Ibrahim Goda
email: ibrahim.goda@uha.fr

Gildas L'hostis

Philippe Guerlain

In-situ non-contact 3D optical deformation measurement of large capacity composite tank based on close-range photogrammetry

Keywords: Industrial measurement, Photogrammetry, FRP composites, Composite tankers, 3D deformation analysis, Hydrostatic loads

Recently, fiber-reinforced composites are widely used in manufacturing of large storage tanks for transportation purposes, thanks to their excellent mechanical and chemical performance, and their good applicability to the shaping of particular geometries. In this contribution, a non-contact 3D optical deformation measurement technique is proposed for monitoring the deformation of carbon-fiber reinforced composite tank subjected to different loading scenarios, which could not be achieved by traditional displacement sensors and resistance strain gauges due to large measuring ranges. This technique is based on the close-range photogrammetry technology, wherein 3D information is extracted from two-dimensional photographs. This is done by positioning artificial reference point markers on the measuring tank before loading, and calculate the 3D coordinates of these markers through analyzing the group photos captured in each loading stage. By tracking and comparing the 3D coordinates of the point markers among different loading stages, the 3D deformation of the tank is obtained. The loading tests comprise both hydrostatic pressure and water-pressurizing tests. The performed in-situ measurements show that the proposed technique can fulfill the efficiency and accuracy requirement of deformation measurement in tank loading tests. This in turn significantly contributes to better understanding the mechanical response at the macroscopic scale, thus improving safety performance.

Introduction

Nowadays, Composite materials are widely used in a variety of commercial and military applications such as automotive industry, aerospace, or marine engineering, due to their numerous advantages, including high mechanical properties and strength, impact resistance, energy absorption capacities, high temperature performance, corrosion resistance, and light weight structural components [START_REF] Bai | Marine Composite Materials and Structure[END_REF][START_REF] Chowdhury | Experimental and finite element studies of bolted, bonded and hybrid step lap joints of thick carbonfibre/epoxypanels used in aircraft structures[END_REF][START_REF] Wang | Ablation damage assessment of aircraft carbon fiber/epoxy composite and its protection structures suffered from lightningstrike[END_REF][START_REF] Kim | Characterization of resistive heating and thermoelectric behavior of discontinuous carbon fiber-epoxy composites[END_REF][START_REF] Bondyra | Design of composite tank covers[END_REF][START_REF] Park | Surface modification of carbon nanotubes for high-performance polymer composites[END_REF][START_REF] Park | Carbon fiber-reinforced polymer composites: preparation, properties, and applications[END_REF][START_REF] Shenoi | Composite Materials for Marine Applications-key Challenges for the Future[END_REF][START_REF] Galanis | Hull Construction with Composite Materials for Ships over 100 m in length[END_REF][START_REF] Marsh | Composites flying high[END_REF]. Their outstanding mechanical properties are largely due to the fact that their microstructure can be adjusted to achieve controlled mechanical properties at the mesoscopic or macroscopic levels [START_REF] Goda | Construction of first and second order grade anisotropic continuum media for 3D porous and textile composite structures[END_REF][START_REF] Goda | Equivalent mechanical properties of textile monolayers from discrete asymptotic homogenization[END_REF]. Most composite materials are multiscale in nature, i.e. the scale of the constituents is of lower order than the scale of the resulting material and structure. To fix the ideas, we speak of the macroscopic scale as the particular scale in which we are interested in (e.g. at structural level), while the lower scales are referred to as microscopic scale and intermediate scale which is also called mesoscopic scale. Reliable prediction of properties or overall response or mechanical behavior in a broader sense of composite materials under various loads and local physical phenomena is of the primary importance for the success of usage of textile composites. The complexity of the structure and the presence of a hierarchy of structural and different length scale levels (fibers, yarns, fabrics, and composite parts) lead to a high complexity of the predictive models, a high level of approximations, and to the high level of uncertainty of the predictions due to accumulations of errors when the model progresses from one hierarchical level to another.

Motivated by frequent inability of purely analytical or complexity of numerical tools to analyze complex problems in composites, this work addresses the applicability of experimental optical techniques to these composite materials. There is in particular a growing interest in the use of fiber reinforced polymer (FRP) composites as high-grade construction materials for various applications that need to be lightweight, yet strong under sometimes harsh service conditions [START_REF] Timmis | Environmental impact assessment of aviation emission reduction through the implementation of composite materials[END_REF][START_REF] Luyckx | Strain Measurements of Composite Laminates with Embedded Fibre Bragg Gratings: Criticism and Opportunities for Research[END_REF][START_REF] Gebremichael | Integration and assessment of fibre Bragg grating sensors in an all-fibre reinforced polymer composite road bridge[END_REF]. FRP composite tanks are a typical example of real engineering application of composites. Such composite tanks have a variety of applications in the chemical, food and drink industries for storing a wide range of materials, some of which are classified as hazardous. They in fact offer significant advantages to the transport industry in terms of increased payload and corrosion resistance compared to conventional metallic tanks. Several companies including Spitzer Eurovrac have lately taken an entirely new path in the development of fiber composite tankers. The FRP tanker truck results in lower unit transportation costs because of larger payloads, less wear on tires and running gears, and lower maintenance costs. Although the manufacturing of composite tanks has been recently spreading in different locations around the world. However, no provisions or guidelines exist in the current codes of practice concerning the design and analysis of these composite structures. Essentially, carbon fibers are used to reinforce these composite tanks because of their exceptional properties such as high specific tensile strength, high modulus, and outstanding wear resistance [START_REF] Xu | Cyclomatrix-type polypho-sphazene coating: improving interfacial property of carbon fiber/epoxy composites and preserving fiber tensile strength[END_REF][START_REF] Newcomb | Processing structure, and properties of carbon fibers[END_REF][START_REF] Wang | Effect of arc spraying power on the microstructure and mechanical properties of Zn-Al coating deposited onto carbon fiber reinforced epoxy composites[END_REF][START_REF] Auras | Wear behaviour microstructure, and dimensional stability of ascast zinc-aluminum/SiC (metal matrix composites) alloy[END_REF][START_REF] Shaukai | Fiber reinforced composite cylindrical vessel with lugs[END_REF]. Carbon-fiber composite tank, made with a special manufacturing technique, is particularly distinguished by its special inherent properties. The result is a lightweight tanker delivering greater payloads with exceptional chemical resistance characteristics to carry a wide range of liquid cargoes. It is worth noting also that at equal strength, carbon fiber makes it possible to save about 800 kg compared to a total weight of 2,000 kg for an aluminium tank. Moreover, its greater heat insulation coefficient reduces condensation risks and hence the formation of crusts. The aforementioned carbon composite tank is the target of the current study. This tank has been manufactured by Spitzer Tanker and is frequently subjected to different working loads. Due to its pressure working environment, deformation characteristics of this type of vessel need to be measured. The feedback from recorded deformations of existing structure in real conditions, can lead to highly valuable information for design criteria. In particular, deformation measurement of an in-service tank should greatly enhance the insight and confidence in the (long-term) behavior of high performance composite tanks. For the above motivations, measuring the field deformation of real-sized tank and its loading capacity under different load conditions are essential. This is the main objective advocated in this work. The present paper starts with a description on the performance of the composite tank under hydrostatic pressure load, following by its performance under water pressurizing loads.

