RECURSIVE BAYESIAN ESTIMATION OF THE ACOUSTIC NOISE EMITTED BY WIND FARMS

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1 RECURSIVE BAYESIAN ESTIMATION OF THE ACOUSTIC NOISE EMITTED BY WIND FARMS Baldwin Dumorier,,3, Emmanuel Vincen,,3 and Madalina Deaconu,3, Inria, Villers-lès-Nancy, F-56, France CNRS, LORIA, UMR 753, Villers-lès-Nancy, F-56, France 3 Universié de Lorraine, LORIA, UMR 753, Villers-lès-Nancy, F-56, France Insiu Elie Caran de Lorraine - UMR 75 ABSTRACT Wind urbine noise is ofen annoying for humans living in close proximiy o a wind farm. Reliably esimaing he inensiy of wind urbine noise is a necessary sep owards quanifying and reducing annoyance, bu i is challenging because of he overlap wih background noise sources. Curren approaches involve measuremens wih on/off urbine cycles and acousic simulaions, which are expensive and unreliable. This raises he problem of separaing he noise of wind urbines from ha of background noise sources and coping wih he uncerainies associaed wih he source separaion oupu. In his paper we propose o assis a black-box source separaion sysem wih a model of wind urbine noise emission and propagaion in a recursive Bayesian esimaion framework. We validae our approach on real daa wih simulaed uncerainies using differen nonlinear Kalman filers. Index Terms Audio source separaion, nonlinear Kalman filering, uncerainies, wind urbine noise. INTRODUCTION Wind energy is one of he mos used susainable energies in he world. The sochasic naure of wind raises numerous research problems including conrol [], shor-erm wind predicion [,3], resource assessmen [] or power curve esimaion [5, 6]. Among he limiing facors of he elecric producion, acousic annoyance has been somewha lef behind in he predicion and conrol field. Ye, complains from inhabians can lead o severe penalies for he owners ha mus ensure he compliance wih he applicable law of he counry where he farm is se. In all counries acousic annoyance is quanified by eiher he oal noise level resuling from all acousic sources which is called ambien noise, or by he acousic emergence [7]. The acousic emergence is he difference beween he ambien noise level and he background noise level due o oher noise sources besides he urbines. I can be seen as he acousic gain brough by he use of wind urbines. The acousic emergence is difficul o esimae because boh he propagaion of he sound of he wind urbines [8] and he background noise rapidly flucuae in an oudoor conex. Nowadays, numerical simulaion and measuremen campaigns are used for ha purpose bu he calculaed emergence is ofen inaccurae because of he sensiiveness of he acousic variables o he fine opology and meeorological condiions [9, ]. To address his problem, he iear projec inroduced an online conrol sysem [] based on permanen sound level meers ha esimae he inensiy of wind urbine noise and background noise in real ime by means of a proprieary audio source separaion sysem using audio inpu only. The oupu of his source separaion sysem is no perfec, hough, since wind urbine noise and background noise ofen exhibi similar specral and spaial characerisics ha make hem difficul o separae. Uncerainies associaed wih source separaion have received some ineres for speech and speaker recogniion [ 6], bu hey have no been sudied for environmenal sounds ye, o he bes of our knowledge. In his paper, we propose a recursive Bayesian esimaion framework for esimaing he inensiy of wind urbine noise and background noise ha joinly akes ino accoun he oupu of a source separaion sysem (considered here as a black box and a model of wind urbine noise emission and propagaion. Our approach has he advanage of considering simulaneously he sound level meer measuremens, he noise emission values provided by urbine manufacurers, and he resuls of audio source separaion and acousic simulaion. We evaluae he suiabiliy of differen nonlinear Kalman filers o solve he esimaion problem. Since he ground ruh is unknown in real condiions, we validae our approach on real daa obained from an acousic compliance sudy of a seleced wind farm o which we added simulaed uncerainies. The res of his paper is organised as follows. In Secion, we presen he background and he noaions. Then we presen he proposed recursive Bayesian model in Secion 3. In Secion, we presen he conduced experimens wih nonlinear Kalman filers esed on semi-simulaed daa. Finally perspecives and discussions are given in Secion 5. hp:// /7/$3. 7 IEEE 556 ICASSP 7

