Method for calculating the physical parameters of a pavement from deflection measurements

Abstract

The invention relates to a computer-implemented method for calculating the physical parameters of a pavement from deflection measurements, the method comprising: (S10) the partitioning of the deflection measurements into different groups of measurements based on the measurement values; and (S20) for each group of measurements, the calculation of the pavement's physical parameters, said calculation comprising (S21) the definition of a reference measurement for the group of measurements; (S23) the calculation, from the reference measurement, of a reference solution for the physical parameter; and (S25) the calculation, from the reference solution, of similar solutions for all measurements in the group. The invention also relates to a system implementing a method for calculating the physical parameters of a pavement from deflection measurements. Figure for the abstract: Fig. 1

Description

Title of the invention: Method for calculating physical parameters of a roadway from deflection measurements Background of the invention

[0001] The present disclosure relates to a method for calculating physical parameters of a roadway based on deflection measurements.

[0002] Road pavements are multi-layer structures that are mechanically stressed by road traffic. The design of pavements to withstand these stresses is generally carried out by a mechanical calculation taking into account the thicknesses of the layers and the properties of the materials (for example, Young's modulus and Poisson's ratio). In order to maintain the pavements, a diagnosis of these properties is necessary to estimate the optimal maintenance solution. This structural diagnosis is generally carried out by exploiting a set of deflection measurements taken at different points of a pavement along a road route. The deflection measurements are used in particular to determine the Young's moduli of the different layers constituting the pavement. We are interested here in an original calculation method making it possible to obtain homogeneous results for a homogeneous set of measurements.

[0003] Generally, during a roadway design study, deflection measurements are carried out along a route of several hundred kilometers with a relatively small spacing, for example approximately 100 m, which implies processing a very large number of measurements. Current methods for calculating physical parameters from deflection measurements perform a calculation of the desired physical parameter for each deflection measurement, which therefore makes them particularly slow and impractical. In addition, several admissible solutions for the physical parameters are generally proposed to the operator to allow him to take into account additional parameters, which requires several calculations per deflection measurement and therefore further slows down the roadway design process while reducing the practicality of the calculation when large volumes of deflection measurements are to be processed.

[0004] Solutions have been proposed to reduce this problem of complexity in processing large amounts of data.

[0005] For example, it has been proposed to group the deflection measurements acquired at different points of the roadway according to their belonging to specific areas of the roadway, see [REF 1]. However, this limits the groupings to measurements acquired at successive points of the roadway.

[0006] There is therefore a need to address the limitations of existing solutions. List of cited documents

[0007] [REF 1] LE BOURSICAUD, Vinciane. New uses of deflection basin measurements to characterize the structural condition of pavements. 2018. Doctoral thesis. Ecole centrale de Nantes, ch. 4, pp. 147-159.

[0008] [REF 2] CHENG, Yizong. Mean shift, mode seeking, and clustering. IEEE transactions on pattern analysis and machine intelligence, 1995, vol. 17, no. 8, pp. 790-799.

[0009] [REF 3] LUENBERGER, DG, “Introduction to Linear and Nonlinear Programming,” Addison-Wesley Publishing Company, Menlo-Park, 1973, ch. 1 & 8-10.

[0010] [REF 4] SOURIOU, David, SIMONIN, Jean-Michel, and SCHMIDT, Franziska. Definition of Optimized Indicators from Sensors Data for Damage Detection of Ins-trumented Roadways. Sensors, 2022, vol. 22, no. 15, p. 5572. Subject matter and summary of the invention

[0011] The present disclosure aims to remedy at least in part these drawbacks.

[0012] To this end, the present disclosure relates to a computer-implemented method for calculating physical parameters of a roadway from deflection measurements. The method comprises: the partitioning of deflection measurements into different measurement groups based on the measurement values; and for each measurement group: the definition of a reference measure of the group of measures; the calculation, from the reference measurement, of a reference solution for the physical parameter; and the calculation, from the reference solution, for each measurement of the group, of a similar solution for the physical parameter.