The traditional displacement sensors and resistance strain gauges can only measure one dimensional deformation at one point in limited measurement range, and it cannot measure the whole field deformation of structure. Traditional sensors are all contact-type device; in many cases their installation on the tested structure is difficult or impossible. Additionally, it would be costly and inopportune to use them for deformation distribution measurement that needs simultaneous measurement at multiple locations. Other complications exist when instrumenting a large-scale structure for testing. This will be time intensive and requires expensive installation equipment. In order to solve these kinds of problems and overcome these drawbacks, we employ a non-contact optical deformation measurement technique to evaluate the structural response of the measured composite tank. The optical technology as a non-contacting measurement technique has gained more attention in the last few decades, mainly because of its non-destructive imaging characteristics with high precision and sensitivity (see e.g., [START_REF] Xu | Rapid 3D surface profile measurement of industrial parts using two-level structured light patterns[END_REF][START_REF] Zhu | A Review of Optical NDT Technologies[END_REF][START_REF] Yang | Deformation behavior analysis of composite structures under monotonic loads based on terrestrial laser scanning technology[END_REF][START_REF] Xu | Monotonic loads experiment for investigation of composite structure based on terrestrial laser scanner measuremen[END_REF][START_REF] Zexiao | Complete 3D measurement in reverse engineering using a multi-probe system[END_REF][START_REF] Cuypers | Optical measurement techniques for mobile and large-scale dimensional metrology[END_REF]). It has seen many advances in the recent years that have manifested itself because of the exceptional advances in computer power and camera sensors. Generally, the optical measurement techniques can be classified into two main categories: (a) approaches that use laser beams and (b) approaches that use white light. Laser surface scanners are based on laser beams, which move across the scanned surface and reflect back to a light sensor [START_REF] Urbanova | Testing photogrammetry-based techniques for threedimensional surface documentation in forensic pathology[END_REF]. The second class works by using white light and is called image based systems. Photogrammetry technique falls into the second group and leverages rays of light that are reflected from a structure. Photogrammetry is a fast, accurate 3D measurement method based on photography. It is used to extract the geometry, displacement, and deformation of a structure using photographs or digital images. With the progress of industry and the need to improve the quality of different products, the practical use of the optical measuring system based on the imaging technique has been increased in various industrial applications [START_REF] Cuypers | Optical measurement techniques for mobile and large-scale dimensional metrology[END_REF][START_REF] Chane | Registration of arbitrary multi-view 3D acquisitions[END_REF][START_REF] Zhao | Precise perimeter measurement for 3D object with a binocular stereo vision measurement system[END_REF]. The most common applications are the quality control and inspection of industrial products [START_REF] Zhao | Precise perimeter measurement for 3D object with a binocular stereo vision measurement system[END_REF][START_REF] Bösemann | Advances in photogrammetric measurement solutions[END_REF][START_REF] Sansoni | State-of-the-art and applications of 3D imaging sensors in industry, cultural heritage, medicine, and criminal investigation[END_REF]. For further details about advances in industrial photogrammetric measurements, the reader is referred to [START_REF] Luhmann | Close range photogrammetry for industrial applications[END_REF]. Moreover, the photogrammetry has been extensively used in the aerospace, civil engineering, wind power blade, and structural monitoring fields [START_REF] Liu | Photogrammetric techniques for aerospace applications[END_REF][START_REF] Ozbek | Feasibility of monitoring large wind turbines using photogrammetry[END_REF][START_REF] Yılmaztürk | Measurement of deflections in buried flexible pipes by close range digital photogrammetry[END_REF][START_REF] Esmaeili | Displacement measurement of the soil nail walls by using close range photogrammetry and introduction of CPDA method[END_REF][START_REF] Valença | Applications of photogrammetry to structural assessment[END_REF][START_REF] Nishiyama | Improved digital photogrammetry technique for crack monitoring[END_REF]. Recently, researchers have used photogrammetry to investigate the dynamic characteristics of structures [START_REF] Lee | 3-D measurement of structural vibration using digital close-range photogrammetry[END_REF][START_REF] Gwashavanhu | Rotating blade vibration analysis using photogrammetry and tracking laser Doppler vibrometry[END_REF]. One of the significant processes in quality control/inspection of an industrial product which can use image-based measurement tools is measuring deformation of the product and evaluate its behavior under loadings. The measured composite tank is a typical large-scale structure which is a multiscale product. In nature, structures with a behavior encompassing interaction on a collection of different scales are a common occurrence. Thus, accounting for these multiscale aspects in analysis is an important issue to be taken into account. Moreover, deformation of such multiscale layered composites under loadings greatly is function of physical laws. But according to the impossibility of identifying all effective factors and modeling their interactions, analytical and numerical approaches do not provide overall good performance. In such situations, physically realistic experiments shall be performed by carrying out field tests and measuring deformations directly. Therefore, in the present paper, a non-contact 3D optical static deformation measurement system is proposed to track the 3D deformation of real-sized composite tank through in-situ experiments in various loading conditions. The composite tank is subjected to different internal loading tests including hydrostatic pressure (tank filled with 52 tonnes of water and subjected to atmospheric pressure) and water-pressurizing test (tank filled with 52 tonnes of water and pressurized to a specific test pressure). The whole field 3D deformation under different loadings is then obtained by tracking the reference point markers on the tank among different stages. The capabilities such as high accuracy and relative rapidity in measuring 3D coordinates of desired points, ability to perform measurement in a continuous space and no need to contact with the surface of the tank at the time of measurement make photogrammetry measuring system a reliable tool for measuring deformations before and after loading tests. To the best of our knowledge, this paper presents the first comprehensive experimental study conducted using a digital photogrammetry system on a large-scale composite tank to capture its macroscopic behavior under internal pressure loading throughout the range of elastic and inelastic response. The rest of the paper is organized as follows. The geometrical configuration, material parameters and supporting conditions for the analyzed composite tank are exposed in Section 2. We introduce in Section 3 the basics of the measurement method and main elements of the measuring system used to assess the mechanical response of the composite tank. Scheme and measurement procedure for composite tank are introduced in Section 4. Experiments and discussions are given in Section 5. We conclude by summary and final remarks in Section 6.

Description of tank geometry, materials, and boundary conditions

This work focuses on experimental evaluations of the structural behavior of the large-capacity carbon composite tank during its internal operating and test pressures. It is therefore necessary to firstly give a brief description about its geometrical and materials parameters that constitute it. This composite vessel is indeed developed and manufactured by Spitzer Eurovrac company which aims at optimizing transportation costs and allowing quick and easy cleaning of the tank's inner walls so as to avoid contamination. The Spitzer group has a world-wide reputation as a specialist in the field of vehicles equipped to discharge powders under air pressure. The group has produced the current composite tipper tank, which discharges via a single outlet at the back of the tank. This tank may be mounted on a trailer or semi-trailer chassis, on a supporting frame, or be used as a road container.

