An automated construction method of finite element model from point cloud data of a steel bridge pier
2024 Volume 5 Issue 1 Pages 7-14
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2024 Volume 5 Issue 1 Pages 7-14
The method was developed to automatically generate an FEM model of a steel highway pier, which is expected to behave in a complex manner during earthquakes, from point cloud data that can measure the three-dimensional shape of the object, without relying on drawings. The FEM model generated by the proposed method (point cloud model) and the FEM model created manually from the information in the drawings (drawing model) were subjected to the same loads and their behaviors were verified. It was found that the point cloud model tended to be slightly lower in terms of yield load, maximum load, and stress distribution near local deformation. There are two possible explanations for this factor: the discrepancy between the actual structure and the drawing due to initial imperfections, or the insufficient accuracy of the proposed method.
A vast number of existing bridges are rapidly aging. Since it is not practical to rebuild all of them at the same time, strategic renewal through life cycle extension is required. To extend the life cycle of bridges, quantitative evaluation of the residual load capacity is being promoted through numerical analysis. As shown in Fig.1, analytical models, such as finite element models, include a beam model that reflects the framework structure, a fiber-based model that enables reasonable structural calculations by applying cross-sectional information to elements of a beam model, a shell model that can consider local buckling by constructing a surface with thickness, and a solid model that reproduces a three-dimensional shape. A fiber model is a reasonable model for load capacity analysis of structures, and a shell model is used when local buckling is dominant. The accuracy of the finite element model configuration (dimensions, materials, and boundary conditions) has been verified through structural experiments and is now being realized with high reproducibility1).
However, the efficiency of an element generation method remains an issue. Construction of a finite element model requires acquisition of member dimensions of a target structure. However, in cases of old bridges, as-build drawings are often unavailable. In addition, conditions of bridges inevitably changed since its construction due to various factors. Therefore, it is necessary to construct a finite element model based on in-situ measured data instead of relying on drawings, but manual measurement is time-consuming and prone to various human errors.
Therefore, the authors focus on point cloud data. Since 3D positions and colors of targets can be acquired as point cloud data in short time and at low cost. It is expected to automatically acquire geometry information of members and quantitatively evaluate local deformation caused by loading. However, as point cloud data is a discrete set of points, processing based on a geometric algorithm is required to obtain the parameters and deformations necessary to construct a finite element model. In the past research, the method to construct fiber-based model of a superstructure of truss bridge was developed2), but a method to construct shell model of substructure of bridge has not yet been developed.
In this paper, the method to automatically generate a finite element model from point cloud data of steel piers of highways, which are expected to behave in a complex manner, and to quantitatively evaluate the deformation under loading. The model constructed by the proposed method is used in loading analysis, and the accuracy of the analysis is evaluated by comparing it with the model generated from the drawings.
The geometry of a 1/5-scale steel pier specimen was measured using point cloud data, at Aichi Institute of Technology. Fig. 2 shows detail of the specimen and Fig. 3 shows the installation of the loading device and specimen. As shown in Fig. 2, the column part has a hollow-section structure with four panels welded together, eight longitudinal ribs and two diaphragms on the inside.
The geometry and positional coordinates of the specimen before the experiment were measured by two methods: "stationary laser measurement" and "handheld laser measurement". Details of the measurement methods and the measured point cloud data are described below.
(1) Stationary laser scanner
The stationary laser scanner, Leica RTC360 (resolution: 6 mm@10 m, error: 1.9 mm@10 m, Fig. 4(a)), was used to measure the whole shape of the specimen. As shown in Fig. 4(b), the origin of the coordinate was set at the vertical projection from the load point to the ground, with the x-axis in the outof-plane direction, the y-axis in the in-plane direction, and the z-axis in the height direction of the specimen. Measurements were taken at four locations (Fig. 4(b)). The measured point cloud data is shown in Fig. 4(c). The number of measured points was 144,340,978 for the entire laboratory, and 8,030,700 for the piers and actuators, with a point density of 70/cm2 to 100/cm2. The measurement time was about 2 minutes per each measured location.
(2) Handheld laser scanner
The handheld laser scanner, HandySCAN BLACK(tm) | Elite (resolution: 0.025 mm@30 cm, error: 0.025 mm@30 cm, Fig. 5(a)), was used to measure the detailed geometry of the column part. Because of its high resolution and small error, the system also aims to acquire weld lines of longitudinal ribs and initial irregularities. The distance from the laser scanner to the object is approximately 30 cm. The entire surface of the column shown in Fig. 5(b) was measured. The measured point cloud data is shown in Fig.5(c). The number of measured points was 4,658,203, with a point density of about 44/cm2 to 100/cm2 for smooth areas and 204/cm2 to 625/cm2 for rough areas. The measurement time was about 20 minutes: marker pasting for self-location estimation was 10 minutes and measurement was 10 minutes.
