1. Introduction
Currently, considerable attention is being given to the development of more accurate deterministic operators, including methods such as the Finite Element Method (FEM) and analytical solution approaches. These approaches take into account the complex relationship between stability and fatigue strength, as well as the influences of initial conditions. Concurrently, it is essential to analyse the influence of various parameters such as material properties, geometry and initial imperfections on the stability capacity by means of these approaches. In general, the validation of the results has to be confirmed by experiments. The fatigue strength of welded structural components and the stability of steel structures such as thin-walled and shell structures are of major importance in steel structures. The buckling behaviour of steel structural components significantly depends on initial geometric imperfections [
1,
2,
3], and the measured geometric imperfections are essential as predefined input values for the calculation using geometrically and materially nonlinear analysis with imperfections included (GMNIA) [
4,
5]. In general, geometric imperfections can be divided into two categories: global and local imperfections, which are the dominant causes of premature global and local instability or buckling, respectively. Most recently, Aktepe and Erkal [
6] reviewed a large number of existing research results and publications concerned with the measurement, identification, prediction and modelling of geometrical imperfections in cold-formed steel components so as to provide useful information about the factors to consider in design and analysis. It was shown that the methodology for modelling geometric imperfections is of paramount importance and is largely dependent on the information available to model the imperfections in the geometry. Furthermore, in the case of welded structures, due to the discontinuous geometry of the weld seam, the stress field at the weld is usually singular, which is a primary factor that complicates the fatigue strength issues of welded joints in steel structures [
7]. Traditional fatigue assessment methods are often based on the ideal geometry defined by the weld toe to describe welds, ignoring the influence of real geometric dimensions on actual stress concentrations and fatigue life predictions [
8]. Therefore, an accurate investigation of these topics in the laboratory is required, as is the successful application of laser scanning technology to obtain the exact geometric dimensions [
9,
10]. Applying accurately measured geometric dimensions and initial geometric imperfections of the specimens in experimental investigations can significantly reduce the scatter of observed results. For example, geometric imperfections play a key role in the buckling of shell structures, which is considered one of the most difficult factors to predict for shell structures [
11]. By accurately measuring the three-dimensional (3D) geometry of the cylindrical shell specimens, it is possible to precisely determine the load-bearing capacity of these shell specimens [
12].
In order to determine the geometric dimensions and/or imperfections of specimens, numerous measurement methods are available, which, in principle, can be divided into two main categories: Contact methods and non-contact methods [
13]. At the beginning of the decade and even before, a contact coordinate measuring machine was often used to record geometric imperfections [
14]. These scanning systems are usually calibrated on a fixed platform and consist of a sonde attached to the end of a mechanical swivel arm. When the sonde touches the surface of the specimen, the scanner determines the spatial position of the sonde by measuring the location with the corresponding sensor. The recorded positions generate a point cloud that can be used to form a 3D model [
15]. Contact methods based on physical movement are generally quite slow and restrict the geometry of the specimens and the size of the structural component to a specific range of lengths. Non-contact methods traditionally use telescopes and theodolites, as well as rulers or callipers, to measure total deviations at several pre-determined cross-sections of scanned specimens [
16]. To overcome these limitations, some of the research teams have turned their focus to non-contact methods based on laser and structured light measurement technology. The principle of 3D laser scanning is that a scanner protrudes a laser beam onto a surface, and the reflected beams back to the scanner are measured and recorded. The laser beam can be projected onto the target object in three different ways: Point, Line and Plane. By measuring the distances and angles of the reflected laser beam, the scanner can create a point cloud of coordinates in three-dimensional space that represents the shape and contours of the scanned specimen. Structured light scanning is a similar technique, except that a few stripes of light are projected onto a 3D-shaped surface, creating single or multiple illuminated lines or patterns of blue light. The displacement of the stripes on the projected 3D surface provides the ability to capture point cloud coordinates for details on the surface of the scanned object [
17].
