Continuous high resolution surface profiling apparatus and method

Abstract

A surface profiler including at least one front support wheel and at least one rear support wheel for travelling along the surface of a profile to be measured, the rotational axes of said wheels being longitudinally spaced, and the wheels contacting the surface being profiled in a collinear manner. A frame carried on the wheels carries at least one inclinometer and at least two vertical distance measuring apparatus such as lasers, and may also carry an optical encoder. The lasers are collinear with each other and with the wheels. incremental to measurements of inclination angles provided by the inclinometer, together with incremental measurements of distance to the surface being measured provided by the lasers, produce a continuous, high resolution mathematical series of elevations representing the surface profile, including reproduction of surface features that are smaller than the distance between the wheels.

Description

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For a point P on the profile function E(x) mid-way between the rotational axes of the wheels and mid-way between the lasers, using principles of differential calculus, the slope at point P is:

$\mathrm{slope}=\frac{dy}{dx}$

For a right angle triangle having point P at its lower corner, the hypotenuse has the slope of a tangential line intersecting P that forms the angle θ with the horizontal plane of the earth. The slope at point P is given by the angle θ. The mean value theorem states that a point P on the profile between the points of contact of the lasers on the profile must have the same slope as that defined by the points of contact of the lasers on the profile. We estimate that this value occurs at the mid-point between the lasers:

$\mathrm{slope}=\sin \left(\theta \right)$ $\sin \theta =\frac{dy}{dx}$

We see that for a very small incremental change in horizontal distance Δx there will be a corresponding very small change in elevation ΔE according to the profile slope at point P as determined by the angle θ. For very small incremental changes in horizontal distance Δx, for example less than 1 mm, and elevation ΔE:

$\sin \theta =\frac{\Delta E}{\Delta x}$

ΔD is the distance travelled by the profiler 10 along the surface being measured. The distance is preferably measured at or very near the mid-point between the lasers for greatest accuracy. Otherwise, a ΔD error may be introduced wherever the slope at the location of the non-contact sensors differs from the slope at the location of the distance sensor. As an example, FIG. 9 illustrates a configuration with a measuring unit remote from the midpoint of the profiler frame. Clearly there can be situations where the midpoint profile is horizontal but the remote distance measuring wheel traverses up a bump or down a dip, where the profile has large positive or negative slope. In this example the distance measuring unit 26 will record a larger value of ΔD than the actual value observed at the mid-point of only ΔD cos ϕ. The opposite may also occur. The ΔD error results in an incorrect calculation of ΔE and an incorrect mathematical series representing the profile elevations.

In summary:

$\sin \theta =\frac{\Delta E}{\Delta D}$ $\Delta E=\mathrm{\Delta Dsin\theta }$ $\mathrm{\Delta E}=\Delta D\sin \left(\alpha +\beta \right)$ $\Delta E=\mathrm{\Delta Dsin}\left(\alpha +{\tan }^{-1}\left(\frac{\left(L_f-L_r\right)}{L}\right)\right)$

And to build a mathematical series accurately representing the profile from m samples of data, starting at elevation E₀, sampled every ΔD_n distance interval, the resulting end distance E_m may be defined as follows:

$E_m=E_0+\sum _{n=1}^m\left({\Delta D}_n\sin \left({\propto }_n+{\tan }^{-1}\left(\frac{\left(L_{\mathrm{fn}}-L_{\mathrm{rn}}\right)}{L}\right)\right)\right)$

E₀ may be taken from existing records for the elevation above sea level of the test site. Alternatively, a relative measure may be sufficient for the purposes of the profile data such that E₀ is set to zero.

In order to build the profile at every n distance interval it is necessary to acquire the values ΔD_n, α_n, L_fn and L_rn from the measuring devices. Therefore, at any given point along the profile, the necessary readings are acquired from the distance measuring unit, the inclinometer and the lasers.

Note that the lasers may be removed from the apparatus, which would continue to function as an accurate profiler using only α_n, therefore making L_fn and L_rn, and consequently β_n, equal to zero. The profiler frequency response would roll off toward and become zero at W.

Calculating the Profile

The data collection process is initiated by the operator, and continues until the operator stops the process. Once stopped, the data collected can be saved to a USB-connected flash drive or other storage device. Also, the operator may perform diagnostics and calculations such as computation of roughness indices such as the IRI.

