Application of Adaptive Kalman Filter in Online Monitoring of Mine Wind Speed

Transcription

1 Aricle Applicaion of Adapive Kalman Filer in Online Monioring of Mine Wind Speed De Huang 1,2, *, Jian Liu 1,2, *, Lijun Deng 1,2, Xuebing Li 2,3 and Ying Song 2,4 1 College of Safey Science & Engineering, Liaoning Technical Universiy, Huludao , China; anheihb03dlj@163.com(l.d.) 2 Key Laboraory of Mine Thermo-moive Disaser and Prevenion, Minisry of Educaion, Huludao , China 3 School of Safey Engineering, Norh China Insiue of Science and Technology, Beijing , China; lxb @126.com(x.l.) 4 College of Managemen Science and Engineering, Shandong Technology and Business Universiy, Yanai , China; songying927@163.com(y.s.) * Correspondence: hunanhd@163.com (D H); liujian@lnu.edu.cn (J.L.); Tel.: (D.H.) Absrac: The underground complicaed esing environmen and he fan operaion insabiliy cause large random errors and ouliers of he wind speed signals. The ouliers and large random errors resul in disorion of mine wind speed monioring, which possesses safey hazards in mine venilaion sysem. Applicaion of Kalman filer in velociy monioring can improve he accuracy of velociy measuremen and eliminae he ouliers. Adapive Kalman Filer was buil by auomaically adjusing process noise covariance and measuremen noise covariance depending on he differences beween measured and expeced speed signals. We analyzed he flucuaion of airflow flow using daa of wind speed flow and disribuion characerisics of he unnel obained by he Laser Doppler Velocimery sysem (LDV) sudies. A sae-space model was buil based on he unnel airflow flucuaions and wind speed signal disribuion. The adapive Kalman Filer was calculaed according o he acual measuremen daa and he Expecaion Maximizaion (EM) algorihm. The adapive Kalman filer was used o shield fluid pulsaion while preserving sysem-induced flucuaions. Using he Kalman filer o rea offline wind speed signal acquired by LDV, he reliabiliy of Kalman filer wind speed sae model and he characerisics of adapive Kalman Filer were invesigaed. Resuls showed ha he adapive Kalman filer effecively eliminaed he ouliers and reduced he roo-mean-squares error (RMSE), and he adapive Kalman filer had beer performance han he radiional Kalman filer in eliminaing ouliers and reducing RMSE. Field experimens in online wind speed monioring were conduced using he opimized adapive Kalman Filer. Resuls showed ha adapive Kalman filer reamen could monior he wind speed wih smaller RMSE compared wih LVD monior. The sudy daa demonsraed ha he adapive Kalman filer is reliable and suiable for online signal processing of mine wind speed monior. Keywords: mine wind speed; Laser doppler velocimery; Kalman filer; expecaion maximizaion algorihm; online monioring. 1. Inroducion One of he basic condiions for mine safey producion is a reliable mine venilaion sysem, especially in coal mine producion. Accurae venilaion parameers mus be esed o ensure effecive venilaion. The air volume is one of he mos imporan parameers for mine venilaion [1]. A presen, mine air volume is calculaed by esing he average wind speed a he unnel es poin secion and he es poin cross-secional area. Therefore, he mine air volume is acually he average wind speed of he roadway es poin secion, or he average wind speed is obained by measuring he average dynamic pressure value of he unnel secion hrough he piezomeer. In order o obain an accurae average wind speed in he unnel secion, some scholars conduced relaed esing and 2019 by he auhor(s). Disribued under a Creaive Commons CC BY license.

