Compression and Analysis of Golden Gate Bridge Sensor Data

Compression and Analysis of Golden Gate Bridge Sensor Data Guilherme Rocha and Bin Yu Statistics Department University of California, Berkeley Joint Work with Shamim Pakzad and Greg Fenves (CE) Sukun Kim, Jim Demmel and David Culler (CS) Outline     Motivation: Structural Health Monitoring About the Golden Gate Bridge About the installed sensor networks Data compression: – – Temperature data compression (lossless) Acceleration (vibration) data need lossy compression modal estimation for monitoring, and meaningful (lossy) compression Physical model for vibration data – – November 5, 2008 page 2 An example   Plate girder bridge (e.g. Minneapolis collapsed bridge) USA Today (Jan. 15, 2008): plates too thin for the pavements and barriers added later November 5, 2008 page 3 Structural Health Monitoring  National Bridge Inventory (DOT Report to Congress, 2004): – – – Approx. 591,000 bridges in the U.S. Approx. 81,000 (~14%) structurally deficient Routine inspections by Federal Highway Adm. (FHWA): • Annually: ~71,000 bridges • Bi-annually: ~490,000 bridges • Every 4 years: ~28,000 bridges  SHM levels (from Bakir et. al., 2007): – – – – Detection (level 1): whether there is damage Localization (level 2): where in the structure Quantification (level 3): how severe Prediction (level 4): remaining life time of damaged structure page 4 November 5, 2008 Structural Health Monitoring  Structural Health Monitoring Strategies: – Direct damage detection: • Visual inspection • X-Rays • etc. – Indirect damage detection: • Detection of changes in dynamic structural behavior: – Natural frequencies – Modes of vibration November 5, 2008 page 5 About the Golden Gate Bridge  Suspension span: 4,200 ft (1,280m) - the longest in the world until 1964 – – Currently 7th longest span Presently, longest span is Akashi-Kaikyo Bridge in Japan (1998)   Total length: 8,981 ft (2,737m) Width: 90 ft (27m) November 5, 2008 page 6 About the Golden Gate Bridge     Costruction: 1933-1937 Open to traffic: May 28, 1937 – San Francisco Chronicle: A thirty-five million dollar steel harp! Chief Engineer: Joseph Strauss Wind forces: – traffic closed to high winds in 6 occasions: 1951, 1982, 1983, 1996, 2005, 2007 – In the 1982 closing, wind force was strong enough to cause visible motion – 1983: Wind gusts of 75MPH (~120Km/h); 2008, 70MPH November 5, 2008 page 7 Instrumentation Our collaborators did the hard work :) Figures by Shamim Pakzad and from web sites November 5, 2008 page 8 Instrumentation Accelerometer Characteristics  Sensor board: – Thermometer Two pairs of accelerometers: • 2 ADXL 202E accelerometers: – Vertical and horizontal – Coarse measurements • 2 Silicon Designs 1221L: – Vertical and horizontal – Finer measurements – Silicon Designs 1221L One thermometer: • temperature for calibration Figure adapted from Kim et. al. (2006) November 5, 2008 ADXL 202E page 9 Instrumentation Accelerometer Characteristics Tables from Kim et. al. (2006) November 5, 2008 page 10 Instrumentation  Hostile Environment: – – – – Gusty wind Strong Fog Rain Strong condensation (sea fog + wind): • Corrosive environment Figure from Kim et. Al. (2006) November 5, 2008 page 11 Instrumentation  Sensing equipment: – – Boards are enclosed in waterproof plastic box Plastic box has holes for antenna and battery cables: • Sealed with silicon adhesives – – Relatively ample supply of energy Communication: • Linear topology exploited: bi-direction antennas Figure from Kim et. Al. (2006) November 5, 2008 page 12 Instrumentation Position of the sensors  There are 81 cables along west span of bridge: – – Sensors installed at position of every other cable (41) Additional sensors installed to reduce packet loss (10) 4 nodes on west and 4 nodes on east tower Figure from Kim et. Al. (2006)  There are 8 sensors installed on south tower: – November 5, 2008 page 13 Time Jittering Synchronization protocol   Deviations from ideal sampling rate: – Capped at 250 s (5% of sampling interval @ 