The following process is used to measure the profile. First, a benchmark survey data may be used to establish the local elevation as E₀ or the starting elevation may simply be set to 0. Then, at suitable time intervals Δt, such as every millisecond, or every incremental distance ΔD, such as every millimeter, a measuring subroutine is initiated, during which the following steps are performed:

1. Acquire all raw data from measuring devices using input hardware interfaces. This step generally involves obtaining information about the angle of the frame 12 from the inclinometer 44 and the distance between each of the lasers 40, 42 and the ground. The data is preferably all acquired substantially simultaneously, for example within one millisecond, because using precise geometry and precise measurements at each position of the profiler along the path will increase the accuracy of the surface profile. Measurements from the is measuring devices are preferably conditioned to remove noise and improve quality prior to performing calculations. Analog voltage signals entering the multi-channel analog to digital converter may be provided anti-aliasing filters. “Anti-aliasing” involves the application of passive resistor-capacitor low pass filters to incoming analog signals to limit the frequencies applied to the inputs of analog to digital converters to one-half of the digital sampling frequency, which is known as the Nyquist frequency, to avoid digitization errors. Digital values derived from the analog to digital converter may be digitally filtered using a band pass digital filter that passes only signal frequencies containing useful information.

2. Determine the distance travelled. In the embodiment shown, this is accomplished by accumulating the counts of electrical pulses from the longitudinal distance measuring unit 26 and dividing by a scaling factor that converts the number of pulses to a distance D_new travelled along the profile, in meters. However, any method suitable to accurately obtain and provide the distance travelled by the profiler may be employed.

3. Determine the incremental distance ΔD travelled. This simply uses the formula:
ΔD=D_new−D_old
where D_old is the distance travelled and stored during the iteration of the measurement subroutine. ΔD may be as small as approximately 1 mm and may vary depending on speed of the profiler but the method is generally independent of speed. The current distance value D_new is stored for use at the next measurement interval as D_old.

4. Convert the data acquired into useful values. This step involves scaling digital values from the analog to digital converter to voltages and then to engineering quantities of angles in radians and distances in meters. The value of α obtained from the inclinometer will be in radians. The distance measured by the front laser distance measuring device is L_f and the distance measured by the rear laser is L_r, both being directed vertically downward and perpendicular to the frame. L_f and L_r from the distance measuring lasers will be converted to meters. The lasers are normally scaled to produce 0 to 10 volts for 16 to 120 mm of distance, but by simple scaling adjustments consisting of adding an offset and inverting the range, it is possible to obtain values of L_f and L_r that represent the distances between the points where the lasers strike the surface of the profile (i.e. along line SL) and the line SW, which extends between the points where wheels contact the surface of the profile pavement. L_f and L_r will have a positive value where the profile is higher than the line SW, and a negative value where the profile is below the line SW.

5. Calculate the nth incremental change in elevation ΔE_n Using the Formula:

${\Delta E}_n={\Delta D}_n\sin \left({\alpha }_n+{\tan }^{-1}\left(\frac{\left(L_{\mathrm{fn}}-L_{\mathrm{rn}}\right)}{L}\right)\right)$

ΔE_n is then added to the accumulated elevation series as:
E_n=E₀+ΔE₁+ΔE₂ . . . +ΔE_n

6. Return to step 1 at the next increment.

The mathematical elevation series created captures within the resulting profile all wavelengths from L to the longest wavelengths of interest. At L, the gain of the device becomes zero. Above L, all frequencies are captured without phase shift or distortion with the result that large and small profile features such as bumps, dips and cracks are captured with correct amplitude and longitudinal distance.

FIG. 6 shows how the addition of dual lasers, in this example being lasers spaced about 25 mm apart mounted to a profiler having a wheelbase of about 250 mm, can extend the short wavelength response over the 25 mm-250 mm range, as compared to an otherwise identical profiler using only an inclinometer, that is where β is always zero because of the absence of lasers to derive β. Overall the performance of this configuration of dual laser/inclinometer profiler is smooth and accurate from 25 mm to effectively infinite millimeters, and in particular provides useful information in the region Δ the wheelbase separation distance W, down to laser separation distance L.