2 simulaion sudy on he average value of single-poin es of unnel by using laser Doppler velocimeer and CFD simulaion heory [2-4]. The resuls showed ha here was a posiive correlaion relaionship beween he wind speed a cerain poins in he roadway secion and he average wind speed in he roadway secion under cerain condiions. The above sudy analyzed he relaionship beween urbulen pulsaion characerisics and cross-secion wind speed and average wind speed. However, he accuracy of he average wind speed is deermined by he precision and accuracy of he single poin es daa. Therefore, i is necessary o ge precise and accurae wind speed for accurae esimaion of secion air volume in he mine. Sensors are usually used for mine daa collecion. The resuls obained by wind speed sensor monioring ofen have large random errors and flucuaions, and ouliers [5]. Filering is he common mehod for sensor signal processing [6, 7]. There is random whie noise in he mine wind speed monioring, which is consisen wih he use condiions of he Kalman filer [8, 9]. Kalman filers are used widely in various fields [10-13]. Kalman filer can rea he disordered and flucuaing daa colleced by he roadway wind speed sensors o ge valid mine wind speed daa for analysis and herefore improve he accuracy of wind speed monior by effecively shielding invalid measuremen values. We analyzed he flucuaion of airflow flow using daa of wind speed flow and disribuion characerisics of he unnel obained by he LDV sudies. A sae-space model was buil based on he unnel airflow flucuaions and wind speed signal disribuion. The adapive Kalman Filer was calculaed according o he acual measuremen daa and he EM algorihm. Using he Kalman filer o rea offline wind speed signal acquired by LDV, he reliabiliy of Kalman filer wind speed sae model and he characerisics of adapive Kalman Filer were invesigaed. Field experimens in online wind speed monioring were conduced using he opimized adapive Kalman Filer, he applicabiliy of he adapive Kalman filer in online monioring of mine wind speed were verified. 2. Adapive Kalman filer 2.1. Sae space model The flow of wind in he underground unnel is very complicaed. Random changes in he sae of he srucure and unknown facors such as he operaion of he mine cars lead o unsable airflow condiions, which would make large wind speed random errors and random flucuaions a he locaion of he wind speed monioring sensors. I is difficul o idenify wheher aleraions are urbulen pulsaions or disurbances caused by sysem movemen. The sae space model is imporan for improving he performance of he Kalman filer. Kalman filer can filer he moniored daa by shielding he flucuaions caused by urbulen pulsaions so ha he oupu of each monioring momen is close o he rue siuaions. Assuming ha T is sampling inerval, he Kalman filer model assumes he rue sae a ime is evolved from he sae a (-1) according o [14]: x = A x + B u + ω (1) where momen A is a sae ransiion model from he sae of he previous momen x ; B is he conrol-inpu model, which is applied o he conrol vecor x 1 o he sae of he u ; ω is he process noise which is assumed ha he mean normal value of zero and he mulivariae normal disribuion of he covariance : ( 0, ) A ime a measuremen Q ω Ν Q ; z of he rue sae x is made according o z = H x + υ (2) where H is he observaion model which maps he rue sae space ino he observed space; υ is he observaion noise which is assumed o be zero mean Gaussian whie noise wih covariance R : υ ~ N(0, R ).

3 The previous ime esimae will be denoed as x ˆ, where he ha denoes esimae, and he super minus is a reminder ha his is he bes esimae prior o assimilaing he measuremen a ime of. The Kalman filering base equaions are given by: where pˆ is he priori esimae error covariance; xˆ ˆ = A x 1+ Bu 1 T pˆ = A p 1A + Q T K ˆ = p H H P H + R xˆ ˆ ˆ = x + K z H x p = ( I K H ) p K T is he Kalman gain. In his sae space model, A = 1, B = 0, H = 1, Q = Q, R = R, where Q and R are consans. And he base equaions are changed o: pˆ = p + Q 1 ˆ = + 1 K p P R xˆ = xˆ + K z xˆ p = ( I K ) p 1 1 where z = v is he measured insananeous wind speed a he es poin a ime, he uni is m/s. xˆ = v ˆ is he es poin o esimae he insananeous wind speed a ime, ha is, he insananeous