The measured tank has a cylindrical shape in horizontal configuration fitted with torispherical cap at the front and hemispherical head at the rear to give better utilization of space and simpler manufacturing. The main geometrical parameters of the tank are illustrated on Fig. 1. They are given as follows: inner diameter is 2515 mm, outer diameter is 2541 mm, total length is 11010 mm, and ferrule (cylinder) length is 8840 mm. The tank has a capacity of 52000 liters and its total mass without support is about 870 kg. In addition, the ferrule (cylinder) span is equipped with 5 manholes distributed equidistantly as shown in Fig. 1. The cylindrical shell of the composite vessel used in the current experiments is manufactured using filament winding technology based on a composite sandwich concept. This is made of carbon/vinylester skins laid up around a soft foam core from Structiso. This core is manufactured by draping fiber glass over a lightweight foam core and tufting fiber glass through the core to form triangulated truss network with specific angles and spacings (see Fig. 2). Such soft foam core provides insulation that keeps the tank from sweating and the goods inside, dry. The following material combinations from the inside to the outside (gelcoat / glass fibers / carbon fibers / foam & glass core / carbon fibers) are involved to produce this cylindrical shell. The mechanical characteristics of these materials are exposed in Table 1. The type of molding used to produce this tank allows indeed to have high volume fractions of reinforcements (overall about 70%). Furthermore, the vinylester resins with volume fractions of about 30% are used as a matrix to manufacture the tank. This kind of resins has in fact outstanding thermal stability and is extremely durable and more resistant to aggressive environments.

Table1. Mechanical properties of the materials used in tank manufacture.

Material

Mass density (kg/m The front and rear heads are produced by reaction injection molding, using glass fibers, carbon fibers and a gelcoat. They are joined to the cylindrical shell by adhesive bonding (structural adhesive), followed by interior and exterior hand lay-up. The laminar construction of the end heads shell is shown in Fig. 3. The Lay-up configuration is as follows: gelcoat/glass/carbon/glass/carbon/glass, with a total thickness of 7.1 mm for the front cap and 6.75 mm for the rear cap. We also show on Fig. 3 the laminar construction and thickness of each layer for the cylindrical shell. It has been constructed with the following material combinations: gelcoat / glass / carbon / carbon /glass / foam Structiso /glass / carbon / carbon /carbon /glass, resulting in a total thickness of 13 mm. We shall afterward describe the setting parameters of the boundary conditions considered in all conducted experiments. The tank is clamped at its rear case on a fixed rigid base A to prevent the movement during the tests. The tank is also supported by two cradles B and C at the front and central hoop. The span between the two cradles is adopted as 4300 mm. The cradles don't exert any longitudinal force on the tank. The global coordinate system as shown in Fig. 3 is defined in such a way that X and Y are the radial directions and Z is the direction along the axis of the cylinder.

In the next section, we introduce the fundamentals of the employed measurement technique and components of the measuring system used to evaluate the response of the tank under internal pressures.

Theory and measuring system

Basics of photogrammetry

Digital photogrammetry is a contactless measurement method that uses a series of images recorded with imaging sensors to identify coordinates of points, patterns, and features in the images or to detect the boundaries of objects.

In broad terms, the photogrammetry technique can be classified based on the type of targets used into point-tracking, digital image correlation, or target-less approaches. The point tracking technique uses photogrammetric cameras to identify the coordinates of discrete points mounted to test structures. For this method, a series of optical targets (usually high contrast circular points or retroreflective targets) are mounted to the structure. The centers of the optical targets are found using an ellipse finding algorithm and the coordinate of the points in 3D space are identified using a triangulation technique. 3D point tracking determines the displacements of the targets by tracking the optical targets in different time stages and comparing their coordinates to the reference or initial stage. For the second category, digital image correlation (DIC) is an optical measurement technique that works based on gray-scale variations of continuous patterns. The area of the test structure must be prepared before the measurement. The surface preparation is usually performed by applying a high contrast stochastic pattern on the structure (typically black and white). The appropriate size of the dots in this method is usually smaller than the optical targets used in 3D point tracking. After surface preparation, a series of pictures are recorded using cameras. The image correlation method works by creating overlapping facets (or subsets) on the total area of interest. Because the stochastic pattern is randomly created, each facet possesses a unique light intensity value and the software can recognize the movement of each unique facet pattern in different stages.

The displacement and strain over the entire area of interest are calculated by correlating each facet to the corresponding facet in the reference stage. For more information about DIC, the reader is referred to a recent review by Pan [START_REF] Pan | Digital image correlation for surface deformation measurement: historical developments, recent advances and future goals[END_REF] that comprehensively summarizes the recent advances of DIC. In the last category, target-less approaches, there is no optical target or pattern to find the deformation of the structure. Authors have used internal features or edges of a structure to identify the object or areas of the object that needs to be tracked. These approaches may not be as accurate as 3D point tracking or digital image correlation, but they have their own advantages when there is not a possibility of mounting optical targets to the structure or patterning the surface [START_REF] Son | Vibration displacement measurement technology for cylindrical structures using camera images[END_REF][START_REF] Gonzalez | Digital Image Processing[END_REF]. Among the three techniques listed above, the 3D point-tracking is the most convenient and practical for large-scale inspection of structures subjected to static mechanical loadings. In fact, the DIC technique provides full-field deformation measurement of objects, but it is limited by the field of view of the cameras and can only measure the response on the parts of the structure that cameras have a line of sight. Thus, this technique cannot be used to measure the displacement of large and complex structures. Therefore, in this research we use the 3D point-tracking approach to track the deformation of the real-sized tank. Although 3D point-tracking is not technically a full-field measurement technique as DIC provides because it measures displacement at discrete points (target points), for all practical purposes it can be considered so because it is relatively easy and inexpensive to mount numerous optical targets to fully cover the structure of interest throughout the field of view. Furthermore, unlike DIC, point tracking does not need patterning of the object and only requires optical targets to be attached to the object that can be easily removed after the measurement. This approach can be applied to virtually any type of the structure without modification or surface preparation.

Proposed system and methods

Our proposed measuring system is based on the TRITOP photogrammetric system developed by the German company GOM. The measuring device is an optical, mobile, measurement system, which precisely determines the 3D coordinates of object target points at quasi-static conditions. Based on this information we are able to calculate the 3D displacements and deformations of objects. Specifically, photogrammetry TRITOP is a large-scale measurement technique that, in fact, is based upon the principle of triangulation per se involves angle measurements. Using TRITOP, the position of a point in 3D space can be determined by triangulating multiple bundles of observation rays. If the spatial orientation of each bundle is known in the object coordinate system (XYZ), the intersection of the rays delivers the desired 3D object point coordinate, as shown in Fig. 4.

Z

Components of the measuring system

The main elements of our measuring system are list as follows: Photogrammetry camera with Wi-Fi image transmission, scale bars, encoded and non-coded reference point markers, highperformance laptop, and TRITOP Professional software, as displayed in Fig. 5.

The process of measuring with the TRITOP system starts with preparation of a measured object. Non-coded reference points are placed on the object, coded reference points and scale bars are placed in the area to be photographed and the whole scene is photographed from multiple positions and angles. The images are transferred to the PC wirelessly and exact coordinates of all coded and non-coded reference points are computed in the software.

The camera and its settings

The imaging camera is one of the main components of the photogrammetric scheme. In this work, Canon EOS-1D X is used for capturing the required images. This camera is based on professional digital reflex camera housing. It is equipped with a manual fixed focus lens and a flashlight. The camera system is factory-verified and certified. This procedure guarantees the measuring accuracy. The system is also self-calibrating and self-checking. The camera is actually calibrated during measurement according to the environment variables (e.g., temperature, humidity) that are present during measurement. This is a significant advantage compared to the systems that are calibrated in laboratory conditions, since laboratory conditions can be very different from conditions at the measurement site. The table below (Table 2) illustrates the technical specifications and setting parameters of the used camera. Two kinds of artificial reference point markers, namely non-coded and coded points are used in our proposed system to simplify image processing and raise an automation level (Fig. 5, right). The material of these markers is an important factor for the ease of use of such a photogrammetric system. It is typical to use a retroreflective material. These targets can be easily identified in the images as the they appear bright and the rest of the image black.

