Sig­nal Pro­cess­ing

The sam­pling the­o­rem, name­ly the Nyquist-Shan­non sam­pling the­o­rem, is a fun­da­men­tal the­o­rem in telecom­mu­ni­ca­tions, sig­nal pro­cess­ing and in­for­ma­tion the­o­ry. It deals with the ques­tion to what ex­tent an ana­log out­put sig­nal can be re­con­struct­ed with­out any er­rors from a time-dis­crete dig­i­tized sig­nal. In order to be able to mea­sure a sig­nal, the sam­pling fre­quen­cy must be at least twice the max­i­mum fre­quen­cy of the ana­log sig­nal to be mea­sured. Other­wise, the so called alias­ing oc­curs.

In sig­nal pro­cess­ing, anti-alias­ing means the ac­tive pre­ven­tion or re­duc­tion of alias­ing ef­fects. Alias­ing ef­fects occur main­ly when the sam­pled sig­nal has high­er fre­quen­cies than half the sam­pling fre­quen­cy. This ef­fect is ex­pressed by the fact that fre­quen­cies high­er than half the sam­pling fre­quen­cy are wrong­ly in­ter­pret­ed as lower fre­quen­cies. To pre­vent alias­ing in tech­ni­cal ap­pli­ca­tions, low-pass fil­ters are used to fil­ter out fre­quen­cies above the half sam­pling fre­quen­cy be­fore sam­pling.

The IfTA AD4 and AD32 mod­ules con­sis­tent­ly im­ple­ment anti-alias­ing with ana­log and dig­i­tal fil­ters.

At high sam­pling rates and many chan­nels, large amounts of data ac­cu­mu­late with­in a short pe­ri­od of time which can hard­ly be stored for longer pe­ri­ods of time nor an­a­lyzed. For ex­am­ple, only the max­i­mum am­pli­tude with­in one minute can be stored, or only the max­i­mum am­pli­tude across all chan­nels can be stored at one time in­stead of stor­ing each chan­nel.

The IfTA DataHub re­al­izes this data ag­gre­ga­tion and al­lows to make large amounts of data vis­i­ble by means of small com­pact over­view files.

The Fast Fouri­er Trans­for­ma­tion is a par­tic­u­lar­ly fast and ef­fi­cient al­go­rithm for cal­cu­lat­ing the dis­crete Fouri­er Trans­for­ma­tion (DFT). Dig­i­tized time-dis­crete sig­nals can be con­vert­ed into their in­di­vid­u­al fre­quen­cy com­po­nents by the Fouri­er trans­form for fur­ther anal­y­sis.

The IfTA Sig­nalMin­er Firmware, which runs in real time on the DSP, and IfTA TrendView­er pro­vide the FFT func­tion­al­i­ty.

What is the ad­van­tage of com­bin­ing on­line & off­line data anal­y­sis?

By com­bin­ing the anal­y­sis of off­line and on­line data in one pro­gram it is pos­si­ble to com­pare cur­rent­ly mea­sured vi­bra­tion pa­ram­e­ters of the mon­i­tored ma­chine with al­ready ex­ist­ing and re­leased mea­sure­ment data. In ad­di­tion to the dy­nam­ic data of the rotor dy­nam­ics, slow­er process vari­ables can also be dis­played in the same plot. Thus com­plex sce­nar­ios can be an­a­lyzed more ef­fi­cient­ly. On the hard­ware side, both slow­er mea­sure­ment cards and mod­ules for bus con­nec­tion are avail­able.

The IfTA Ar­gusOMDS sets stan­dards for the de­tailed and com­plete anal­y­sis of the vi­bra­tion be­hav­ior of ro­tors.

An order in ro­tat­ing ma­chines is de­fined as a mul­ti­ple of the ro­ta­tion­al speed (1st order = 1 x ro­ta­tion­al speed, 2nd order = 2 x ro­ta­tion­al speed, ..., n x ro­ta­tion­al speed). The order anal­y­sis ex­am­ines order-de­pen­dent phe­nom­e­na such as un­bal­ance or fric­tion over a changed ro­ta­tion­al speed.

For order track­ing, a sig­nal with dis­crete val­ues de­pend­ing on the an­gu­lar po­si­tion of the wave is cal­cu­lat­ed using re­sam­pling tech­niques. This sig­nal is trans­formed via FFT into the order do­main in­stead of the fre­quen­cy do­main. There­fore, there is no smear­ing of order-de­pen­dent phe­nom­e­na and they can be iden­ti­fied and re­solved more eas­i­ly.

IfTA TrendView­er of­fers order track­ing as an op­tion­al cal­cu­la­tion.

In re­sam­pling, a dis­crete sig­nal is rewrit­ten to other time-dis­crete data points. It is main­ly used as a prepa­ra­tion for order track­ing, where a sig­nal is re­sam­pled de­pend­ing on the an­gu­lar po­si­tion of the wave.