Xun Li
email: xun.li@erdw.ethz.ch

Theodor Becker

Nele Börsing

Dirk-Jan Van Manen

Andrew Curtis

Johan Robertsson

IMMERSIVE WAVE CONTROL EXPERIMENTS USING NON-ISOTROPIC SOURCES: LABORATORY APPLICATIONS

A physical experiment can be fully linked and immersed within a virtual (numerical) domain through the real-time exchange of boundary conditions between the experiment and the numerical simulation. Such immersive wave control experimentation relies on active sources deployed around a physical domain (e.g., a water tank) to change its boundary condition. However, in theory, the control algorithm requires sources with an isotropic radiation pattern, while physical sources typically exhibit angledependent radiation characteristics. This discrepancy can be overcome by a processing method carried out in the frequency-wavenumber (f-k) domain if the source radiation pattern is known. Here we show the measured radiation pattern of a custom-built Bender-mode X-spring (BMX) type piezoelectric source that will be used in underwater acoustic immersive wave experimentation. We measure the half-space radiation pattern of the BMX source that is mounted at the center of a steel plate with a transversely deployed planar receiver surface. The acquired data is redatumed to that corresponding to receivers deployed along a semi-circle and the source at the origin. The BMX source shows a non-negligible radiation pattern with the highest energy at normal and decreasing power gradually to its perpendicular. The measured radiation pattern will be incorporated into the 3-D physical implementation of immersive wave experimentation.

INTRODUCTION

For laboratory wave propagation experimentation, the concept of immersive boundary conditions [START_REF] Vasmel | Immersive experimentation in a wave propagation laboratory[END_REF] has emerged in recent years, originating from the method of exact boundary conditions used in numerical modeling [START_REF] Van Manen | Exact wave field simulation for finite-volume scattering problems[END_REF][START_REF] Givoli | Nonreflecting boundary conditions based on kirchhoff-type formulae[END_REF]. Immersive wave experimentation involves deploying active sources around the physical boundary of a closed domain (e.g., water tank), enabling to fully immerse the domain into a surrounding virtual medium. Figure 1 shows a twodimensional (2-D) setup for immersive experimentation where sources on the active boundary S emt cancel outgoing waves (e.g., ray path 1 or its reflection along ray path 3) and produce in-going waves (e.g., ray path 4) that result from the wavefield interactions with the surrounding virtual medium. The produced in-going waves are also canceled when arriving at S emt . Wave cancellation and production apply to first and higher-order scattered waves between the physical and virtual domains, producing an illusion within the physical domain that waves propagate seamlessly in the combined two domains. The setup includes (1) a recording surface S rec consisting of closely spaced receivers (blue dots), (2) a rigid boundary (red rectangle) surrounding the physical domain, (3) emitters (red dots) mounted on the rigid boundary (i.e., emitting surface S emt ). The black star denotes an internal source generating wavefields for acoustic experiments. Such a physical laboratory for immersive wave control experimentation is currently constructed in the Exploration and Environmental Geophysics Group at the Swiss Federal Institute of Technology (ETH), Zurich. Immersive boundary conditions have been physically implemented in an airfilled 1-D waveguide as a proof-of-concept [START_REF] Becker | Immersive Wave Propagation Experimentation: Physical Implementation and One-Dimensional Acoustic Results[END_REF] and also in a 2-D acoustic waveguide between two closely-spaced plates [START_REF] Becker | Immersive wave propagation experiments in a two-dimensional acoustic waveguide[END_REF][START_REF] Becker | Real-time immersion of physical experiments in virtual wave-physics domains[END_REF] while for a 3-D domain such as a water tank, the implementation is on-going work. For that purpose, custom-built acoustic piezoelectric sources, pressure hydrophones, amplifiers, and a high-performance computing and control unit based on field-programmable gate array (FPGA) have been manufactured and undergone extensive testing [START_REF] Börsing | Acoustic immersive experimentation through real-time control of boundary conditions[END_REF].

