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 the physical parameters of a pavement from deflection measurements. Background of the invention

[0001] The present exposition relates to a method for calculating the physical parameters of a pavement based on deflection measurements.

[0002] Road pavements are multi-layered structures that are subjected to mechanical stresses from road traffic. Pavement design to withstand these stresses is generally performed using mechanical calculations that take into account the layer thicknesses and material properties (for example, Young's modulus and Poisson's ratio). To maintain pavements, an analysis of these properties is necessary to determine the optimal maintenance solution. This structural analysis is generally carried out by using a set of deflection measurements taken at different points along a road route. These deflection measurements are used in particular to determine the Young's moduli of the different layers constituting the pavement. This paper focuses on an original calculation method that provides consistent results for a consistent set of measurements.

[0003] Generally, during a pavement design study, deflection measurements are taken along a route of several hundred kilometers with 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, making them particularly slow and impractical. Furthermore, several acceptable solutions for the physical parameters are generally proposed to the operator to allow for the consideration of additional parameters, which necessitates multiple calculations per deflection measurement and thus further slows down the pavement design process while reducing the practicality of the calculation when large volumes of deflection measurements need 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 deflection measurements acquired at different points of the pavement according to their belonging to specific areas of the pavement, see [REF 1]. However, this limits the groupings to measurements acquired at successive points of the pavement.

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

[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. Object and summary of the invention

[0011] The present exposition aims to remedy at least some of these drawbacks.

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

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

[0014] Although the present exposition is primarily concerned with the calculation of a physical parameter at different points of a pavement, this should be interpreted as including the calculation of at least one physical parameter at each of these points, and may therefore include the calculation of a plurality of physical parameters characteristic of the pavement at each point of measurement of the pavement.

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

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

[0017] Moreover, according to some examples, the Poisson coefficients of each layer are known, in particular from knowledge of the materials composing these layers.

[0018] In the present description, the step of calculating the physical parameters of the pavement from pavement 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 computation time and computing power; therefore, it is particularly advantageous to reduce the number of times it is performed when dealing with pavement deflection data. Furthermore, after performing several back-calculations of solutions, it is generally necessary to validate each solution obtained to harmonize all the solutions. This step, which is generally carried out by a calculation engineer, is also time-consuming.

[0019] With the present invention, it is possible to perform the back-calculation of a physical parameter from a deflection measurement only once per group of measurements, thereby accelerating and simplifying pavement diagnostics by reducing the number of back-calculations required. As a result, the computing power and time required are reduced, and a large number of deflection measurements can be processed 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, and then the solutions corresponding to the other measurements in the group are determined from the reference solution. The back-calculation step is therefore performed 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 their values, thus forming groups of measurements comprising measurements with similar values. Therefore, it is possible to determine solutions similar to the reference solution within a group to obtain the solutions corresponding to the other deflection measurements in the group.

[0022] In the present exposition, pavement deflection measurements can be obtained from a file containing deflection data or can be taken directly from a pavement using a deflection measurement instrument, for example a falling weight deflectometer (generally designated as FWD, from the English acronym "Falling Weight Deflectometer").

[0023] According to some examples, each deflection measure comprises a plurality of deflection sub-measures forming a deflection vector that corresponds to a basin of deflection at a point in the pavement; and the following steps of the process are applied to one or more of the sub-measures forming the deflection vector.

[0024] According to some examples, the partitioning of deflection measurements into different measurement groups based on measurement values ​​includes the classification of deflection measurements with respect to an average value of 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, that is, with respect to an average deflection vector calculated over a set of measurements. Furthermore, a group of measurements can also be defined with respect to a representative (deflection) basin, that is, a basin that best represents the deflection measurements constituting a deflection basin. In particular, the representative basin may include a deflection vector that is closest to the average basin, for example, in the least-squares sense.