poin wind speed afer Kalman filer processing, he uni is m/s Adapive parameer adjusmen Process noise covariance Q and measuremen noise covariance filer performance improvemen [8]. Inappropriae R and Q R 1 (3) (4) are imporan for Kalman make poor performance of he Kalman filer in eliminaing ouliers and reducing random errors [15]. In pracical applicaions, he R and Q are difficul o be deermined. Only by consanly adjusing R and Q can he Kalman filer achieve he bes performance. EM algorihm is a mehod for finding maximum likelihood esimaion parameers from incomplee daa ses [16]. This mehod is widely used o deal wih incomplee daa such as defecs, runcaion, and noise [17]. According o he deviaion beween he observed and esimaed values, Kalman's orhogonaliy and wind speed esimaion error, using he EM algorihm o achieve process noise covariance and measuremen noise covariance adapive adjusmen can improve Kalman's filering performance. The purpose of he Kalman-EM algorihm is o find a se of parameers = ( QR,, 0, 0) ha maximize he probabiliy P( ), mean and variance, respecively. z of Kalman performance. Where 0 0 ; 0: T 1 are he iniial Using 0: o represen 1 E( x z 0: T1 ), and o represen 0: Var ( 0: T1 ) E ( ) is he mahemaical expecaion of and filer recursively forwards o obain: x z, where Var is he variance of. Then he Kalman

4 where 10 = 0, 10 = This gives he expressions of Q = 0 0 = 0: 1 10: 1 0: 1 = 10: 1 + K ( I K ). To ge max P( ; ) and 1 ( R ) K( z ) = + 0: 1 0: 1 = + 0: 0: 1 0: 1 = Q 0: 0: 1 z, need o perform backward recursion: 0: T 1 ( )( ) 1 J 1 = 10: 1 0: 1 = + J x x = + J 10: T 1 10: 1 1 0: T 1 0: 1 10: T 1 10: 1 1 0: T 1 0: 1 1 R : T 2 1 Q = + + J J T : T 1 0: T : T 1 0: T 1 0: T : T : T : T 1 ( )( ) 1 1 T 0: T 1 0: T 1 0: T 1 T = 0 R = z z + (8) The insananeous wind speed can be obained by recursively calculaing he basic equaion (4) of he Kalman filer using he parameers calculaed by equaions (7) and (8). E ( z ˆ x 1) 0.05 (9) P ( ˆ R + Cov z x 1) If he consrain condiion of (9) is saisfied, he es value z a ime is a normal value, oherwise z is oulier, a his ime, he esimaed value is used as he rue value a ime o updae he process noise covariance and he measuremen noise covariance. 3. Experimen The mine wind speed monioring is inerfered by he complex and variable es environmen, here are many unknown disurbance facors in he wind speed monioring signal in acual producion. The wind speed signal ha moniored is difficul o deermine he performance of he Kalman filer. Therefore, he experimenal monioring of he wind speed signal is carried ou using a laser Doppler velocimery sysem wih high measuremen accuracy and less influence from exernal disurbance facors. The obained offline signals were processed by a convenional Kalman filer and an adapive Kalman filer for comparing he performance of he Kalman filer in reducing random errors and rejecing ouliers. Bu in he producion process, off-line wind speed signal processing is difficul o mee he needs of real-ime monioring of mine wind speed, real-ime filering of wind speed monior signals is required. Therefore, he experimenal mine was used for he field es o deermine he feasibiliy and applicaion performance of he adapive Kalman filer in mine wind speed online monioring LDV experimenal model The mine wind speed LDV es experimenal equipmen and model are shown in Figure 1. A square experimenal model was used. The model had a proporion of 1:20, a secion inner diameer of 0.2 m and a lengh of 15 m. To race he airflow, he smoke wih an average paricle diameer of fewer han 2 μm is used as he racer paricles. Speed measuremen precision reaches 0.1%. During J (5) (6) (7)