Immersive wave experimentation requires monopolar sources deployed on the emitting surface S emt in Fig. 1. However, a physical source (e.g., a piezoelectric transducer) projects waves that do not conform to the theoretically-required monopolar radiation pattern, which causes controlled wavefields to deviate from those desired, especially at high emitting frequencies for which source directivity is typically more pronounced than at low frequencies (< 1 kHz). Ref. [START_REF] Li | Compensating for source directivity in immersive wave experimentation[END_REF] proposed a frequencywavenumber (f-k) processing method that can compensate for the source radiation pattern in immersive wave experimentation. The method involves incorporating the measured source radiation pattern into the pre-computed Green's functions used for wavefield extrapolation, which has been validated in a 2-D synthetic experiment with control sources on S emt that exhibit non-monopolar radiation patterns [START_REF] Li | Compensating for source directivity in immersive wave experimentation[END_REF].

In this paper, we show the radiation pattern of a BMX source and discuss the practical application of the source directivity compensation method. In Section 2, we review the theory of immersive boundary conditions that can account for source radiation pattern. We then show the acquisition geometry for measuring the radiation pattern of a BMX source in the laboratory and introduce the necessary processing methods for obtaining the radiation pattern from the measurement. In Section 3, we show the measured radiation pattern, and in Section 4, we discuss the practical usage of these directive sources in immersive wave experimentation. We conclude the paper with an outlook for building a 3-D laboratory for immersive wave experimentation in Section 5.

METHOD 2.1 Immersive wave experimentation

Active sources surrounding a closed rigid boundary can fully control the acoustic wavefield inside based on the following IBC term [START_REF] Broggini | Immersive boundary conditions: Theory, implementation, and examples[END_REF]:

P IBC (x , t) = - S emt G p (x , t, x emt , 0) * v n (x emt , t) dS (1)
where the Green's function G p (x , t, x emt , 0) denotes a pressure source at x emt (at time 0) and a pressure receiver at an arbitrary point x inside the experimental domain. The normal to the emitting surface S emt is denoted by n, and the symbol * refers to convolution in time t. Eqn. [START_REF] Vasmel | Immersive experimentation in a wave propagation laboratory[END_REF] implies that the time signatures for these boundary sources at x emt are the normal particle velocities v n (x emt , t) of the waves that have traveled seamlessly between the physical and virtual domains, without scattering caused by the rigid boundary.

The normal particle velocity v n [in Eqn. (1)] at S emt is extrapolated from the interior propagating waves (i.e., particle velocities and pressures at the recording surface S rec ) using the Kirchhoff-Helmholtz integral [START_REF] Van Manen | Exact wave field simulation for finite-volume scattering problems[END_REF][START_REF] Miller | On perfect cloaking[END_REF]:

v n (x emt , t) = S rec [G(x emt , t, x rec , 0) * v m (x rec , t) + Γ(x emt , t, x rec , 0) * p(x rec , t)] • m dS. (2)
Here, G and Γ are the monopolar and dipolar Green's functions, respectively, with direction m normal to S rec . In a physical experiment, Eqn. ( 2) is computed in real time such that the wavefield extrapolation is faster than waves traveling between S rec and S emt [START_REF] Becker | Immersive Wave Propagation Experimentation: Physical Implementation and One-Dimensional Acoustic Results[END_REF].

As previously noted, physical control sources may exhibit non-isotropic radiation characteristics and hence do not comply with the theory of immersive boundary conditions, which require monopolar sources deployed on the rigid boundary [as denoted by G p in Eqn. ( 1)]. To compensate for the source radiation pattern, Ref. [START_REF] Li | Compensating for source directivity in immersive wave experimentation[END_REF] apply a f-k processing method to the pre-computed Green's functions in Eqn. [START_REF] Van Manen | Exact wave field simulation for finite-volume scattering problems[END_REF]. Here for simplicity, we only show the processing scheme for the monopolar Green's function G, and the same procedure applies to the dipolar Green's function Γ. We show the f-k processing method in a 2-D geometry which can be extended to a 3-D laboratory application.

We start by (Fourier) transforming the Green's function G(x emt , t, x rec , 0) in Eqn. ( 2) to the frequencywavenumber (f-k) domain denoted by Ĝ(k, f, x rec ). The spatial axis x emt corresponds to wavenumber k while t corresponds to frequency f . We then process the transformed Ĝ in the f-k domain:

Ĝ(k, f, x rec ) = Ĝ(k, f, x rec ) Ŵ (π -θ, f ) (3)
where Ŵ (π -θ, f ) are the directive matched filters in the frequency domain (denoted by the symbolˆ), and the angle π -θ implies that the compensation of the source radiation pattern applies in the direction of wave reflection at the active source boundary S emt for out-going waves (ray path 3 in Fig. 1), and this compensation works also well for in-going waves (see Ref. [START_REF] Li | Compensating for source directivity in immersive wave experimentation[END_REF]). Provided that S emt is composed of planer surfaces, the angle θ is given as θ = π/2 + arcsin(ck/f ) where c is the wavespeed of the medium (i.e., water).