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

[0027] According to some examples, the step of partitioning the deflection measurements into different groups of measurements based on the measurement values ​​includes partitioning the deflection measurements such that the difference between two measurements in the same group is strictly less than a known limit. This limit may be a measurement uncertainty, for example, a measurement uncertainty related to a measuring instrument used to acquire the deflection measurements.

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

[0029] According to some examples, the partitioning of deflection measurements into different measurement groups based on measurement values ​​involves applying a grouping algorithm to the deflection measurements. Applying the grouping algorithm can result in defining the measurement groups as Gaussian distributions based on measurement values, with the widths and standard deviations of said Gaussian distributions being adjusted to maximize the expected value of each measurement belonging to one of the measurement groups.

[0030] According to some examples, the calculation step, starting from the reference measurement, of a reference solution, includes the use of at least one of the following methods: gradient algorithm; and Newton-Schneider algorithm. Raphson. This step may also include the use of a sampling method within a range of acceptable values.

[0031] According to some examples, the step of calculating a reference solution for the physical parameter from the reference measurement includes 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 the reference solution in the following steps of the process.

[0032] Acceptable solutions can, for example, be obtained using several different methods that are more or less suited to several specific pavement criteria. This allows 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 calculation step, starting from the reference solution, of solutions for all the measures in the group includes calculating solutions similar to the reference solution using an indicator method. The indicator method is described, for example, in the context of monitoring damage to an instrumented pavement in [REF 4].

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

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

[0036] Consequently, the present exposition 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 process as described above.

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

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

[0039] The information medium can be any entity or device capable of storing the program. For example, the medium 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 drive. The medium may also include a solid-state drive (SSD) storage medium.

[0040] On the other hand, the information medium may be a transmissible medium such as an electrical or optical signal, which may be transmitted via an electrical or optical cable, by radio, or by other means. The program described herein may, in particular, be downloaded from an Internet-type network. Brief description of the drawings

[0041] Other features and advantages of the invention will become apparent from the following description of embodiments of the invention, given by way of non-limiting examples, with reference to the accompanying figures, in which: • [Fig.1] is a schematic illustration of the steps of the present process, according to certain embodiments; • [Fig.2] is a functional block diagram illustrating the operation of the present process according to certain embodiments. Detailed description of the invention

[0042] Figure 1 schematically represents steps in the present method for calculating physical parameters from deflection measurements. Figure 1 shows that, in certain examples, the present method comprises the following steps: S10: Partitioning the deflection measurements into different measurement groups based on the measurement values; S20: Calculating physical parameters for each measurement group. Step S20 specifically includes the following steps: S21: Defining a reference measurement for the measurement group; S23: Calculating, from the reference measurement, a reference solution for the physical parameter; S25: Calculating, from the reference solution, solution physical parameters for all measurements in the group.

[0043] Fig. 2 represents examples of the operation of the present process.

[0044] One or more physical parameters, defined as the solutions 109, are thus determined from a set of deflection measurements 101 of a pavement. Rather than performing a calculation of the physical parameter(s) from each deflection measurement (back-calculation), as is generally the case in the prior art, the present method proposes to first perform a partition of 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 only one back-calculation per group of measurements 103.

[0045] According to some 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. Next, 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 process, 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 obtained using a falling mass deflectometer. The falling mass deflectometer generally consists of a force sensor and a plurality of geophones located at fixed distances from a mass pressing on the pavement. Each geophone allows the acquisition of a deflection measurement; thus, the set of several geophones in a deflectometer allows the acquisition of a plurality of measurements forming a deflection vector, commonly called a "deflection basin."

[0048] Deflection measurements are taken along a route via a series of measurement points along the route. It is possible to take a single deflection measurement per point on the route or to repeat the measurement several times at the same point. When measurements are repeated at the same point, each measurement at that point is generally considered 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 preceding expression; F j is the force applied during the measurement of index "j"; d"™'' is the geophone measurement vector (commonly called the "deflection vector"); and Fm is the average force applied.

