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Wireless sensors as a tool to explore avalanche internal dynamics: Experiments at the Weissflühjoch Snow Chute
Cold Regions Science and Technology 65 (2011) 242–250
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Cold Regions Science and Technology j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / c o l d r e g i o n s
Wireless sensors as a tool to explore avalanche internal dynamics: Experiments at the Weissflühjoch Snow Chute I. Vilajosana a,d,⁎, J. Llosa b, M. Schaefer c, E. Surin̂ach d, X. Vilajosana e a
WorldSensing, Clos de Sant Francesc 21, 08034, Barcelona, Spain Universitat Oberta de Catalunya IN3-Internet Interdisciplinary Institute Parc, Mediterrani de la Tecnología, Av. del Canal Olímpic s/n, 08860 Castelldefels, (Barcelona), Spain WSL, Swiss Federal Institute for Snow and Avalanche Research SLF, CH-7260, Davos Dorf, Switzerland d Grup dAllaus (RISKNAT), Dept. Geodinàmica i Geofísica, Fac. de Geologia, Universitat de Barcelona, Martí i Franquès s/n, 08028 Barcelona, Spain e Universitat Oberta de Catalunya, Estudis d'Informàtica, Multimèdia i Telecomunicació, Rambla Poblenou 156, 08018 Barcelona, Spain b c
a r t i c l e
i n f o
Article history: Received 23 February 2010 Accepted 28 September 2010 Keywords: Snow avalanche Wireless sensors Accelerometer Speed
a b s t r a c t Specially designed wireless accelerometers units were used in a series of experiments at the snow chute operated by the SLF at Weissflühjoch (Switzerland) during 2008–2009 winter. The purpose of the experiment was to evaluate the best design and the performance of these innovative instruments to provide information on the internal dynamics of flowing snow. The wireless accelerometers were placed in the snow chute starting zone prior to the experiments and traveled within the flow when the avalanche was released. The characteristics of the units (size and density) allow them to evolve like active particle tracers. Acceleration measurements obtained at 85 Hz in the different experiments were analyzed. The analysis methods used include Empirical Mode Decomposition and Kalman filtering techniques. The developed methodologies were used to obtain reliable speed and position values from the single 2D acceleration measurements. The obtained results were compared to independent speed and position measurements. The results show to be in agreement with that obtained from independent speed measurements from optoelectronic sensor arrays and video images and open a new perspective for future avalanche research. The extracted information could provide valuable data related to internal dynamics of the avalanche. Small-scale chutes are the ideal scenario to test these new technologies. Moreover, we consider these sites essential to develop and test new instrumentation (to be deployed), in the future, in full-scale experiments. In addition, the experiments performed show for the first time the potential of the wireless technologies and wireless sensors to study snow avalanches. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Over the last 80 years, avalanche-dynamics models have been increasingly used in land-use planning and for the design of protecting structures that are able to resist avalanche impact. These models have been improved by taking more and more processes into account to better describe snow avalanche motion. To keep on refining these models and develop more robust avalanche physical description it is essential to obtain more information on avalanche dynamics. In the last decades the measuring equipment of the main test sites in Europe and USA were renovated (Ammann, 1999), (Lied et al., 2002), (Dent et al., 1998). Test sites were equipped with monitoring systems to get new insights on the avalanche physical parameters (e.g., front velocity, flow depth, mass balance, and density).
⁎ Corresponding author. WorldSensing, Clos de Sant Francesc 21, 08034, Barcelona, Spain. Tel.: + 34 699 896471. E-mail address: [email protected] (I. Vilajosana). 0165-232X/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.coldregions.2010.09.011
However, acquiring data on high-speed phenomena still remains a challenge. The description of the avalanche behavior needs to be supported by physical observations measured during chute and fullscale experiments (Dent et al., 1998). Classical methods such as image processing techniques give useful information on the shape and velocity of the avalanche, but they cannot track the internal structure. Non-intrusive methods (e.g., Doppler radar) give access to the internal structure of an avalanche but the obtained signals are difficult to interpret (Issler, 2003). Static sensors for measuring the impact pressure or snow density are also of common use but they only yield information at fixed places and their interpretation needs supplementary information (velocity measurements, density (Gauer et al., 2007)). In the last decade, a new generation of instruments has been used to study snow avalanches. Louge et al. (1997) have developed a capacitance probe that can be calibrated to measure snow density. Radar techniques have been improved to yield more accurate speed estimates (Gauer et al., 2007 and Rammer et al., 2007). Development of commercially available Laser Scanner systems allowed to obtain accurate measurements on avalanche mass balance (Sailer et al.,
I. Vilajosana et al. / Cold Regions Science and Technology 65 (2011) 242–250
2008) which was inconceivable some years ago. Ground Based SAR radars have also been successfully used to monitor avalanche activity (Martínez-Vázquez and Fortuny-Guasch, 2005). In addition, smallscale experiments in laboratory chutes have become increasingly popular and a large number of experiments have been carried out in the past years (Issler, 2003), (Dent et al., 1998). It is obvious that experiments under controllable and reproducible conditions become the ideal scenery for developing new measuring techniques especially for snow avalanche research. As an example, the usage of high-speed cameras has been popularized in chute experiments. Their measurements combined with new data processing methodologies brought successful results related to avalanche dynamics (McElwaine and Nishimura, 2001), (Biancardi et al., 2005). There is also a unique approach to nonintrusively track a particle in the avalanche flow that was presented in a series of two papers by Dave and Bukiet (1998) and Dave et al. (1998). Specifically, they proposed a system, which is based on the principle of magnetic induction coupling and consists of small transmitters mounted inside the particle being tracked and a set of receiving antennae surrounding the experimental apparatus. In Part I of the sequence of two papers, they focus on the theoretical aspects, in particular, on developing a computational technique to solve the inverse problem of finding the three-dimensional position as well as orientation of the particle from the voltages induced in the antennae. In the second part (Dave et al., 1998) they focus on the system development, including all hardware and data acquisition aspects. In that work, (Dave and Bukiet, 1998) they demonstrate the wide applicability of the system due to its non-intrusive nature, especially when optical tracking techniques are not feasible. However, the system presents also some drawbacks. Mainly the requirement of using multiple receiving antennae limits the applicability to chute experiments where antennae could be easily installed. Nowadays, emerging technologies have the potential to provide environmental information in an unprecedented scale. For example, the wireless sensor networks which were developed for military purposes (Warneke et al., 2001) have presented a tremendous increase of application in many fields due to their specific characteristics: low power, low cost and wireless communications. These characteristics are what also made them very “attractive” for exploring natural phenomena. In this work this technology will be used to obtain information from the internal dynamics of snow avalanches. The University of Barcelona (UB) Avalanche Group in collaboration with the Distributed Systems and Computer Networks at the Open University of Catalonia (UOC) are developing a new type of sensors that will overcome the current limitations imposed by avalanche nature. The main objective is to track the motion of each sensor while flowing in the avalanche body as if they were snow clods and in addition, to measure complementary properties (temperature, density). It is obvious that such an ambitious goal requires a clear road map and previous experimentations under more controlled conditions. In this sense, the large snow chute of the WSL Swiss Federal Institute of Snow and Avalanche Research (SLF) located at Weissflühjoch, Switzerland becomes an ideal scenario for testing this technology. In this paper we present a series of experiments at the Weissflühjoch Snow Chute, where specifically designed WSN nodes were released inside the avalanche flow. Specifically, we focus on the determination of the position of the sensors as a function of time when they travel in the flow. 2D accelerometers connected to a wireless micro-device were employed as a first attempt to use wireless technology for snow avalanche dynamics studies.