FIG. 7 is a more specific example of the results from a profiler to which dual lasers have been added. The profiler, which has the same dimensions as that in the FIG. 6 example, is now able to measure the shape and amplitude of a bump on the profile having a half cycle sinusoidal shape with width of 160 mm. Without the addition of the dual lasers to the profile calculation, laser-derived angle β would always be zero and would not affect the profile. Using only the inclinometer, the wheels would contact points on the profile, spaced apart by W, tilt the frame and provide the inclinometer slope
Correction and Compensation

The measurement of the surface profile is accomplished using a combination of inclinometer measurements and laser measurements. The inclinometer is able to measure profile independently of the laser measurements using the formula:
ΔE=ΔD sin(α)

However, as shown in FIG. 8, when the wavelength λ of any surface feature is equal to or is less than W, the inclinometer alone loses effectiveness, and the profiler is incapable of accurately detecting these features. Where the feature wavelength λ is equal to W, the profiler remains horizontal relative to the plane of the earth at all positions on the profile so the angle α measured by the inclinometer remains constantly at zero, meaning the response gain of the profiler is zero at this wavelength. The use of the lasers therefore extends the wavelength range of the invention into the range of λ between W and L, enabling high resolution measurement of surface features. For features having wavelengths λ between W and L, the combination of inclinometer and lasers work together to measure the profile using the formula:

$\Delta E=\mathrm{\Delta Dsin}\left(\alpha +{\tan }^{-1}\left(\frac{\left(L_f-L_r\right)}{L}\right)\right)$

FIG. 10 is a graph showing the contributions of the inclinometer alone and lasers alone, as compared to using the dual laser and inclinometer combination of the invention.

In practice, despite efforts to accurately calibrate and balance the front and rear lasers, it is possible that L_f will not equal L_r when the profiler is placed on a perfectly straight surface with or without tilting relative to the horizontal plane of the earth. Also for very long wavelength sine wave profiles, the distance measuring lasers “see” a straight line and produce no L_fL_r or β signal. FIG. 10 shows that at 20 times W (5 m where W is 0.25m), the contribution of the lasers to the total profile, or their gain, is nearly zero compared to the inclinometer which is nearly 1.0. At 20 times W, the L_f and L_r signals will be very small relative to the resolution of the lasers or the analog to digital converters or will be buried in noise inherent in data acquisition systems. This may result in poor performance of the profiler if the long wavelength component of the L_fL_r or β signal is not removed. Therefore it may be necessary to wavelength high pass filter L_f and L_r or the term:

$\beta ={\tan }^{-1}\left(\frac{\left(L_f-L_r\right)}{L}\right)$
using a high pass digital filter with a cutoff wavelength of approximately 20 times W. This involves filtering in the distance domain (cycles/meter) rather than the frequency domain (cycles/second) and requires the ΔD values to be fairly constant. In this way, even if L_f-L_r or β is not exactly equal to zero for a perfectly straight profile, there will be no non-zero value of β that causes the profile elevation to wander and result in large elevation errors at the end of the profile, since the high pass digital filter will make L_f and L_r or β equal to zero for very long wavelengths. Filtering out very long wavelengths from the β signal as described requires the wheels and lasers be collinear to ensure the component of the profile contributed by the inclinometer is aligned with the component of the profile contributed by the lasers particularly through the crossover region at 20 times W.

A typical inclinometer is basically an accelerometer that responds to the direction of the acceleration of gravity using a pendulum that is balanced to the zero position by a miniature torque motor. The electrical current to the torque motor required to maintain the pendulum in the zero position is proportional to the sine of the angle of inclination and is the source of the voltage signal produced by the inclinometer. Such devices are also sensitive to acceleration of the inclinometer along the sensitive axis, such as may be caused by the operator pushing on the handle of the profiler to start it moving, and pulling on the handle to stop it. The inclinometer will also be sensitive to the normal acceleration and deceleration inherent in the walking motion of the operator. In order to correct this sensitivity, it may be necessary to calculate a compensating signal using high resolution distance information from the optical encoder or other distance measuring device, if the information is available. By differentiating the distance signal D twice, an acceleration signal A can be derived. This differentiation may be performed on the digital representation of distance obtained from the distance measuring unit. By appropriately scaling this acceleration with constant k, an equal and opposite compensation signal can be added to the inclinometer signal i to eliminate this issue. Specifically this is accomplished as follows:

• • dD/dt=velocity V
  • dV/dt=acceleration A
  • i_corrected=i_uncorrected−k A

In some cases, the longitudinal inclinometer produces an errant signal when tilted in the transverse direction, a characteristic known as cross-axis error. Cross-axis error is caused by misalignment between the axis of the sensing accelerometer element in the longitudinal inclinometer with its enclosure, or misalignment between the enclosure of the inclinometer with the longitudinal axis of the profiler. Either misalignment exposes the sensing accelerometer element to tilting in the transverse direction. As best shown in FIG. 11, if a transversely-aligned (or cross-axis) inclinometer 45 is provided to measure the angle χ between the horizontal plane of the earth and the frame in the transverse direction, it may provide information to correct the longitudinal inclinometer angle α for cross-axis error. The correction is applied to the voltage output from the inclinometer prior to conversion to angle. The longitudinal inclinometer voltage V_αis compensated for cross-axis error as follows.