[0051] In some 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 below a limit set by the road engineer and generally slightly above 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, related to the standard deviation). In order to obtain a satisfactory decomposition, the expected value of belonging to the set of Gaussians is maximized. In particular, in some embodiments, the process is initialized by choosing two central values ​​for the Gaussians (for example, two values ​​close to the value minimal among all values ​​in set 101). We then calculate the expected value of belonging to the two Gaussian distributions for each measure in set 101 as a function of the measure value. We then vary the centers

[0053]

[0054]

[0055]

[0056]

[0057] and the widths of the Gaussians to calculate new membership probabilities (in the middle). The chosen decomposition is the one that maximizes the probability of belonging to 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 performance of the instrument used to acquire the measurements. It is therefore advantageous to verify that the decomposition is correct. Otherwise, it is possible to extract information indicating that the number of groups is not suitable for the set 101 of measurements to which this method is applied.For example, when using the process, it is possible to use this information to warn the road engineer in charge of the calculation, and to offer him various correction options such as the possibility of increasing the number of measurement groups 103 into which to distribute the measurements of 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 corridor is constructed from a "mean basin" of deflection, that is, from a mean deflection vector derived from all the 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 using the following expression. V jwm jnoyen L / Jj (h - ..... A corridor centered on this average is then determined, the corridor being characterized by a given width, X. The value of the corridor 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 relative to this zone representing an average basin in order to define groups of measurements. For example, measurements entirely within this zone are considered to constitute a first group of 103 measurements {M_i}. In addition, 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 ​​within the zone) are further classified. (lower and upper than the zone) are then considered to construct, using the same method, three additional groups 103 of measurement populations. The process is repeated iteratively until each measurement in 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 that 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 that minimizes this difference is retained to define the center of a measurement group, to which all the measurements contained within 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] Step S10 of the partitioning of the present method can be applied to a single deflection measurement at a point on the pavement or to a plurality of deflection sub-measurements defining a deflection vector representative of a deflection basin in an area of ​​the pavement. These options depend in particular on the type of device used to acquire the pavement deflection measurements.

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

[0062] In step S23, the calculation of 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, sampling within 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, starting from a single reference measurement 105, a plurality of admissible solutions 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 selected solution remains, in this case, dependent on the expertise of the road engineer, which increases the adaptability and accuracy 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 may, for example, be based on an indicator method, see [REF 1].

[0066] In this indicator method, weighting functions are sought in order to maximize the sensitivity of an indicator derived from measurements to a physical parameter while minimizing its sensitivity to other physical parameters. The functions are chosen to allow the calculation of an indicator 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 pavement deflection. In this case, the solutions will be varied in the same direction (constant sign variation) 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 circumstances. For example, the variation factor, a, can be weighted to account for the stiffness of each layer. This will result in a different variation in the solution for each layer. The variation method used can also be based on classic indicators (LLI, BLI) known in the field of deflection measurements rather than on the maximum deflection.

[0071] Although the present description has been made with reference to a specific embodiment, it is evident that various modifications and changes can 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 mentioned can be combined in additional embodiments. Therefore, the description and drawings should be considered in an illustrative rather than restrictive sense.

Claims

Demands

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

2. A method according to claim 1, wherein 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 such 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 according to the measurement values ​​comprises: - the classification of 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 according to the measurement values ​​comprises the application of a grouping algorithm to the deflection measurements, the grouping algorithm resulting in the definition of the measurement groups as Gaussian distributions according to the measurement values, the widths and standard deviations of said Gaussian distributions being adjusted to maximize the expected mathematical membership of each measurement in one of the measurement groups.

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

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

7. A 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 the reference solution in the subsequent steps of the method.

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

9. A method according to any one of the preceding claims, wherein: - each deflection measure comprises a plurality of deflection sub-measures forming a deflection vector that corresponds to a deflection basin at a point in the pavement; and - the following steps of the method are applied to one or more of the sub-measures forming the deflection vector.

10. A system for calculating the physical parameters of a pavement implementing the method according to any one of claims 1 to 9.

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