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sensor arrays, load cells, high-speed camera, and ultrasonic sensor (Tiefenbacher & Kern, 2004). The SLF Snow Chute is described in more detail in Tiefenbacher and Kern (2004). A schematic picture of the chute is provided in Fig. 1. The chute consists of a 10 m long reservoir, a 10 m long acceleration section followed by a 4 m long measurement section and, finally, a 6 m long run-out zone. In the experiments the slope of the two uppermost moveable sections of the chute was set to 45°. The slope of the measurement section was 40° and in the run-out zone was 8°. In the acceleration section and the measurement section rubber mats cover and roughen the smooth running surface of the chute. The rubber mats have a width of 6 cm and a stream wise spacing of 2.5 cm. In the experiments snow stuck in the void spaces and sliding conditions similar to natural avalanches were produced. Up to 15 m3 of snow was released from the storage part by opening a shutter door forming artificial avalanches. The front velocities of the test avalanches were in the range of 6 m/s to 14 m/s obtained from optoelectronic sensors and video images and flow heights up to 1 m were generated depending on the filling volume and snow properties. The snow chute reservoir was filled with considerable effort of manpower: snow surrounding the chute was shoveled in by hand. Before each experiment the snow density and snow temperature inside the reservoir were measured and grain sizes and forms were determined. The air temperature was measured as well. The wireless units used in this experiment are based on a commercial development platform for wireless sensor network applications. Specifically, the core of each wireless sensor node is based on the telosb platform (Polastre et al., 2005). The telosb is used as a node on the wireless sensor network. It features a Texas Instruments MSP430 microcontroller, 48 Kbytes of program memory, 10 Kbytes of static RAM, 1 Mbyte of external flash memory, and a 2.4-GHz Chipcon CC2420 IEEE 802.15.4 radio. The telosb was designed to run TinyOS (TinyOs: Operating System, web page http://tinyos.net/). The election of the telosb platform is justified because the MSP430 microprocessor provides several configurable ports that easily support external devices. The large amount of flash memory available in that device was useful for buffering the collected data. In each unit the sensor used was an accelerometer MMA6260Q (http://www.freescale.com/). It is a 2 axis capacitive micro-machined accelerometer featuring signal conditioning, a 1-pole low pass filter and temperature compensation. This sensor has a linear output with high signal to noise ratio, low power consumption and high sensitivity. The typical sensitivity is 800 mV/g with a characteristic acceleration range of ± 1.5g. The accelerometer used is capable of measuring accelerations over a
2. Instruments and experimental site The large snow chute located at Weissflühjoch 2670 M.A.S.L. is equipped with different type of sensors including optoelectronic
Fig. 1. Scheme showing the snow chute geometry and position of the available sensors.
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bandwidth of 1.5 kHz for all three axes. The analog output is sampled using the microcontroller's embedded 12 bit A/D converter. A single sensor node was constituted by the sensor board, the interface board and a battery holder with two AA batteries. These parts, were housed inside a rugged PVC weatherproof and watertight case (Fig. 2). Care was taken in the sensor design to have a sensor density ranging from 200 kg / m3 to 500 kg / m3 to ensure that the sensors remain on the avalanche surface. The whole software was developed using the TinyOS 2.x (TinyOs: Operating System, web page http://tinyos.net/) operating system. TinyOS is a wireless sensor network specific operating system that follows an event-driven programming model. The programming language is nesC which is an extension of C that incorporates the concept of components and bidirectional interfaces. Components allow programmers to encapsulate the behavior of the different parts of the program independently. The communication between the components was achieved by the use of bidirectional interfaces. This approach makes the collaboration between different programmers easier, ensures cleaner code, and facilitates reutilization. Four different experiments were carried out during the period 02/ 02/2008 and 02/04/2008. In each experiments, after filling up the reservoir and tilting up the chute to its maximum inclination (45°), two units were placed over the snow surface, 1.5 to 3 m uphill the gate. Once the gate was opened the units released with the flow traveling downslope as particle clods. The sensor data were time stamped to have a common base of time to facilitate comparison between the different units. Apart of the data from the available sensors, video images, shear force measurements at the base of the avalanche and velocity obtained with two independent measurement systems were recorded during the experiments. Fig. 3 shows snapshots of the small-scale dry-mixed avalanche released on 02/04/2008 (Experiment 4.2.2). Red circles indicate the position of the two units. 3. Methodology Acceleration readings from the two axis accelerometers were analyzed to obtain the velocity and position of the unit inside the avalanche flow. It is well known that accelerometers are very good to provide local accelerations. However, they are inaccurate to provide velocity and position estimates through direct numerical integration (Britting, 1971). Accelerometers measure the force per unit of mass acting on a body along a specific sensing direction. The vector sum of this force per unit of mass and the gravity acceleration, is the inertial acceleration of the body, which is the value of our interest. To this end we developed a methodology based on the Empirical Mode
Decomposition (Huang et al., 1998), and Kalman filtering (Kalman, 1960) to estimate the velocity and position of the sensors along the path minimizing the different sources of error. Specifically, we focused on filtering out the gravity component effects from the data. Numerical integration errors, and random errors from sensor collisions with surrounding snow clods and chute walls were also considered. Empirical Mode Decomposition (EMD) was used to subtract the gravity component from the acceleration readings. Essentially, this methodology allows decomposing any data set into a finite number of intrinsic mode functions (IMFs) which constitute the empirically determined basis for our data. Each IMF represents a simple oscillatory mode similar to a component in the Fourier-based methodology. The EMD explores temporal variations in the characteristic time scale of the data and in consequence, it is adaptive to nonlinear and nonstationary data processes like the inclination of the snow surface running downhill the chute. The crucial step in the application of this data analysis technique is to determine the independent IMF through an iterative process, which was first described by Huang et al. (1998) and is summarized below. The main idea behind this methodology is to determine the different time scales that are present in the data. Three methods for measuring the time scales were defined in Huang et al. (1999): the time between successive zero crossings, the time between successive extremes, and the time between successive curvature extremes. In each case, the time interval is a local measure of the time variation of the events. Extremes and curvature intervals show a local time scale that indicates whether the data cross the zero line or not. The aim of the process is to define a local time scale of oscillation that starts at one extreme, crosses zero, and reaches the extreme of the opposite sign. The period of this oscillation gives the characteristic time scale. It is local and represents only one mode of oscillation. An iterative procedure is used to determine the different IMF from the data. The first step consists of identifying all the local extremes. All the obtained local maxima are connected by a cubic spline line as the upper envelope. The same procedure is repeated for the minima values to produce the lower envelope. The arithmetical mean between the maxima and the minima envelopes is designated as m1(t), and the difference between the data X(t) and m1(t) becomes the first component, h1(t) i.e.: X ðt Þ−m1 ðt Þ = h1 ðt Þ
ð1Þ
Ideally, h1(t) should be the first IMF extracted from our data. However, local heterogeneities in the time series (small changes in curvature, data overshoots and undershoots) underlie hidden local
Fig. 2. Waterproof packaging and sensor node. Unit size 14 × 8 cm.
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Fig. 3. Snapshots of the first instants of one experiment. Red circles indicate the deployed sensors.