(1) Requirement of the FEM model
This chapter describes the development of a method to automatically generate finite element models from the point cloud data described in Chapter 2. The finite element model generated is based on a fiber-based model, but shell models are generated for hollow-section column, longitudinal ribs, and diaphragms, where local buckling may dominate. Therefore, the finite element model as shown in Fig. 6 is generated. In this experiment, the beam model of the specimen is assumed to be a rigid beam model because the beam section of the specimen can be considered almost as a rigid body. So, the column model is generated from highly accurate point cloud data measured by the handheld laser scanner, while the beam model is derived from point cloud data measured by the stationary laser scanner. The finite element model is directly generated from point cloud without creating geometric models, as the focus of this research is solely on load capacity analysis.
(2) Detection of nodes and elements (fiber-based model)
In the first step, nodes and elements of the fiberbased model are detected from the measured point cloud data of the specimen including actuators.
a) Position of ribs and diaphragms
As shown in Fig. 6, this specimen contains diaphragms and longitudinal ribs inside the column. As these are invisible from outside, their shapes cannot be measured in the point cloud. But their positions can be detected by slight bulges caused by welding.
As shown in Fig. 7, when the normal vectors obtained from the point cloud data measured with the handheld laser scanner are separated into horizontal and vertical angles, different features can be seen only near the welding position. By approximating these points as straight lines using the RANSAC method3) (the method to detect parametric models by excluding the influence of outliers), the lines of the diaphragm and longitudinal ribs can be obtained. The centroids of the four intersections of the lines of diaphragms at the same height can be used to obtain the central axis of the column section (Fig. 8).
b) Modeling of a beam
In order to model the beam section, it is necessary to detect the central axis of the beam. Therefore, the point cloud data is divided into planer segments using the region growing method4), a clustering method that adds adjacent points with close normal vector and curvature parameters in the point cloud data to the same group. The centroid, normal vector, and area are calculated for each divided segment, and these are used to identify the segment it corresponds to. The handhole segments, which are located at the front and back of the beam, are extracted, and the axes through the center of the beam are obtained by mapping the handholes located at the front and back and taking the midpoint of the center of each figure (Fig. 9).
c) Detection of load point
The actuator used in this experiment is cylindrical shape, and the load point is obtained by utilizing the property that the intersection of the load lines of two actuators corresponds to the load point. The parameters of the linear equation of central axis and the radius of the cylinder can be obtained from actuator segments by fitting them to the cylinder based on the RANSAC method. The actuator segments can be detected based on the normal vector thresholds, which one of the xyz components is not prominent and distributed. Considering the possibility that the two lines may be in a torsional position, the intersection is defined as the midpoint of the line segment that is orthogonal to the two lines and has the minimum distance between the two lines (Fig. 10).
(3) Modeling of column part (shell model)
The next step is to generate a model of the column part. Since the column part is composed of four panels, inner longitudinal ribs, and diaphragms, parameters related to them are obtained from the point cloud data.
First, starting from the bottom of the column part, cross sections are sliced at equal intervals along the central axis of the column part. Next, the joint points of the panels on the four sides of the column part and the welding points of the longitudinal ribs are detected from the intersections of the obtained cross sections and the lines of the aforementioned longitudinal ribs. The positions of the panel joints and longitudinal rib welding points are corrected to prevent overlap due to the thickness of adjacent shells. The panel is then divided into equally spaced sections between the two joint points or longitudinal rib welding points. This process is repeated for the sliced cross section to create a single shell by connecting four adjacent nodes (Fig. 11).
Nodes obtained by linear interpolation of the line segments connecting the joint points or longitudinal rib welding points may not reflect the actual shape such as initial irregularities. Therefore, point cloud data is used to correct the shape to the actual shape. In the method of searching and replacing the nearest neighbor points to a node in the point cloud data of a column part, there is a possibility of obtaining oblique neighbor points due to gaps in the points. Therefore, the node is adjusted to project to the local plane around the obtained neighbor point (Fig. 12).
The shell model of a longitudinal rib is generated by sampling nodes perpendicular to the line segment connecting two longitudinal rib welding points on the same plane, starting from the aforementioned longitudinal rib welding point. The generated models shows as Fig. 13.
(4) FEM model generation result
The proposed method was implemented in the development environment shown in Table 1. The point cloud data measured by the stationary laser scanner and the point cloud data measured by the handheld laser scanner were input, resulting in a computation time of approximately 2.5 minutes. Material and load conditions are entered in the analysis software.
Because it was difficult to obtain the thickness of each member and the height of the longitudinal ribs with the measurement method used in this paper, the values read from the drawings (Fig. 2) were applied to these values.
(1) Analysis conditions
The finite element model generated by the proposed method from the measured point cloud data of the specimen (referred to as the "point cloud model") and the finite element model created manually from the drawings (referred to as the "drawing model") were subjected to the same loads as in the loading experiment to confirm their behavior. The difference between the two models is the coordinate of the nodes in the shell model for the column part and the fiberbased model for the beams. Other models (element division, modeling of joints, etc.), loading conditions, restraint conditions are the same for both models.
