CN113897865B - Concrete combined box girder pre-assembly quality evaluation method based on EMD - Google Patents

Concrete combined box girder pre-assembly quality evaluation method based on EMD Download PDF

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CN113897865B
CN113897865B CN202111161690.5A CN202111161690A CN113897865B CN 113897865 B CN113897865 B CN 113897865B CN 202111161690 A CN202111161690 A CN 202111161690A CN 113897865 B CN113897865 B CN 113897865B
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data
assembled
quality
assembly
emd
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CN113897865A (en
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杜永军
刘泓佚
徐林
唐志强
胡名良
吴文清
周小燚
王新雅
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Wuxi City Key Construction Project Management Center
Wuxi Traffic Construction Engineering Group Co ltd
Southeast University
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Wuxi City Key Construction Project Management Center
Wuxi Traffic Construction Engineering Group Co ltd
Southeast University
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    • E—FIXED CONSTRUCTIONS
    • E01—CONSTRUCTION OF ROADS, RAILWAYS, OR BRIDGES
    • E01D—CONSTRUCTION OF BRIDGES, ELEVATED ROADWAYS OR VIADUCTS; ASSEMBLY OF BRIDGES
    • E01D21/00—Methods or apparatus specially adapted for erecting or assembling bridges
    • E—FIXED CONSTRUCTIONS
    • E01—CONSTRUCTION OF ROADS, RAILWAYS, OR BRIDGES
    • E01D—CONSTRUCTION OF BRIDGES, ELEVATED ROADWAYS OR VIADUCTS; ASSEMBLY OF BRIDGES
    • E01D19/00—Structural or constructional details of bridges
    • E—FIXED CONSTRUCTIONS
    • E01—CONSTRUCTION OF ROADS, RAILWAYS, OR BRIDGES
    • E01D—CONSTRUCTION OF BRIDGES, ELEVATED ROADWAYS OR VIADUCTS; ASSEMBLY OF BRIDGES
    • E01D19/00—Structural or constructional details of bridges
    • E01D19/02—Piers; Abutments ; Protecting same against drifting ice
    • E—FIXED CONSTRUCTIONS
    • E01—CONSTRUCTION OF ROADS, RAILWAYS, OR BRIDGES
    • E01D—CONSTRUCTION OF BRIDGES, ELEVATED ROADWAYS OR VIADUCTS; ASSEMBLY OF BRIDGES
    • E01D2/00—Bridges characterised by the cross-section of their bearing spanning structure
    • E01D2/04—Bridges characterised by the cross-section of their bearing spanning structure of the box-girder type
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/13—Architectural design, e.g. computer-aided architectural design [CAAD] related to design of buildings, bridges, landscapes, production plants or roads
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q50/00—Systems or methods specially adapted for specific business sectors, e.g. utilities or tourism
    • G06Q50/08—Construction
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
    • Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
    • Y02P90/30—Computing systems specially adapted for manufacturing

Abstract

The application relates to a concrete combined box girder pre-assembly quality evaluation method based on EMD. The method comprises the following steps: inputting bridge pier data and bridge pier data related to pre-assembly quality evaluation of bridge piers and bridge piers; performing virtual assembly on the beam body data and the pier data according to a default assembly scheme to obtain various assembled data; and analyzing by adopting an evaluation function according to each item of assembled data, describing the condition of a quality detection subentry in the whole area in a probability statistics mode, and calculating a weighted sum to calculate a pre-assembled quality evaluation value based on EMD (empirical mode decomposition) and obtain a whole assembly quality evaluation result, so that the assembly quality of the whole area can be reflected, meanwhile, the comprehensive influence of various factors on the final pre-assembled quality evaluation can be considered, and the limitation of calculating standard detection content by simply utilizing point cloud data is avoided. The method provides a detection item of the matching degree of the corresponding surface by using the point cloud data so as to comprehensively reflect the relative deviation between the adjacent beam bodies.

