Calculating the Trend Data

Transcription

1 LASER INTERFEROMETER GRAVITATIONAL WAVE OBSERVATORY - LIGO - CALIFORNIA INSTITUTE OF TECHNOLOGY MASSACHUSETTS INSTITUTE OF TECHNOLOGY Techncal Note LIGO-T B - D 3/29/07 Calculatng the Trend Data Davd Barker, Rolf Bork, Alex Ivanov and Danel Sgg Dstrbuton of ths draft: all Ths s an nternal workng note of the LIGO Project. LIGO Hanford Observatory P.O. Box 1970 S9-02 Rchland, WA Phone (509) FAX (509) E-mal: nfo@lgo.caltech.edu Calforna Insttute of Technology LIGO Project - MS Pasadena CA Phone (626) Fax (626) E-mal: nfo@lgo.caltech.edu LIGO Lvngston Observatory LIGO Lane Lvngston, LA Phone (504) FAX (504) E-mal: nfo@lgo.caltech.edu Massachusetts Insttute of Technology LIGO Project - MS NW Cambrdge, MA Phone (617) Fax (617) E-mal: nfo@lgo.mt.edu www: fle C:\User\Danel\Detector\cds\trend\trend.fm - prnted March 29, 2007

2 1 SUMMARY The standard trend format s a composte of 5 values: the mean, the mnmum, the mum, the rms and the number of data ponts whch were used to compute the data pont. Ths format s useful to summarze analog channels whch are sampled at a much hgher rate. It s however neffcent for bt encoded dgtal values as well as a trend channels whch are not derved from a hgher samplng rate. We propose to ntroduce 2 new trend formats: ) verson 2 of the current format whch wll be used for all analog channels, and ) a new dgtal trend format to store trends of bt encoded values. 1.1 ANALOG TREND CHANNELS Verson 2 The man new feature for verson 2 trend fles s an optmzed storage format. The followng changes are ncorporated: ) Trends by default store the standard devaton rather than the root-mean-square. Ths allows the use of sngle precson floatng pont values for all trend values (wth the excepton of the number of ponts whch s a 32 bt nteger), ) Trends can omt the mnmum, the mum and the standard devaton, f the number of ponts s exactly 1,.e., the channel samplng rate s equal to the trend rate. )Second trend can be omtted f t doesn t provde any useful nformaton. Ths s manly the case for montor processes whch have averagng constants longer than a second. However, mnute trend must always be provded f a second trend s wrtten. v) Trend frames are sgnfcantly longer n duraton and use compresson by default. Second trends are stored n one hour long frames and mnute trends are stored n one day long frames. To support the onlne system trends can stll be wrtten as shorter frames (1 mnute and 1 hour, respectvely), but must be converted to the longer format by an background program whenever enough data has been accumulated. A trend reader should support the rms by calculatng ts value on-the-fly. Verson 1 Verson 1 trend frames are calculated at one-second and one-mnute ntervals. The one-second trend s stored n one mnute long frame fles, whereas the one-mnute trend s stored n one hour long frame fles. Trend channels are denoted by ther correspondng channel name extended by a suffx descrbng the statstcal quantty they represent. For each recorded channel the trend data conssts of the number of ponts (.n ), the mean value (.mean ), the root-mean-square value (.rms ), the mnmum value (.mn ) and the mum value (. ). Addtonally, the standard devaton (.stddev ) can be calculated from the above values as needed. The extenson can be omtted, f the channel s sampled at the rate of the trend and does not contan mnmum, mum and standard devaton values. In ths case t s smply a slow channel. page 2 of 9

3 Trend readers A general purpose trend reader should support the followng features: ) Readng both verson 2 and 1, ) Calculatng the rms or standard devaton on-the-fly, )Automatcally generate trends at lower rates f requested, v) Beng able to ntegrate multple trends generated n parallel by ndependent sources. The onlne trend reader may also support: ) A propretary trend format to grant fast access, ) The ablty to read short and long trends (to facltate the onlne wrter). If a trend channels s requested wthout a specfacton of an extenson, the mean shall be returned. 1.2 DIGITAL TREND CHANNELS The new format of dgtal trend channels s optmzed to store bt encoded values. A trend s derved from a channel wth hgher samplng rate by decmaton and by by computng a bt mask whch marks the bts whch were changed. Both the decmated value and the change mask are stored as 32 bt unsgned ntegers. For each recorded channel the dgtal trend data conssts of the decmated value (.val ) and the change mask (. ). If a trend channels s requested wthout a specfacton of an extenson, the value shall be returned. The extenson can be omtted, f the channel s sampled at the rate of the trend and does not contan a change mask. In ths case t s smply a slow channel. 2 ANALOG ONE-SECOND TREND Only vald data ponts are ncluded nto calculatng the one-second trend. If no vald data ponts exst wthn the one second boundary, the one-second trend s nvald for ths nterval; ths s ndcated by settng N 0. All data ponts n verson 2 are stored as sngle precson floatng pont numbers wth the excpeton of N whch s stored as a 32 bt nteger. 2.1 CONVENTIONS The followng conventons were chosen (quanttes marked by an x have to be present n the frame fle, quanttes marked by o are requred f N > 1, and quanttes marked by are calculated on-the-fly): vers. 1 vers. 2 Number of ponts N x o 1 s Data ndex 1, 2, 3, Data ponts x page 3 of 9