maxima or minima, which can be extracted if, in the next step, we consider h1(t) to be our data. h1 ðt Þ−m11 ðt Þ = h11 ðt Þ
ð2Þ
where m11(t) is the mean value of the new envelope obtained from h1(t). This iterative procedure is called Sifting, and basically aims to eliminate riding waves from the data and make the data profiles more symmetric. The Sifting procedure can be repeated k times until h1k is obtained as IMF. This h1k(t) is considered the first component of the data, c1(t), and it would be much more symmetric than h1(t). c1 ðt Þ = h1k ðt Þ
ð3Þ
The Sifting process, however, should be applied with care owing that too many Sifting steps could convert the resulting IMF in a pure frequency-modulated signal of constant amplitude. In order to guarantee that the final IMF obtained from the Sifting process has enough physical meaning a stopping criterion was determined by Huang et al. (1999). These authors suggested that an appropriate stopping criterion could be achieved simply by limiting to three the repetition of Sifting steps in which the same number of zero crossings and extremes is obtained. Once the stopping criteria are satisfied, the first component contained in the data, c1(t), is determined. It represents the finest scale (highest frequency) contained in the data. Removing this component from the data X(t) we obtain r1(t) r1 ðt Þ = X ðt Þ−c1 ðt Þ
ð4Þ
Since r1(t) still contains information on the longer period scales, it is treated in a similar way as the data and the Sifting procedure is repeated until the remainder becomes a monocomponent signal and no more components can be extracted. After this procedure our data can be represented as the sum of N orthogonal modes and a remainder. N
X ðt Þ = ∑ cj ðt Þ + rN ðt Þ j=1
ð5Þ
In our case, we observed that the remainder corresponds to the gravity component due to the path curvature and hence this IMF could be filtered out from the data. Once the gravity component was removed from the data, the Kalman filtering technique based on a ballistic model (Kalman, 1960) was used to estimate the velocity and the position of the sensors. In this case we assume the sensor as a mass block traveling on the slope. Elementary laws of physics say that the relationship between the velocity in one step vk and the one in the following time step vk + 1 is: vk
+ 1
= vk + ak ⋅ΔT
ð6Þ
where ak is the acceleration in time step k and ΔT the interval of time. However, a more realistic equation for vk + 1 taking into account the velocity noise due to collisions with snow clods and random collisions with the surrounding snow is: vk
+ 1
= vk + ak ⋅ΔT + ek
ð7Þ
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3 ΔT 2 is called the transition matrix, B = 4 2 5 the ΔT input matrix, C = ½ 1 0 the measurement matrix, zk the measurement noise and yk the position measurement. We assume that the process noise, wk, and the measurement noise, zk, follow a Gaussian distribution with zero mean and no correlation exists between them. In consequence, the measurement noise and process noise covariance matrices Sm and Sp could be obtained as:
1 where A = 0
considering an additional term ek for the velocity noise (we assume the velocity noise to be a random variable that changes with time). A similar equation can be derived for the position x: xk + 1 = xk + vk ⋅ΔT +
uk ⋅ΔT 2
2
ð8Þ
+ wk
where wk is the position error. According to these equations we can define a state vector rk that consists of the position and velocity vectors: rk = ½vk xk
T
Since the measured output is the unit position, a linear system of equations can be written as follows:
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imf6 imf5 imf4 imf3 imf2 imf1 signal
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ð11Þ
where wT and zT indicate the transpose of the w and z random noise vectors, and E(⋅) means the expected value.
ð10Þ
a 7 6.5 6
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Sw = E w ⋅wT T Sz = E z ⋅z
ð9Þ
rk + 1 = A ⋅rk + B ⋅ ak + wk yk = C ⋅rk + zk
ΔT 1
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Time(s) Fig. 4. a) and b), IMF of the acceleration readings from 30 s of data prior to an avalanche test. c) Top: detrended acceleration readings, middle calculated slope angle, bottom, velocity and position obtained using the EMD and Kalman filtering combined methodology.
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At this point we can use Kalman filtering estimation equations as presented by (Welch & Bishop, 2001). Kk = APk C
T
−1 T CPk C + Sz
ð12Þ
rˆk
+ 1
= A rˆk + Bak + Kk yk + 1 −C rˆ k
Pk
+ 1
= APk A + Sw −APk C Sz CPk A
T
T −1
T
ð13Þ ð14Þ
where matrix K is called the Kalman gain and P is the estimation error covariance (Kalman, 1960). The generic term of the state estimate equation at time kð rˆk Þ derives the state estimate at time k + 1 which is only A times the state estimate at time k, plus B times the known input at time k. The second term in Eq. (13) is called the correction term and it represents the amount by which to correct the propagated state estimate due to the process and the measurement errors. In the experiments, we used as an acceptable position error estimate 0.3 m. The commanded acceleration was obtained from the accelerometer readings. The acceleration noise was set as one standard deviation of the acceleration readings. Acceleration noise was obtained from each independent sensor and experiment from the analysis of 2 s of data recorded before each experiment. In that period the sensors were laying on the snow surface. In Fig. 4 an example of the application of the EMD and Kalman filtering combined methodology is presented. Figs. 4a and b show the different IMF from 30 s of acceleration data obtained prior to an avalanche test release. Note that the different intrinsic mode functions are presented in Blue and the residual in Red. We attribute the latter to the gravity component. This fact allows us to eliminate gravity component effects from the data. In Fig. 4c, the accelerometer raw data and the slope angle determined from the slope normal component acceleration readings are presented. At the lowest part of the figure, the detrended slope tangential acceleration readings filtered out using the Kalman filter are presented. As a result estimates of the sensor position and velocity laying on the surface of the snow were obtained. Fig. 4c shows that the obtained velocity remains zero for about 26 s highlighting the potential of this methodology to minimize numerical integration errors when determining velocity and position from direct integration of acceleration readings. 4. Data analysis and results
Fig. 5. Normal (green) and tangential (blue) acceleration readings from the experiment 2.2.1 released on 02/02/2008 (right) and from the experiment 4.4.2 released on 02/04/ 2008. The arrow shows the instant of the avalanche release.
Data from the experiments released on winter 2008–2009 at the Weissflühjoch Snow Chute using wireless accelerometers were analyzed. In Fig. 5, the normal and the tangential accelerations obtained in the experiment 2.2.1 released on 02/02/2008 and the experiment 4.4.2 released on 02/04/2008 are presented. Avalanche kg 2.2.1 was a fresh snow dry avalanche with a snow density of 0:233 m 3 and a snow temperature of − 8.7°. Avalanche 4.4.2 was a dense wet kg avalanche with a snow density of 0:466 m 3 and a snow temperature of − 8°. The initial (approx) 5.5 s of data corresponds to the sensors laying on the snow surface before the experiment. Note that the slope angle, θ, can be recovered from these readings assuming that at = g ⋅ cos(θ) (because the inertial acceleration is 0). After opening the gate, (arrows Fig. 5a and b), a sudden decrease of the force per unit of mass is observed in the time series of the normal and tangential components. This decrease corresponds, as expected, to an increase of the inertial acceleration undergone by the unit. In both experiments, during the first 2 s of motion the sensors traveled in a straight line in the flow (observed from video images). The motion of the sensors in this window of time (5–7 s) shows an erratic shifting between acceleration and deceleration phases.
This behavior is also observed in the other experiments, not presented here. The mean retarding acceleration, however, is rather constant. This behavior was also observed in full-scale avalanches analyzing Doppler radar measurements (Gauer et al., 2007). During the most stable phase of the measurements in Experiment 2.2.1 the mean retarding acceleration, aret is 3.7m / s2 (from 5.4 to 6.4 s Fig. 5a). If we assume for simplicity aret = g ⋅ sin(θ) − μ ⋅ cos(θ) and θ = 45° results μ = 0.24. For the 4.4.2 experiment the mean retarding acceleration is 0.84m / s2 (from t = 5.5 s to t = 6.5 s) which yields a Coulomb friction coefficient of μ = 0.44. The obtained values of μ seem reasonable according to the type of flow and snow released. In both experiments after a period of stability, the acceleration becomes more erratic due to the impacts of the sensors with the chute, snow clods and sensor rotation. Afterwards, the dynamic component of acceleration becomes zero again showing that the units stopped. Note that the unit stayed upside down as indicated by the negative value of the measured acceleration. In Fig. 6 the velocity (dashed line) and position (continuous line) estimates of the two sensors released in the 4.4.2 experiment are
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Sensor Position and Velocity Experiment 4.2.2
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Time (s) Fig. 6. Wireless sensor velocity (dashed lines), position error (red lines), and position (continuous lines) for the experiment 4.4.2. Squares and triangles show position estimates obtained from video images.
presented. Raw position estimates are also depicted in red dotted lines. For comparison purposes, in the same figure the position estimates from simultaneously obtained video images are also presented (squares and triangles). The position estimates from the video images show good agreement with those obtained from the wireless sensors. Complementary punctual speed measurements using optoelectronic sensor arrays were used to track the velocity of the sensors at the wedge (Fig. 1). The pink line in Fig. 6 indicates the wedge position where punctual speed estimates were obtained. The velocity profiles obtained for the 4.4.2 experiment from the array of optoelectronic sensors are shown in Fig. 7. The data from the optoelectronic sensor array corresponds to a time averaged velocity profile over the avalanche event. The error bars correspond to one standard deviation of the velocity signals in the time window. The comparison between the velocity estimates obtained using inflow sensors and from optoelectronic sensor array measurements show that inflow sensors provide higher speed estimates than optoelectronic sensors. This result was expected according to the different velocities measured: Whereas the inflow sensors were traveling on top of the flow about
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velocity in m/s Fig. 7. Velocity profiles obtained from the optoelectronic sensors (bars) in mixed snow test avalanche released on 02/04/2008 (exp. 4.4.2).