200Hz) Delay in data reading within a node: • Data reading waits until memory write ends Temporal jitter: – – Controlled by use of high performance TinyOS components Difference in the time of reading across different nodes: • Variation in the crystal of processors in different nodes • Imperfect time synchronization  Spatial jitter: – – Controlled by using FTSP (Flooding Time Sync. Protocol) page 14 November 5, 2008 Transmitted Data  Data set: – – – 8 minutes @ 100Hz = 48,000 readings 5 readings/sample @ 2 Bytes each = 10 Bytes/reading Total transmitted volume: 480 KBytes Uncompressed data rate 1KB/sec: • 2 bytes/sample (for both temperature and acceleration) • 5 samples/reading (1 temperature, 4 acceleration) • 100 readings/sec (sampling frequency: 100 Hz)  Volume of data: – – – Temperature data currently makes up for 20% of byte vol. Acceleration data makes up for 80% of byte volume Temperature Data Description of data  Temperature: – – Slow variation (@100-200Hz) Small and infrequent jumps 1,000 readings – Run length code provides good lossless compression: • 94% reduction in number of bytes transmitted (conservative) Histogram # of points with temperature change Worst case: Change in 1,278 points (out of 48,000) November 5, 2008 page 17 Temperature Run Length Code  Run Length coding: – – Transmit first reading in full precision (2 bytes) Transmit packets only when change occurs: • Each packet contains: – Number of time steps since last change – Temperature variation • Packet size: – Adjustable – A conservative choice: 4 bytes Temperature Data Compression Run Length Code  Assumptions (conservative): 4 bytes/reading – 16 bit representation of temperature variation • larger observed temperature variation: 3000 units – – 1 bit for sign of temp. variation 15 bit representation of run length • More than enough to present overflow: – Maximum observed run length: 1370 units • 11 bits are probably enough Temperature Data Compression Run Length Code  Data volume: – – current: 48,000 readings x 2 Bytes / 480 sec = 200 Bps run length coding: • Each data point corresponds to a change in temperature • Each data point contains 4 Bytes of data • Worst case observed (by our coding): – (1,278 x 4 Bytes + 2 Bytes) / 480 sec ~ 11 Bps – Volume reduction: 94.5% • Average case (49 sensors): – (967 x 4 Bytes + 2 Bytes) / 480 sec ~ 8.1 Bps – Volume reduction: 95.9% Acceleration Data Compression  Possibly useful facts: – – – Temporal correlation (LMS tried, more on this later) Physical model for the data Redundant measurements: Vertical Coarse scale Finer Scale Accelerometer 3 Accelerometer 1 Horizontal Accelerometer 4 Accelerometer 2 Acceleration Data Compression In progress  Low pass filtering: – – Currently all data is transmitted Expert knowledge: • For most civil structures, fundamental frequencies below 10Hz • low-pass filtering is used  Correlation of the series in neighboring sensors: – Particularly convenient to explore in bridge setting: • Good correspondence of network topology and correlation structure November 5, 2008 page 22 Acceleration Data Compression Adaptive filtering  Use of LMS to implement predictive coding – Xt+1 predicted from: – The weight vector wt is determined adaptively: November 5, 2008 page 23 Acceleration Data Compression Adaptive filtering with LMS  Experiments were conducted – On the sensor readings for two different nodes • Nodes with the higher R2 for AR models were used – Node 30 – Node 45 – Different number of lags: • “p” set to values between 1 and 250 – Different settings for : • 100; 500; 1,000; 10,000 and 15,000  Standard deviation of the residual series: – – At best 60% of standard deviation of “raw” series In most cases, above 80% of standard deviation of “raw” series page 24 November 5, 2008 Acceleration data compression The series to which LMS was applied November 5, 2008 page 25 Acceleration data compression The series to which LMS was applied November 5, 2008 page 26 Acceleration data compression LMS: (STD residuals/STD series) November 5, 2008 