Error sensitivity of the connected vehicle approach to pavement performance evaluations

Transcription

1 Pre-Print Manuscript of Article: Bridgelall, R., Rahman, T., Daleiden, J. F., Tollier, D., Error sensitiity of the connected ehicle approach to paement performance ealuations, International Journal of Paement Engineering, pp. 1-6, March 8, 016. Error sensitiity of the connected ehicle approach to paement performance ealuations Raj Bridgelall 1, Md Tahmidur Rahman, Jerome F. Daleiden 3, Dener Tollier 4 Upper Great Plains Transportation Institute, North Dakota State Uniersity, Fargo, ND, USA Fugro Roadware Inc., Austin, TX, USA 1 Raj Bridgelall (Corresponding Author): P.O. Box , Plano, TX, 75086; Phone ; raj@bridgelall.com Fugro Roadware, Inc., 8613 Cross Park Drie, Austin, TX 78754; Phone: ; trahman@fugro.com 3 Jerome F. Daleiden: Fugro Roadware, Inc., 8613 Cross Park Drie, Austin, TX 78754; Phone: ; jdaleiden@fugro.com 4 Dener Tollier: P.O. Box 6050, Fargo, ND 58108; Phone ; dener.tollier@ndsu.edu The Uniersity Transportation Centre, a program of the United States Department of Transportation, sponsored this research through its Mountain Plains Consortium (MPC) under grant DTRT1-G-UTC08. Abstract The international roughness index is the prealent indicator used to assess and forecast road maintenance needs. The fixed parameters of its simulation model proide the adantage of requiring relatiely few traersals to produce a consistent index. Howeer, the static parameters also cause the model to under-represent roughness that riders experience from profile waelengths outside of the model s response range. A connected ehicle method that uses a similar but different index to characterize roughness can do so by accounting for all ibration waelengths that the actual ehicles experience. This study characterizes and compares the precision of each method. The field studies indicate that within 7 traersals, the connected ehicle approach could achiee the same leel of precision as the procedure used to produce the international roughness index. For a gien ehicle and segment lengths longer than 50 meters, the margin-of-error diminished below 1.5% after 50 traersals, and continued to improe further as the traersal olume grew. Practitioners deeloping new tools to ealuate paement performance will benefit from this study by understanding the precision trade-off to recommend best practices in utilizing the connected ehicle method. Keywords: connected ehicle; GPS; inertial profiler; measurement precision; paement management; probe ehicles; ride quality; smartphone Raj Bridgelall et al. Page 1/18

2 1 Introduction Transportation agencies rely on the regular reporting of paement performance to prioritize maintenance needs. Existing methods of smoothness (or roughness) characterizations that use the international roughness index (IRI) are difficult or impractical to apply on unpaed roads and in most urban settings (Karamihas 015). In particular, interrupted flow conditions generally diminish the accuracy of the present data collection methods. These deficiencies coupled with the relatiely high cost to acquire, maintain, and operate inertial profilers has motiated the search for alternatie methods. Subsequently, transportation agencies are ealuating connected ehicle approaches because of their potential to proide affordable, continuous, and network-wide coerage. Connected ehicle methods rely on the inertial and geospatial position data from common on-board accelerometers and GPS receiers. The authors preiously deeloped and demonstrated the road impact factor (RIF) transform to process oluminous data from connected ehicle sources (Bridgelall 014a). The transform is a mathematical model that integrates the inertial, speed, and geospatial position data streams across a gien segment length to produce a roughness index called the RIF-index. Other work described the theories and experiments showing that within any selected speed band, RIF-indices are directly proportional to the IRI (Bridgelall 014b). Practitioners hae long recognized that the IRI mischaracterizes roughness that riders experience (Ahlin and Granlund 00). Specifically, the fixed quarter-car (Golden Car) parameters and the precise reference speed of the IRI procedure result in a spatial waelength bias (Papagiannakis 1997). Traersing spatial waelengths at different speeds produce temporal waelengths at frequencies that coincide with the resonant modes of ehicle suspension system to amplify ride roughness (ak, Degrande and ombaert 011). Raj Bridgelall et al. Page /18