[0013] The similar solutions thus obtained therefore form a set of physical solution parameters for the measurements of the measurement group.

[0014] Although the present disclosure primarily concerns the calculation of a physical parameter at different points of a roadway, this must be interpreted as including the calculation of at least one physical parameter at each of these points, which may therefore include the calculation of a plurality of physical parameters characteristic of the roadway at each measurement point of the roadway.

[0015] The physical parameters of the roadway which are calculated from the deflection measurements may for example be the Young's modulus of the roadway, or the Young's moduli of one or more layers constituting the roadway.

[0016] According to certain examples, the number and / or the thicknesses of the layers constituting the roadway are known. The number and / or the thickness of the layers constituting the roadway can in particular be determined beforehand by a known suitable measurement of the qualified person.

[0017] Furthermore, according to certain examples, the Poisson's ratios of each layer are known, in particular from knowledge of the materials composing these layers.

[0018] In the present disclosure, the step of calculating physical parameters of the roadway from roadway deflection measurements is an estimation that can be described as a “back-calculation” of said physical parameters. This step is generally demanding in terms of calculation time and computing power, so it is particularly advantageous to reduce the number of times it is performed when processing roadway deflection data. In addition, after performing several solution back-calculations, it is generally necessary to validate each solution obtained to harmonize all of the solutions. This step, which is generally performed by an engineer in charge of the calculation, is also demanding in terms of time.

[0019] With the present invention, it is possible to back-calculate a physical parameter from a deflection measurement only once per group of measurements, which therefore speeds up and simplifies roadway diagnosis by reducing the number of back-calculations to be performed. Thus, the computing power and computing time required are reduced and it is possible to process a large number of deflection measurements efficiently.

[0020] In particular, with the present method, a reference solution is back-calculated for a group of measurements from a reference measurement of the group, then the solutions corresponding to the other measurements of the group are determined from the reference solution. The back-calculation step is therefore carried out only once per group of measurements, using the reference measurement.

[0021] The step of determining the other physical parameter solutions from the reference solution advantageously uses the fact that the measurements have been partitioned according to the measurement values, thus constituting groups of measurements comprising measurements of similar values. Thus, it is possible to determine solutions similar to the reference solution of a group to obtain the solutions corresponding to the other deflection measurements of the group.

[0022] In the present disclosure, the roadway deflection measurements may be obtained from a file containing deflection data or may be taken directly from a roadway using a deflection measuring instrument, for example a falling weight deflectometer (generally referred to as FWD, from the English acronym “Falling Weight Deflectometer”).

[0023] According to some examples, each deflection measurement comprises a plurality of sub-deflection measurements forming a deflection vector that corresponds to a basin. of deflection at a point on the roadway; and the following steps of the method are applied to one or more of the sub-measures forming the deflection vector.

[0024] According to some examples, partitioning the deflection measurements into different measurement groups based on the values ​​of the measurements includes classifying the deflection measurements relative to an average value of the deflection measurements.

[0025] In particular, with the present method, a group of measurements can be defined with respect to an average (deflection) basin of a set of deflection measurements, i.e. with respect to an average deflection vector calculated on a set of the measurements. Furthermore, a group of measurements can also be defined with respect to a representative (deflection) basin, i.e. a basin best representing the deflection measurements constituting a deflection basin. In particular, the representative basin can comprise a deflection vector which is closest to the average basin, for example in the least squares sense.

[0026] According to some examples, the classification may also be carried out by defining an average zone of deflection values ​​containing the average basin. This zone may be characterized by a zone width, for example equal to the measurement uncertainty or defined with respect to the measurement uncertainty.