5 he experimen, he laser ransmier emied 6 beams of laser and he laser was combined ino 3 beams of laser hrough a probe, he colors were green, blue and purple, respecively, for esing fluid velociy in he X, Y, and Z direcions, where X is he flow direcion, Y is he exension direcion, and Z is he verical direcion. The laser probes were fixed on he 3D coordinae frame and he pich of he probe was conrolled by a compuer, and movemen accuracy was up o 0.001mm LDV experimenal Figure 1. Experimenal model and equipmen of LDV The LDV experimen is a non-conac measuremen mehod wih a more accurae es resul ha reflecs he rue sae of he fluid[18]. The es poin is placed a a poin where a fully developed flow sae is reached[5], and 10 imes he cross-secion of he air inle,. The arrangemen of he measuring poins and he cross-secion are shown in Figure 2. The experimenal sampling ime is 10s. The fan was urned on when all he equipmen was ready, and esing sared 10 minues afer he fan was on. The experimen was carried ou under ideal condiions in which he wind flow was sable, and he environmen was free from exernal inerference Field experimen Figure 2. Tes model and is cross secion In order o verify he pracicaliy and accuracy of Kalman filer in online monioring of mine wind speed, field experimens were conduced in he experimenal mine of Liaoning Technology Universiy. Figure 3 shows he experimenal plan. Experimenal mine was a recangular secion wih a uni of m. The measuring poins were placed 60m away from he damper 2 and he corner of he roadway, 0.5m away from he roof of he roadway and 1.5m away from he wall of he unnel. The wind speed sensor model was used KDF9403, and is es range was m/s. The fan ran for more han 10 minues before collecing daa a he measuring poin. A his ime, he damper 1 was closed, and in order o ensure he sabiliy of he fan as much as possible, he wind window of he

6 damper 1 is opened, as shown in Fig. 4(a). The damper 2 was fully opened sae, as shown in Fig. 4(b). Afer he measuring poins colleced he daa for 15 minues, he damper 1 was fully opened, remaining in he same sae as he damper 2, while daa collecion coninued. Daa collecion coninued and he es was erminaed afer 15 minues. Figure 3. The experimen of mine floor plan 4. Resuls 4.1. Offline filer process resuls Figure 4. Field experimen of mine air door Afer he Kalman filer offline processing, he average values of wind speed were almos equal o hose obained he LDV es, bu he RMSEs were hugely reduced (Table 1). The RMSE was obained using he mean of wind speed as a reference in he sampling ime T. The average value of he wind speed es resuls in 10s was 3.308m/s, and he RMSE was 0.299m/s. There was no oulier in he 1 o 4s (Figure 5), RMSE was 0.286m/s. There was an oulier in he 4 o 6s es (Figure 6), RMSE was m/s. Afer radiional Kalman filer processing, he average value wihin 10s was 3.308m/s and he RMSE was 0.108m/s. he RMSE in 1-4s was 0.079m/s, while in 4-6s was m/s. Afer adapive Kalman filer processing, he average value wihin 10s was 3.307m/s and he RMSE was 0.012m/s. he RMSE in 1-4s was 0.004m/s, while in 4-6s was 0.018m/s. Table 1. Resuls of es and Kalman filer signal processing 1-4s 4-6s 0-10s values RMSE( m/s) mean(m/s ) RMSE( m/s) mean( m/s) RMSE( m/s) mean( m/s) LDV Tradiional filer Adapive filer

7 Following he radiional Kalman filer process, he wind speed signal ended o be sable, bu i was difficul o eliminae he abnormal poin in he wind speed signal. Afer he adapive Kalman filer processing, he wind speed signal flucuaed around he average value, and he flucuaion range was 3.28m/s-3.34m/s, indicaing relaively sable (Figure 5-7). Figure 5. Experimen resuls wihou ouliers in 1s-4s and he consequences of filering Figure 6. Experimen resuls wih ouliers in 4s-6s and he consequences of filering 4.2. Field experimen resuls Figure 7. Wind speed signal and he consequences of filering in 10s The field experimen resuls showed ha even if he sysem was no adjused or moved, he signal moniored by he sensor flucuaed largely, and he flucuaion range was m/s (Figure 8). Before he dampers was closed, he average value of wind speed was 2.83m/s, he RMSE was m/s, and he average value of wind speed in he s is 2.83m/s, and he RMSE is 0.119m/s. Following he adapive Kalman filer, he mean of wind speed was 2.82m/s, and he RMSE was 0.017m/s in he firs 5minues. The average value was 2.83m/s, and he RMSE was reduced o 0.009m/s in he s (Table 2). Afer he damper 2 was opened, he experimen was coninued for 15 minues. The resuls showed ha he wind speed had a slow downward rend, and he rend of decline afer he adapive Kalman filer reamen was more obvious (Figure 9). Afer he damper