$V_{\alpha c}=V_{\alpha }+S_{\alpha \mathrm{to}\chi }x\frac{V_{\chi -}{V}_{\chi \mathrm{offset}}}{S_{\chi }}$

• • where:
  • V_αc is the longitudinal inclinometer voltage, after compensation, in volts;
  • V_αis the longitudinal inclinometer voltage, before compensation, in volts;
  • S_{α to χ}is the longitudinal inclinometer's (or α's) sensitivity to tilting in χ direction in volts/G, determined empirically;
  • V_χis the transverse, or cross-axis, inclinometer voltage in volts;
  • V_{χ offset} is the transverse inclinometer voltage output measured when the inclinometer is set horizontal relative to the plane of the earth in volts, determined empirically; and
  • S_χis the full range sensitivity of the transverse inclinometer in volts/G.

Then the cross-axis compensated angle α is given by:

$\alpha ={\sin }^{-1}\frac{V_{\alpha c}}{S_{\alpha }}$
where S_α is the full range sensitivity of the longitudinal inclinometer in volts/G.

The present invention, given its high accuracy and repeatability, while finding uses in several industries and for many purposes, will be of particular value in both the contract management of new surface construction and as a reference standard for certification of other instruments.

The foregoing embodiment of the invention has been described as a rolling/walking profiler, having an operator to physically move the apparatus along the surface being profiled. However, it is also contemplated to provide a motorized drive mechanism for the apparatus, which can move the apparatus along the surface at a controllable speed. In a further alternative, the apparatus may comprise appropriate attachment means by which it can be attached to a motorized vehicle, which will then move the apparatus along the surface to be profiled, such as by towing or pushing.

In the foregoing specification, the invention has been described with reference to specific embodiments thereof. However, the scope of the claims should not be limited by the preferred embodiments set forth in the examples, but should be given the broadest interpretation consistent with the description as a whole. The specification and drawings are, accordingly, to be regarded in an illustrative rather than a restrictive sense.

Claims

1. A surface profiling apparatus comprising:

a frame;

a plurality of wheels supporting said frame, at least two of said wheels being separated by a distance W and being aligned to contact a surface being profiled in a longitudinally collinear manner;

a longitudinal distance measuring apparatus supported by said frame;

a longitudinal inclination measuring apparatus supported by said frame to measure an angle α between said frame and said surface; and

at least two vertical distance measuring devices, said vertical distance measuring devices being collinear with said collinear wheels and separated by a distance l.

2. The surface profiling apparatus of claim 1 wherein said vertical distance measuring devices are equidistant from the mid-point of said frame.

3. The surface profiling apparatus of claim 1 wherein each of said vertical distance measuring devices is a laser.

4. The surface profiling apparatus of claim 3 wherein said lasers are attached to said frame at a specified separation, and wherein said separation is shorter than the distance W.

5. The surface profiling apparatus of claim 3 wherein said lasers are equidistant from the mid-point of said frame.

6. The surface profiling apparatus of claim 1, wherein said longitudinal distance measuring apparatus is positioned between said collinear wheels.

7. The surface profiling apparatus of claim 1 wherein said longitudinal distance measuring apparatus is positioned between said vertical distance measuring apparatuses.

8. The surface profiling apparatus of claim 1, wherein said longitudinal distance measuring apparatus is rotationally linked to an axle of one of said wheels.

9. The surface profiling apparatus of claim 8 wherein said longitudinal distance measuring apparatus is an optical encoder.

10. The surface profiling apparatus of claim 1 wherein said longitudinal inclination measuring apparatus is an inclinometer.

11. The surface profiling apparatus of claim 1 further comprising a motorized drive adapted to move the profiling apparatus along the surface to be profiled.

12. The surface profiling apparatus of claim 1 further comprising attachment means by which the apparatus may be attached to a motorized vehicle to move the apparatus along the surface to be profiled.