3 The RIF-transform precludes waelength bias by reporting the roughness that riders actually experienced at the speed that they traelled, and in their real ehicles (Bridgelall 015). Unlike the IRI that uses a precise speed of 80 km h -1, the RIF-transform uses the actual speed traelled. Therefore, the notation for RIF-indices includes a subscript to indicate the aerage traersal speed in a speed band. Preious studies described the tradeoff in selecting the width of the speed band, and the number of traersals needed to achiee some desired leel of precision (Bridgelall 015). The aerage RIF-index from a specified speed band is analogous to the aerage IRI reported from multiple traersals of a facility. As anticipated, the fixed quarter-car model and the precise reference speed of 80 km h -1 results in a relatiely high consistency of IRI reporting. Conersely, the connected ehicle method reflects ariations in the actual speed, suspension system behaiour, and sensor characteristics. The main objecties of this study are to: (1) characterize the practically achieable precision of the connected ehicle method, () identify the dominant parameters that contribute to precision dilution, (3) ealuate the relatie impacts from each parameter, and (4) quantify the number of traersals needed to report RIF-indices with the same leel of precision as the IRI procedure. Preious work examined the impact from ariations in accelerometer sample rate, ehicle speed, and suspension system performance for a typical mix of ehicles in the traffic stream. Those studies found that the dilution of precision becomes insignificant when the sample rate of the accelerometer exceeds 64 Hertz (Bridgelall 015), and when the traersal olume exceeds 50 (Bridgelall 014b). The method of this study isolates the Raj Bridgelall et al. Page 3/18

4 impact from ariation in the analysed traersal path by fixing the accelerometer sample rate to a alue much higher than 64 Hertz, using the same ehicle for multiple traersals, and traeling the same test segment with more careful speed regulation. Practitioners deeloping new tools to ealuate paement performance will benefit from this study by understanding the trade-off to produce guidelines for best practices when deploying the connected ehicle methods. The organization of this paper is as follows: the next section will reiew the RIFtransform and theoretically characterize the significance of factors that dilute the precision of measurements. The third section will describe the field experiments conducted to quantify the relatie impact from ariations in the analysed traersal path. The fourth section will discuss the trade-off in precision and traersal olume as a function of the minimum segment length analysed. The final section will summarize and conclude the study. The connected ehicle approach to measuring paement roughness Gien the highly specialized area of paement performance ealuations, few other researchers hae deeloped methods to transform sensor data from connected ehicles to characterize roughness. Preious work that attempted to relate the accelerometer signal to the IRI witnessed a speed dependency but did not establish a mathematical characterization to explain the behaiour obsered (Dawkins et al. 011, Du et al. 014). Related research inestigated participatory sensing approaches that would identify clusters of roughness reports from riders to suggest the locations of possible anomalies such as potholes (Byrne et al. 013). Methods that directly analyse the accelerometer signal stream from indiidual ehicles used short-time spectral transforms to identify the signatures of anomalies (Ayenu- Raj Bridgelall et al. Page 4/18

5 Prah and Attoh-Okine 009). Some methods attempt to recoer the road profile by double integration of the accelerometer signal (Islam et al. 014, Nomura and Shiraishi 015). Approaches that are more recent inestigated signal classification ia machine learning techniques to identify possible anomalies (Rajamohan, Gannu and Rajan 015). The next sections reiew the connected ehicle method of characterizing paement roughness in terms of the RIF-index. Preious work (Bridgelall et al. 014) established that the fusion of sensor data from many connected ehicles is a primary factor in its superiority oer other approaches that can afford ery few traersals. The deriation of a model to characterize the indiidual error contributors will establish a framework to guide the design of field experiments and the data processing to quantify the proportional error contributions..1 Inertial signal transformation For indiidual ehicle traersals, the RIF-transform produces a measure of localized roughness such that 1 N 1 n0 z[ n] n R g t (1) where the RIF-index R is the aerage g-force magnitude experienced per unit of distance when traelling at an aerage speed of (Bridgelall 014a). An on-board accelerometer produces the ertical acceleration g z[n] for signal sample n of N total samples. A speed sensor produces the instantaneous traersal speed n. Preious research established that the aerage sample period δt should be at least 64 Hertz (Bridgelall 014b). Increasing the sample rate beyond 64 Hertz does increase the leel of measurement consistency for a Raj Bridgelall et al. Page 5/18