8 was opened for abou 2 minue, he wind speed remained a around 0.87 m/s, and he RMSE decreased by 0.07 m/s. Table 2. Real-ime monioring of experimenal mine wind speed and resuls of Kalman filering values Firs 15 minues s RMSE(m/s) mean(m/s) RMSE(m/s) mean(m/s) Monior Adapive filer Figure 8. Field monioring and filering resuls in 220s-280s Figure 9. Field monioring and filering resuls in 10 minues including sysem changed. 5. Discussion Sudies on wind speed es by laser Doppler velocimery sysem, he resuls showed ha even in he relaively sable and ideal experimenal condiions, he wind speed of he es poins in he pipeline also had random flucuaions, and ouliers. The reason for he oulier may be ha he fan did no run compleely sable, or he racer paricles were no observed a he ime of daa acquisiion. The Kalman filer offline processing on he wind speed signal reduced he RMSE, bu couldn compleely remove he oulier of he signal. The adapive Kalman filer could no only reduce he RMSE, bu also eliminae he ouliers of he wind speed signal. Resuls showed ha he performance of he adapive Kalman filer is beer han he radiional Kalman filer (Figure 6). The field experimen resuls showed ha here was a random disurbance in he online monioring wind speed of he measuremen poins in he unnel. Even when he sysem had no changes, he moniored wind speed signals were no so smoohly sable as hose obained under LDV experimenal condiions. The reasons for such observaions migh be volage insabiliy, which causes changes of he fan operaing condiions, or he naural wind flow in he air inle, which affeced he wind speed. The adapive Kalman filer reamen reduced he RMSE grealy. When he sysem is changing, he adapive Kalman filer can quickly reflec he real change process, insead of reaing he acual change value as he oulier (Figure 9). Therefore, he adapive Kalman filer can be applied for mine wind speed online monioring signal processing.

9 Comparison of he RMSEs obained in he wind speed monioring and he filer processing revealed ha he RMSE a he sampling ime wihou ouliers was smaller han ha a he sampling ime wih ouliers. When he number of ouliers was consan, he longer he sampling ime is, he more accurae he experimen resuls are, which is in line wih he law of signal processing [19]. Resuls proved he reliabiliy of es sysems, models, and mehods. In he case where he es sysem does no change, and no ouliers occur, he mean value of he moniored speed during he sampling ime is generally equal o he mean value of he filered speed. Daa showed ha he monioring mehods commonly used in engineering have a cerain reliabiliy. However, he occurrence of abnormal poins and he ime and locaion of sysem changes are unknown, herefore, in acual applicaions, here may be some errors ha cause he sensor o alarm under normal condiions, which resuls in he emergency rescue program, or he alarming sysem fails o respond o a real emergency condiion, which resuls in safey issues. The wind speed signal filered by he adapive Kalman filer, when here is a wild value, in he case ha he sysem does no change, he signal a each monioring momen is close o he mean of signal a he sampling ime. when he sysem changes, he filered signal can give a corresponding response. As a resul, adapive Kalman filer can quickly reflec he real wind speed a each measuring poin. The wind speed and oher parameers a he measuring poin can ensure he safey of producion a each monioring ime and ensure he safe and effecive producion of he mine. The Kalman filer predics he moniored values based on a small number of measuremens [9]. Applying he Kalman filer o mine wind speed online monioring signal processing can provide shor-erm wind speed online predicion in he even of an acciden or failure of he venilaion sysem, ensure he wind speed moniored a every momen, and i can also provide some reference clues for he rescue work in he acciden. Compared he resuls of previous researchers' experimens on mine wind speed using LDV, he mine wind speed es conforms o he uncerainy principle. The wind speed signal resuls conform o he normal disribuion, and he signal pulsaion has lile correlaion wih he wind speed and sampling ime. Their experimen resuls are consisen wih he LDV examinaion resuls of his research. The wind speed values in previous sudy were he average wind speed in he sampling