The non-coded reference point type is used for determining the 3D coordinates. It is a selfadhesive marker with a background of black color and a circle of white color in the center. Due to this fact, there is a high contrast between the colors black and white. On the other hand, the coded reference markers are used to determine the 3D space and camera positions (orientation). They ensure an image set that can be evaluated and allow for automatic calculation of the camera positions. They are referred to as concentric-ring coded point that also has a white central circle, especially surrounding discrete ring sections and a unique ID (identification). The coded reference points are provided in two different forms either as individual markers or located on orientation crosses. Each orientation cross is equipped with 9 coded reference point markers. This in turn allows for applying coded markers easily and fast to the measuring object of large scale. Within the orientation crosses, one cross shows markers with the IDs 360 to 368 and is labeled with a green X and a blue Y (Fig. 6). This orientation cross determines the global coordinate system (XYZ) of the measuring project in 3D computation. By positioning this cross accordingly in the measuring project, we prealign the resulting coordinate system. To achieve a high measuring accuracy, it is essential when taking an image to see as many coded reference point markers spread over the entire object as possible.

Fig. 6. Orientation cross to determine the coordinate system (XYZ).

The photogrammetric measurement has in fact no dimensions, consequently photograph contains no information about the size of the photographed object. This means that without a known distance in the measurement there is no way of knowing the size of the object depicted. To scale the measurement, we must have at least one known distance. If we know the actual coordinates beforehand of some targeted points, we can compute the distances between these points and use these to scale the measurement. Thus, we may use a scale bar with point targets on it and measure this along with the object. The distance between the targets on the bar is known and can be used to scale the measurement. In our measuring system, two scale bars are used for determining the dimensions and observe the measuring accuracy (see Fig. 5). The advantage of using such two scale bars is that the software checks the scale bars with respect to each other and thus guarantees a high measuring accuracy.

Essentially, the position of the scale bars can be arranged, so that they are completely or partially visible in the captured images and should not be placed directly beside each other.

Depending on the temperature of the measurement environment, the lengths of the scale bars change. The length here refers to the distance between two non-coded reference point markers on the scale bar. The scale bars are calibrated at a certain temperature (20 °C). The software can compensate the length changes of the scale bars. Therefore, we shall enter the current ambient temperature on the scale bars in the photogrammetry settings, in order to take into account thermal expansion. In general, TRITOP system can provide a high measurement accuracy of 0.01 mm/m.

Processing flow of the proposed photogrammetry system

Pinhole imaging model

As mentioned earlier, the photogrammetry is a 3D measurement approach that uses photographs to establish the geometrical relationship between a 3D object and its 2D photographic images. Its fundamental mathematical model is based upon the pinhole camera model, as illustrated in Fig. 7. This model describes the mathematical relationship between the coordinates of a point in 3D space and its projection onto the image plane of a camera. In Fig. 7, P is the object point, Q is the image point, O is the projection center, S is the principal point of camera, and the distance between O and S is the camera focal length that is expressed as f. The collinearity equations express the fact that the perspective center of the camera O, the object point P and its observation Q in the image plane lie on the same line, as shown in Fig. 7. The following collinearity equations form the relationship between the 3D spatial coordinates of an object point (X, Y, Z) and the corresponding 2D spatial coordinates for an image (x, y) of that object. , etc. are the elements of the 3×3 rotation matrix m mapping the orientation of the object coordinate system onto that of the camera coordinate system. When the interior (or intrinsic) and exterior (or extrinsic) parameters of camera are given and the two corresponding image points are known, 4 equations can be constructed according to the above equation and the 3D coordinates of object point P can be calculated, the least square method is employed to find out the optimal solution. TRITOP Camera requires taking 4 starting calibration photographs, from the same position and in the same direction, while rotating the camera by approximately 90° after each photograph. Camera calibration is used to determine a set of intrinsic and extrinsic parameters of camera that relate a 3D object to its 2D images. Intrinsic parameters define the geometric and optical characteristics of the camera while extrinsic parameters describe the location and orientation of the camera reference frame with respect to a known global reference frame.

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) O O O O O O O O O O O O Z Z m Y Y m X X m Z Z m Y Y m X X m f y Z Z m Y Y m X X m Z Z m Y Y m X X m f x - + - + - - + - + - - = - + - + - - + - + - - = 33

Workflow of the proposed TRITOP software

The photogrammetric workflow of our TRITOP software firstly processes the images to identify the 2D coordinates of all reference point markers, then uses the coded reference points in the images to accomplish the reconstruction of all the points by epipolar line geometric constraint, and lastly it calculates 3D coordinates of the points using bundle block adjustment method with relative control. Accordingly, the distances between marker points located on the object can be determined precisely. Fig. 8 shows the workflow of the software. After capturing the images, the software recognizes the reference points applied on the measuring object and locate their image coordinates. Target point matching is the process of locating and uniquely indexing the same image point in all recorded images. Coded point matching (localization) can be easily realized due to their

Point recognition and matching

Image acquisition

Image points 3D reconstruction

Bundle block adjustment

Scale bar identification 3D points coordinates unique identification information. Conversely, the uncoded points are difficult to be matched correctly, because they don't have identification codes. For uncoded point matching, epipolar geometry is often used as restriction of matching. The epipolar geometry means that for a point in one image, the corresponding points in other images are constrained on epipolar lines which depend only on the camera's intrinsic parameters and the relative orientation. In order to enhance the accuracy of non-coded point matching, combination of multiple camera positions and outer epipolar constraint of multiple images are required. After target point recognition and matching, all corresponding points and their coordinates are determined. In addition, through camera calibration, the intrinsic and extrinsic parameters of the cameras have already been obtained. Then the 3D coordinates of all points can be reconstructed using the triangulation method. For triangulation to take place, the camera needs to shoot the object from different positions in the surrounding space, with a partially overlapping image area. The software has to be based on the bundle block adjustment principle in order to solve the equations of projective mapping. The bundle adjustment is an optimization technique that is often used as the last step in reference point-based 3D reconstruction algorithm, following the prior steps of point detection and matching. This technique involves simultaneously refining the 3D coordinates of all points describing the scene geometry as well as the parameters of the relative positions and the optical characteristics of the employed camera, according to an optimality criterion involving the corresponding image projections of all reference points.