2 . BACKGROUND AND NOTATIONS.. Acousic variables We assume ha acousical engineers have se sound level meers in differen locaions indexed by j {,..., J}. Each sound level meer measures he ambien noise b,j, i.e. he oal noise level a locaion j and ime in A-weighed decibels (dba. Each ime corresponds o a period of min. The ambien noise is he sum of he wind urbine noise l,j and he background noise r,j a locaion j and ime. These wo signals are assumed o be uncorrelaed and o sum up on a linear scale (W/m [7] which gives in dba: ( b,j = log l,j r,j +. ( Furhermore, he acousic emergence e,j is defined as e,j = b,j r,j. ( This quaniy represens he increase of he noise level due o he wind urbines and i has he meaning of an a poseriori signal-o-noise raio... Acousic model Besides acousic measuremens, acousic simulaions are conduced o predic he wind urbine noise l,j wih he help of he acousic noise emission curves of he urbine manufacurer. These simulaions are conduced by means of specific sofware such as Daakusik cadnaa, ha uses ray-racing o simulae he propagaion. To reduce he number of simulaions, he variables c and o ha respecively represen he urbine command variables (pich angle, ec and he meeorological variables (wind speed and direcion, are reduced o a small number of number of discree values denoed by C = {c,..., c N } and O = {o,..., o N } and he following acousic formula is generally considered [8]: l,j log ( I i a o,i,j x c,o,i. (3 where i {,..., I} indexes he wind urbines, x c,o,i is he noise emied by urbine i in dba ha boh depends on he command c in use and on he meeorological condiions o, and a o,i,j is an aenuaion facor beween wind urbine i and sound level meer j which depends on he meeorological condiions o only..3. Measuremens and uncerainies Finally, we assume ha a source separaion sysem separaes he wind urbine noise and background noise signals and produces an esimae of he background noise level a each locaion and ime. Neiher he acousic model nor he sound hp:// level measuremens and he source separaion oupus are exac: hey suffer from uncerainies. To disinguish hem from he ground ruh values, we adop he following noaions. b,j and r,j respecively denoe he sound level measuremen of b,j and he audio source separaion esimae of r,j. They are sacked across locaions ino J vecors b and r. x c,o,i, a o,i,j, and r,j respecively denoe he real values of urbine noise emission, propagaion, and background noise. They are sacked across urbines and/or locaions ino an I vecor x, an IJ vecor a, and a J vecor r. We denoe by z = [b T r T ] T he overall J observaion vecor and by y = [x T a T r T ] T he overall (IJ+I+J sae vecor. Finally, w v denoes he uncerainy relaed o a given variable v, ha is he deviaion from he ground ruh. 3. BAYESIAN ESTIMATION The aim of he proposed Bayesian approach is o refine he prior disribuion resuling from he acousic model hanks o he observaions ha comprise of he measured ambien noise and he oupus of he source separaion sysem. The poserior disribuion is hen inferred hanks o he Bayes heorem [9]. In order o define he likelihood and he prior disribuion, we model he uncerainies of he sysem as Gaussian random variables. This assumpion is suiable since wind urbine manufacurers, sound level meer manufacurers, and simulaion sofware sysemaically quanify uncerainies using sandard deviaions on he dba scale. 3.. Prior For he prior, we use a firs order auo-regressive moving average wih exernal oupu vecors (ARMAX model [] for he emission, he propagaion and he background noise: x F x x + G x m x + w x y = a = F a a + G a m a + w a. ( F r r + G r m r + w r r This model akes ino accoun boh he emporal correlaions (via he marices F x, F a, and F r and he mean values m x, m a, and m r derived from he acousic sudies (via he marices G x, G a, and G r. The marices F x, F a, F r, G x, G a, and G r can be deermined by learning in principle, even hough we haven ried his ye and we chose a simple random walk model for r (F x = as well as simple model for he propagaion (G x = and G a =. 3.. Likelihood For he likelihood, we consider he following model: ( I b,j = log a,i,j x,i r,j + i + w b,j (5 r,j = r,j + w r,j + w b,j. (6 557