6 gien traersal olume, but with diminishing returns beyond 100 Hertz. For situations when speed ariation is not a dominant factor in precision dilution, the expression for the RIF-transform is simplified by replacing the instantaneous speed with the aerage speed such that 1 N 1 n0 z[ n] R g t () et the linear energy density be defined as gz 1 N 1 n0 z[ n] E g t (3) that is, the signal energy per meter traelled. Hence, the units are in joules per meter when the output of the accelerometer signal is a oltage. Subsequently, for an aerage speed, the simplified RIF-transform is gz R E. (4) In the triial case where the traersal speed is zero, the RIF-index must be zero. It is important to distinguish this expression from the root-mean-square (RMS) of the signal samples. That is, the RMS is the square root of the signal energy per unit of time rather than distance. Substituting RMS of the accelerometer signal. That is, T into Equation () reeals the relationship with the R 1 T N 1 n0 g z[ n] t g (5) z_rms where T is the total traersal time of segment, traeling at the aerage speed. This subtle distinction is important and critical to expressing the non-linear behaiour of the Raj Bridgelall et al. Page 6/18

7 accelerometer output at different speeds.. Variance in measurements For a constant speed and a fixed quarter-car, the IRI will ary with differences in the eleation profile measurements among traersals. Howeer, ariations in the RIF-indices will include the effects of speed fluctuations. Other sources of errors include ariations in the traersal path, inertial sample interal, and ehicle suspension responses. From the classical theory of error propagation (Papoulis 1991), the standard deiation of the RIF- index, R is: R R R E gz Var R R E gz E gz E (6) where is the ariance of the batch mean speed among traersals. The coariance of the batch mean speed and the ertical acceleration signal energy is denoted the partial deriaties indicated in Equation (6) yields: E. Ealuating R E gz Var E (7) gz E Egz where E gz and are the aerages of the linear energy density of the ertical acceleration signal and the batch mean speed among traersals, respectiely..3 Proportional contribution to the spread in RIF-indices From equation (7), the proportional error contribution from ariations in speed is Raj Bridgelall et al. Page 7/18

8 E gz (8) R Therefore, the proportional contribution from the remaining errors E will be E 1. E gz (9) R We define the residual error E as all contributions to the spread in RIF-indices that result from ariations other than speed. Hence, gien a precise speed, the residual errors will reflect ariations in the traersal path, fluctuations in the sample interal, and ariations in the ehicle suspension response. Using the same ehicle and sensor for all traersals will minimize ariations in the suspension behaiour and the sample interal, respectiely. Therefore, ariations in the length and position of the traersal path would expectedly dominate the aggregate error obsered..4 Geo-fence triggering Connected ehicles use geo-fences to establish the lateral positions from where agencies wish to characterize and report roughness (Bridgelall 015). As shown in figure 1, a lateral geo-fence at position 0 identifies the start of the data section to be analysed. For a fixed GPS update rate, the actual starting position in the geospatially tagged data stream will ary about the precise geo-fence position as illustrated in figure 1. The final data point will be located at an interpolated segment length n such that n n 0 ktk (10) k1 Raj Bridgelall et al. Page 8/18

9 where k and t k are the instantaneous speed and time updates for the k th inertial sample. Figure 1 illustrates this data acquisition approach for two different path lengths a and b such that b >> a. Each line represents the geospatial position and length of the segment to be analysed from traersal data stream n. The length of the error interal σ depends on the GPS update rate, the statistics of the GPS position estimate, and the traersal speed. The corresponding ariations in traersal path positions and lengths translate to ariations in the RIF-indices reported. [Figure 1 near here]. Figure 1 illustrates a hypothetical eleation profile that would produce obious ariations in RIF-indices for the shorter path a, but not for the longer path b. That is, the shorter paths shown include the anomalies to arying degrees. Therefore, the corresponding a a set of RIF-indices R [ 1] R [ n] will reflect the proportion of the rough spot that the analysed path coers. Conersely, the longer path always includes all of the anomalies. Therefore, for fixed path lengths, the RIF-indices for the longer path in this scenario will exhibit no ariation. 3 Case studies The Minnesota Road Research Facility (MnROAD) is an outdoor laboratory that the Minnesota Department of Transportation operates in the U.S. to test the performance of different paement types (MnROAD 015). On June 10, 015, the authors used a certified and approed inertial profiler to collect simultaneously eleation profile and ertical acceleration data from a 70-meter section of Cell 40 to produce the IRI and RIF-indices, respectiely. The paement analysis ia ehicle electronic telemetry (PAVVET) application (app) for a smartphone (Bridgelall 014c) collected the inertial and speed data Raj Bridgelall et al. Page 9/18