Scheme and measurement procedure of the composite tank

With the increasing complexity of composite structures, it is crucial to investigate their deformation behavior and assess their safety performance. In this section we use the noncontact image based 3D point-tracking technique explored in the previous section to track the deformation of the real-sized composite tank. Practically, 3D point-tracking approach can be considered as a full-field displacement measurement technique because it can measure the displacement at huge discrete optical points, which can easily be mounted on the tank to entirely cover the surface of interest throughout the field of view. The potential advantages for the employed method in deformation tracking of the large scale tank comprise 3D full-field displacement distributed over a very large area, eliminate the expensive sensors and timeconsuming wiring and the need for large-channel data acquisition systems. Testing of large composite tanks for transport is very important because such containers can explode if they fail under pressure. Strength can optionally be tested by measuring permanent deformation of these tanks. In this study, the composite tank is tested experimentally under different internal loading conditions. The experiments are conducted to investigate the deformation throughout the range of elastic and inelastic response. The detection of deformation means to detect the changes in form, direction and displacement of structures. This is done by tracking the reference point markers mounted on the tank at different loading stages: before loadings, under loadings, and after removing the loads. At each loading stage, the 3D coordinates of the point markers are reconstructed and the coordinate systems of different stages are aligned together by means of global transformation. The whole field 3D deformation or displacement under different load level can then be obtained by tracking the homologous point markers among different stages. In the course of all measurement loading stages, the composite tank remains fixed at its rear case and simply-supported by the two cradles at the front and central hoop of the tank. Attaching the tank to the cradles in a simply-supported manner is a convenient way of installation. Hence, the simply-support boundary condition is adopted in the static pressure loading tests setup.

Tank preparation and shooting techniques for a single stage

The system adopts image processing and photogrammetry technology to reconstruct the 3D coordinates of the discrete reference points applied to tank surface. No matter what is the measurement stage, every measuring process consists of the following steps:

• Preparation: non-coded and coded reference point markers are placed directly on the surface of the tank. When positioning the point markers, we make sure that they are positioned stable and shouldn't not move in the measuring stage and they are well distributed and creating lines of points is avoided. The material thickness of the markers is automatically compensated. Enormous non-coded points are actually applied everywhere on the positions that need to be measured in such a way that they cover the entire structure and be somewhat so dense. About 127 Individual coded points and 33 orientation crosses (among them one cross determines the coordinate system) are distributed over the tank in a way enables us to see as many coded points as possible when shooting an image. The individual coded markers are distributed in the zones that are in fact difficult to be photographed, especially at the top and bottom of the tank. These coded markers are not necessary as a measuring point but rather to link the different photographs with each other. Fig. 9 shows the real composite tank and the disposition of the reference points and orientation crosses. In each measuring stage, the scale bars are the reference for determining the dimensions. Ideally, the scale bars fit 1:1 to the measuring object. For the scaling purpose, two reference standards of 2 m length are used. These standards are placed next to the tank and parallel to each other (Fig. 9). • Image acquisition: before starting the measurement photographs, the camera needs to be calibrated for computing the optical distortion of the camera lens and the position of the principle point. Therefore, four calibration images are firstly taken 90° rotated against each other. The images are sent wirelessly to the computer for processing. Afterwards, typical multi-image acquisition procedure contemplates taking photos around the tank from different directions and different height levels. During image recording, it is the goal to capture as many reference points spread over the entire tank as possible in order to achieve a high measuring accuracy. In particular, the following considerations should be taken into account to obtain high-quality images so that the software will be able to reliably and precisely evaluate reference points and image sets:

-In each image at least 5 coded reference points must be visible because the software needs at least this number to precisely compute the camera positions. -The reference point must be visible in at least 3 different images so that software can automatically and precisely determine the 3D coordinates of a non-coded reference point. -In each image used in photogrammetric measurement, software needs to identify at least 5 previously photographed coded reference points, so it could be possible to orientate photograph in a common coordinate system. -A minimum distance to the measuring tank surface depending on the camera focal length and height of tank should be chosen. -Avoid taking photos at similar points of view.

-The top parts of the tank should be acquired from an elevated point using a hand ladder or alternative. -Vast number of overlapping photos with highly redundant reference points in each photo shall be acquired. -The measured tank is a large and complex measuring object that needs a sufficient amount of overlap between adjacent images. Particularly complex zones in the recording of tank's surfaces are the front and rear caps, which combine particular geometries and surfaces with the presence and variance of curved form at their connections to the cylindrical shell. In this case, connecting images are especially important, for example, the right and the left side as well as the front and the rear side of the tank body. -The illumination conditions of the tank should be optimized as much as possible to increase the potential applications of the measurement. An additional aspect to consider to ensure good photograph is that the flash is switched on if the lighting condition is poor. • Measurements: After preparation of the tank and the scene, the measurement photographs are taken and continuously transmitted to the computer via WiFi. When the software receives the first images, the search for the reference point markers in the images starts. After enough photographs are taken, using built-in function "computing measurement series", the 3D computation of the reference points is carried out automatically. This computation consists of several functional and optimization processes in order to obtain precise 3D measuring data. During the computation, the ellipses are identified (measure image points), the reference points and the scale bars are identified, a 3D pre-and postorientation of the images is carried out based on the coded reference points, and the bundling is optimized. Fig. 10 shows the recognized reference points (coded and noncoded points) in the 3D view of the measured tank in the initial stage (without loading). Furthermore, we display in Fig. 11 the 2D camera images and 3D measuring data together in the 3D view. As a matter of further illustration, Fig. 12 displays a small camera for the sensor position of each individual measurement in the 3D view. Thus we have a good overview of the different camera positions from which we measured the tank when it was empty. In this case, a total of about 300 photographs are acquired at approximately 3-5 m away from the point targets depending on the zone being photographed. With prior knowledge of the tank's bottom surface and its complexity, few images are taken severely at approximately 1 m away from the reference points due to the extremely constrained working space.

Accuracy assessment of the measurements

One of the most important issues in tank measuring process is the estimation of the measuring precision, including its uncertainty and the accuracy and probability of the measurements (confidence intervals). We can assess the quality of the photogrammetry images directly for the individual tank images or for the entire photogrammetry project at each loading stage, so that we can decide which images are missing or which we need to repeat. The most important information about the individual image measurement is explained as follows.

Image oriented: if enough coded reference points are identified in the image, the image can be oriented in 3D space. Additionally, if the identified number of coded points in the image is less than 5 points, the image might not be oriented in 3D space. Overexposed points: if the number of overexposed reference points is > 1, a warning is displayed. Average point contrast: the average point contrast of the reference points might be too low or too high. The warning threshold is at < 10% and > 80%.

Point distribution: in order to compute the distortion parameters of the camera lens, enough images of the coded reference point markers are required. Therefore, the distribution of the reference points used in one image should be filling the entire image format. If the points are concentrated in just one image area, the computation for the image orientation might be less precise. The warning threshold is at < 15%. Average point deviation: the average image point deviation is displayed in pixels. The warning threshold is at 0.2 pixels. Likewise, to assess the overall quality of the entire photogrammetry measurement series of the tank at each loading stage, the following are the most important criteria that describe the quality of the image set: Average image point deviation: if the value of the average deviation of all image points is ≥ 0.08 pixels, a warning is displayed. Minimum observation angle: if a reference point (coded or non-coded) has an observation angle of ≤ 3.5°, a warning is displayed.

Average scale bar deviation: the warning threshold value of the average deviation of the two scale bars used in each measurement series is determined using the following mathematical formula: [scale bar length (mm)/50000]+5µm. For all measurements conducted in this work either at the individual images or entire measurement series in all loading stages of the tank, both images and image set recorded are evaluated in good quality and generally comply with the quality requirements of the application software. Therefore, the accuracy of the employed technique in this study is found to be competent and sufficient for the measurement of such large scale tank. As an illustration of the accuracy of our measurements, we present in Table 3 the quality information attained for three measurement series after bundling the images and scaling the results at three different loading situations; without pressure, hydrostatic pressure, and modified hydrostatic pressure. When we come across the analysis of the obtained values of scale bar deviations given in Table 3, we find for instance in the initial situation that the error on the two scale bars of 2 m after bundling and scaling the measurements is about 0.03 mm. This could be related to 0.03 mm/2m or 0.16 mm over a distance of 11 m the whole length of the measured tank. This makes the current technique well suited to high accuracy measurement of large, complicated objects like the underlying tank.