Ŵ (θ, f ) = M p (θ, f )/ M p (θ, f ). (4)
Finally, the processed Green's functions G (and also Γ) in Eqn.

(3) are transformed back to the time-space (t-x) domain and further used in wavefield extrapolation [Eqn. [START_REF] Van Manen | Exact wave field simulation for finite-volume scattering problems[END_REF]] such that source directivity is compensated.

Acquisition geometry for radiation patterns

Figure 3 shows the piezoelectric sources and pressuresensitive hydrophones that are used in 3-D immersive wave experimentation [START_REF] Börsing | Acoustic immersive experimentation through real-time control of boundary conditions[END_REF]. The pressure-sensitive receivers on the recording surface are custom-built piezoelectric hydrophones with negligible directivity [START_REF] Börsing | Acoustic immersive experimentation through real-time control of boundary conditions[END_REF]. The sources are Bender mode X-spring (BMX) type of piezoelectric transducers, which can generate acoustic waves with high output power across the frequency range 1-20kHz [START_REF] Willard | Acoustic Transducer Design for Active Reflection Cancellation in a Finite Volume Wave Propagation Laboratory[END_REF][START_REF] Willard | Acoustic transducer design for active reflection cancellation in a finite volume wave propagation laboratory[END_REF][START_REF] Delany | Bender transducer design and operation[END_REF].

These BMX transducers are mounted flush in a rigid steel plate, which must be included in the measurement of source directivity due to its influence on the radiation pattern [START_REF] Li | Compensating for source directivity in immersive wave experimentation[END_REF]. The BMX source is built in close collaboration with the Walker Department of Mechanical Engineering at the University of Texas (UT) at Austin and the Applied Research Laboratories UT Austin [START_REF] Willard | Acoustic Transducer Design for Active Reflection Cancellation in a Finite Volume Wave Propagation Laboratory[END_REF].

Instead of using the ideal acquisition geometry in Fig. 2, we use the geometry shown in Fig. 4 where one active BMX source emits waves at the center of the rigid steel plate with the receivers arranged in the X-Y plane that contains the source. This measurement only works for source radiation pattern with transverse isotropy, which can be inferred from the manufacture of the BMX source with round front face, shown in Fig. 3(c). Hence, directivity only exists along the direction towards the normal of the emitting surface (or the front face of the source) [START_REF] Börsing | Acoustic immersive experimentation through real-time control of boundary conditions[END_REF][START_REF] Willard | Acoustic Transducer Design for Active Reflection Cancellation in a Finite Volume Wave Propagation Laboratory[END_REF]. Figure 5 shows the locations of the source and receivers in the X-Y plane, and this geometry covers a large (angular) aperture to characterize the source radiation pattern.

Redatuming of recorded data

The Cartesian coordinate for the locations of the source and receivers in Fig. 5 can be transformed into the radiation angle θ against the source-receiver distance as shown in Fig. 6. Here, we follow a spherical wave spreading model [START_REF] Wapenaar | Elastic Wave Field Extrapolation: Redatuming of Single-and Multi-Component Seismic Data[END_REF]:

p(ω, r) = S(ω)e -ikr r ( 5
)
where p(ω, r) is the pressure recorded at distance r from a point source, i is the imaginary unit, and S(ω) is the frequency spectrum of the source signature. We redatum the recorded data to the semi-circle (as shown in Fig. 2) with radius r 0 = 0.45 m: where p c (ω, r 0 ) is the pressure after redatuming. Finally, the results are transformed back to the time domain to yield p c (t, r 0 ). The amplitude and phase variation of p c (t, r 0 ) in different directions θ represent the source radiation pattern.

p c (ω, r 0 ) = p(ω, r) r 0 r e ik(r0-r) (6)