10 at a mean sample rate of 93 Hertz, which was the maximum that the deice could practically achiee. The deice internally established a mean GPS update interal of approximately 1 second. The app collected data with the smartphone secured into a holster attached to the dashboard. The mean traersal speed of the inertial profiler was 80 km h -1. Table 1 summarizes the IRI and RIF-indices deried from the measurements. The inertial profiler was aailable to collect data for only N = 9 traersals. Operating errors on two of the traersals resulted in smartphone data losses, so those entries are not aailable in the table. [Table 1 near here]. To examine the data consistency, the analysis incorporated a larger PAVVET data set aailable from an experiment conducted on Cell 40 three months prior (Bridgelall et al. 016). The data set contained 53 traersal samples from a 011 Cherolet Traerse. The mean speed was 68 km h -1 (~4 mph) and the PAVVET app settings were identical. Table characterizes the roughness from the 70-meter traersals (last row), and the roughness across shorter length subsets (10-, 30-, 5-, and 50-meters) taken about the centre of the 70- meter segment. [Table near here]. The relatie margin-of-error (MOE) for the distribution of N T random ariables (Papoulis 1991), with significance within a (1-)% confidence interal, MOE (1-α), is MOE 1 t1 /, df (11) N T The t-score for a normalized cumulatie t-distribution with df degrees of freedom is t 1 /,df. The mean alue of the ariables is μ, and σ is the standard deiation. Hence, Raj Bridgelall et al. Page 10/18

11 MOE 95 is a relatie measure of the amount of spread about the mean alue for samples that fall within the 95% confidence interal. For example, the row before the last row of Table indicates that for the 50-meter segment, there was a 1.34% MOE 95 in measuring the RIFindex. Furthermore, a.8% ariation in speed (standard deiation/mean) accounted for 31.7% of the error, but the residual factors dominated at 68.3% contribution. Table 3 summarizes the error in GPS position tags relatie to the geo-fence. The mean error μ from the inertial profiler experiments were a factor (Δ μ ) of 1.36 times greater than the mean error from the prior experiments using the Cherolet Traerse. Similarly, the six-sigma error spread σ was a factor (Δ σ ) of.35 times greater. [Table 3 near here]. The proportional contribution of residual factors E to the spread in RIF-indices was more substantial for the inertial profiler experiments. The speed coefficient of ariation (CV), for the Cherolet Traerse was a factor of.31 times greater than the speed CV for the inertial profiler. Howeer, the error from residual factors, particularly GPS tagging errors, dominated in both cases. In fact, the use of a smartphone speed sensor may hae een resulted in an oer-estimation of the relatie contribution from speed errors. Therefore, using an actual connected ehicle speed sensor will retain the conclusion that errors from residual factors dominate. In addition to alidating the expectations from the theoretical deelopment, these experiments reeal the degree of relatie sensitiities to each of the dominant factors that users should expect in practice. Raj Bridgelall et al. Page 11/18

12 4 Results and discussion Figure plots the histogram of RIF-indices calculated from the inertial profiler (table 1) and the 011 Cherolet Traerse for the 70-meter traersal path length (table ). It is eident that the mean alues of the distributions practically agree. That is, the mean RIFindex from the inertial profiler and the Cherolet Traerse were and 0.181, respectiely. Speed ariations from the inertial profiler contributed only 1.7% to the spread in RIF-indices whereas the traersal path ariations from GPS position tagging errors contributed 98.3% to the error spread (table 3). GPS tagging errors were less seere for the experiments inoling the Cherolet Traerse, but there was more speed ariation. Hence, speed ariations contributed substantially more (39%) to the spread in RIF-indices from the Cherolet Traerse. Neertheless, in both cases the residual errors E dominated. This reciprocal relationship in residual error contributions from the spread in GPS position tagging σ relatie to speed ariations alidates the expectation from equation (9). [Figure near here]. Figure also plots the least squares fits of a Student t-distribution to the histograms. The t-distribution is appropriate for hypothesis testing of fewer than 30 samples, and approaches the Gaussian distribution for larger sample sizes (Agresti and Finlay 009). The significance alue for a chi-squared test statistic (χ ) of the agreement with the fit is n Ok Ek. (1) E k1 k The random ariables O k are the histogram alues obsered in bin k and E k are the expected alues of the hypothesized distribution. The significance alues for RIF-indices from the inertial profiler and Cherolet Traersal samples were 77.9% and 98.4%, respectiely. Raj Bridgelall et al. Page 1/18