Experimental results and discussions

In this research, a semi-automated photogrammetric modeling approach is applied through the extensive computation platform of TRITOP 2016. The software interactively or automatically detected and referenced the reference points positioned on the tank surface in each captured image, before all of the images were oriented for the solution of points 3D information. The output 3D point information of the whole tank is checked and post-processed for the missing or wrongly marked and referenced points.

We aim now at evaluating the overall mechanical response in the elastic regime of the composite tank exposed to loadings. To do so, the tank is tested experimentally under different internal pressure situations; this includes hydrostatic pressure and water-pressurizing or modified hydrostatic pressure. In the hydrostatic case, the tank is filled with water, so the introduced hydrostatic load is the static pressure from the water inside the tank (non-moving fluid), which acts on the internal structure of the tank. Whereas, in the water-pressurizing situation, the tank is filled with water and then pressurized to a certain test pressure typically 2 bar (service pressure) and 3 bar (proof pressure). Service testing is the test at normal operating conditions and utilizing service fluid as the test medium. The proof pressure test consists of subjecting the tank to a maximum test pressure of 3 bar and inspecting the pressurized tank for deformations. Note that in order to create the necessary pressure during the water pressure tests. One obvious possibility is to utilize the mains water supply, and in this case the available pressure from the waterline is 3 bar maximum. The water pressure is directly measured using pressure gauge mounted on the top of the tank. We next expose the process of measurement experiment of the entire tank with different load situations as following:

1. Using the handheld camera, we record a series of about 300 images from different directions and positions around the tank when it is under empty load (without load). 2. The recorded images are transmitted via Wifi to the software, and from these images the 3D coordinates of reference point markers are computed (about 6700 points). The obtained 3D result is set as the basic (reference) stage. 3. Fill the tank with 52 tonnes of water and leave the manholes mounted on top of the tank opened up, thus exposing the water surface to atmospheric pressure. Wait until the deformation is stable and then take a set of photos of this stage which is defined as the second stage (about 317 photographs are acquired). In this stage the tank is deformed by the hydrostatic force, which is the total pressure acting on the tank surface that is in contact with the water at rest. 4. Repeat the second step to compute the 3D coordinates of the markers. In this stage approximately 6800 points have been measured. 5. The water filled tank is then pressurized to internal operating pressure of 2 bar.

Afterwards we wait till the deformation become stable and then take a series of photos of this stage as the third stage; more than 350 images are oriented. 6. Repeat the second step to compute the 3D coordinates of the markers. In this stage more than 6900 non-coded points have been measured. 7. We further increase the pressure of the water filled tank to a maximum test pressure of 3 bar. When the deformation is stable, a group of images are taken (more than 370 photos are acquired) and step 2 is repeated to compute the 3D coordinates of point markers (about 7200 non-coded points). The obtained result is defined as the fourth stage. 8. Each loading stage listed above is captured in its own original coordinate system, so we use an alignment cross to define the position of the coordinate system. Based on the nine corresponding coded points on the cross, all points can be aligned in the global coordinates. In fact, different loading measurements should lie in the same coordinate system to make it possible to compare it. The software sets result in arbitrary coordinate system. In order to be able to use the 3D measuring data to carry out deformation evaluation, measurements need to be transformed into a defined coordinate system. There are actually different transformation methods. However, an alignment cross is presently preferred depending on the measuring tank and the data available. The entire project now contains four measurement series corresponding to the four different loading stages. While aligning the coordinate systems to each other by alignment cross, we set the stage behavior for transformation throughout the stages to separate stage transformations mode. By this mode of transformation, the coordinate system of the project gets a fixed relationship to the measuring tank. Therefore, we can analyze the deformation of the tank regardless of the movement (the global movement is already removed); the software compensates the global movement of the tank in space over the stages. So far, measurement coordinates alignment of different loading stages of the tank is carried out before they are inter-compared. We are now in the stage of calculation and display the obtained deformations. Due to tank loadings, the deformations over multiple static load stages in the space compared with the beginning state of empty tank can be calculated. The 3D displacement or deformation of any point n in the space can be calculated by subtracting the corresponding 3D coordinates component before and after deformation based on the point component creation of those key points on the tank, as follows:

{ } It can be seen from the results of all loading stages that the distributions of displacement field are non-homogenous. The main reason is that the composite sandwich materials and carbon fiber composite with anisotropic characteristics from which the tank is manufactured result in a complex deformation state. Under the action of internal pressure, the deformations of the composite tank are actually influenced by some inherent mesostructures such as interface between the fiber and matrix, and deformation of fiber and matrix itself.

Experimental results in Figs. 13b-d show the tendency, for the cylindrical portion and both tori-and hemispherical ends to expand by a different amount of deformation under the action of internal pressure. So owing to difference in stress, the two main portions (cylindrical and spherical ends) expand by a different amount. This incompatibly of deformations may cause a local bending and sheering stresses in the vicinity of the joint. Properly curved ends are used for this composite tank to ensure physical continuity between the ends and the cylindrical portion. We further create deviation labels to represent the discrete color deviations around the connection between the cylinder and caps, see Fig. 14. With these deviation labels, we numerically visualize the local deviations. It is noticed that these deviations are not significant and distributed rather uniformly along the circumference. From the above results, we can assess the overall mechanical response of the composite tank. We notice from Fig. 13b that the hydrostatic pressure test results in a symmetric pattern of deformation of the tank in YZ plane with significant deformation produced at the top of the cylindrical portion (ferrule) near the manholes with a maximum displacement deviation value of 27 mm.

In addition, the hydrostatic pressure load leads the deformation along the ferrule (between the two caps) at the middle line L (see Fig. 3) to be distributed in a quadratic scheme as illustrated in Fig. 15. The selected section line in Fig. 15 is located on the tank cylinder and aligned along the length of the tank. Along this longitudinal line L the displacement deviations profile varies between 6 mm and 16 mm with a maximum that occurs almost in the center. The results obtained in Fig. 15 provide important information regarding the displacement distribution on an essential section line in the tank. The displacements of the discrete points on the measurement surface are also displayed in Fig. 15b as function of section length. We can also check the displacement deviations for each coordinate direction individually in order to investigate in which direction the deformation is predominant since this is a vital step in designing and analysis against failure. The hydrostatic pressure associated with the contained liquid leads to high deformation level in the radial direction along the right and left L parts of the cylinder as shown in Fig. 16a as well as a centralized zone of localized severe deformation at the top of the cylindrical portion as illustrated in Fig. 16b. On the other hand, hydrostatic pressure promotes a lower level of deformation in the longitudinal direction as displayed in Fig. 16c simply because of its resistance to deformation in this direction due to the large length of the tank in axial direction compared to the diameter. Similarly, a smaller level of deformation is produced at the top of the ferrule surface in the circumferential direction (see Fig. 16a), whereas a relatively larger amount of deformation is generated in the same direction along the right and left parts of the ferrule (Fig. 16a). We notice as a general trend that the deformation in the radial direction is predominant in comparison to the circumferential deformation as with this composite tank having thickness to diameter less than 1:150. In order to measure the deformation response under hydrostatic pressure along the circumference in the middle of the cylinder at which large deformation occurs, we create a section A through the tank (Fig. 3) using a plane parallel section. This enables one to create analysis in 2D and hence understanding well how the displacement deviations are distributed around the circumference of the ferrule due to the internal hydrostatic load (see Fig. 17). Note that for the magnitude of displacement distribution, the highest and lowest values occur, respectively, at the top and bottom and they act in downward directions. The distribution displayed on both right and left portions of the created section shows that the displacement almost varies quadratically and downwardly inclined (Fig. 17a). We further investigate the contribution of each displacement component in each coordinate direction that leads to the contour plot of displacement magnitude given in Fig. 17a. Fig. 17b shows the overlay plots of individual displacements in X, Y, and Z directions. It is obvious that the noteworthy deformation is largely promoted along the radial direction. When we come across the analysis of results obtained at different loading situations illustrated in Fig. 13 we observe that the modified hydrostatic pressure test at 2 bar (Fig. 13c) exhibits a reduction of maximum and minimum deformations by about 33% and 62% respectively compared to the hydrostatic pressure situation. This demonstrates better performance of water-pressurizing tank against static pressure loading as compared to the water filled tank.