50 cm from the bottom of the avalanche, the velocity profiles obtained from the optoelectronic sensors show velocities from the bottom of the flow (first 8–10 cm) where boundary effects are more important. The velocity profiles obtained from the 4.4.2 event show 8 m/s as the maximum speed. The maximum speed obtained from wireless sensors at the wedge for the two sensors are 12.5 m/s and 14 m/s respectively. The physical parameters obtained for the dry avalanche released on 02/02/2008 (exp. 2.2.1) are shown in Fig. 8. In a similar representation as Fig. 6 the velocity (dashed line) and position (continuous line) estimates of the two sensors released are presented. Again position estimates from video images show significant agreement with wireless sensor estimates. In Fig. 9 the velocity profile obtained from the array of optoelectronic sensors is presented. The velocity profile from this event shows a maximum velocity of 6.5 m/s at 7.5 cm from the ground. Speed estimates from wireless sensors at the wedge show again higher values (9.5 m/s). 5. Conclusions Specially designed wireless accelerometer units were used in a series of experiments at the snow chute operated by the SLF at Weissflühjoch (Switzerland). The main goal was to evaluate their capability to provide information on the internal dynamics of flowing snow. The experiments showed the validity of the sensors to be deployed in small-scale avalanche experiments. The units demonstrated to be robust and able to intercommunicate wirelessly between few centimeters under the snow. Data from 4 different experiments were obtained, however in this paper only two of them are presented. A methodology based on the Empirical Mode Decomposition (Huang et al., 1998) and Kalman filtering (Kalman, 1960) was developed to determine the position and the velocity of the sensors traveling inside the flow from the acceleration readings. Reproducibility was observed in the acceleration readings from the different experiments. Acceleration measurements during the initial stages of motion showed an erratic oscillation along the main driving force as also observed by Gauer et al. (2007) in full-scale avalanches based on Doppler radar measurements. Position estimates obtained from the acceleration readings showed good agreement with the independent position estimates obtained from video images. Wireless sensor velocity estimates were also compared to velocity estimates from correlation of
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Sensor Position and Velocity Experiment 2.2.1
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Time (s) Fig. 8. Wireless sensor velocity (dashed lines), position error (red lines), and position (continuous lines) for the experiment 2.2.1. Squares and triangles show position estimates obtained from video images.
optoelectronic sensor array measurements. In all the cases wireless sensor estimates showed higher values than that of optoelectronic sensors. This fact is attributed to the higher position in the flow of the wireless sensors in relation with the optoelectronic sensors. Wireless sensors were traveling on the flow surface (about 50 cm above the ground) and the optoelectronic sensors measured the shearing layer ranging from 0 cm to 10 cm. Overall, the results show to be in agreement with that obtained from independent speed measurements from optoelectronic sensors and video images and open a new perspective for future avalanche research. The information provided by the units shows the potential of new technologies to provide valuable data related to internal dynamics of snow avalanches. Tracer sensors like the ones presented here if combined with non-intrusive systems like proposed by Dave and Bukiet (1998) and Dave et al. (1998) could provide a pseudo-Lagrangian perspective on the flow dynamics as they are transported along with the flow. We believe, that such sensors are crucial for studying the flow dynamics as they have typically provided much better temporal resolution than non-invasive methods. Moreover, they could provide better detail of the vertical structure of the flow at-a-point. Future experiments shall go in this direction, especially at small-scale chutes. 0.08 0.07
flow depth in m
0.06 0.05 0.04 0.03 0.02 0.01 0
2
3
4
5
6
7
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velocity in m/s Fig. 9. Velocity profiles obtained from the optoelectronic sensors (bars) in dry snow test avalanche released on 02/02/2008 (exp. 2.2.1).
We consider small-scale sites essential to develop and test new instrumentation (to be deployed), in the future, in full-scale experiments. In addition, the experiments performed show for the first time the potential of the wireless technologies and wireless sensors to study snow avalanches. Acknowledgements We are indebted to our colleagues at the SLF for their help in our shoveling stage. We also would like to thank the financial support of projects MICINN: DALMASA (CGL2006-06596/BTE), and Consolider (CSD2006-00041). I.V is supported by a Torres Quevedo grant from the Spanish Ministerio de Ciencia e Innovacin 2008-03-08109. References Ammann, W.J., 1999. A new Swiss test-site for avalanche experiments in the Valle de la Sionne. Cold Regions Science and Technology 30 (1–3), 3–11. Biancardi, A., Ghilardi, P., Pagliardi, M., 2005. Automatic mask extraction for PIV-based dam-break analysis. IbPRIA 2, 705–712. Britting, K.R., 1971. Inertial Navigation System Analysis. Wiley, New York. 116–119. Dave, R.N., Bukiet, Bruce G., 1998. Nonintrusive rigid body tracking technique for dry particulate flows. Part I. Theoretical aspects. Review of Scientific Instruments 69 (10), 3598–3605. doi:10.1063/1.1149145. Dave, R.N., Voicy, J., Agarwal, J., Gupta, V., 1998. Non-intrusive rigid body tracking technique for dry particulate flows, Part II: practical aspects and implementation. Review of Scientific Instruments 69 (10), 3606–3613. Dent, J., Burrel, K., Schmidt, D., Louge, M., Adams, E., Jazbutis, T., 1998. Density, velocity and friction measurements in a dry snow avalanche. Annals of Glaciology 26, 247252. Gauer, P., Issler, D., Lied, K., Kristensen, K., Iwe, H., Lied, E., Rammer, L., Schreiber, H., 2007. On full-scale avalanche measurements at the Ryggfonn test site, Norway. Cold Regions Science and Technology, Amsterdam 50 (1–3), 55–71. Huang, N.E., Shen, Z., Long, S.R., Wu, M.C., Shih, E.H., Zheng, Q., Tung, C.C., Liu, H.H., 1998. The empirical mode decomposition method and the Hilbert spectrum for non-stationary time series analysis. Proceedings of the Royal Society of London 454, 903–995. Huang, N., Shen, Z., Long, S., 1999. A new view of nonlinear water waves: the Hilbert Spectrum. Annual Reviews in Fluid Mechanics 31, 417–457. http://www.freescale.com/. Issler, D., 2003. Experimental information on the dynamics of dry-snow avalanches. In: Hutter, K., Kirchner, N. (Eds.), Dynamic response of granular and porous materials under large and catastrophic deformations: Lecture Notes in Applied and Computational Mechanics, 11, pp. 109–160. Kalman, R.E., 1960. A new approach to linear filtering and prediction problems. Transaction of the ASME Journal of Basic Engineering 82, 35–45. Lied, K., Moe, A., Kristensen, K., Issler, D., 2002. Snow Avalanche Research Programme SIP-6. Ryggfonn. Full scale avalanche test site and the effect of the catching dam. Technical Report 581200-35, Norwegian Geotechnical Institute. Louge, M.Y., Steiner, R., Keast, S., Decker, R., Dent, J., Schneebeli, M., 1997. Application of capacitance instrumentation to the measurement of density and velocity of flowing snow. Cold Regions Science and Technology 25 (1), 47–63.