page 27 Acceleration data compression LMS: (STD residuals/STD series) November 5, 2008 page 28 Lossy compression for statistical analysis In information theory, lossy compression is about reducing bits of data -- the meaning of data is NOT taken into account. Lossy compression for statistical analysis needs a different metric for measuring loss -- what matters is the precision lost in estimating a meaningful model (or parameters). If we know the data model, we know what to keep… November 5, 2008 page 29 Meaningful compression of vibration data The goal is structural monitoring hence we need to decide on what information is crucial for this task. Ideally, we’d establish modes of the bridge and monitor any deviation from normal modes. Minimally, this mode information has to be transmitted. Possibly other information as well in case the chosen estimation method is not working well. November 5, 2008 page 30 Physical Model for Vibration Lumped components  Masses: – Model inertia – Force proportional to acceleration: • Newton’s law  Dashpots: – Model dampening – Force proportional to speed: • Viscous friction  Springs: – Model stiffness – Force proportional to displacement • Young’s law November 5, 2008 page 31 Physical Model for Vibration A simplified vibrating system November 5, 2008 page 32 Physical Model for Vibration A simplified vibrating system From Newton’s Law: Hence: November 5, 2008 page 33 Physical Model for Vibration A simplified vibrating system Collecting equations for all blocks: with: November 5, 2008 page 34 Physical Model for Vibration Cont. time state space representation  Define, the state variable as:  The state space representation of the vib. system:  We observe the acceleration: November 5, 2008 page 35 Physical Model for Vibration System dynamics in continuous time  From the dynamic equation: – State evolution obeys Stochastic Diff. Eq. (SDE): – Assuming the random excitation to be: with dW t Gaussian and “covariance matrix” , the solution of the above SDE satisfies (Oksendal, 1998): November 5, 2008 page 36 Physical Model for Vibration System dynamics in discrete time  Letting: a discrete time representation of the system is:  Our goal is to obtain dynamic properties: – Focus on estimating A and C matrices. page 37 November 5, 2008 System Identification Different methods  Methods for model identification: – SRIM: System Realization from Information Matrix • Juang, 1997: Journal of Guidance, Control and Dynamics • Based on state space model (second order method) Future: – State-space model: MLE or Bayesian November 5, 2008 page 38 Using the data Model Identification using SRIM  Recall the discrete time state space representation:  Define:  From discrete time state space representation: November 5, 2008 page 39 Using the data Model Identification using SRIM  Let:  We must have: November 5, 2008 page 40 Using the data Model Identification using SRIM  identification: – – Any invertible linear map of state variable is a state variable Hence A and x are not unique • Let: • If x has (intra-temporal) conditional covariance xx|u, write the spectral decomposition xx|u= RR’ and define to obtain one state representation with diagonal covariance. November 5, 2008 page 41 Using the data Model Identification using SRIM  SRIM Estimates:  Modal parameters: – – – Modal frequencies: arg(eigenvalues of A)/(2t) Damping ratios: 1-exp{[abs(eigenvalues of A)-1]/(t)} Modes of vibration: C • where stems from the Schur decomposition A = ’ page 42 November 5, 2008 Using the data Model Identification using SRIM  Issues: – – – Choice of p (number of lags) Choice of d (state space dimension) Behavior in small samples November 5, 2008 page 43 Model Identification using SRIM Simulation results  Simulation set-up: – – – System with 5 unit masses (m j=1Kg, for all j) Forces are i.i.d. standard Gaussian random variables Stiffness: • k12=k23=k45=160 N/m, k34=40 N/m, k01=k05=15 N/m – Dampening (Raleigh’s simplification): • S =  K, with  = 510-3 (units: Ns/m) November 5, 2008 page 44 