RESULTS

Figures 7(a) and (b)

show the data measured in underwater experiments using the geometry given in Fig. 4 and the data redatumed using Eqn. ( 6), respectively. The source signature of the BMX source is a Ricker wavelet with peak frequency 6 kHz, and the wavespeed of water is c = 1488 m/s. The first events in the redatumed time series [Fig. 7(b)] have almost identical arrival times, indicating that the propagation of direct waves in the water tank is well described by the spherical spreading model. A strong ringing effect does exist after the expected first arrival in the recorded data. This ringing is undesired and pollutes the measurement of the phase variation in different directions, complicating the estimation of the source radiation pattern. Hence, Eqn. ( 4) can be further simplified, and we only focus on the amplitude variation for the radiation pattern. For the redatumed data shown in Fig. 7(b), we first calculate the envelope using Hilbert transform [START_REF] Korn | Mathematical Handbook for Scientists and Engineers: Definitions, Theorems, and Formulas for Reference and Review[END_REF], which eliminates the phase variation in different directions. The maximum amplitude values of these envelopes are plotted against the directions θ, as shown in Fig. 8. This radiation pattern is symmetric with maximum energy in the normal direction (θ = 90 • ) and decreasing emitted energy to its perpendicular, which is expected in a BMX type source [START_REF] Willard | Acoustic Transducer Design for Active Reflection Cancellation in a Finite Volume Wave Propagation Laboratory[END_REF]. We also verify that the change of the redatuming radius r 0 does not change the shape of the amplitude variation trend in Fig. 8 (not shown here).

The obtained radiation pattern in Fig. 8 is not evenly sampled in the radiation angle θ. To overcome this fact, we interpolate the acquired pressure data for equally spaced radiation angles using Modified Akima Cubic Hermite interpolation [START_REF]Interpolation for 2-d gridded data in meshgrid format[END_REF][START_REF] Cheregi | A comparison between akima and hermite type cubic spline with minimal quadratic oscillation in average[END_REF], and repeat the estimation of the source radiation pattern, as shown in Fig. 9. The radiation angles θ are resampled with 1 • interval from θ = 10 • to 170 • .

DISCUSSION

The radiation pattern of transducers typically depends on the signal frequency or wavelength. As for wavelengths on the order of the transducer dimensions, the geometry of the source affects the radiation pattern [START_REF] Li | Compensating for source directivity in immersive wave experimentation[END_REF]. Hence, the compensation of the source directivity is frequency-dependent, and the frequency range of the measurement of the radiation pattern must match the operating frequency range of immersive experimentation.

The ringing tails that exist in the recorded data [Fig. 7(b)] may not be suppressed or compensated by the proposed deconvolution in Eqn. (4) and is considered as artefacts, which should be removed from the data. Naive deconvolution between the data with ringing tails and the analytical traces results in the directive matched filters that if convolving with the pre-computed Green's functions, generate undesired source emission at the emitting surface S emt . This ringing effect is probably caused by the (nonlinear) coupling between the rigid steel boundary and the physical source and hence cannot be removed by a linear filter. Considering this source characteristic, we plan to first compensate for the amplitude variation in the measured source radiation pattern. The deconvolution in Eqn. ( 4) becomes a simple division, and the directive matched filters become scalars/ratios varying for waves traveling in different directions. In this case, the source compensation method takes only (source) amplitude variation in different directions into account, which should effectively remove the undesired effect caused by directive sources used in immersive wave experimentation [START_REF] Li | Compensating for source directivity in immersive wave experimentation[END_REF]. The wave phase variation in different directions from a directive physical source is often quite weak or even negligible [START_REF] Börsing | Acoustic immersive experimentation through real-time control of boundary conditions[END_REF]. We only measure the radiation pattern of a single source and assume the radiation pattern only varies little among the batch of sources such that the measured radiation pattern and further computed directive matched filters can be used to compensate for the directivity of all the sources. In the future laboratory work, we will first test whether this radiation pattern is consistent enough across all the BMX sources. Alternatively, the directivity compensation method still holds if radiation patterns are different for all sources (with some modification, see Ref. [START_REF] Li | Compensating for source directivity in immersive wave experimentation[END_REF]). Since the sources need to be mounted on the rigid steel boundary to be measured with the radiation patterns, we need a more effective acquisition geometry or scheme for the measurement, considering that the water tank is limited with its size, and we should avoid boundary reflection present in the data for radiation patterns.