3 We model he ambien noise b,j measured by he sound level meer a locaion j as a Gaussian deviaion from he real ambien noise b,j expressed as a nonlinear funcion of he sae variables wih ( (3. Similarly, we model he background noise r,j esimaed by he source separaion algorihm as a Gaussian deviaion from he rue r,j. The source separaion uncerainy w r, and he measuremen uncerainy w,j b are,j srongly correlaed wih each oher since source separaion is performed from he same sound level meer inpu. Therefore he overall observaion covariance is given by: [ σ Σ z = b I J σb I ] J σb I J (σb + σ r I J wih I J he ideniy marix of size J Recursive Bayesian model The proposed formulaion now fis wih he recursive Bayesian filering framework. We can summarize ( (6 wih he general recursive Bayesian esimaion model (7 (prior y = Fy + Gm y + w y (8 (likelihood z = h(y + w z (9 wih h he nonlinear funcion in (5 (6, and recursively infer he poserior disribuion of he sae variables by he general filering equaions p(y z : = p(y y p(y z : dy ( p(y z : p(z y p(y z : ( wih z : = {z,..., z } he se of observaions up o ime... Daa. EXPERIMENTS AND RESULTS We validaed our approach on daa colleced by VENATHEC SAS on a wind farm locaed in he norh-eas of France. For privacy reasons, he name and exac locaion of he wind farm are no menioned. The wind farm is composed of 6 wind urbines (Vesas V MW and 5 measuremen locaions were se up. In his paper, we consider 9 h of measuremens ha correspond o 5 ime frames of min. Since he ground ruh is unknown in real condiions, we generaed he es daa as follows. For background noise, we considered he real series r measured when he urbines are sopped. For noise emission and propagaion, we considered he mean values m x and m a provided by he urbine manufacurer and cadnaa, respecively, and generaed x and a by adding random Gaussian uncerainies w x and w a. We hen generaed observaions z using (9 wih random Gaussian measuremen and separaion uncerainies w b and w r. Such a simulaion procedure is common in he wind urbine acousics communiy. The uncerainies were assumed o be emporally and spaially uncorrelaed and independen of i and j. Hence, we omi indices i and j in he following. We generaed wo daases. The firs daase conains 5 es cases wih all 6 urbines and 5 measuremen locaions. The sandard deviaions σ x, σ a, and σ r of he uncerainies w x, w a, and w r are chosen in {.5,.5,.5, 3.5,.5} and all combinaions of values are considered. These are plausible values encounered in pracice. In he second daase, σ x, σ a, and σ r are fixed o 3.5, bu subses of o 6 urbines and o 5 measuremen locaions are seleced, resuling in 3 es cases. For boh daases, he sandard deviaion σb of he measuremen uncerainy w b is fixed o.5 db, ha is he sandardized value for Type sound level meers []... Tesed nonlinear Kalman filers We processed hese daa using various nonlinear Kalman filers wih he following values for he model parameers. We se F x = I, F a = I, F r =, G x =, G a =, and G r = I. The covariance of w y was defined as σxi J Σ y = σai IJ. ( Σ r wih Σ r he covariance marix of r r measured when he urbines are sopped. The values of m x, m a, σ x, σ a, and σ r were se as above. The assumpions behind hese seings are also common in he wind urbine acousics communiy. The Kalman filer [] implemens he general recursive Bayesian filer in ( (. I provides updae rules for he poserior mean ŷ and covariance ˆΣ y of he sae vecor y given he sequence of observaions z : up o ime. In he case of a linear funcion h, hese updae rules are exac. In our specific problem, he funcion h is nonlinear, hence we evaluaed hree differen approximaions : he exended Kalman filer [3], he unscened Kalman filer [] and he cenral difference Kalman filer [5]. The firs one is he mos common approximaion: i relies on firs-order Taylor developmen of h around a single poin, namely he esimaed sae mean. When he covariance is large or h is srongly nonlinear i poorly approximaes he poserior disribuion and he esimaion can be weak. The wo oher filers are ingenious improvemens of he exended Kalman filer based on saisical linearisaion. They approximae he prior disribuion wih a number of well-chosen poins ha are propagaed hrough he nonlineariy o capure he mean and covariance. The wo filers slighly differ in he choice of he poins and he way hey reconsruc he mean and covariance..3. Evaluaion merics We evaluaed he resuls by means of he roo mean square error (RMSE beween he esimaed background noise value 558