[0027] According to certain examples, the step of partitioning the deflection measurements into different groups of measurements according to the values ​​of the measurements comprises partitioning the deflection measurements such that a difference between two measurements of the same group is strictly less than a known limit. This limit may be a measurement uncertainty, for example a measurement uncertainty linked to a measurement instrument used to acquire the deflection measurements.

[0028] According to some examples, the reference measurement of the measurement group is one of the measurements of the measurement group or a pseudo-measurement calculated from the measurements of the group, for example an average value of the measurements of the group. By pseudo-measurement, it is understood that this value is not measured directly but is calculated from directly measured values.

[0029] In some examples, partitioning the deflection measurements into different measurement groups based on the measurement values ​​includes applying a clustering algorithm to the deflection measurements. Applying the clustering algorithm may result in defining the measurement groups as Gaussian distributions based on the measurement values, wherein the widths and standard deviations of said Gaussian distributions are adjusted to maximize the mathematical expectation of each measurement belonging to one of the measurement groups.

[0030] According to certain examples, the step of calculating, from the reference measurement, a reference solution, comprises the use of at least one of the following methods: gradient algorithm; and Newton- Raphson. This step may also include the use of a sampling method within a range of permissible values.

[0031] According to certain examples, the step of calculating a reference solution for the physical parameter from the reference measurement comprises calculating several admissible solutions for the physical parameter from the reference measurement; and selecting a retained solution from among the admissible solutions, said retained solution being used as a reference solution in the following steps of the method.

[0032] The admissible solutions can, for example, be obtained with several different methods which are more or less adapted to several particular criteria of the roadway. This thus leaves the choice to the engineer in charge of determining the physical parameter to choose the solution resulting, for example, from the most suitable method.

[0033] According to some examples, the step of calculating, from the reference solution, solutions for all the measurements of the group comprises calculating solutions similar to the reference solution using an indicator method. The indicator method is described, for example, in the context of monitoring the damage of an instrumented pavement in [REF 4].

[0034] The present disclosure also relates to a system for calculating physical parameters of a roadway implementing the present calculation method.

[0035] In a particular embodiment, the different steps of the calculation method are determined by computer program instructions.

[0036] Consequently, the present disclosure also relates to a program on an information medium, this program being capable of being implemented in an estimation device or more generally in a computer, this program comprising instructions adapted to the implementation of the steps of an estimation method as described above.

[0037] This program may use any programming language, and be in the form of source code, object code, or code intermediate between source code and object code, such as in a partially compiled form, or in any other desirable form.

[0038] The present disclosure also relates to an information medium readable by a computer or by a microprocessor, and comprising instructions of a program as mentioned above.

[0039] The information carrier may be any entity or device capable of storing the program. For example, the carrier may include a storage means, such as a ROM, for example a CD ROM or a microelectronic circuit ROM, or a magnetic recording means, for example a floppy disk or a hard disk. The carrier may also include a storage means of the solid state disk (SSD) type.

[0040] Furthermore, the information medium may be a transmissible medium such as an electrical or optical signal, which may be conveyed via an electrical or optical cable, by radio or by other means. The program according to the present disclosure may in particular be downloaded from a network of the Internet type. Brief description of the drawings

[0041] Other characteristics and advantages of the invention will emerge from the following description of embodiments of the invention, given as non-limiting examples, with reference to the appended figures, in which: • [Fig.l] is a schematic illustration of the steps of the present method, according to certain embodiments; • [Fig.2] is a functional block diagram illustrating the operation of the present method according to certain embodiments. Detailed description of the invention

[0042] [Fig.l] schematically represents steps of the present method for calculating physical parameters from deflection measurements. [Fig.l] shows that, in certain examples, the present method comprises the following steps: S10: Partitioning the deflection measurements into different measurement groups according to the values ​​of the measurements; S20: Calculating physical parameters for each group of measurements. Step S20 comprises in particular the following steps: S21: Defining a reference measurement of the group of measurements; S23: Calculating, from the reference measurement, a reference solution for the physical parameter; S25: Calculating, from the reference solution, physical parameter solutions for all the measurements of the group.