Description

Concrete combined box girder pre-assembly quality evaluation method based on EMD
Technical Field
The application relates to the technical field of bridge structures, in particular to a concrete combined box girder pre-assembly quality assessment method based on EMD.
Background
In order to ensure the assembly quality of the concrete combined box girder and prevent the assembly construction difficulty caused by production construction errors, a virtual pre-assembly mode is generally adopted for carrying out pre-assembly simulation and verifying the assembly quality. The virtual simulation assembly is based on the steps of acquiring the shape characteristics of the beam body by means of a three-dimensional laser point cloud technology, assembling the beam body by means of a virtual pre-assembly technology, and evaluating the assembly quality of the beam body.
However, the quality assessment of the concrete structure pre-assembly currently only has independent detection items in the specification, most of the methods only consider local geometric deviation at partial nodes, and the method has great limitations: firstly, the quality condition of the whole assembly body cannot be comprehensively reflected; secondly, noise in the calculation region may have a large influence on the result; thirdly, data loss caused by occlusion and the like in the actual scanning process may cause that the result cannot be obtained.
Disclosure of Invention
In view of the above, there is a need to provide an EMD-based method for evaluating the pre-assembly quality of a concrete composite box girder, which can solve the above-mentioned disadvantages.
An EMD-based concrete combined box girder pre-assembly quality assessment method comprises the following steps:
inputting bridge pier data and bridge pier data related to pre-assembly quality evaluation of bridge piers and bridge piers;
performing virtual assembly on the beam body data and the pier data according to a default assembly scheme to obtain various assembled data;
and analyzing by adopting an evaluation function according to the assembled data, describing the condition of the quality detection subentries in the whole area in a probability statistics mode, and calculating a weighted sum to calculate a pre-assembled quality evaluation value based on the EMD distance so as to obtain the integral evaluation result of the whole assembled quality.
In one embodiment, the step of virtually assembling the beam body data and the pier data according to a default assembly scheme to obtain each assembled item of data includes:
when the longitudinal center lines of all the beam bottom surfaces coincide with the connecting lines of the central points of the cushion stones correspondingly counted into the support data and keep horizontal in the transverse direction, the middle points of the longitudinal center lines of the beam bottom surfaces coincide with the middle points of the connecting lines of the central points of the cushion stones correspondingly counted into the support data, and all assembled data are obtained.
In one embodiment, the step of analyzing the assembled data by using an evaluation function and then calculating a weighted sum to calculate a pre-assembly quality evaluation value based on an EMD distance to obtain an overall evaluation result of the overall assembly quality includes:
and analyzing the point cloud data based on the assembled data, and calculating a weighted sum to calculate a pre-assembled quality evaluation value based on the EMD distance, describing the deviation of a quality evaluation item in a probability distribution form, and obtaining an integral evaluation result of the overall assembling quality with statistical significance, which is obtained by calculating the point cloud data.
In one embodiment, the evaluation parameters of the pre-assembled quality assessment value at least comprise a wet joint component assessment value, a support deviation component assessment value and a corresponding surface matching degree component assessment value.
According to the EMD-based concrete combined box girder pre-assembly quality evaluation method, girder body data and pier data of piers and girder bodies related to pre-assembly quality evaluation are input; performing virtual assembly on the beam body data and the pier data according to a default assembly scheme to obtain various assembled data; and analyzing by adopting an evaluation function according to each item of assembled data, describing the condition of a quality detection subentry in the whole area in a probability statistics mode, calculating a weighted sum to calculate a pre-assembled quality evaluation value based on an EMD distance, and obtaining an integral evaluation result of the whole assembling quality, so that the assembling quality of the whole area can be reflected, meanwhile, the comprehensive influence of various factors on the final pre-assembled quality evaluation can be considered, and the limitation of calculating standard detection content by simply utilizing point cloud data is avoided. The method provides a detection item of the matching degree of the corresponding surface by using the point cloud data so as to comprehensively reflect the relative deviation between the adjacent beam bodies.