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Martínez-Vázquez, A., Fortuny-Guasch, J., 2005. Avalanche and snowfall monitoring with a ground-based synthetic aperture radar. Fringe 2005 workshop. Proceedings of the conference held 28 November–2 December, 2005 in Frascati, Italy. McElwaine, J., Nishimura, K., 2001. Ping-pong ball avalanche experiments. Annals of Glaciology 32 (1), 241–250. Polastre, P., Szewczyk, R., Culler, D., 2005. Telos: enabling ultra-low power wireless research. Proceedings of the 4th international symposium on Information processing in sensor networks, Los Angeles, California, USA. Rammer, L., Kern, M.A., Gruber, U., Tiefenbacher, F., 2007. Comparison of avalanchevelocity measurements by means of pulsed Doppler radar, continuous wave radar and optic methods. Cold Regions Science and Technology, Amsterdam 50 (1–3), 35–54.
Sailer, R., Fellin, W., Fromm, R., Juerg, P., Rammer, L., Sampl, P., Schaffhauser, A., 2008. Snow avalanche mass balance calculation and simulation model verification. Annals of Glaciology 48 (1), 183–192. Tiefenbacher, F., Kern, M., 2004. Experimental devices to determine snow avalanche basal friction and velocity profiles. Cold Regions Science and Technology 38 (1), 17–30. TinyOs: Operating System, web page http://tinyos.net/. Warneke, B., Last, M., Liebowitz, M., Pister, K., 2001. Smart dust: communicating with a cubic-millimeter. Computer 34, 44–51. Welch, G., Bishop, G., 2001. An introduction to the Kalman Filter, SIGGRAPH 2001 Course. http://www.cs.unc.edu/welch/kalman/kalmanIntro.html.
Contents lists available at ScienceDirect
Cold Regions Science and Technology j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / c o l d r e g i o n s
Wireless sensors as a tool to explore avalanche internal dynamics: Experiments at the Weissflühjoch Snow Chute I. Vilajosana a,d,⁎, J. Llosa b, M. Schaefer c, E. Surin̂ach d, X. Vilajosana e a
WorldSensing, Clos de Sant Francesc 21, 08034, Barcelona, Spain Universitat Oberta de Catalunya IN3-Internet Interdisciplinary Institute Parc, Mediterrani de la Tecnología, Av. del Canal Olímpic s/n, 08860 Castelldefels, (Barcelona), Spain WSL, Swiss Federal Institute for Snow and Avalanche Research SLF, CH-7260, Davos Dorf, Switzerland d Grup dAllaus (RISKNAT), Dept. Geodinàmica i Geofísica, Fac. de Geologia, Universitat de Barcelona, Martí i Franquès s/n, 08028 Barcelona, Spain e Universitat Oberta de Catalunya, Estudis d'Informàtica, Multimèdia i Telecomunicació, Rambla Poblenou 156, 08018 Barcelona, Spain b c
a r t i c l e
i n f o
Article history: Received 23 February 2010 Accepted 28 September 2010 Keywords: Snow avalanche Wireless sensors Accelerometer Speed
a b s t r a c t Specially designed wireless accelerometers units were used in a series of experiments at the snow chute operated by the SLF at Weissflühjoch (Switzerland) during 2008–2009 winter. The purpose of the experiment was to evaluate the best design and the performance of these innovative instruments to provide information on the internal dynamics of flowing snow. The wireless accelerometers were placed in the snow chute starting zone prior to the experiments and traveled within the flow when the avalanche was released. The characteristics of the units (size and density) allow them to evolve like active particle tracers. Acceleration measurements obtained at 85 Hz in the different experiments were analyzed. The analysis methods used include Empirical Mode Decomposition and Kalman filtering techniques. The developed methodologies were used to obtain reliable speed and position values from the single 2D acceleration measurements. The obtained results were compared to independent speed and position measurements. The results show to be in agreement with that obtained from independent speed measurements from optoelectronic sensor arrays and video images and open a new perspective for future avalanche research. The extracted information could provide valuable data related to internal dynamics of the avalanche. Small-scale chutes are the ideal scenario to test these new technologies. Moreover, we consider these sites essential to develop and test new instrumentation (to be deployed), in the future, in full-scale experiments. In addition, the experiments performed show for the first time the potential of the wireless technologies and wireless sensors to study snow avalanches. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Over the last 80 years, avalanche-dynamics models have been increasingly used in land-use planning and for the design of protecting structures that are able to resist avalanche impact. These models have been improved by taking more and more processes into account to better describe snow avalanche motion. To keep on refining these models and develop more robust avalanche physical description it is essential to obtain more information on avalanche dynamics. In the last decades the measuring equipment of the main test sites in Europe and USA were renovated (Ammann, 1999), (Lied et al., 2002), (Dent et al., 1998). Test sites were equipped with monitoring systems to get new insights on the avalanche physical parameters (e.g., front velocity, flow depth, mass balance, and density).
⁎ Corresponding author. WorldSensing, Clos de Sant Francesc 21, 08034, Barcelona, Spain. Tel.: + 34 699 896471. E-mail address: [email protected] (I. Vilajosana). 0165-232X/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.coldregions.2010.09.011
However, acquiring data on high-speed phenomena still remains a challenge. The description of the avalanche behavior needs to be supported by physical observations measured during chute and fullscale experiments (Dent et al., 1998). Classical methods such as image processing techniques give useful information on the shape and velocity of the avalanche, but they cannot track the internal structure. Non-intrusive methods (e.g., Doppler radar) give access to the internal structure of an avalanche but the obtained signals are difficult to interpret (Issler, 2003). Static sensors for measuring the impact pressure or snow density are also of common use but they only yield information at fixed places and their interpretation needs supplementary information (velocity measurements, density (Gauer et al., 2007)). In the last decade, a new generation of instruments has been used to study snow avalanches. Louge et al. (1997) have developed a capacitance probe that can be calibrated to measure snow density. Radar techniques have been improved to yield more accurate speed estimates (Gauer et al., 2007 and Rammer et al., 2007). Development of commercially available Laser Scanner systems allowed to obtain accurate measurements on avalanche mass balance (Sailer et al.,
I. Vilajosana et al. / Cold Regions Science and Technology 65 (2011) 242–250
2008) which was inconceivable some years ago. Ground Based SAR radars have also been successfully used to monitor avalanche activity (Martínez-Vázquez and Fortuny-Guasch, 2005). In addition, smallscale experiments in laboratory chutes have become increasingly popular and a large number of experiments have been carried out in the past years (Issler, 2003), (Dent et al., 1998). It is obvious that experiments under controllable and reproducible conditions become the ideal scenery for developing new measuring techniques especially for snow avalanche research. As an example, the usage of high-speed cameras has been popularized in chute experiments. Their measurements combined with new data processing methodologies brought successful results related to avalanche dynamics (McElwaine and Nishimura, 2001), (Biancardi et al., 2005). There is also a unique approach to nonintrusively track a particle in the avalanche flow that was presented in a series of two papers by Dave and Bukiet (1998) and Dave et al. (1998). Specifically, they proposed a system, which is based on the principle of magnetic induction coupling and consists of small transmitters mounted inside the particle being tracked and a set of receiving antennae surrounding the experimental apparatus. In Part I of the sequence of two papers, they focus on the theoretical aspects, in particular, on developing a computational technique to solve the inverse problem of finding the three-dimensional position as well as orientation of the particle from the voltages induced in the antennae. In the second part (Dave et al., 1998) they focus on the system development, including all hardware and data acquisition aspects. In that work, (Dave and Bukiet, 1998) they demonstrate the wide applicability of the system due to its non-intrusive nature, especially when optical tracking techniques are not feasible. However, the system presents also some drawbacks. Mainly the requirement of using multiple receiving antennae limits the applicability to chute experiments where antennae could be easily installed. Nowadays, emerging technologies have the potential to provide environmental information in an unprecedented scale. For example, the wireless sensor networks which were developed for military purposes (Warneke et al., 2001) have presented a tremendous increase of application in many fields due to their specific characteristics: low power, low cost and wireless communications. These characteristics are what also made them very “attractive” for exploring natural phenomena. In this work this technology will be used to obtain information from the internal dynamics of snow avalanches. The University of Barcelona (UB) Avalanche Group in collaboration with the Distributed Systems and Computer Networks at the Open University of Catalonia (UOC) are developing a new type of sensors that will overcome the current limitations imposed by avalanche nature. The main objective is to track the motion of each sensor while flowing in the avalanche body as if they were snow clods and in addition, to measure complementary properties (temperature, density). It is obvious that such an ambitious goal requires a clear road map and previous experimentations under more controlled conditions. In this sense, the large snow chute of the WSL Swiss Federal Institute of Snow and Avalanche Research (SLF) located at Weissflühjoch, Switzerland becomes an ideal scenario for testing this technology. In this paper we present a series of experiments at the Weissflühjoch Snow Chute, where specifically designed WSN nodes were released inside the avalanche flow. Specifically, we focus on the determination of the position of the sensors as a function of time when they travel in the flow. 2D accelerometers connected to a wireless micro-device were employed as a first attempt to use wireless technology for snow avalanche dynamics studies.