The addition of pressure is shown to improve the performance of water filled tank in terms of less deformation and more globally distributed loading. This can be explained by that the water filled tank submitted to pressure may cause both a phase change of water and redistribution of internal and kinetic energy over the tank surface. Water pressure indeed gives a non-conservative loading that is always normal to the surface. In such situation, the mechanical energy does not remain constant but decreases due to the presence of frictional forces that act to reduce the mechanical energy in the system. Moreover, from Figs. 13c andd, it can be seen that the symmetric pattern of deformations no longer exists as in case of hydrostatic pressure load. This experiment also reveals that the maximal displacements occur at the top of structure along the left side of the front half of the tank. In addition, increasing water pressure from 2 bar to 3 bar has in fact little or no noticeable influence on the overall behavior of the tank surface.

Now we turn to investigate the overall response of the composite tank throughout the range of inelastic behavior. To do so, we perform the following steps 1. The pressure of water filled tank is reduced from 3 bar to 0 bar, so that the pressure inside the tank is completely removed and the tank is only under action of hydrostatic pressure (due to water). A group of images are then acquired and 3D coordinates of point markers are computed. The result is defined as the fifth stage. 2. The hydrostatic pressure load is removed by emptying the tank, then we take a series of photos and the 3D coordinates of point markers are thereafter computed. This stage is considered as the sixth stage. 3. The coordinate systems of different deformation stages are registered together via the global transformation points. The deformation in the space in different states can then be calculated and displayed.

We next construct eight virtual extensometers for measuring strains of 3D tank at different positions contactlessly. To measure strain, or more specifically, the change in length of an object, we need a 2-point distance with a defined length. The distance between the initial point and the end point constitutes the length of the extensometer. With distance checks, we can analyze how the distance between two surface points deviates from a reference value. Distance deviations and strain between key points located on the tank surface at different places, e.g. top surface, front and rear heads, and along the diameter (see Fig. 18) are measured before adding pressure to water filled tank (second stage, Fig. 18a) and after removing the pressure (fifth stage, Fig. 18b) and then compared to each other. This is carried out to explore the effect of introducing 3 bar pressure load on the inelastic response of the composite tank. Similarly, deformations at the same locations are measured after the loads are totally removed from the tank (sixth stage, Fig. 18c), then compared to the beginning state of empty tank (reference stage at which the deformation is zero) to examine the effects of applied pressures that may cause permanent deformation. The experimental observations for both situations show indeed very minor plastic deformation in the tank. The differences in length changes between the initial and final hydrostatic pressure phase as well as between the reference stage and final stage after emptying the tank do not exceed 1 mm. Table 4 shows the detailed information of measurement results for the considered eight distances depicted in Fig. 18. In Table 4, ∆L stands for the deviation of a distance in the 3D space, ∆L X,Y,Z represents the deviation in the individual coordinate directions X, Y, and Z, εl=∆L/L 0 is the quotient of length change and reference length of a distance in the 3D space, εl x,y,z =∆L X,Y,Z /L 0X,Y,Z stands for the quotient of length change and reference length of a distance in the individual coordinate directions X, Y, and Z. In general, it can be seen from these results that the tank materials under internal applied pressures are resistant to permanent deformation. Upon removal of load, the composite tank reverts back to its initial size and no permanent material's shape change occurred in the tank. The obtained results are information rich, reliable and provided in different locations on tank surface, enabling detailed 3D deformation analysis of large scale composite tank.

Considerable insights in the nature of the elastic behavior observed in Table 4 can be obtained, making small displacement gradient theory be adopted for the deformation analysis of the underlying structure which is typically built from relatively stiff elastic materials like carbon fiber, since a common goal in the design of such composite structures is to minimize their deformation under typical operating pressures. In this work, pressure testing was carried out using water. The reason for this is because water is virtually incompressible (as other liquids) and only a small quantity of energy needs to be introduced to increase the pressure significantly. Air, however, (like all gases) is compressible and, as a result, much more energy has to be put into the gas to raise its pressure. Thus, pneumatic tests are potentially more dangerous than hydrostatic because of the higher level of potential energy. Hydrostatic pressure is indeed an important issue for such composite tank. The tank walls have to be constructed to resist this pressure under all conditions and at all levels of water storage. So that, pressure tests were performed under the maximum capacity of the tank (52 tonnes of water) to evaluate the deformation level induced by the introduced internal loadings, thereby confirming the mechanical strength of the tank, and thus ensuring the safety and reliability of the underlying tank.

On the basis of the optical measurement results obtained, it can be noticed that the potential influence factors of the present method are the changes in lighting of the environment and the quality of recorded photographs. In spite of careful planning prior to the actual field site image acquisition, few problems surfaced during the operation, especially those that were related to the characteristics of the closed space workshop (e.g. poor lighting, dim sunlight, and insufficient space around the tank); obviously with higher quality image and more suitable environment, a better accuracy can be obtained. The whole placement of optical targets and photo taking operations in this study involved two persons, and it took approximately 5 days to complete the measurements: 2 days were fully devoted into the tank preparation and targeting operation, and another 3 days were required for the photograph taking and end-of-project cleaning processes. Since enormous discrete optical points are adhered on the tank to entirely cover the surface of interest so that the deformation can be measured over a very large area. A large number of images that require a large amount of time were actually necessary to obtain both accurate measurements and the 3D model of the tank with a little manual intervention.