Drawings
FIG. 1 is a schematic flow chart of a method for evaluating the pre-assembly quality of a concrete composite box girder based on EMD in one embodiment;
FIG. 2 is a data diagram of a beam side point cloud in one embodiment and an embodiment thereof;
FIG. 3 is a schematic diagram of coordinates of an embodiment support point and an embodiment data thereof;
FIG. 4 is a diagram illustrating default construction rules in one embodiment;
FIG. 5 is a schematic illustration of a construction effect in one embodiment;
FIG. 6 is a schematic flow chart of a method for evaluating the pre-assembly quality of a concrete composite box girder based on EMD in another embodiment;
FIG. 7 is a diagram illustrating the partitioning of regions in the wet seam width partition evaluation value calculation, in accordance with one embodiment;
FIG. 8 is a diagram illustrating a representative point set matching method, according to an embodiment;
FIG. 9 is a diagram illustrating a boundary point determination method according to an embodiment;
FIG. 10 is a diagram illustrating region partitioning in computation of corresponding face matching degree partition estimates, in accordance with an embodiment;
FIG. 11 is a diagram illustrating a side point cloud projection method in calculating a corresponding surface matching degree subitem evaluation value according to an embodiment;
FIG. 12 is a diagram illustrating EMD definition of discrete probability distributions in one embodiment.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the present application is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present application and are not intended to limit the present application.
In one embodiment, as shown in fig. 1, there is provided an EMD-based method for evaluating the pre-assembly quality of a concrete composite box girder, comprising the steps of:
and S220, inputting bridge pier data and bridge pier data related to pre-assembly quality evaluation of the bridge piers and the bridge piers.
According to the table 8.7.2-1 and the table 8.7.2-2 in JTG F80-1-2017 Highway engineering quality inspection and assessment Standard (first volume civil engineering), the following concrete bridge assembly inspection items are taken: the wet joint width, bearing center offset and adjacent beam top elevation difference total three items. According to the three items, the input beam body data comprises: all the point cloud data of each beam side and the support supporting point coordinates designed on the beam, the input pier data comprises: the coordinates of the center point of the pad, which are included in the support data, are three groups of data, and the geometric meaning of each group of data is schematically shown in fig. 2 to 3 and part of the data in the embodiment is shown in fig. 2. And extracting beam data and pier data from the pier columns and the beam point cloud, and inputting the beam data and the pier data as initial data.
And S240, virtually splicing the beam body data and the pier data according to a default splicing scheme to obtain various spliced data.
In one embodiment, the step of virtually splicing the beam body data and the pier data according to a default splicing scheme to obtain spliced data comprises the following steps: when the longitudinal center lines of all the beam bottom surfaces coincide with the connecting lines of the center points of the cushion stones correspondingly counted in the support data and are kept horizontal in the transverse direction, the middle points of the longitudinal center lines of the beam bottom surfaces coincide with the middle points of the connecting lines of the center points of the cushion stones correspondingly counted in the support data, and all assembled data are obtained.
The default splicing scheme refers to a scheme of placing the beam bodies on proper beam positions according to the number of the beam bodies and the designed sequence. The assembly rule is schematically shown in fig. 4, namely, it is assumed that the longitudinal center lines of all beam bottom surfaces are coincident with the connecting lines of the central points of the corresponding cushion stones taking the data of the supports into account and are kept horizontal in the transverse direction. Meanwhile, the middle point of the longitudinal center line of the bottom surface of the beam body coincides with the middle point of the connecting line of the center points of the cushion stones correspondingly counted in the data of the support. The assembly rule is schematically shown in fig. 4, and the assembly effect in one embodiment of the present application is shown in fig. 5. Further, as shown in fig. 6, virtual pre-assembly quality evaluation is performed according to the assembled data items and the beam side point cloud data, so as to obtain an evaluation value of wet joint components, an evaluation value of support deviation components and an evaluation value of corresponding surface matching degree components.