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sensor arrays, load cells, high-speed camera, and ultrasonic sensor (Tiefenbacher & Kern, 2004). The SLF Snow Chute is described in more detail in Tiefenbacher and Kern (2004). A schematic picture of the chute is provided in Fig. 1. The chute consists of a 10 m long reservoir, a 10 m long acceleration section followed by a 4 m long measurement section and, finally, a 6 m long run-out zone. In the experiments the slope of the two uppermost moveable sections of the chute was set to 45°. The slope of the measurement section was 40° and in the run-out zone was 8°. In the acceleration section and the measurement section rubber mats cover and roughen the smooth running surface of the chute. The rubber mats have a width of 6 cm and a stream wise spacing of 2.5 cm. In the experiments snow stuck in the void spaces and sliding conditions similar to natural avalanches were produced. Up to 15 m3 of snow was released from the storage part by opening a shutter door forming artificial avalanches. The front velocities of the test avalanches were in the range of 6 m/s to 14 m/s obtained from optoelectronic sensors and video images and flow heights up to 1 m were generated depending on the filling volume and snow properties. The snow chute reservoir was filled with considerable effort of manpower: snow surrounding the chute was shoveled in by hand. Before each experiment the snow density and snow temperature inside the reservoir were measured and grain sizes and forms were determined. The air temperature was measured as well. The wireless units used in this experiment are based on a commercial development platform for wireless sensor network applications. Specifically, the core of each wireless sensor node is based on the telosb platform (Polastre et al., 2005). The telosb is used as a node on the wireless sensor network. It features a Texas Instruments MSP430 microcontroller, 48 Kbytes of program memory, 10 Kbytes of static RAM, 1 Mbyte of external flash memory, and a 2.4-GHz Chipcon CC2420 IEEE 802.15.4 radio. The telosb was designed to run TinyOS (TinyOs: Operating System, web page http://tinyos.net/). The election of the telosb platform is justified because the MSP430 microprocessor provides several configurable ports that easily support external devices. The large amount of flash memory available in that device was useful for buffering the collected data. In each unit the sensor used was an accelerometer MMA6260Q (http://www.freescale.com/). It is a 2 axis capacitive micro-machined accelerometer featuring signal conditioning, a 1-pole low pass filter and temperature compensation. This sensor has a linear output with high signal to noise ratio, low power consumption and high sensitivity. The typical sensitivity is 800 mV/g with a characteristic acceleration range of ± 1.5g. The accelerometer used is capable of measuring accelerations over a
2. Instruments and experimental site The large snow chute located at Weissflühjoch 2670 M.A.S.L. is equipped with different type of sensors including optoelectronic
Fig. 1. Scheme showing the snow chute geometry and position of the available sensors.
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bandwidth of 1.5 kHz for all three axes. The analog output is sampled using the microcontroller's embedded 12 bit A/D converter. A single sensor node was constituted by the sensor board, the interface board and a battery holder with two AA batteries. These parts, were housed inside a rugged PVC weatherproof and watertight case (Fig. 2). Care was taken in the sensor design to have a sensor density ranging from 200 kg / m3 to 500 kg / m3 to ensure that the sensors remain on the avalanche surface. The whole software was developed using the TinyOS 2.x (TinyOs: Operating System, web page http://tinyos.net/) operating system. TinyOS is a wireless sensor network specific operating system that follows an event-driven programming model. The programming language is nesC which is an extension of C that incorporates the concept of components and bidirectional interfaces. Components allow programmers to encapsulate the behavior of the different parts of the program independently. The communication between the components was achieved by the use of bidirectional interfaces. This approach makes the collaboration between different programmers easier, ensures cleaner code, and facilitates reutilization. Four different experiments were carried out during the period 02/ 02/2008 and 02/04/2008. In each experiments, after filling up the reservoir and tilting up the chute to its maximum inclination (45°), two units were placed over the snow surface, 1.5 to 3 m uphill the gate. Once the gate was opened the units released with the flow traveling downslope as particle clods. The sensor data were time stamped to have a common base of time to facilitate comparison between the different units. Apart of the data from the available sensors, video images, shear force measurements at the base of the avalanche and velocity obtained with two independent measurement systems were recorded during the experiments. Fig. 3 shows snapshots of the small-scale dry-mixed avalanche released on 02/04/2008 (Experiment 4.2.2). Red circles indicate the position of the two units. 3. Methodology Acceleration readings from the two axis accelerometers were analyzed to obtain the velocity and position of the unit inside the avalanche flow. It is well known that accelerometers are very good to provide local accelerations. However, they are inaccurate to provide velocity and position estimates through direct numerical integration (Britting, 1971). Accelerometers measure the force per unit of mass acting on a body along a specific sensing direction. The vector sum of this force per unit of mass and the gravity acceleration, is the inertial acceleration of the body, which is the value of our interest. To this end we developed a methodology based on the Empirical Mode
Decomposition (Huang et al., 1998), and Kalman filtering (Kalman, 1960) to estimate the velocity and position of the sensors along the path minimizing the different sources of error. Specifically, we focused on filtering out the gravity component effects from the data. Numerical integration errors, and random errors from sensor collisions with surrounding snow clods and chute walls were also considered. Empirical Mode Decomposition (EMD) was used to subtract the gravity component from the acceleration readings. Essentially, this methodology allows decomposing any data set into a finite number of intrinsic mode functions (IMFs) which constitute the empirically determined basis for our data. Each IMF represents a simple oscillatory mode similar to a component in the Fourier-based methodology. The EMD explores temporal variations in the characteristic time scale of the data and in consequence, it is adaptive to nonlinear and nonstationary data processes like the inclination of the snow surface running downhill the chute. The crucial step in the application of this data analysis technique is to determine the independent IMF through an iterative process, which was first described by Huang et al. (1998) and is summarized below. The main idea behind this methodology is to determine the different time scales that are present in the data. Three methods for measuring the time scales were defined in Huang et al. (1999): the time between successive zero crossings, the time between successive extremes, and the time between successive curvature extremes. In each case, the time interval is a local measure of the time variation of the events. Extremes and curvature intervals show a local time scale that indicates whether the data cross the zero line or not. The aim of the process is to define a local time scale of oscillation that starts at one extreme, crosses zero, and reaches the extreme of the opposite sign. The period of this oscillation gives the characteristic time scale. It is local and represents only one mode of oscillation. An iterative procedure is used to determine the different IMF from the data. The first step consists of identifying all the local extremes. All the obtained local maxima are connected by a cubic spline line as the upper envelope. The same procedure is repeated for the minima values to produce the lower envelope. The arithmetical mean between the maxima and the minima envelopes is designated as m1(t), and the difference between the data X(t) and m1(t) becomes the first component, h1(t) i.e.: X ðt Þ−m1 ðt Þ = h1 ðt Þ
ð1Þ
Ideally, h1(t) should be the first IMF extracted from our data. However, local heterogeneities in the time series (small changes in curvature, data overshoots and undershoots) underlie hidden local
Fig. 2. Waterproof packaging and sensor node. Unit size 14 × 8 cm.