Model Identification using SRIM Simulation results  Dynamic characteristics: Mode 1 2 3 4 5 November 5, 2008 Frequency 1.29 Hz 2.04 Hz 3.14 Hz 4.50 Hz 4.54 Hz Damping Ratio 0.152 0.338 0.623 0.866 0.870 page 45 Model Identification using SRIM Simulation results  Geometric characteristics (mode shapes): Mode 2, Nat. Freq. = 2.04 Hz Mode 3, Nat. Freq. = 3.14 Hz Mode 1, Nat. Freq. = 1.29 Hz Mode 4, Nat. Freq. = 4.50 Hz Mode 5, Nat. Freq. = 4.54 Hz November 5, 2008 page 46 Model Identification using SRIM Simulation results  Est. frequencies: 1st mode of vibration (1.29 Hz) November 5, 2008 page 47 Model Identification using SRIM Simulation results  Est. frequencies: 2nd mode of vibration (2.04Hz) November 5, 2008 page 48 Model Identification using SRIM Simulation results  Est. frequencies: 3rd mode of vibration (3.14 Hz) November 5, 2008 page 49 Model Identification using SRIM Simulation results  Est. frequencies: 4th mode of vibration (4.50 Hz) November 5, 2008 page 50 Model Identification using SRIM Simulation results  Est. frequencies: 5th mode of vibration (4.54 Hz) November 5, 2008 page 51 Model Identification using SRIM Simulation results: est. modes of vib.  1st mode of vibration (4.54 Hz) Lags spanning 0.4s (40 lags @ 100Hz) Using state space dim. = 6 Using state space dim. = 10 Using state space dim. = 20 Lags spanning 1.2s (120 lags @ 100Hz) Using state space dim. = 6 Using state space dim. = 10 Using state space dim. = 20 November 5, 2008 page 52 Model Identification using SRIM Simulation results: est. modes of vib.  2nd mode of vibration (2.04 Hz) Lags spanning 0.4s (40 lags @ 100Hz) Using state space dim. = 6 Using state space dim. = 10 Using state space dim. = 20 Lags spanning 1.2s (120 lags @ 100Hz) Using state space dim. = 6 Using state space dim. = 10 Using state space dim. = 20 November 5, 2008 page 53 Model Identification using SRIM Simulation results: est. modes of vib.  3rd mode of vibration (3.14 Hz) Lags spanning 0.4s (40 lags @ 100Hz) Using state space dim. = 6 Using state space dim. = 10 Using state space dim. = 20 Lags spanning 1.2s (120 lags @ 100Hz) Using state space dim. = 6 Using state space dim. = 10 Using state space dim. = 20 November 5, 2008 page 54 Model Identification using SRIM Simulation results: est. modes of vib.  4th mode of vibration (4.50 Hz) Lags spanning 0.4s (40 lags @ 100Hz) Using state space dim. = 6 Using state space dim. = 10 Using state space dim. = 20 Lags spanning 1.2s (120 lags @ 100Hz) Using state space dim. = 6 Using state space dim. = 10 Using state space dim. = 20 November 5, 2008 page 55 Model Identification using SRIM Simulation results: est. modes of vib.  5th mode of vibration (4.54 Hz) Lags spanning 0.4s (40 lags @ 100Hz) Using state space dim. = 6 Using state space dim. = 10 Using state space dim. = 20 Lags spanning 1.2s (120 lags @ 100Hz) Using state space dim. = 6 Using state space dim. = 10 Using state space dim. = 20 November 5, 2008 page 56 Model Identification using SRIM Simulation results  Est. dampening ratio: 1st mode of vibration (1.29 Hz) November 5, 2008 page 57 Model Identification using SRIM Simulation results  Est. dampening ratio: 2nd mode of vibration (2.04 Hz) November 5, 2008 page 58 Model Identification using SRIM Simulation results  Est. dampening ratio: 3rd mode of vibration (3.14 Hz) November 5, 2008 page 59 Model Identification using SRIM Simulation results  Est. dampening ratio: 4th mode of vibration (4.50 Hz) November 5, 2008 page 60 Model Identification using SRIM Simulation results  Est. dampening ratio: 5th mode of vibration (4.54 Hz November 5, 2008 page 61 Future directions:  How to reduce bias of SRIM’s damping ratio estimation regularization and choice of p in the eigen-analysis and in LS for A?  SRIM on real data how to choose d?  Other methods for modal estimation and compare with SRIM comparison metrics: distance to true parameters in simulations, and prediction performance  On-line SRIM modal estimation on-line PCA is needed distributed computation November 5, 2008 page 62