[0043] [Fig.2] shows examples of operation of the present method.

[0044] One or more physical parameters, defined as the solutions 109, are therefore determined from a set of deflection measurements 101 of a roadway. Rather than performing a calculation of the physical parameter(s) from each deflection measurement (back-calculation), as is generally the case in the state of the art, the present method proposes to first partition the set of measurements 101 into different groups of measurements 103 according to the values ​​of the deflection measurements. Then, the solutions 109 are calculated for each group of measurements 103 by performing a single back-calculation per group of measurements 103.

[0045] According to certain examples, reference measurements 105 are defined for each group of measurements 103. Then reference solutions 107 are calculated (back-calculation) for each reference measurement 105. Then, for each group of measurements 103, the solutions 109 corresponding to all the measurement values ​​of the group are calculated from the reference solutions 107.

[0046] In the first step S10 of the method, a set 101 of deflection measurements is decomposed (partitioned) into different groups 103 of measurements according to the measurement values. Different variants are possible for carrying out this step.

[0047] In a specific example, the deflection measurements are measurements obtained by a falling mass deflectometer. The falling mass deflectometer is generally composed of a force sensor and a plurality of geophones located at fixed distances from a mass pressing on the roadway. Each geophone allows the acquisition of a deflection measurement, thus the set of several geophones of a deflectometer allows the acquisition of a plurality of measurements forming a deflection vector, commonly called a “deflection basin”.

[0048] Deflection measurements are made along a route according to a succession of measurement points on the route. It is possible to make a single deflection measurement per point on the route or to repeat the measurement several times at the same point. When the measurements are repeated at the same point, each measurement at this point is generally considered to be independent of the others.

[0049] In some examples, a normalization step is performed to normalize the measurement and ensure that variations in applied force do not affect the accuracy of the measurement. In this case, the average force (over all measurement points) applied is calculated, and then the ratio of the deflection forces is determined, for example according to the following expression:

[0050] In the previous expression; F j is the force applied during the measurement of index “j”; d"™'' is the vector of the geophone measurements (commonly called “deflection vector”); and Fm is the average force applied.

[0051] In certain examples, the decomposition step S10 aims to separate the set 101 of deflection measurements {M} into different groups 103 (subset) of measurements {M_i} such that the difference between two measurements of the same subset {M_i} remains lower than a limit set by the road engineer and generally slightly higher than the measurement uncertainty of the device used to acquire the deflection measurements on which the present method is used.

[0052] In a specific example, the aim is to obtain a given number, n, of groups. To do this, the population of deflection measurements will be decomposed into n Gaussians characterized by a central value (for example the mean) and a width (for example linked to the standard deviation). In order to obtain a satisfactory decomposition, the mathematical expectation of belonging to the set of Gaussians is maximized. In particular, in certain embodiments, the process is initialized by choosing two central values ​​for the Gaussians (for example two values ​​close to the value minimum among all the values ​​of the set 101). We then calculate the mathematical expectation of belonging to the two Gaussians for each measurement of the set 101 as a function of the value of the measurement. We then vary the centers

[0053]

[0054]

[0055]

[0056]