Currently, 3D laser scanners are widely used in experimental investigations in steel structures to capture the geometric dimensions of specimens. In this decade, Zhao et al. developed a platform for measuring geometric imperfections of cold-formed steel members based on laser scanning technology [
18] and proposed a novel method for feature recognition to distinguish and extract geometric properties, such as corner points and planes from target scanned specimens [
19,
20]. For Box-T beams with complex cross-section profiles and difficult-to-measure geometric imperfections, Zhang et al. [
21] used a handheld 3D laser scanner to measure the entire geometric profiles of Box-T girders. More recently, Meng et al. [
13] explained the typical 3D scanning workflow using a typical I-shaped structural steel profile specimen nearby. Additionally, numerous studies have utilised 3D scanning to obtain accurate weld details for evaluating the fatigue behaviour of welded joints. For example, Ghahremani et al. [
22] used a handheld laser scanner to determine the geometric dimensions of treated welded joints. Niederwanger et al. [
23,
24] applied 3D laser scanning to obtain the real weld geometries and introduced the geometric information into the evaluation to reduce the scatter of fatigue life due to geometry variations for each weld of different specimens. More recently, Shojai et al. [
25] investigated structural steel specimens of offshore wind support structures with pitting using a 3D scanner and analysed the influence of the pitting corrosion and related stress concentrations on the fatigue strength of the support structures. In the framework of experimental investigations in steel structures, especially for the determination of specimen geometries and the characterisation of geometric imperfections, the use of 3D scanning is discussed by means of application examples [
26]. Handheld laser scanners prove to be simple and user-friendly in practice, but they are relatively expensive. Moreover, the accuracy as well as the algorithms embedded in them are not fully transparent for the user. The efficient, simple and meaningful transfer of the measured point cloud information into the finite element (FE) model is still a challenge for structural components of different sizes, such as steel beams of several metres or weld seams of a few millimetres.
In this paper, a self-developed 3D laser scan platform based on laser triangulation is used to capture specimen dimensions using point clouds. The specimens include steel beams with web openings to investigate buckling behaviour [
27], cylindrical shell specimens with a diameter of up to 1.6 m [
28], and weld seams of the cross-weld specimen. The procedures for post-processing of the point clouds and the general steps for transforming the point cloud information into an FE model are presented in detail. Finally, the test results are compared with the simulation results.
2. Principles of 3D Scanning and Scan Platform Design
This section first explains the basics of 3D scanning and introduces the functional principle of the self-built 3D scanning platform. Then, it describes in detail the process by which the 3D coordinates of the point cloud can be optimally generated for the experimental specimen.
2.1. Three-Dimensional Laser Scan Platform with Different Coordinate Systems
Using a laser scanner for 3D measurement involves two basic tasks: (i) the measurement of the spacing between the distance sensor and the measured object; (ii) the determination of the relative movement between the distance sensor and the tested object and the accurate recording of the path of the movement. The determined distances and paths of movement form a point cloud of coordinates in three-dimensional space that represent the shape and contours of the scanned specimen. According to the previously explained principles, a fully automated 3D scan platform design idea is proposed. During the scanning process, two stepper motors with transmission devices such as threaded spindles enable the relative movement between the distance sensor and the object to be measured. By measuring the clearances through the distance sensor and the parameters of the two stepper motors in relation to the current position of the distance sensor, a three-dimensional coordinate system can be created to determine the relative positions between the measured points.
To enable the synchronised operation of these hardware components, an Arduino Uno board is used to control the scanning process and set up the data transmission, according to
Figure 1. The control programme is written in C++ using the Arduino (IDE) software (
https://www.arduino.cc/en/software) and uploaded to the Arduino Uno board via the USB serial port. By setting predefined parameters in the control program, such as the speed of the stepper motors, the frequency of the analogue voltage readings from the stepper motors and the laser distance sensor, different dimensions of the scanned specimens can be set, and the resolution of the point cloud can be varied. The highest resolution of the stepper motor and corresponding driver is 8000 steps per revolution. One rotation of the thread moves the screw nut by 5 mm. This means that the parameter accuracy of the stepper motor is 5/8000 mm. With appropriate parametric settings, such as the stepper motor speed being 200 rpm and the scanned point cloud grid being 10 mm × 10 mm, high accuracy can be achieved at comparatively high scanning speeds, providing an optimum balance between speed and accuracy of the scanning process. The position of a spatial point is first represented using analogue signals from a distance sensor and a stepper motor.