And step S260, analyzing by adopting an evaluation function according to each item of assembled data, describing the condition of a quality detection item in the whole area in a probability statistics mode, and calculating a weighted sum to calculate a pre-assembled quality evaluation value based on an EMD distance so as to obtain an integral assembled quality evaluation result.
In an embodiment, the step of analyzing the assembled data by using an evaluation function and then calculating a weighted sum to calculate a pre-assembly quality evaluation value based on an EMD distance to obtain an overall evaluation result of the overall assembly quality includes: and analyzing the point cloud data based on the assembled data, and calculating a weighted sum to calculate a pre-assembled quality evaluation value based on the EMD distance, describing the deviation of a quality evaluation item in a probability distribution form, and obtaining an integral evaluation result of the overall assembling quality with statistical significance, which is obtained by calculating the point cloud data.
The evaluation parameters of the pre-assembly quality evaluation value at least comprise a wet joint component evaluation value, a support deviation component evaluation value and a corresponding surface matching degree component evaluation value. In order to reflect the overall assembling quality condition and utilize rich information contained in the data volume of the point cloud data, the assembling quality can be described by adopting a statistical method according to a large amount of point cloud data in the application.
Firstly, point cloud data of the side surfaces of the beams in the assembled state are divided according to regions and then are subjected to statistical analysis. Taking the mean value of all point cloud data point coordinates in each area as a representative point of the area can convert the side face of the whole beam into a representative point set which is relatively less in number and relatively more uniform in distribution, as shown in fig. 7 (in order to ensure the display effect, the point cloud density in fig. 7 is subjected to sparse processing). Meanwhile, the division scale of the region can be adjusted according to the required precision, and the value is recommended to be 5-10 times of the average distance of the point cloud so as to ensure that enough data points exist in the region. For point clouds on the two side faces of the beam body of the same wet joint, the two representative point sets are matched, so that the points in the two representative point sets correspond to each other as far as possible, the sum of the distances between the matched representative points is minimum, and a schematic diagram is shown in fig. 8. At the moment, the representative point sets of the two are matched and converted into the minimum weight matching problem of the bipartite graph, so that the minimum weight matching problem of the bipartite graph is solved by adopting a conventional KM algorithm. In this way, the wet seam width can be obtained everywhere over the entire area by calculating the horizontal distance between the corresponding points. Statistically, the distribution of the whole width data meets the normal distribution surrounding the mean value, so the mean value and the variance are calculated, and the discrete wet joint width value in the whole area is converted into a continuous normal distribution model for description.
And secondly, introducing corresponding surface matching degree to describe the corresponding degree of the side surfaces of the two adjacent beam bodies in the spatial position, and reflecting the corresponding deviation of the side surfaces of the correspondingly assembled beam bodies in the longitudinal direction and the vertical direction. At this time, the internal point cloud has no influence on the evaluation of the correspondence, so that it is necessary to extract boundary points for evaluation. The classification and identification of the boundary point are mainly determined by the maximum included angle formed by the connecting line of a certain point and its neighboring points, and when the maximum included angle is greater than a certain threshold (the threshold is generally close to 180 °), the point is determined as the boundary point, as shown in fig. 9. And then according to the method for calculating the wet joint, performing region division on the boundary point data of the side surfaces of the beams, fitting the boundary point in each region into a line segment in the region, taking the midpoint of the line segment as a representative point of the region, and forming a representative point set of the region as shown in fig. 10 (in order to ensure the display effect, the density of point clouds in fig. 10 is subjected to sparse processing). Different from the calculation of the width of the wet joint, when the matching degree of the corresponding surfaces is calculated, the side surfaces of two adjacent beam bodies are projected to the same plane, the influence of the transverse slope in the longitudinal direction is deducted, and then the beam bodies are divided in the same region division mode, as shown in fig. 11, the matching at this time does not need to use a KM algorithm, only the representative points of the side surfaces of the two beam bodies in the same region are matched, and then the longitudinal and vertical coordinate deviation is converted into a continuous two-dimensional normal distribution model for description.