Conclusion and final remarks

In this contribution, an innovative, non-invasive measurement technology, based on photogrammetric detection has been applied to experimentally estimate the structural properties of large-capacity composite tank. This technique allows an accurate reconstruction of the 3D shape of the tank from a number of freehand digital pictures taken from different angles and positions. A triangulation process, based on the correlation of the digital images, yields 3D coordinates of designated reference point markers located on the tank surface. The 3D coordinates are computed through an algorithm that post-processes the data by simultaneously recognizing and triangulating the target points pasted on the tank, resecting the pictures and self-calibrating the camera. Although the size of the tank in this work was very large and structurally complex, all conducted measurements were evaluated in high quality and complied with the quality requirements of the application software. Through tracking the point markers pasted on the composite tank and calculating the displacement of 3D coordinates of the markers, the whole 3D deformation is obtained in all loading stages. The structural performance of the tank under actions of hydrostatic pressure and water pressurizing loadings was experimentally investigated in this paper. The static loading was applied by filling the tank by fluid to assert static pressure on the tank. In this pressure case, a large field of 3D displacement and/or strain of the tank were obtained from the test and compared to the initial stage of empty water tank. The hydrostatic pressure test was followed by water pressurizing tests through raising the pressure of the water filled tank from zero to a certain test pressure, typically 2 bar and 3 bar. It has been found that the water pressurizing test exhibits a reduction of tank deformation compared to the hydrostatic pressure situation; this indeed demonstrates better performance of water-pressurizing tank contrary to the water filled tank situation. The knowledge of hydrostatic pressure effects on the solid domain of tanks and their interdependence under pressure loading is significant for the safe and economic design of composite resistant containers.

According to the analysis of all experimental results conducted in this work, the following conclusions can be drawn:

• Compared with other conventional and modern techniques, photogrammetry is proven to be a time-saving and cost-effective method for deformation measurement of large scale composite structure. Since photogrammetry basically consists in applying adhesive reference point markers and taking a set of 2D photographs, it has several advantages in terms of reduced cost and intrusion, as well as in terms of easiness of setup and measurement.

• The target points positioned on measured tank are very light and thin so that they will not interfere with the deformation of tank itself. • According to the deformation under different load tests measured by the present method, reasonable explanations of the deformation during the loading test is gained and a feasible solution to improve the safety of the tested composite tank is found, which indicate that the proposed method is very useful. • For the above-mentioned reasons, photogrammetry is a reference in the composite tank area measurement field for the future and is clearly an efficient technique for tanker companies. This method opens a new research field that addresses, for instance, new kinds of composite containers (more complex), advances in the automation of the photogrammetric process and optimisation of the acquisition process. • This study could also provide some valuable references for large field deformation measurement in engineering applications.

Fig. 1 .

 1 Fig. 1. 2D sketch of the geometrical characteristics of the composite tank. Units in mm.

Fig. 2 .

 2 Fig. 2. Schematic illustration of the schemes to form the triangulated core.

Fig. 4 .

 4 Fig. 4. Working principle of photogrammetry TRITOP: coordinate determination of reference points by triangulating bundles of observation rays from different images.

Fig. 5 .

 5 Fig. 5. Hardware composition of the proposed measurement system.

Fig. 7 .

 7 Fig. 7. Central perspective projection on which the photogrammetric model for the camera is based. P is an object point in 3D space, which is projected through the perspective centre O onto the projection plane where it creates the image point Q.

Fig. 8 .

 8 Fig. 8. Computational flow of TRITOP software.

Fig. 9 .

 9 Fig. 9. The real composite tank and placement of non-coded points, individual coded points, orientation crosses, and scale bars.

Fig. 10 .

 10 Fig. 10. Recognized coded and non-coded reference points for the tank in the initial stage.

Fig. 11 .

 11 Fig. 11. Oriented photogrammetry images in the 3D view and recognized reference points together for the tank.

Fig. 12 .

 12 Fig. 12. Displayed sensor positions in the 3D view.

.Fig. 13 .

 13 Fig. 13. 3D graphics mode of the magnitude and direction of the displacement in different loading situations.

Fig. 14 .

 14 Fig. 14. Displacement with enabled deviation labels at the joint between the cylinder and rear head (a) and front head (b).

Fig. 15 .

 15 Fig. 15. Magnitude of displacement along line L on the tank subjected to hydrostatic pressure.

Fig. 16 .

 16 3D displacement deviations in individual coordinate directions.

  (a) Magnitude of displacement (b) Overlay plots of displacement in X, Y, and Z directions

Fig. 17 .

 17 Fig. 17. Displacement distribution around the circumference of the ferrule due to hydrostatic pressure.

Fig. 18 .

 18 Fig. 18. Strain measurements between target points at different places on the tank surface in 3D space.

Table 2 .

 2 Technical

	Parameter	Value
	Image size	Approx. 18 mega pixel
	Image width	5184 pixels
	Image height	3456 pixels
	Principle point offset 0 each
	Shutter speed	1/250 s
	Camera focal length	25.00 mm
	Pixel size	6.90 µm
	Binarization offset	5
	3.2.1.2. Coded and non-coded reference point markers and scale bars

specifications and setting parameters of the used photogrammetry camera, Canon EOS-1D X.

Table 3 .

 3 Quality parameters of the photogrammetry measurement series obtained for three

	loading cases
	3D data	Without	Hydrostatic	Modified hydrostatic
		pressure	pressure	pressure
	Minimum observation angle (°)	3.61	4.71	4.20
	Average image point deviation (pixel)	0.0513	0.0641	0.0718
	Average reference point deviation (mm)	0.0368	0.0432	0.0479
	Average scale bar deviation (mm)	0.0290	0.040	0.0365

Table 4 .

 4 Deformation measurements at different locations on the tank surface

				Before adding pressure to water filled tank
		1	2	3	4	5	6	7	8
	-1.055 12.195 0.724 22.226 7.537 -1.638 3.504 -13.141 3.518 0.686 ∆L X (mm) -0.326 12.278 -0.475 22.225 7.557 0.122 ∆L (mm) -6.177 -0.772 0.298 -4.805 1.512 -14.287 ∆L Y (mm) 2.334 -1.918 1.009 0.428 -0.009 -1.379 -0.421 1.097 ∆L Z (mm) -1.118 -0.121 -0.049 0.477 0.007 0.872 0.299 -0.040 0.139 -0.632 εl (%) -0.330 0.482 -0.113 0.872 0.302 0.068 0.139 0.132 εl X (%) 3.359 -5.457 -1.293 -12.686 0.098 -2.090 8.076 -0.725 εl Y (%) εl Z (%) -0.051 -0.054 0.009 1.708 -0.036 -0.034 -0.328 0.266
			After removing pressure from water filled tank
		1	2	3	4	5	6	7	8
	-0.842 13.349 0.589 22.976 6.659 -1.806 4.287 -13.310 4.289 0.838 ∆L X (mm) 0.025 13.446 -0.162 22.974 6.660 0.171 ∆L (mm) -6.793 -1.139 0.394 -5.155 1.802 -14.583 ∆L Y (mm) 2.446 -2.184 0.889 0.546 0.015 -1.530 -0.192 1.460 ∆L Z (mm) -0.924 -0.182 -0.039 0.522 0.005 0.902 0.264 -0.044 0.170 -0.640 εl (%) 0.026 0.528 -0.038 0.902 0.266 0.095 0.170 0.161 εl X (%) 3.520 -6.214 -1.422 -18.710 0.129 -2.243 9.618 -0.740 εl Y (%) εl Z (%) -0.043 -0.082 0.008 2.178 0.063 -0.038 -0.150 0.354
				Remove load by emptying the tank
		1	2	3	4	5	6	7	8
	∆L (mm)	0.205 0.505	0.691 0.258	-0.070 0.395	0.769 0.289

Acknowledgment

The authors of this paper would like to acknowledge and appreciate the support provided by Spitzer Eurovrac to accomplish this work.