ime [5], while he curren sudy used he insananeous wind speed, which was he wind speed value afer Kalman filer reamen a he sampling momen. According o he es resuls, when he sabiliy of he esing sysem is free from exernal inerference, he average wind speed obained by LDV during he sampling ime is close o he insananeous wind speed following Kalman filer reamen. However, when he sysem is changed, he average wind speed is no equivalen o he insananeous wind speed. Researchers on vehicle speed monioring have applied LDV speed measuremen sysem o vehicle speed monior. The adapive Kalman filer was used o process he measuremen resuls. Turnable experimens and field es revealed ha he adapive Kalman filer could eliminae he measured ouliers, and he RMSE was reduced by 0.370cm/s and 0.021m/s, respecively [20]. The difference beween he curren sudy and he vehicle speed monior sudy is ha he measuremen of he vehicle running speed was adjused adapively for he acceleraion variance and he measuremen noise variance using he curren sae space model analysis. Our sudy was o solve he process noise variance and observaion noise variance by using he EM algorihm o find he opimal parameers, hereby achieve he purposes of reducing he errors, eliminaing he wild values and he condiion of he Kalman filer convergence. The curren sudy has some shorcomings, parameer opimizaion of process noise variance and observaion noise variance is a non-convex opimizaion process, and non-convex opimizaion of parameers using he EM algorihm can easily lead o local opimizaion. Therefore, he choice of proper iniial values for process noise variance and observaion noise variance is imporan in adapive Kalman filers. Our research analyzed he performance of Kalman filering. Bu he reasons for he occurrence of ouliers and flucuaions of wind speed were no analyzed horoughly. This sudy only invesigaed reamen of wind speed signals in mine venilaion. To achieve real-ime dynamic monioring and warning of he safey of he venilaion sysem, i should also monior oher imporan parameers of he mine venilaion sysem[21] and perform correlaed filering and noise reducion reamen.

10 In he acual producion of he mine, circulaing venilaion, unreliable venilaion faciliies, unsafe venilaion sysems, air leakage, insufficien air supply and series venilaion all may cause mine disasers a any ime [22]. One of he imporan parameers for hese phenomena is he venilaion air volume of he mine. I is necessary o obain he accurae wind speed value of he es poin. The adapive Kalman filer can filer he signals moniored online o obain real-ime values by eliminaing ouliers and reducing RMSE. In addiion o he processing of wind speed signals, i is sill necessary o sudy he feasibiliy of adapive Kalman filer in processing signals of imporan venilaion parameers such as gas and wind pressure [23]. Under viable condiions, he scienific heory of mine venilaion safey shall be applied o conduc safey monioring of mine venilaion sysem o achieve he purposes of reducing he probabiliy of accidens and ensure he safe and effecive producion of mines. 6. Conclusion The Kalman filer can eliminae ouliers caused by versaile and unpredicable environmens and monioring insrumen failures, and i can reduce he random errors of he wind speed signal. As a resul, he accuracy of he insananeous wind speed monior can be improved. The adapive Kalman Filer can be reached by adapive adjusmen of process noise variance and observaion noise variance. The Kalman filer processing resuls of he offline signals obained by he Doppler velocimery sysem show ha he performance of he adapive Kalman filer is beer han ha of he radiional Kalman filer. The online processing of he adapive Kalman filer for he online wind speed signal monioring in he experimenal mine shows ha he adapive Kalman filer no only improves he accuracy of insananeous wind speed monioring bu also predics he shor-erm wind speed. The adapive Kalman filer is feasible in he online monioring signal processing of mine wind speed, which can improve he abiliy of he venilaion sysem o idenify unsafe facors and saes. Therefore, he adapive Kalman filer is suiable for mine wind speed online monioring signal processing. Auhor Conribuions: Concepualizaion, Jian Liu; Daa curaion, De Huang and Lijun Deng; Formal analysis, De Huang; Funding acquisiion, Jian Liu; Mehodology, Lijun Deng; Resources, Jian Liu; Validaion, Xuebing Li and Ying Song; Wriing original draf, De Huang; Wriing review & ediing, Jian Liu, Xuebing Li and Ying Song. Funding: This research was funded by he Naional Naural Science Foundaion of China ( ). Acknowledgmens: D.H. is graeful for he experimenal equipmen of Professor L.J. and he experimenal design and suppor of X.L. and Y.S. Conflics of Ineres: The auhors declare no conflic of ineres. References 1. Harman, H. L.; Mumansky, J. M.; Ramani, R. V.; Wang, Y. J., Mine venilaion and air condiioning. John Wiley & Sons: Li, X. B.; Liu, J.; Song, Y.; Wu, G.; Zhang, M. X., On he conversion beween he mean airflow velociy and ha of he individual poin in he underground mine unnels. Journal of Safey and Environmen 2018, 18, (1), Song, Y.; Liu, J.; Li, X. B.; Liu, Y. H., Experimen and numerical simulaion of average wind speed disribuion law of airflow in mine unnel. China Safey Science Journal 2016, 26, (6), Xu, J., Fluid machinery and fluid mechanics: 4h Inernaional Symposium (4h ISFMFE). Tsinghua Universiy Press and Springer: Liu, J.; Li, X. B.; Song, Y.; Gao, K.; Deng, L. J., Experimenal sudy on uncerainy mechanism of mine air velociy and pressure wih non-exernal disurbance. Journal of China Coal Sociey 2016, 41, (06), Cheng, D. Q.; Qian, J. S.; Zhou, T.; Li, W. J., A high-speed response linkage model for inegraed monioring sysem a coal mine based on inellecualized daa analysis. Procedia Earh and Planeary Science 2009, 1, (1),

11 7. Huang, Y. R.; Cheng, W. J.; Tang, C. L.; Wang, C. L., Sudy of muli-agen-based coal mine environmenal monioring sysem. Ecological Indicaors 2015, 51, Brown, R. G.; Hwang, P. Y. C., Inroducion o random signals and applied Kalman filering: Wih MATLAB exercises. 4h ed. / by Rober Grover Brown ed.; John Wiley: Grewal, M. S.; Andrews, A. P., Kalman filering: Theory and pracice using MATLAB / Mohinder S. Grewal, Angus P. Andrews. 3rd ed. ed.; Wiley: Candiani, G.; Carnevale, C.; Finzi, G.; Pisoni, E.; Vola, M., A comparison of reanalysis echniques: applying opimal inerpolaion and Ensemble Kalman Filering o improve air qualiy monioring a mesoscale. The Science of he oal environmen 2013, , Louka, P.; Galanis, G.; Sieber, N.; Karinioakis, G.; Kasafados, P.; Pyharoulis, I.; Kallos, G., Improvemens in wind speed forecass for wind power predicion purposes using Kalman filering. Journal of Wind Engineering and Indusrial Aerodynamics 2008, 96, (12), Şimşek, E. H.; Güleç, F.; Kavuşu, H., Applicaion of Kalman filer o deerminaion of coal liquefacion mechanisms using discree ime models. Fuel 2017, 207, Zhang, Q., Adapive Kalman filer for acuaor faul diagnosis. Auomaica 2018, 93, Kalman, R. E., A New Approach o Linear Filering and Predicion Problems. Journal of Basic Engineering 1960, 82, (1), Zarchan, P.; Musoff, H., Fundamenals of Kalman filering: A pracical approach / Paul Zarchan, Howard Musoff. 3rd ed. ed.; American Insiue of Aeronauics and Asronauics: Dempser, A. P.; Laird, N. M.; Rubin, D. B., Maximum Likelihood Esimaion from incomplee observaions. J. Roy. Sais. Soc. B 1977, 39, Do, C. B.; Bazoglou, S., Wha is he expecaion maximizaion algorihm? Naure Bioechnology 2008, 26, (8), Kao, S.; Io, H.; Ichikawa, T.; Kagami, M., Laser doppler velocimeer. In Google Paens: Proakis, J. G., Digial signal processing: principles algorihms and applicaions. Pearson Educaion India: Fan, Z.; Sun, Q.; Du, L.; Bai, J.; Liu, J., Applicaion of adapive Kalman filer in vehicle laser Doppler velocimery. Opical Fiber Technology 2018, 41, Muduli, L.; Mishra, D. P.; Jana, P. K., Applicaion of wireless sensor nework for environmenal monioring in underground coal mines: A sysemaic review. Journal of Nework and Compuer Applicaions 2018, 106, Ma, J.; Dai, H., A mehodology o consruc warning index sysem for coal mine safey based on collaboraive managemen. Safey Science 2017, 93, Mishra, P. K.; Praik; Kumar, M.; Kumar, S.; Mandal, P. K., Wireless real-ime sensing plaform using vibraing wire-based geoechnical sensor for underground coal mines. Sensors and Acuaors A: Physical 2018, 269,