These analogue signals are converted into digital signals by an analogue/digital conversion circuit within the Arduino Uno board. For data saving and post-processing, the digital signals must be communicated to the PC via the USB serial port. Here, a programme developed in Matlab® 2022b automates this procedure. When performing 3D scans of the measurement specimens, the selection of the appropriate 3D coordinate system plays a major role, as this has a direct influence on the accuracy of the scan results, the complexity of the processing and the user-friendliness for subsequent applications. The determination of the scan path and the coordinate system depends on the practical requirements, the properties of the scanner as well as the geometry of the specimen to be scanned.
From a theoretical point of view, three parameters of orthogonal coordinates can describe the positional information of a point in three dimensions. Thus, these scanning systems have to provide only three parameters at any time point. By repeating with the predefined interval, the parameters for generating a three-dimensional coordinate point cloud can be obtained. In this paper, the position values of the two stepper motors and the distance sensor are adopted as three return parameters of the developed 3D scan platform. These parameters can be determined by simple mathematical operations to obtain the required point clouds. By employing this approach, two scan measurement systems can be established based on the characteristics of the scanned specimen and the scanning method, utilising cylindrical coordinates and Cartesian coordinates as foundations.
Figure 2 presents the scan platform set-up established in this study for cylindrical circular shells.
The initial geometric imperfections in the web of a steel beam can be described as the difference between a point on the web and the corresponding point on perfect specimens. It should be noted that due to the scanning process and coordinate representation, 3D scanners based on the cylindrical coordinate system will not be suitable for capturing complete point cloud data from large flat surfaces such as the web of a structural beam. For steel structural component specimens that are relatively flat and without a large area of curvature, a measuring system on the plane of the Cartesian coordinate system (as shown in
Figure 3) is suitable, as any two axes can form a plane in this coordinate system. This makes it possible to measure the initial geometric imperfections of the web in the structural beam specimen with this scanner system. In order to enhance scanning efficiency and data acquisition, two distance sensors will be employed.
Figure 3 illustrates the approximate trajectory of the laser distance sensor as it moves along the web of the beam specimen.
As illustrated in
Figure 4, the geometric imperfections at the welding joint can be captured by extracting geometric features. Specifically, the thickness of the weld seam is determined through an analysis of the weld toe and leg lengths, as well as the dimensions of the transition area. Although all four welds of the cross-welded specimen can be obtained simultaneously by turning the specimen, rotation of the specimen will cause the base steel plate to obscure the weld detail. The 3D scanner, which is based on a Cartesian coordinate system and, as shown in
Figure 3, allows horizontal and vertical movement of the distance sensor. Therefore, this scanning procedure is, in general, suitable for scanning steel structural girders as well as for welded specimens based on the baseplate cross-section. The generation of a Cartesian coordinate system for steel beam and weld joint specimens is comparatively uncomplicated, as the three parameters returned by the measuring system correspond to three orthogonal coordinate axes.
2.2. Verification and Calibration of the 3D Laser Scan Platform and Error Analysis
The 3D scanning platform utilises the Panasonic® HG-C1200 laser sensors (Panasonic Industry Co., Ltd. Osaka, Japan)to obtain the distance between the measuring device and the specimen via non-contact methods. According to product instructions, the measurement range and accuracy of the laser distance sensor are ±80 mm and 0.2 mm, respectively. Note that the analogue/digital conversion circuitry on the Arduino Uno board only provides 10 bits of resolution, i.e., 1024 different values. Therefore, the accuracy of the entire measurement system is limited to the range of the maximal value between 0.2 mm and mm at the hardware level. Nevertheless, it should be noted that the actual accuracy may deviate from the theoretical accuracy of a 3D scan platform. Various factors during the scanning process can influence the actual accuracy, such as the environmental conditions, the stability and reliability of the scan platform, the calibration, the reflection behaviour of the scanned object and possible measurement errors.