As shown in Fig. 14, a dead load of a superstructure (540kN) was first applied to the load point, followed by a forced displacement (0.2 m) in the out-ofplane direction (x-axis direction).
(2) Results
Fig. 15 shows the load-displacement curves of the point cloud model and the drawing model at the load point position, and Fig. 16 shows the stress contour and deformation when the horizontal displacement in the out-of-plane direction is 0.2m. As can be seen, it was confirmed that the point cloud model and the drawing model show almost the same behavior, indicating the possibility of generating a finite element model from the point cloud data. On the other hand, Fig. 15 shows that the point cloud model has a slightly lower yield load and maximum load than the drawing model, and Fig. 16 shows that the point cloud model has a slightly lower stress distribution in the neighborhood where concentrated deformation occurs.
(3) Limitations and considerations
In this paper, the possibility of structural analysis using a finite element model automatically generated from point cloud data is demonstrated. The reasons for the slight differences in load-displacement curves and stress contour near some local buckling are thought to be caused by different configuration between the two models. In other words, point cloud model have captured initial irregularities of about 1.2mm, or the modeling accuracy of the proposed method was insufficient. However, since no comparison with the results of loading experiments has been made, further consideration will be given by comparing the results with loading experiments in the future. Currently, displacement evaluation in loading experiments involves checking local deformation by hand or by applying a tape measure, or by setting up a displacement meter for a single point or a straight line, and it is difficult to say that evaluation is performed quantitatively on an area basis. So, a new quantitative evaluation method for local deformation using point cloud data is necessary. It can be expected to deepen discussion by comparing with loading experiments in the future.
Although the proposed method was able to detect the positions of longitudinal ribs and diaphragms inside the columns, it was difficult to obtain the thickness of the plates. As shown in Fig. 17, welding is performed at two welding points on both sides of each plate, but the bulged welding points are not at the edges of the plate but slightly outside, and the method of obtaining the distance between the two welding lines yields a value larger than the actual plate thickness. However, there is a possibility that the thickness of longitudinal ribs and diaphragms can be acquired based on the measured panel thickness because they are correlated with the panel thickness in the design criteria. Furthermore, if success or failure in jointing panels can be detected from measured point cloud data, panel thickness can be acquired and the finite element model containing thickness of members and height of longitudinal ribs is automatically constructed from point cloud data.
The proposed method in this paper was used handholes’ positions in the beam section, but there are steel piers without handholes. Furthermore, there are steel piers with inconsistent beam cross-sections. In order to increase the versatility of the proposed method, it is necessary to develop a method that can handle steel piers with various shapes, as shown in Fig. 18. In addition, the proposed method uses a number of geometric algorithms for processing point cloud data, and the threshold parameters are currently set to reasonable values through trial and error for each case study. If a method to set appropriate parameters for geometric algorithms applicable to steel piers of various shapes can be developed, the versatility of the proposed method is expected to be further improved.
In this paper, a method to construct finite element models by efficiently obtaining member cross-sections and member structures without using drawings by utilizing point cloud data is proposed, and loading analysis using a specimen of steel highway bridge piers, which are expected to behave in a complex manner is performed. The following are the findings obtained.
1) A method for accurately obtaining the geometry and member dimensions of the specimen (point cloud data acquisition method using stationary laser measurement and handheld laser measurement) is proposed.
2) A method to construct a finite element model from the acquired information is established.
3) A computer code that can automatically generate an analytical model from point cloud data is developed.
4) Comparing the point cloud model constructed from the point cloud data and the drawing model created from the drawings, the trends of the load-displacement curves were similar for both models, but slight differences were observed in the initial slope and load carrying capacity.
Finally, the challenges of this study and future research would be discussed. In this paper, the finite element model was automatically generated from the point cloud data of steel piers. However, there is room for improvement in versatility, as the thickness and width of longitudinal ribs could not be automatically obtained, and some types of steel piers are assumed to be inapplicable. In addition, structural experiments have been conducted, but their response values have not yet been evaluated, so further consideration will be given through comparison with loading tests in the future. In this case, it is expected that the content of the discussion will be further deepened by using an areal and quantitative displacement evaluation method based on point cloud data as an alternative method to the current displacement evaluation method of loading experiments.
This research was supported by JACIC 2022-6, Nao Hidaka. The point cloud data used in this research were measured by Mr. Naofumi Hashimoto, Kameda Corporation, in structural experiments at Nagoya Expressway Public Corporation, Nagoya Institute of Technology, and Aichi Institute of Technology, with the cooperation of Dr. Moriaki Suzuki and Dr. Yoshiyuki Shimaguchi, Aichi Institute of Technology. We also thank Ms. Maki Iwamura of the Earthquake Engineering Research Center, Inc. for her guidance in constructing the analytical model.