13 Therefore, the chi-squared tests cannot reject the hypothesis that the distribution of RIFindices follows the classic distribution because the significance alues are much greater than 5%. This result proides confidence that the precision will continue to increase with the eer-increasing traersal olume of connected ehicles. Figure 3a proides further eidence that the MOE 95 for both the IRI and the RIFindex diminishes with increasing traersal olume. The MOE 95 for RIF-indices diminished below 1.5% as the traersal olume approached 50. In fact, for the 70-meter segment, the RIF-transform achieed the same leel of precision as the IRI procedure (4.4%) within seen traersals. Reducing the segment length by half increased the influence from GPS tagging errors as expected. Consequently, the RIF-index for the shorter segment required more than double the number of traersals (from 7 to 17) to achiee the same leel of precision as the IRI procedure. Figure 3b plots the MOE 95 for the RIF-indices (left axis) as a function of segment length. The exponential decrease to a point of diminishing returns indicates that the influence from GPS errors wane substantially for segment lengths that are greater than 50-meters. The proportional contribution from residual errors (right axis) diminishes exponentially from nearly 100% for 10-meter long segments to approximately 61% for the 70-meter long segments. [Figure 3 near here]. Oerall, this result indicates that the larger traersal olumes from connected ehicle enironments will yield eer-increasing leels of precision for any segment length, but the consistency will improe more rapidly for segments longer than 50 meters. 5 Summary and conclusions Affordable and scalable methods of measuring localized roughness enable improed Raj Bridgelall et al. Page 13/18

14 efficiencies and effectieness in the practice of paement asset management. Howeer, the prealent approach that relies on laser-based inertial profilers and the IRI is relatiely expensie to deploy for continuous network leel ealuations. Connected ehicle methods proide an attractie alternatie, but the approach requires higher traersal olume to achiee the same leel of precision as the IRI procedure. This study characterized the error contributors for the connected ehicle approach and conducted case studies to assess the conditions needed to achiee a desired leel of consistency. The IRI achiees relatiely high precision within few traersals because the procedure that produces the index uses a fixed quarter-car and a precise traersal speed. Conersely, connected ehicles rely on geo-fence triggering based on the geospatial position estimates from on-board GPS receiers. Therefore, ariations in position tagging the inertial data stream lead to larger ariations in the longitudinal traersal path analysed. Additionally, the roughness index deried from connected ehicle data reflects ariations in the actual ehicle suspension behaiour, traersal speed, and sensor parameters. The field studies conducted found that the connected ehicle approach could achiee the same leel of precision as the IRI procedure within 7 traersals. The results further indicate that for a gien ehicle and segment lengths larger than 50-meters, the margin-of-error in estimating RIF-indices diminished below 1.5% as the traersal olume exceed 50. Future research will utilize the connected ehicle method to examine the waelength composition of different paement types and establish a relationship with the power spectral density reported using the IRI procedure. Raj Bridgelall et al. Page 14/18