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Fig. 3. Snapshots of the first instants of one experiment. Red circles indicate the deployed sensors.
maxima or minima, which can be extracted if, in the next step, we consider h1(t) to be our data. h1 ðt Þ−m11 ðt Þ = h11 ðt Þ
ð2Þ
where m11(t) is the mean value of the new envelope obtained from h1(t). This iterative procedure is called Sifting, and basically aims to eliminate riding waves from the data and make the data profiles more symmetric. The Sifting procedure can be repeated k times until h1k is obtained as IMF. This h1k(t) is considered the first component of the data, c1(t), and it would be much more symmetric than h1(t). c1 ðt Þ = h1k ðt Þ
ð3Þ
The Sifting process, however, should be applied with care owing that too many Sifting steps could convert the resulting IMF in a pure frequency-modulated signal of constant amplitude. In order to guarantee that the final IMF obtained from the Sifting process has enough physical meaning a stopping criterion was determined by Huang et al. (1999). These authors suggested that an appropriate stopping criterion could be achieved simply by limiting to three the repetition of Sifting steps in which the same number of zero crossings and extremes is obtained. Once the stopping criteria are satisfied, the first component contained in the data, c1(t), is determined. It represents the finest scale (highest frequency) contained in the data. Removing this component from the data X(t) we obtain r1(t) r1 ðt Þ = X ðt Þ−c1 ðt Þ
ð4Þ
Since r1(t) still contains information on the longer period scales, it is treated in a similar way as the data and the Sifting procedure is repeated until the remainder becomes a monocomponent signal and no more components can be extracted. After this procedure our data can be represented as the sum of N orthogonal modes and a remainder. N
X ðt Þ = ∑ cj ðt Þ + rN ðt Þ j=1
ð5Þ
In our case, we observed that the remainder corresponds to the gravity component due to the path curvature and hence this IMF could be filtered out from the data. Once the gravity component was removed from the data, the Kalman filtering technique based on a ballistic model (Kalman, 1960) was used to estimate the velocity and the position of the sensors. In this case we assume the sensor as a mass block traveling on the slope. Elementary laws of physics say that the relationship between the velocity in one step vk and the one in the following time step vk + 1 is: vk
+ 1
= vk + ak ⋅ΔT
ð6Þ
where ak is the acceleration in time step k and ΔT the interval of time. However, a more realistic equation for vk + 1 taking into account the velocity noise due to collisions with snow clods and random collisions with the surrounding snow is: vk
+ 1
= vk + ak ⋅ΔT + ek
ð7Þ
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3 ΔT 2 is called the transition matrix, B = 4 2 5 the ΔT input matrix, C = ½ 1 0 the measurement matrix, zk the measurement noise and yk the position measurement. We assume that the process noise, wk, and the measurement noise, zk, follow a Gaussian distribution with zero mean and no correlation exists between them. In consequence, the measurement noise and process noise covariance matrices Sm and Sp could be obtained as:
1 where A = 0
considering an additional term ek for the velocity noise (we assume the velocity noise to be a random variable that changes with time). A similar equation can be derived for the position x: xk + 1 = xk + vk ⋅ΔT +
uk ⋅ΔT 2
2
ð8Þ
+ wk
where wk is the position error. According to these equations we can define a state vector rk that consists of the position and velocity vectors: rk = ½vk xk
T
Since the measured output is the unit position, a linear system of equations can be written as follows:
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b
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Residual imf11 imf10
imf6 imf5 imf4 imf3 imf2 imf1 signal
0.1 0 -0.1
ð11Þ
where wT and zT indicate the transpose of the w and z random noise vectors, and E(⋅) means the expected value.
ð10Þ
a 7 6.5 6
2
Sw = E w ⋅wT T Sz = E z ⋅z
ð9Þ
rk + 1 = A ⋅rk + B ⋅ ak + wk yk = C ⋅rk + zk
ΔT 1
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Time(s) Fig. 4. a) and b), IMF of the acceleration readings from 30 s of data prior to an avalanche test. c) Top: detrended acceleration readings, middle calculated slope angle, bottom, velocity and position obtained using the EMD and Kalman filtering combined methodology.
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At this point we can use Kalman filtering estimation equations as presented by (Welch & Bishop, 2001). Kk = APk C
T
−1 T CPk C + Sz
ð12Þ
rˆk
+ 1
= A rˆk + Bak + Kk yk + 1 −C rˆ k
Pk
+ 1
= APk A + Sw −APk C Sz CPk A
T
T −1
T
ð13Þ ð14Þ
where matrix K is called the Kalman gain and P is the estimation error covariance (Kalman, 1960). The generic term of the state estimate equation at time kð rˆk Þ derives the state estimate at time k + 1 which is only A times the state estimate at time k, plus B times the known input at time k. The second term in Eq. (13) is called the correction term and it represents the amount by which to correct the propagated state estimate due to the process and the measurement errors. In the experiments, we used as an acceptable position error estimate 0.3 m. The commanded acceleration was obtained from the accelerometer readings. The acceleration noise was set as one standard deviation of the acceleration readings. Acceleration noise was obtained from each independent sensor and experiment from the analysis of 2 s of data recorded before each experiment. In that period the sensors were laying on the snow surface. In Fig. 4 an example of the application of the EMD and Kalman filtering combined methodology is presented. Figs. 4a and b show the different IMF from 30 s of acceleration data obtained prior to an avalanche test release. Note that the different intrinsic mode functions are presented in Blue and the residual in Red. We attribute the latter to the gravity component. This fact allows us to eliminate gravity component effects from the data. In Fig. 4c, the accelerometer raw data and the slope angle determined from the slope normal component acceleration readings are presented. At the lowest part of the figure, the detrended slope tangential acceleration readings filtered out using the Kalman filter are presented. As a result estimates of the sensor position and velocity laying on the surface of the snow were obtained. Fig. 4c shows that the obtained velocity remains zero for about 26 s highlighting the potential of this methodology to minimize numerical integration errors when determining velocity and position from direct integration of acceleration readings. 4. Data analysis and results
Fig. 5. Normal (green) and tangential (blue) acceleration readings from the experiment 2.2.1 released on 02/02/2008 (right) and from the experiment 4.4.2 released on 02/04/ 2008. The arrow shows the instant of the avalanche release.
Data from the experiments released on winter 2008–2009 at the Weissflühjoch Snow Chute using wireless accelerometers were analyzed. In Fig. 5, the normal and the tangential accelerations obtained in the experiment 2.2.1 released on 02/02/2008 and the experiment 4.4.2 released on 02/04/2008 are presented. Avalanche kg 2.2.1 was a fresh snow dry avalanche with a snow density of 0:233 m 3 and a snow temperature of − 8.7°. Avalanche 4.4.2 was a dense wet kg avalanche with a snow density of 0:466 m 3 and a snow temperature of − 8°. The initial (approx) 5.5 s of data corresponds to the sensors laying on the snow surface before the experiment. Note that the slope angle, θ, can be recovered from these readings assuming that at = g ⋅ cos(θ) (because the inertial acceleration is 0). After opening the gate, (arrows Fig. 5a and b), a sudden decrease of the force per unit of mass is observed in the time series of the normal and tangential components. This decrease corresponds, as expected, to an increase of the inertial acceleration undergone by the unit. In both experiments, during the first 2 s of motion the sensors traveled in a straight line in the flow (observed from video images). The motion of the sensors in this window of time (5–7 s) shows an erratic shifting between acceleration and deceleration phases.