13. The surface profiling apparatus of claim 1, further comprising an operator interface to control said profiling apparatus.

14. The surface profiling apparatus of claim 13 wherein said interface is associated with a cabinet associated with said frame.

15. The surface profiling apparatus of claim 14 wherein said cabinet houses operational equipment, said operational equipment being selected from the group consisting of: one or more internal sensors, a power supply, power level monitor, signal conditioning equipment, real time clock, distance pulse counters, digital input/output and multi-channel 16 bit analog to digital converter, computer and non-volatile memory.

16. The surface profiling apparatus of claim 1, further comprising a transverse inclination measuring apparatus, supported by said frame and oriented substantially perpendicular to said longitudinal inclination measuring apparatus, to measure a transverse angle χ between said frame and said surface.

17. A method of profiling a surface using a surface profiling apparatus mounted on a plurality of wheels, at least two of said wheels being aligned to contact the surface in a longitudinally collinear manner, the method comprising:

acquiring data relating to:

a longitudinal distance ΔD travelled by said profiler surface profiling apparatus from a longitudinal distance measuring apparatus mounted on said profiler surface profiling apparatus;

an angle α of said profiler surface profiling apparatus relative to a horizontal plane intersecting said surface at a location of one of said wheels where a point of the wheel, a vertical line and a line collinear with a diameter of the wheel intersect, from a longitudinal inclination measuring apparatus comprising a first inclinometer mounted on said profiler surface profiling apparatus; and

a vertical distance l_f between said profiler surface profiling apparatus and said surface from a first vertical distance measuring apparatus mounted on said profiler surface profiling apparatus;

a vertical distance l_r between said frame and said surface from a second vertical distance measuring apparatus mounted on said profiler surface profiling apparatus;

said first and second vertical distance measuring apparatuses being mounted collinearly with said wheels and separated by a distance l;

calculating an incremental change in surface elevation ΔE, using the formula:

18. The method of claim 17, wherein said method is applied at periodic intervals.

19. The method of claim 18 wherein said periodic intervals are at time increments, Δt.

20. The method of claim 19 wherein Δt is 1 millisecond.

21. The method of claim 18 wherein said periodic intervals are at longitudinal distance increments, ΔD.

22. The method of claim 21 wherein ΔD is 1 millimeter.

23. The method of claim 17, wherein said step of acquiring data further comprises acquiring data relating to a transverse angle χ of said profiler relative to surface profiling apparatus between a horizontal plane above said surface and a line transverse to a longitudinal axis of a frame of said surface profiling apparatus, from a transverse inclination measuring apparatus comprising a second inclinometer supported by mounted on said profiler surface profiling apparatus to correct said angle α for cross-axis error.

24. The method of claim 23, wherein said method is applied at periodic intervals.

25. The method of claim 24 wherein said periodic intervals are at time increments, Δt.

26. The method of claim 25 wherein Δt is 1 millisecond.

27. The method of claim 24 wherein said periodic intervals are at longitudinal distance increments, ΔD.

28. The method of claim 27 wherein ΔD is 1 millimeter.

29. A method of profiling a surface using a surface profiling apparatus mounted on a plurality of wheels, at least two of said wheels being aligned to contact the surface in a longitudinally collinear manner, the method comprising:

moving the profiler surface profiling apparatus a longitudinal distance increment ΔD;

obtaining a vertical distance l_f between said surface profiling apparatus and said surface from a first vertical distance measuring device, and a vertical distance l_r between said surface profiling apparatus and said surface from a second vertical distance measuring device, said first and second vertical distance measuring apparatuses being mounted on said surface profiling apparatus collinearly with said at least two wheels and separated by a distance l;

calculating a first angle β between said vertical distances l_f, l_r and said distance l using the formula:

30. The method of claim 29, wherein said method is applied at periodic intervals.

31. The method of claim 30 wherein said periodic intervals are at time increments, Δt.

32. The method of claim 31 wherein Δt is 1 millisecond.

33. The method of claim 30 wherein said periodic intervals are at longitudinal distance increments, ΔD.

34. The method of claim 33 wherein ΔD is 1 millimeter.

35. The method of claim 29 comprising the further step of correcting said angle α for cross-axis error using a transverse angle χ, said transverse angle χ being obtained from a transverse inclination measuring apparatus supported by comprising a second inclinometer mounted on said profiler surface profiling apparatus.