15 References The authors would also like to express their sincere appreciation to Mr. Thomas Burchett of Fugro Roadware for his contribution in data collection at MnROAD facilities. References Agresti, A., and Finlay, B., 009. Statistical Methods for the Social Sciences. 4th. City: Upper Saddle Rier: Pearson Prentice Hall Ahlin, K. and Granlund, N.J., 00. Relating road roughness and ehicle speeds to human whole body ibration and exposure limits. Int. J. Paement Eng., 3 (4), Ayenu-Prah, A.Y. and Attoh-Okine, N.O., 009. Comparatie study of Hilbert Huang transform, Fourier transform and waelet transform in paement profile analysis. Vehicle Syst. Dyn., 47 (4), Bridgelall, R., 014a. Connected ehicle approach for paement roughness ealuation. J. Infrastruct. Syst., 0 (1), 1-6. Bridgelall, R., 014b. Inertial sensor sample rate selection for ride quality measures. J. Infrastruct. Syst., 1 (), 1-5. Bridgelall, R., 014c. A participatory sensing approach to characterize ride quality. In: J.P. ynch, K-W. Wang, and H. Sohn, ed. Proc. SPIE 9061, Sensors and smart structures technologies for ciil, mechanical, and aerospace systems, 8 March 014, San Diego. Bellingham: International Society for Optics and Photonics (SPIE). Bridgelall, R, Precision bounds of paement distress localization with connected ehicle sensors. J. Infrastruct. Syst.,1 (1) 1-7. Bridgelall, R., Huang Y., Zhang Z., and Deng F., 016. Precision enhancement of paement roughness localization with connected ehicles. Meas. Sci. Technol., 7 () Byrne, M., Parry, T., Isola, R., and Dawson, A., 013. Identifying road defect information from smartphones. Road Transp. Res., (1), Dawkins, J., Bely, D., Powell, B., and Bishop, R., 011. Inestigation of Paement Maintenance Applications of Intellidrie. Pooled Fund Study, Charlottesille, Virginia: Uniersity of Virginia. Du, Y., iu, C., Wu, D., and Jiang, S., 014. Measurement of International Roughness Index by using z-axis accelerometers and GPS. Math. Probl. Eng., (014), Islam, S., Buttlar, W.G., Aldunate, R.G., and Varik, W.R., 014. Measurement of paement roughness using Android-based smartphone application. Transport Res. Rec., (457), Karamihas, S.M., 015. Measuring, Characterizing, and Reporting Paement Roughness of ow- Speed and Urban Roads. Research in Progress, Washington, D.C.: Transportation Research Board of the National Academies. Accessed October 1, ak, M.A., Degrande, G., and ombaert, G., 011. The influence of the paement type on groundborne ibrations due to road traffic. In: G. De Roeck, G. Degrande, G. ombaert and G. Müller, ed. Proc. 8th Intl. Conf. on Structural Dynamics. euen, Belgium: EURODYN Raj Bridgelall et al. Page 15/18

16 MnROAD, 015. Safer, Smarter, Sustainable Paements Through Innoatie Research. Brochure, Monticello, MN: Minnesota Department of Transportation. Nomura, T., and Shiraishi, Y., 015. A method for estimating road surface conditionsns with a smartphone. Int. J. Informatics Society, 7 (1), Papagiannakis, A.T., The Need for a New Paement Roughness Index; RIDE. International Truck & Bus Meeting & Exposition. Washington, D.C.: Society of Automotie Engineers International. Papoulis, A., Probalility, random ariables, and stochastic processes. New York: McGrawfor road Hill. Rajamohan, D., Gannu, B., and Rajan, K.S., 015. MAARGHA: a prototype system condition and surface type estimation by fusing multi-sensor data. ISPRS Int. J. Geo-Information, 4 (3), Zhou, Z., iu, W.Q., Huang, Y., Wang, H.P., Huang, M.H., and Ou, J.P., 01. Optical fiber Bragg grating sensor assembly for 3D strain monitoring and its case study in highway paement. Mech. Syst. Signal Pr., 8 (4), Figure 1. Measurement ariability decreases with longer analysis segments. Raj Bridgelall et al. Page 16/18

17 Figure. Distribution of RIF-indices from each ehicle for the 70-meter segment. a) MOE 95 45% 40% 35% 30% 5% 0% 15% 10% 5% 0% IRI Profiler = 70 m RIF Chey = 70 m RIF Chey = 35 m b) MOE 95 RIF Chey η E Contribution from Residual Factors Traersals Segment length (meters) Figure 3. Margin-of-error as a function of traersal olume and segment length. Raj Bridgelall et al. Page 17/18

18 Table 1. Roughness characterizations from the inertial profiler. N IRI 70 R80 (m/km) (g/m) (m s -1 ) (m s -1 ) Table. Roughness characterization from the Cherolet Traerse. R 68 MOE R 95 E gz E (m) (g/m) (g/m) (%) (m s -1 ) (m s -1 ) (Joules) (%) (%) E E E E E Table 3. Position error in GPS reference tags from the 70-meter segment traersals. Probe Vehicle N μ σ Δ μ Δ σ E (m) (m) (m) (m) (m s -1 ) (m s -1 ) (%) (%) Inertial Profiler Cherolet Traerse Raj Bridgelall et al. Page 18/18