t)* – movement dose for time t.

Crest factor (*CrestFactor*), vibration dose (*VDV*) and movement dose (*MSDV*) are the parameters of remedial acceleration:

*remedial acceleration RMS a_{w}*: translational or angular vibration averaged by time is determined by the formula:

- a
_{w}(ξ) – current value of remedial acceleration (translational or angular) as a time function ξ;

- Т – period of measurements.

*remedial acceleration level L_{w}:* The level of remedial acceleration RMS, dB, is determined by the formula:

- a
_{w}– remedial acceleration RMS, m/s^{2};

- а
_{0}– acceleration reference value, 10^{-6}m/s^{2}.

*current RMS value of remedial acceleration текущее a_{w,θ}(t):* RMS value of remedial acceleration at moment of time t is determined by the formula:

- a
_{w}(ξ) -current value of remedial acceleration at the moment of time ξ; - θ – integration time;
- t – current time.

Note- as an approximation of linear averaging you can use exponential averaging, which is determined by the following formula:

- τ – exponential averaging time constant.

*maximum short-term RMS value (of remedial acceleration) MTVV:* Maximum value of current RMS value of remedial acceleration for integration period θ, which is equal to 1 second.

*movement dose MSDV:* Value, represented by remedial acceleration RMS square integral a

_{w}(t), m/s

^{1,5}, which is determined by the formula:

where Ф – is a total period of time during which low-frequency oscillations are observed (these very oscillations cause motion sickness).

Notes:

1 Movement dose can be obtained from RMS value remedial acceleration value by multiplication by the ratio Ф^{1/2}.

2 Unless otherwise specified, impact time Ф is considered to be equal to T.

*vibration dose VDV:* Value, which represents an integral of remedial acceleration fourth power aw(t), m/s

^{1,75}and is determined by the formula:

where Ф – is the total duration of vibration impact.

Notes

1. Vibration dose is more sensible to peak acceleration values than the RMS. Доза вибрации более чувствительна к пиковым значениям ускорения, чем среднеквадратичное значение.

2. Unless otherwise specified, impact time Ф is considered to be equal to measurements duration T.

*TimeShift (, t)* – time shift by the channel, for a particular period in seconds.

The figure below shows the operation of *TimeShift *function. As a source signal, there is used a function *SinGen* (Formula1). Timeshift is set for an interval of 0,1 s (Formula2).

*ThreshD ( , const)* – bottom limit of channel constant. I.e. all the values that are less than the constant level are substituted by it.

*ThreshU ( , const)* – top limit of channel constant. I.e. all the values that are more than the constant level are substituted by it.

in order to set a negative value as a constant, one can use postfix inversion operator.

The figure below shows a result of *ThreshD* and *ThreshU *functions operation. As a source signal, a triangular signal is used – it has an amplitude of ±300 mV (Formula 1). The bottom limit is -150 (Formula 2), the top limit: 150 (Formula 3).

*IncRise ( )* – fronts counter (transitions from 0 to 1).

*IncFall (*) – cut-off counter (transitions from 1 to 0).

It is necessary to use the logical functions *Equal* and *Greater*. The figure below shows an example of transitions counter operation. It is based on saw-shaped signal *TriGen*.

*ImpWidthPos( )* – width of positive pulse in seconds.

*ImpWidthNeg( ) *– width of negative pulse in seconds.

It is necessary to use logical functions *Equal* and *Greater*.

The figures below show an example of functions *ImpWidthPos* and *ImpWidthNeg *operation.