4 The number of data ponts wthn one second nterval s equal to the sample rate of the correspondng channel. In verson 2, only the mean has to be present f the trend s derved from a mn sngle data pont, or f one can safely assume N 1, and σ s 0. For example, a channel sampled at 1 Hz would produce a reduced second trend only, but a full mnute trend wth mean, mum, mnmum and standard devaton. 2.2 FORMULAE The one-mnute trend s calculated as follows: Mean x x Maxmum x x o s mn Mnmum x x o s rms RMS x x s Standard devaton σ s o N 1 1. Default s x 1 { x mn mn { x rms x σ s rms ( x 1 s ) 2 ( ) 2 page 4 of 9

5 3 ANALOG ONE-MINUTE TREND Only vald one-second trend ponts are ncluded nto calculatng the one-mnute trend. If no vald one-second trend ponts exst wthn the one mnute boundary, the one-mnute trend s nvald for ths nterval (ndcated by N 0 ). All data ponts n verson 2 are stored as sngle precson floatng pont numbers wth the excpeton of N whch s stored as a 32 bt nteger. 3.1 CONVENTIONS The followng conventons were chosen (quanttes marked by an x have to be present n the frame fle, quanttes marked by o are requred f N > 1, and quanttes marked by are calculated on-the-fly): vers. 1 vers. 2 Number of ponts x o 1 Number of one-second ponts n m Data ndex 1, 2, 3, n m One-second data ponts ( ) Mean x x Maxmum x o Mnmum mn x o RMS rms x Standard devaton σ m o N 1 1. f omtted assume. page 5 of 9

6 3.2 FORMULAE The one-mnute trend s calculated as follows: n m 1 ( ) n m ( ) ( ) 1 {( ) mn mn {( ) n m rms 1 rms ( ) ( ) 1 σ m rms ( x 1 m ) 2 ( ) 2 Snce the mnute trend s calculated from the one-second trend, t avods floatng pont round-off errors when addng a large number of terms. 4 ANALOG TREND OVER OTHER INTERVALS A trend whch averages over multple one-second or one-mnute ponts can be calculated ondemand usng the one-second or the one-mnute trend, respectvely. For example, a ten-mnute trend would average over 10 one-mnute trend data ponts. All data ponts are transferred as sngle precson floatng pont numbers wth the excpeton of N whch s stored as a 32 bt nteger. 4.1 CONVENTIONS The followng conventons were chosen (quanttes marked by an x have to be present n the frame fle, quanttes marked by o are requred f N > 1, and quanttes marked by are calculated on-the-fly): page 6 of 9

7 ndex denotng new bnnng h Number of ponts Number of one-mnute ponts/ Number of one-second ponts n h Data ndex 1, 2, 3, n h One-mnute data ponts ( ) Mean Maxmum Mnmum mn RMS rms Standard devaton σ h 4.2 FORMULAE The arbtrary bnned trend s calculated as follows: n h 1 ( ) n h ( ) ( ) 1 {( ) mn mn {( ) n h rms 1 rms ( ) ( ) 1 page 7 of 9

8 σ h rms ( x 1 h ) 2 ( ) 2 5 DIGITAL SECOND TREND For the vast majorty of bt encoded values the one second samplng rate s the natural acquston rate and there s no need for decmaton and for computng the change mask. For the few bnary channels whch are aqured at a faster rate, we use the followng conventon (quanttes marked by an x have to be present n the frame fle, quanttes marked by o are requred f N > 1, and quanttes marked by are calculated on-the-fly): Number of ponts Data ndex 1, 2, 3, Data ponts x Decmated Change Mask dec x o The formulae are as follows: dec x 1 ( x 2 xor x 1 ) ( x 3 xor x 1 ) ( x Ns xor x 1 ) 6 DIGITAL MINUTE TREND the followng conventon (quanttes marked by an x have to be present n the frame fle, quanttes marked by o are requred f N > 1, and quanttes marked by are calculated onthe-fly): Number of ponts Data ndex 1, 2, 3, Data ponts ( ) page 8 of 9

9 Change mask n second trend Decmated Change Mask ( ) dec x o The formulae are as follows: dec ( (( ) 2 xor ( ) ( (( ) 3 xor ( ) (( ) Nm xor ( ) ( ) 2 ( ) 3 ( ) Nm A dgtal trend wth a rate other than second or mnute can be calculated from the same equatons. page 9 of 9