The amplitude radiation pattern, shown with data points in Fig. 8, contains some outliners. The data points that deviate from the general trend of the radiation pattern (for θ = 90 • ) correspond to the receivers closest to the source. However, no near-source effect theoretically exists in acoustic pressure recordings from a point source [START_REF] Parkes | The Marine Seismic Source[END_REF]. These deviations may be caused by the fact that the physical source has a finite dimension and cannot be considered as a perfect point source. This issue remains to be investigated in the laboratory, but currently, we can remove these data points as outliers.

OUTLOOK

We presented the measured radiation pattern of a custombuilt BMX-type source in an underwater acoustics laboratory. The source radiation pattern is significantly non-isotropic, which does not fit into the requirement of monopoles in the theory for immersive wave experimentation. In the next step, we will first finish the implementation of the single-sided immersive boundary condition in a 3-D water tank, shown as in Fig. 3(a). Then we assess the effect caused by source directivity, especially when using high emitting frequencies (> 2kHz). We can incorporate our measured source radiation pattern into immersive wave experimentation using the theory proposed in Ref. [START_REF] Li | Compensating for source directivity in immersive wave experimentation[END_REF]. We might repeat measurements at some point once we can get rid of the ringing effect for the current BMX sources such that the phase variation in different directions can also be compensated. Finally, we will demonstrate the f-k compensation method in the real laboratory in one-sided/full 3-D experiments.

Figure 1 .

 1 Figure 1. Schematic of immersive wave experimentation. The setup includes (1) a recording surface S rec consisting of closely spaced receivers (blue dots), (2) a rigid boundary (red rectangle) surrounding the physical domain, (3) emitters (red dots) mounted on the rigid boundary (i.e., emitting surface S emt ). The black star denotes an internal source generating wavefields for acoustic experiments.

Figure 2 .

 2 Figure 2. Ideal geometry for the measurement of source radiation patterns (2-D view). The green dot denotes the source mounted on a rigid boundary while the blue dots (hydrophones) are arranged along a semi-circle (or a hemisphere in 3-D) with the same distance r 0 to the source. Ideally, the radiation pattern can be measured as pressure responses in different directions θ with the geometry shown in Fig. 2. The directive matched filters are calculated from the trace-to-trace deconvolution between the

Figure 3 .

 3 Figure 3. (a) Photo of one-sided immersive wave experimentation containing planar source and receiver arrays in a 3-D water tank. (b) Pressure-sensitive hydrophones (receivers) with front and back views. These receivers are held by a lattice of 3 mm-thick rods. (c) Bender-mode Xspring piezoelectric source with the housing flange (5 cm diameter).

Figure 4 .

 4 Figure 4. Actual geometry used to measure the radiation pattern of a BMX source in the underwater acoustic laboratory. The planar receiver array is on the same X-Y plane (or same Z-level) with the active source.

Figure 5 .Figure 6 .

 56 Figure 5. Geometry used to measure the radiation pattern of a BMX source, with view on X-Y plane. The red dot denotes the active BMX source and blue dots denote the receivers.

Figure 7 .

 7 Figure 7. (a) Pressure data recorded with the geometry shown in Figs. 4 and 5. (b) Redatumed data at a uniform radius r 0 = 0.45 m with the geometry shown in Fig. 2.

Figure 8 .

 8 Figure 8. The source radiation pattern of the BMX source.

Figure 9 .

 9 Figure 9. The source radiation pattern of the BMX source including interpolation of the acquired data to yield evenly spaced angles θ.

10.48465/fa.2020.0070

e-Forum Acusticum, December 7-11, 2020

ACKNOWLEDGMENTS

This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No 694407).