[0057] and the widths of the Gaussians to calculate new probabilities of membership (in the middle). The decomposition retained is that which maximizes the probability of membership in the two Gaussians of the set of points (at the bottom). Once the decomposition of the measurements into different groups 103 has been obtained, it is possible to verify that the Gaussians defining the groups 103 have variances close to the metrological performances of the device used to acquire the measurements. It is therefore advantageously possible to verify that the decomposition is correct. Otherwise, it is possible to remove information indicating that the number of groups is not adapted to the set 101 of measurements to which the present method is applied.For example, when using the method, it is possible to use this information to warn the road engineer in charge of the calculation, and offer him various correction options such as the possibility of increasing the number of measurement groups 103 into which to distribute the measurements of the set 101 of measurements. In another specific example, the decomposition of the set 101 of measurements into different groups 103 of measurements is obtained based on the measurement uncertainty, X, of the apparatus used to acquire the deflection measurements on which the present method is used. In a first variant of the example, a spindle is constructed from a deflection "mean basin", i.e. from a mean deflection vector derived from all deflection measurements along a route. For example, the mean deflection vector, ^°yen^ can be calculated from the (normalized) deflection vectors, dnf>m, obtained at N measurement points along a route with the following expression. V jwm jnoyen L / Jj (h - ..... A spindle centered on this average is then determined, the spindle being characterized by a given width, X. The value of the spindle width used is for example defined by the road engineer in charge of the calculation with regard to the metrological performance of the device used for the measurements. The measurements are then classified with respect to this zone representing an average basin in order to define groups of measurements. For example, the measurements entirely included in this zone are considered to constitute a first group 103 of measurements {M_i}. In addition, the populations above the zone (comprising only values ​​above the zone), below the zone (comprising only values ​​below the zone), and across the zone (comprising both values ​​in lower and higher than the spindle) are then considered to construct, by the same process, three additional groups 103 of measurement populations. The process is repeated iteratively until each measurement of the set 101 belongs to a group 103 of measurements.

[0058] In a second variant, a mean shift algorithm is used to search for dense measurement groups of width equal to the measurement uncertainty, X, see for example [REF 2].

[0059] In particular, an initial measurement point is chosen and the average of the measurements which are at a distance from this point less than the measurement uncertainty, X, is calculated. The same average is then calculated for the other points and the point which minimizes this deviation is retained to define the center of a group of measurements, to which all the measurements contained in the interval, X, belong. The measurements belonging to the group thus defined are then removed from the set of measurements to be partitioned before repeating the process as many times as necessary to define the other measurement groups with the remaining measurements.

[0060] The partitioning step S10 of the present method can be applied to a single deflection measurement at a point on the roadway or to a plurality of deflection sub-measurements defining a deflection vector representative of a deflection basin in an area of ​​the roadway. These options depend in particular on the type of device used to acquire the deflection measurements of the roadway.

[0061] In step S21, the calculation of reference measurements 105 for the measurement groups 103 can be performed by directly choosing one of the measurements of the group 103 or by applying a particular function to the deflection measurements of the group. In particular, it is possible to choose the average of the deflection measurements of the measurement group as the reference measurement 105 of the measurement group 103.

[0062] In step S23, the step of calculating a reference solution for the physical parameter from the reference measurement of the measurement group can be carried out in various ways. This can in particular be carried out with known methods based, for example, on different mathematical optimization methods (gradient algorithm, Newton-Raphson algorithm, samplings in a range of admissible values), see for example [REF3], chap. 8, pp. 259-266 & chap. 10, pp. 299-234.

[0063] Furthermore, according to certain examples, from a single reference measurement 105, a plurality of admissible solution proposals are proposed for the physical parameter. Depending on the large number of possible solutions for a given reference measurement, different algorithms can be tested. The choice of the solution retained in this case remains a function of the expertise of the road engineer, which increases the adaptability and precision of the present method.

[0064] In step S25, for each group 103 of measurements, the solutions 109 corresponding to the deflection measurements other than the reference measurement 105 are calculated by varying the reference solution 107 obtained by a certain increment.

[0065] The variation method used can for example be based on an indicator method, see [REF 1].

[0066] In this indicator method, weighting functions are sought in order, on the one hand, to maximize the sensitivity of an indicator derived from the measurements to a physical parameter while minimizing its sensitivity to other physical parameters. The functions are chosen to allow an indicator to be calculated for each physical parameter. The variations of these indicators are linear with respect to the variations of the physical parameter in the vicinity of the reference solution 107.