This behavior is also observed in the other experiments, not presented here. The mean retarding acceleration, however, is rather constant. This behavior was also observed in full-scale avalanches analyzing Doppler radar measurements (Gauer et al., 2007). During the most stable phase of the measurements in Experiment 2.2.1 the mean retarding acceleration, aret is 3.7m / s2 (from 5.4 to 6.4 s Fig. 5a). If we assume for simplicity aret = g ⋅ sin(θ) − μ ⋅ cos(θ) and θ = 45° results μ = 0.24. For the 4.4.2 experiment the mean retarding acceleration is 0.84m / s2 (from t = 5.5 s to t = 6.5 s) which yields a Coulomb friction coefficient of μ = 0.44. The obtained values of μ seem reasonable according to the type of flow and snow released. In both experiments after a period of stability, the acceleration becomes more erratic due to the impacts of the sensors with the chute, snow clods and sensor rotation. Afterwards, the dynamic component of acceleration becomes zero again showing that the units stopped. Note that the unit stayed upside down as indicated by the negative value of the measured acceleration. In Fig. 6 the velocity (dashed line) and position (continuous line) estimates of the two sensors released in the 4.4.2 experiment are
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presented. Raw position estimates are also depicted in red dotted lines. For comparison purposes, in the same figure the position estimates from simultaneously obtained video images are also presented (squares and triangles). The position estimates from the video images show good agreement with those obtained from the wireless sensors. Complementary punctual speed measurements using optoelectronic sensor arrays were used to track the velocity of the sensors at the wedge (Fig. 1). The pink line in Fig. 6 indicates the wedge position where punctual speed estimates were obtained. The velocity profiles obtained for the 4.4.2 experiment from the array of optoelectronic sensors are shown in Fig. 7. The data from the optoelectronic sensor array corresponds to a time averaged velocity profile over the avalanche event. The error bars correspond to one standard deviation of the velocity signals in the time window. The comparison between the velocity estimates obtained using inflow sensors and from optoelectronic sensor array measurements show that inflow sensors provide higher speed estimates than optoelectronic sensors. This result was expected according to the different velocities measured: Whereas the inflow sensors were traveling on top of the flow about
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50 cm from the bottom of the avalanche, the velocity profiles obtained from the optoelectronic sensors show velocities from the bottom of the flow (first 8–10 cm) where boundary effects are more important. The velocity profiles obtained from the 4.4.2 event show 8 m/s as the maximum speed. The maximum speed obtained from wireless sensors at the wedge for the two sensors are 12.5 m/s and 14 m/s respectively. The physical parameters obtained for the dry avalanche released on 02/02/2008 (exp. 2.2.1) are shown in Fig. 8. In a similar representation as Fig. 6 the velocity (dashed line) and position (continuous line) estimates of the two sensors released are presented. Again position estimates from video images show significant agreement with wireless sensor estimates. In Fig. 9 the velocity profile obtained from the array of optoelectronic sensors is presented. The velocity profile from this event shows a maximum velocity of 6.5 m/s at 7.5 cm from the ground. Speed estimates from wireless sensors at the wedge show again higher values (9.5 m/s). 5. Conclusions Specially designed wireless accelerometer units were used in a series of experiments at the snow chute operated by the SLF at Weissflühjoch (Switzerland). The main goal was to evaluate their capability to provide information on the internal dynamics of flowing snow. The experiments showed the validity of the sensors to be deployed in small-scale avalanche experiments. The units demonstrated to be robust and able to intercommunicate wirelessly between few centimeters under the snow. Data from 4 different experiments were obtained, however in this paper only two of them are presented. A methodology based on the Empirical Mode Decomposition (Huang et al., 1998) and Kalman filtering (Kalman, 1960) was developed to determine the position and the velocity of the sensors traveling inside the flow from the acceleration readings. Reproducibility was observed in the acceleration readings from the different experiments. Acceleration measurements during the initial stages of motion showed an erratic oscillation along the main driving force as also observed by Gauer et al. (2007) in full-scale avalanches based on Doppler radar measurements. Position estimates obtained from the acceleration readings showed good agreement with the independent position estimates obtained from video images. Wireless sensor velocity estimates were also compared to velocity estimates from correlation of
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optoelectronic sensor array measurements. In all the cases wireless sensor estimates showed higher values than that of optoelectronic sensors. This fact is attributed to the higher position in the flow of the wireless sensors in relation with the optoelectronic sensors. Wireless sensors were traveling on the flow surface (about 50 cm above the ground) and the optoelectronic sensors measured the shearing layer ranging from 0 cm to 10 cm. Overall, the results show to be in agreement with that obtained from independent speed measurements from optoelectronic sensors and video images and open a new perspective for future avalanche research. The information provided by the units shows the potential of new technologies to provide valuable data related to internal dynamics of snow avalanches. Tracer sensors like the ones presented here if combined with non-intrusive systems like proposed by Dave and Bukiet (1998) and Dave et al. (1998) could provide a pseudo-Lagrangian perspective on the flow dynamics as they are transported along with the flow. We believe, that such sensors are crucial for studying the flow dynamics as they have typically provided much better temporal resolution than non-invasive methods. Moreover, they could provide better detail of the vertical structure of the flow at-a-point. Future experiments shall go in this direction, especially at small-scale chutes. 0.08 0.07
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We consider small-scale sites essential to develop and test new instrumentation (to be deployed), in the future, in full-scale experiments. In addition, the experiments performed show for the first time the potential of the wireless technologies and wireless sensors to study snow avalanches. Acknowledgements We are indebted to our colleagues at the SLF for their help in our shoveling stage. We also would like to thank the financial support of projects MICINN: DALMASA (CGL2006-06596/BTE), and Consolider (CSD2006-00041). I.V is supported by a Torres Quevedo grant from the Spanish Ministerio de Ciencia e Innovacin 2008-03-08109. References Ammann, W.J., 1999. A new Swiss test-site for avalanche experiments in the Valle de la Sionne. Cold Regions Science and Technology 30 (1–3), 3–11. Biancardi, A., Ghilardi, P., Pagliardi, M., 2005. Automatic mask extraction for PIV-based dam-break analysis. IbPRIA 2, 705–712. Britting, K.R., 1971. Inertial Navigation System Analysis. Wiley, New York. 116–119. Dave, R.N., Bukiet, Bruce G., 1998. Nonintrusive rigid body tracking technique for dry particulate flows. Part I. Theoretical aspects. Review of Scientific Instruments 69 (10), 3598–3605. doi:10.1063/1.1149145. Dave, R.N., Voicy, J., Agarwal, J., Gupta, V., 1998. Non-intrusive rigid body tracking technique for dry particulate flows, Part II: practical aspects and implementation. Review of Scientific Instruments 69 (10), 3606–3613. Dent, J., Burrel, K., Schmidt, D., Louge, M., Adams, E., Jazbutis, T., 1998. Density, velocity and friction measurements in a dry snow avalanche. Annals of Glaciology 26, 247252. Gauer, P., Issler, D., Lied, K., Kristensen, K., Iwe, H., Lied, E., Rammer, L., Schreiber, H., 2007. On full-scale avalanche measurements at the Ryggfonn test site, Norway. Cold Regions Science and Technology, Amsterdam 50 (1–3), 55–71. Huang, N.E., Shen, Z., Long, S.R., Wu, M.C., Shih, E.H., Zheng, Q., Tung, C.C., Liu, H.H., 1998. The empirical mode decomposition method and the Hilbert spectrum for non-stationary time series analysis. Proceedings of the Royal Society of London 454, 903–995. Huang, N., Shen, Z., Long, S., 1999. A new view of nonlinear water waves: the Hilbert Spectrum. Annual Reviews in Fluid Mechanics 31, 417–457. http://www.freescale.com/. Issler, D., 2003. Experimental information on the dynamics of dry-snow avalanches. In: Hutter, K., Kirchner, N. (Eds.), Dynamic response of granular and porous materials under large and catastrophic deformations: Lecture Notes in Applied and Computational Mechanics, 11, pp. 109–160. Kalman, R.E., 1960. A new approach to linear filtering and prediction problems. Transaction of the ASME Journal of Basic Engineering 82, 35–45. Lied, K., Moe, A., Kristensen, K., Issler, D., 2002. Snow Avalanche Research Programme SIP-6. Ryggfonn. Full scale avalanche test site and the effect of the catching dam. Technical Report 581200-35, Norwegian Geotechnical Institute. Louge, M.Y., Steiner, R., Keast, S., Decker, R., Dent, J., Schneebeli, M., 1997. Application of capacitance instrumentation to the measurement of density and velocity of flowing snow. Cold Regions Science and Technology 25 (1), 47–63.
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