After normal distribution descriptions of the wet joint width and the corresponding face matching degree are obtained, threshold distribution is set as reference standards of the two normal distribution descriptions according to specification requirements of tables 8.7.2-1 and 8.7.2-2 in road engineering quality inspection assessment standard (first civil engineering) of JTG F80-1-2017. For wet joint width, JTG F80-1-2017 ″ "highway engineering quality test assessment standards (first civil engineering project)" in the specifications of table 8.7.2-1 and table 8.7.2-2, the error should be within ± 20mm, and assuming that 20mm is 95% of the quantile of the threshold distribution, i.e., 1.96 σ =20mm, and 0mm is the center of the standard distribution, the threshold distribution N (μ, σ) of wet joint width can be obtained 2 ) N (0,104); for the degree of matching of the corresponding surface, in the specifications of tables 8.7.2-1 and 8.7.2-2 in JTG F80-1-2017 highway engineering quality inspection and assessment standard (first volume of civil engineering), the size deviations in the longitudinal and vertical directions are all limited to ± 10mm, so that 10mm is taken as 95% of the quantile point of the threshold distribution, and the threshold distribution N (μ) of the degree of matching of the corresponding surface is obtained (μ 1 ,μ 2 ,σ 1 2 ,σ 2 2 ,ρ)＝N(0,0,26,26,0)。
Finally, the generalized "distance" of the two probability distributions is estimated, which can be measured by using the EMD (Earth Mover's distance) distance, i.e. the Wasserstein distance between the two probability distributions, for the discrete probability distributions, it is equivalent to considering the histogram of the probability distributions as a soil heap, and converting one soil heap form to another soil heap form, also called dozing distance, with the minimum transportation cost, as shown in fig. 12. And for a continuous normal distribution, the EMD distance is W = ((mu-mu') 2 +(σ-σ’) 2 ) 1/2 . In this case, an ideal distribution N (0,0) is assumed, i.e., a state in which there is no deviation at all. By calculating the EMD distance from the actual distribution and the threshold distribution to the ideal distribution and dividing the actual distribution and the threshold distribution, the statistical evaluation value E can be calculated for the wet joint width and the corresponding surface matching degree width And E match . When the evaluation value of the components after division is less than 1, the integral distribution condition is considered to be better than the specification requirement, and the smaller the evaluation value is, the better the evaluation value is; on the contrary, the overall distribution is considered to be inferior to the specification requirement, and the larger the subentry evaluation value is, the worse the integral distribution is.
Further, JTG F80-1-2017, in the Standard of quality inspection and assessment of Highway engineering (first volume of civil engineering), table 8.7.2-1 and table 8.7.2-2, three test items required in the specification: wet joint width, bearing center offset, and adjacent beam top height difference. Because the data of the bearing center deviation are generally less, the significance of the statistical result is not great, and the method of directly averaging is adopted to divide the data by 5mm required by the specification to obtain the subentry evaluation value E bear . Similarly, if the evaluation value of the component is less than 1, the overall distribution condition is considered to be better than the specification requirement, and the smaller the evaluation value is, the better the evaluation value is; on the contrary, the overall distribution is considered to be inferior to the specification requirement, and the larger the subentry evaluation value is, the worse the integral distribution is. So far, all three detection items have corresponding subentry evaluation values. On one hand, the three-term evaluation values can reflect the quality detection results of all the terms; on the other hand, the evaluation function F (E) is designed width ,E match, E bear )＝αE width +βE match +γE bear . And the values of the three components are taken as required, so that the value of alpha + beta + gamma =1, and the evaluation value of the overall assembly quality detection of the beam body can be obtained. And the value also has the property of the above subentry evaluation value and has a negative correlation with the assembling quality.