[0067] The variation method used can also be based on the maximum deflection of the roadway. In this case, the solutions will be varied in the same direction (variation of constant sign) and in proportions similar to the variation of the maximum deflections.

[0068]

[0069]

[0070] For example, if a given measure, , among the group of measures has a variation with respect to the reference measurement, which is characterized by a factor a such that * a , then the homogeneous solution corresponding to said measurement can be estimated as a function of the reference solution from the following expression: Ej = Eref*a Flexural stiffness may or may not be taken into account depending on the case. For example, the variation factor, a , may be weighted to account for the stiffness of each layer. This will result in a variation in the solution that is different for each layer. The variation method used can also be based on classical indicators (LLI, BLI) known in the field of deflection measurements rather than on maximum deflection.

[0071] Although the present disclosure has been described with reference to a specific exemplary embodiment, it is obvious that various modifications and changes may be made to these examples without departing from the general scope of the invention as defined by the claims. Furthermore, individual features of the various embodiments recited may be combined in additional embodiments. Therefore, the description and drawings should be considered in an illustrative rather than restrictive sense.

Claims

Claims

1. A computer-implemented method for calculating physical parameters of a roadway from deflection measurements, the method comprising: - (S 10) partitioning the deflection measurements (101) into different groups of measurements (103) based on the values ​​of the measurements; and - (S20) for each group of measurements (103), calculating physical parameters of the roadway, said calculation comprising: - (S21) defining a reference measurement (105) of the group of measurements (103); - (S23) calculating, from the reference measurement (105), a reference solution (107) for the physical parameter; and - (S25) calculating, from the reference solution (107), for each measurement of the group of measurements (103), a similar solution (109) for the physical parameter.

2. Method according to claim 1, in which the step (S 10) of partitioning the deflection measurements into different groups of measurements according to the values ​​of the measurements comprises: - partitioning the deflection measurements in such a way that a difference between two measurements of the same group is strictly less than a known limit.

3. A method according to claim 1 or 2, wherein the step (S 10) of partitioning the deflection measurements into different measurement groups based on the values ​​of the measurements comprises: - classifying the deflection measurements with respect to an average value of the deflection measurements.

4. A method according to any one of claims 1 to 3, wherein the step (S 10) of partitioning the deflection measurements into different measurement groups based on the measurement values ​​comprises applying a clustering algorithm to the deflection measurements, the clustering algorithm resulting in the measurement groups being defined as Gaussian distributions based on the measurement values, the widths and standard deviations of said Gaussian distributions being adjusted to maximize the mathematical expectation of each measurement belonging to one of the measurement groups.

5. A method according to any one of claims 1 to 4, wherein the reference measurement of the group of measurements is one of the measurements of the measurement group or a pseudo-measurement calculated from the measurements in the measurement group.

6. A method according to any one of claims 1 to 5, wherein the step (S23) of calculating, from the reference measurement, a reference solution, comprises using at least any one of the following methods: gradient algorithm; Newton-Raphson algorithm; and sampling within a range of permissible values.

7. Method according to any one of claims 1 to 6, wherein the step (S23) of calculating a reference solution for the physical parameter from the reference measurement comprises: - calculating several admissible solutions for the physical parameter from the reference measurement; and - selecting a retained solution from among the admissible solutions, said retained solution being used as a reference solution in the following steps of the method.

8. A method according to any one of claims 1 to 7, wherein the step (S25) of calculating, from the reference solution, for each measurement of the group of measurements, a similar solution for the physical parameter, comprises calculating solutions similar to the reference solution using an indicator method.

9. A method according to any preceding claim, wherein: - each deflection measurement comprises a plurality of deflection sub-measurements forming a deflection vector which corresponds to a deflection basin at a point on the roadway; and - the following steps of the method are applied to one or more of the sub-measurements forming the deflection vector.

10. System for calculating physical parameters of a roadway implementing the method according to any one of claims 1 to 9.

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