Diego Vinasco-Alvarez
email: diego.vinasco-alvarez@univ-lyon2.fr

John Samuel
email: john.samuel@cpe.fr

Sylvie Servigne
email: sylvie.servigne@insa-lyon.fr

Gilles Gesquière
email: gilles.gesquiere@univ-lyon2.fr

Towards a semantic web representation from a 3D geospatial urban data model

Keywords: 3D urban data conceptual models, Semantic Web, Interoperability, CityGML, RDF, GeoSPARQL

L'urbanisation est un processus d'évolution continue qui est actuellement étudié par nombre de chercheurs. Les modèles d'information de la ville, multi-sources et multidimensionnels, sont souvent utilisés pour comprendre le paysage urbain, qui est en constante évolution. Ces modèles peuvent cependant poser des problèmes d'interopérabilité et de perte de données lors de conversions, souvent nécessaires pour permettre leur intégration. Aujourd'hui, nous pouvons nous baser sur des modèles conceptuels qui peuvent aider à traiter les pertes de données lors de conversions, et peuvent également contribuer à préserver l'interopérabilité des données. Ce type d'approche modèle-centrée permet de définir une représentation commune. Récemment, un mouvement vers la représentation de données basée sur les graphes et la sémantique a gagné en popularité pour répondre aux problèmes d'interopérabilité. Dans un premier temps, pour illustrer notre approche, nous considérons CityGML, un standard de représentation des informations urbaines en 3D. Nous proposons une stratégie pour convertir la sémantique du modèle conceptuel de CityGML vers des ontologies et, ensuite, en formats web sémantiques pour faciliter l'intégration. Nous proposons également une méthode pour convertir et stocker les instances CityGML en individus RDF qui respectent l'ontologie générée. L'approche proposée permet de pallier le déficit d'information sémantique résultant de la traduction directe de différents types de données en graphe, tels que RDF.

ABSTRACT. Urbanization is a continuous evolution process that is currently studied by a number of researchers. Multi-source and multidimensional city information models are often used to MOTS-CLES : Modèle conceptuel de données urbaines 3D, Web sémantique, Interopérabilité, CityGML, RDF, GeoSPARQL

understand the ever-changing urban landscape. These models may encounter issues with interoperability and data-loss if conversion is required for integration. Today we can base ourselves on conceptual models which can help deal with data losses during conversion and may also help preserve data interoperability. This kind of model-driven approach can be useful as common representation. Recently, a movement towards graph and semantic based data representations has also grown in popularity to respond to these issues. As a first step, we consider CityGML, a common standard that can be used to represent 3D urban information. We propose a strategy for converting the semantics of CityGML conceptual model into ontologies and later to semantic web formats to facilitate integration. In addition, we propose a method for converting and storing CityGML instances into RDF individuals that respect the generated ontology. This proposed approach overcomes the loss of semantic information resulting from the direct translation of different types of data into graphs such as RDF.

Introduction

The urban landscape is a complex and heterogeneous source of information. The anthropization and urbanization of modern cities have brought into the fold various actors, issues, and systems that all have complicated interconnections and dependencies both on local and global scales. The data-driven approaches used to represent and model these urban environments often depend on multi-source and multidimensional urban data, which consists of a variety of different information coming from multiple actors and organizations [START_REF] Barbosa | Structured Open Urban Data: Understanding the Landscape[END_REF]. For example, city governments have different departments for handling different subjects or issues like water and sewage, pollution, traffic, energy, etc. [START_REF] Rochet | Urban lifecycle management: A research program for smart government of smart cities[END_REF]. Sometimes these organizations release open datasets using their own internally defined business formats or using formats that conform to a specific use-case as opposed to more generic or widely used standards, thus making it difficult to get an integrated view of the data from multiple sources.

In response to the limits of using internal formats, we are now seeing the growing use of geospatial and 2D/3D urban data standards. Different international organizational bodies (OGC, ISO, W3C...) propose standards and release conceptual data models for their standards to ensure that the data is represented uniformly by the users, thereby giving open datasets an aspect of interoperability. Take for example, the CityGML standard 1 released by the Open Geospatial Consortium (OGC), a city information model used for 3D urban modeling to represent city objects at different levels of detail.