To investigate the actual accuracy and working reliability of the 3D scanner, a high-precision aluminium plate polished with abrasive paste, which can be considered almost completely flat, is used as a perfect reference scanning specimen, as shown in
Figure 5. By analysing the scanned point cloud results, it can be clearly seen that there are noticeable differences in the measured laser sensor value between the two different sensor movement directions on the 3D scanning platform based on the Cartesian coordinate system. This is probably due to the fact that the stiffness of the horizontal linear guide is not infinite, and as the laser distance sensor accelerates and decelerates, the slight distortion of the horizontal guide is not completely consistent in the two directions of motion, which results in a difference in the sensor measurements. In order to overcome the hardware shortcomings of the scanning platform, the measurements in the two directions are checked separately, and the values of the laser distance sensor in the two directions have to be corrected for a difference of about 0.5 mm in the post-processing of the point cloud data.
For the verification of the actual accuracy of the 3D scanner, the deviation of the original scanned data compared to the reference plane of the perfect specimen is taken into consideration. In this paper, the uncertainty band of 95% probability (quantile) is employed to determine the measurement accuracy. To graphically illustrate this estimate of accuracy and confidence interval, a histogram of the scanned results is plotted, and the mean value and the boundaries of the 95% confidence level are marked on the graph, as shown in
Figure 6. From the diagram, it can be seen that the confidence interval is [−0.221, 0.221], which means that the actual accuracy of the scanner is about ±0.22 mm. The measurement accuracy is close to and slightly greater than the described theoretical accuracy.
5. Conclusions
This paper illustrates a common analytical framework for mapping point cloud information into numerical models based on spatial relationships, thereby integrating 3D laser scanning technology with FE modelling. Through meticulous experimentation and methodological development, the study has shown that the advanced scanning platform developed is capable of capturing accurate geometric dimensions and imperfections of a variety of steel components, offering significant improvements in the predictive capabilities of numerical simulations for stability and fatigue risk assessments in steel structures. Different coordinate systems are developed within the scanning system to ensure accurate scanning dimensions for different types of specimens in steel structures. Through the investigation of three kinds of specimens, namely weld details, steel girders and cylindrical shells, the stability and fatigue behaviour of steel structural components are examined. Post-processing procedures for the obtained point clouds are presented, including the construction of a refined FE model and the establishment of the spatial relationship between FE nodes and point clouds. This allows for simplification of the geometric dimensions obtained from the scanning process by accounting for coordinate deviations of the FE nodes. Finally, the processed point cloud information is integrated into the numerical model using advanced mapping algorithms.
Through comparative experimental investigations, the results affirmed that automatic processing and correction of the point cloud with the developed algorithm, followed by the application of tailored mapping algorithms, enable a high-fidelity transfer of scanned data into the numerical model. By utilising the point cloud data to include these imperfections in FE models, the study has contributed to reducing the variability in observed outcomes and enhancing the reliability of stability and fatigue strength predictions. The comparison between the experimental findings and the simulated results derived from 3D-scanned FE models demonstrated a congruence within a narrow margin, indicating that the approach could reliably predict the performance of different steel components. Furthermore, research has addressed the technical difficulties of translating 3D scan information into FE models for complex steel structures. The detailed study of geometric imperfections and their influence on stability and fatigue risk provides valuable insights into material behaviour under practical conditions, thereby providing an empirical basis for experimental investigation on structural specimens of steel structures. By demonstrating the practicality of the developed scanning platform, the study also provided a comprehensive methodological framework for transforming scanned data into actionable FE model inputs. This development holds promise for a wide variety of applications, including, but not limited to, the accurate characterisation of welded joints and the buckling analysis of thin-walled structures. Moreover, the integration of 3D scanning methods, which accurately capture the geometric dimensions of specimens before and after testing, with Digital Image Correlation (DIC) techniques for full-field measurement of displacement and strain on the specimen surface, forms a comprehensive system for geometric feature perception during experimental procedures. This advanced approach to measurement and acquisition provides researchers with a deeper insight into the mechanical behaviours of structural components during experimental studies.