According to the EMD-based concrete combined box girder pre-assembly quality evaluation method, girder body data and pier data of piers and girder bodies related to pre-assembly quality evaluation are input; performing virtual assembly on the beam body data and the pier data according to a default assembly scheme to obtain various assembled data; and analyzing by adopting an evaluation function according to each item of assembled data, describing the condition of a quality detection subentry in the whole area in a probability statistics mode, calculating a weighted sum to calculate a pre-assembled quality evaluation value based on an EMD distance, and obtaining an integral evaluation result of the whole assembling quality, so that the assembling quality of the whole area can be reflected, meanwhile, the comprehensive influence of various factors on the final pre-assembled quality evaluation can be considered, and the limitation of calculating standard detection content by simply utilizing point cloud data is avoided. The method provides a detection item of the matching degree of the corresponding surface by using the point cloud data so as to comprehensively reflect the relative deviation between the adjacent beam bodies.
It should be understood that, although the steps in the flowchart of fig. 1 are shown in order as indicated by the arrows, the steps are not necessarily performed in order as indicated by the arrows. The steps are not performed in the exact order shown and described, and may be performed in other orders, unless explicitly stated otherwise. Moreover, at least a portion of the steps in fig. 1 may include multiple sub-steps or multiple stages that are not necessarily performed at the same time, but may be performed at different times, and the order of performance of the sub-steps or stages is not necessarily sequential, but may be performed in turn or alternately with other steps or at least a portion of the sub-steps or stages of other steps.
All possible combinations of the technical features in the above embodiments may not be described for the sake of brevity, but should be considered as being within the scope of the present disclosure as long as there is no contradiction between the combinations of the technical features.
The above-mentioned embodiments only express several embodiments of the present application, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the concept of the present application, which falls within the scope of protection of the present application. Therefore, the protection scope of the present patent shall be subject to the appended claims.

Claims (4)

1. The method for evaluating the pre-assembly quality of the concrete combined box girder based on EMD is characterized by comprising the following steps:
inputting bridge pier data and bridge pier data related to pre-assembly quality assessment of bridge piers and bridge bodies, wherein the bridge body data comprises: all the point cloud data of each beam side and the support supporting point coordinates designed on the beam, wherein the pier data comprises: calculating the coordinate of the central point of the pad stone of the support data;
performing virtual assembly on the beam body data and the pier data according to a default assembly scheme to obtain various assembled data;
and analyzing by adopting an evaluation function according to each item of assembled data, describing the condition of a quality detection subentry in an integral area in a probability statistics mode, and calculating a weighted sum to calculate a pre-assembled quality evaluation value based on the EMD distance so as to obtain an integral evaluation result of the integral assembling quality.
2. The method of claim 1, wherein the step of virtually assembling the beam body data and the pier data according to a default assembly scheme to obtain each assembled item of data comprises:
when the longitudinal center lines of all the beam bottom surfaces coincide with the connecting lines of the center points of the cushion stones correspondingly counted in the support data and are kept horizontal in the transverse direction, the middle points of the longitudinal center lines of the beam bottom surfaces coincide with the middle points of the connecting lines of the center points of the cushion stones correspondingly counted in the support data, and all assembled data are obtained.
3. The method of claim 1, wherein the step of analyzing the assembled data by using an evaluation function to describe the quality detection sub-items in the whole area in a probabilistic manner, and then calculating a weighted sum to calculate a pre-assembled quality evaluation value based on the EMD distance to obtain a whole evaluation result of the whole assembly quality comprises:
and analyzing the point cloud data based on the assembled data, and calculating a weighted sum to calculate a pre-assembled quality evaluation value based on the EMD distance, describing the deviation of a quality evaluation item in a probability distribution form, and obtaining an integral evaluation result of the overall assembling quality with statistical significance, which is obtained by calculating the point cloud data.
4. The method of claim 1 or 2, wherein the parameters for evaluating the pre-assembled quality assessment value comprise at least a wet joint component assessment value, a support deviation component assessment value and a corresponding surface matching component assessment value.
CN202111161690.5A 2021-09-30 2021-09-30 Concrete combined box girder pre-assembly quality evaluation method based on EMD Active CN113897865B (en)

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