Measuring functions

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/s²;

• а₀ – acceleration reference value, 10^-6 m/s².

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.

• Formula program
• Constants (in Formula program)
• Operations (in Formula program)
• Mathematical functions (in Formula program)
• Channels (in Formula program)
• Filters (in Formula program)
• Deterministic signals (in Formula program)
• Algorithms (in Formula program)