4 ˆr and he ground ruh r and he log-likelihood of he ground ruh r given he poserior disribuion of he background noise, assumed o be Gaussian wih mean ˆr (subvecor of ŷ and covariance ˆΣ r (submarix of ˆΣ y. We also compued he RMSE and he log-likelihood of he emergence, where he ground ruh e was obained from y and he poserior mean ê and covariance ˆΣ e were obained by propagaing ŷ and ˆΣ y hrough he nonlineariy via he nonlinear Kalman filer under es. RMSE separaion sd (a 3 model sd 5.. Resuls Tables and repor he average RMSE on he background noise esimae and he emergence esimae. The former is similar o he inrinsic sandard deviaion of he sound level meer (σb =.5 db, while he laer is much smaller due o he fac ha he measuremen uncerainy w b on b and r cancels when subracing hose wo quaniies from each oher. I is also much smaller han he average uncerainy of he source separaion sysem (.5 db. The cenral difference Kalman filer appears o perform bes in erms of RMSE, however he poserior covariance is underesimaed so ha he unscened Kalman filer yields a beer log-likelihood. Filer RMSE log-likelihood source separaion esimae (wihou Kalman filer exended filer unscened filer cenral difference filer.6. 5 Table. Average RMSE and log-likelihood of he background noise esimae on he firs daase. Filer RMSE log-likelihood source separaion esimae (wihou Kalman filer exended filer unscened filer cenral difference filer Table. Average RMSE and log-likelihood of he emergence esimae on he firs daase. Figure shows he dependency of he RMSE on he uncerainies in he daa and on he number of wind urbines and measuremen locaions. As expeced, hanks o he fusion of he model uncerainies and he separaion uncerainies operaed by he nonlinear Kalman filer, he RMSE on he emergence esimae decreases wih he uncerainies in he daa and i is always smaller han he sandard deviaion of he separaion sysem, excep for (σ x, σ a, σ r = (3.5, 3.5,.5 and (σ x, σ a, σ r = (.5,.5,.5 where he cenral difference approximaion is poor. Also, he RMSE increases wih he number of wind urbines and decreases wih he number of measuremen locaions. RMSE number of wind urbines 5 3 number of measuremen poins (b Fig.. RMSE of he emergence esimae as a funcion of (a he sandard deviaions σ x and σ a of he model uncerainies and he sandard deviaion σ r of he source separaion sysem on he firs daase and (b he number of measuremen locaions and wind urbines on he second daase. The cenral difference Kalman filer is used. 5. CONCLUSION In his paper, we proposed a recursive Bayesian esimaion framework adaped o he conex of wind farms in order o improve a black-box source separaion sysem. The proposed framework leverages he noise emission values provided by urbine manufacurers and he resuls of acousic simulaion. Our experimens showed ha he cenral difference Kalman filer provides he lowes average RMSE on he emergence esimae and ha his average RMSE is almos always smaller han he uncerainy of he source separaion sysem alone. Fuure work includes addressing he poor performance of he cenral difference Kalman filer when he separaion uncerainies are small and he model uncerainies are large, for insance by using ieraed Kalman [6] or paricle filers [7]. 6. ACKNOWLEDGEMENT This work was done wih he collaboraion and he suppor of VENATHEC SAS. In paricular, he auhors hank Jeremy Schild and Parice Cornu from Venahec SAS for heir implicaion. Experimens presened in his paper were carried ou using he Grid 5 esbed, suppored by a scienific ineres group hosed by Inria and including CNRS, RENATER and several Universiies as well as oher organizaions (see hps:// 559

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