Another aspect of urban data is the underlying n-dimensional structure. For a long time, 2D maps, aerial views, and cadastral views were used for the management of the urban lifecycle. With the growing availability of 3D data, thanks to new data acquisition processes (LIDAR, photogrammetry...), numerous applications are now possible with 3D urban data (Biljecki 2015). Recently, some urban data models also take into account the changes of cities as they evolve over time in addition to spatial information [START_REF] Chaturvedi | A REQUIREMENT ANALYSIS ON EXTENDING SEMANTIC 3D CITY MODELS FOR SUPPORTING TIME-DEPENDENT PROPERTIES[END_REF][START_REF] Jaillot | Delivering time-evolving 3D city models for web visualization[END_REF][START_REF] Samuel | Representation of concurrent points of view of urban changes for city models[END_REF], thereby adding the temporal dimension (4D). These models help historians and city planners visualize and contextualize the impacts previous key projects have had on the development of a city. Such studies require an integration of the urban models with document corpus consisting of project plans, newspaper articles, archives etc. However, it is challenging to integrate data from different sources with different standards for providing an integrated urban view [START_REF] Biljecki | CityGML Application Domain Extension (ADE): overview of developments[END_REF][START_REF] Ohori | Processing BIM and GIS Models in Practice: Experiences and Recommendations from a GeoBIM Project in The Netherlands[END_REF].

Semantic web models are now being used increasingly to ensure interoperability among multiple data sources [START_REF] Malinverni | A semantic graph database for the interoperability of 3D GIS data[END_REF][START_REF] Nuninger | Linking Theories, Past Practices, and Archaeological Remains of Movement through Ontological Reasoning[END_REF][START_REF] Tran | Towards a semantic framework for exploiting heterogeneous environmental data[END_REF]. Due to its increasing popularity, a number of tools are now available to transform data in legacy formats to semantic web formats but, as said by C. Claramunt in [START_REF] Claramunt | Ontologies for geospatial information: Progress and challenges ahead[END_REF]) "3D models and Building Information Models should be fully integrated. However, any transformation must conform to the original conceptual model used for developing the standard or risk inconsistent or semantically incomplete representations [START_REF] Bohring | Mapping XML to OWL ontologies[END_REF].

In this work, we take into consideration a model-centric approach for transformation of urban data into ontological and graph formats. We demonstrate our approach with CityGML, particularly making use of open data from the metropole of Lyon. Our approach is detailed in this article. Section 2 presents the problem statement of model-centric urban data transformation in detail. Section 3 presents the existing state of the art. Taking the case study of CityGML, we detail our approach in Section 4. However, the focus of our work is not limited to transforming CityGML, but to link data from other sources, especially those based on open standards. These perspectives are discussed in section 5. Section 6 concludes the article.

Problem Statement

Managing and analyzing urban data is complex because different stakeholders and different entities produce these data, sometimes in silos. City administrators and urban planners often require an integrated view of these data for analyses and for obtaining meaningful insights for daily routine tasks and future planning. Take for example, urban planners who wish to construct a new high-rise building in a particular sector, need to have information on the other structures present around the proposed building. Such information may help them to study the impact on visibility of historical buildings of interest, analyze the reduced or increased sunshine or shadows because of the new construction. All these studies require data from multiple sources, such as the terrain information, 3D structures of urban objects, position of celestial bodies at different points of times etc.

However, the task of integrating urban data from multiple sources remains very difficult. Additionally, the various standards used to model this data evolve based on the growing requirements of the domain users. New versions of standards need to be released. Sometimes, the data released under previous versions is incompatible with the newer versions. Hence, any semantic web representation solution for an integrated view of urban data must deal with the heterogeneous data from multiple sources as well as their evolution.

Concerning 3D geospatial urban data models, many approaches propose directly translating different data formats into graphs, such as RDF, without taking into account the underlying conceptual model, and consequently omit semantic information during translation, weakening the initial model. The question is therefore to propose an approach that allows the preservation of the semantics of a 3D urban model when converting into a semantic web representation.

State of the art

There are growing efforts to ensure semantic interoperability across heterogeneous data from diverse multiple sources. To obtain an integrated view, one commonly used approach is to transform the data from one data format to a common format by making use of data transformers. Stylesheets like XSLT, JSONT are commonly used for this purpose. However, some of these stylesheets are written on demand basis and may not be available on the internet for use. This means that if the users want to reuse and reproduce some of the results based on the transformed data, they may not be able to achieve it, especially if transformers follow different methodologies. In addition, information loss is another major problem during data transformation [START_REF] Levina | Assessing Information Loss in EPC to BPMN Business Process Model Transformation[END_REF]. It is important to take into consideration the initial conceptual models used for the conception of the modeling.

Several information modeling techniques exist in the literature [START_REF] Bork | A survey of modeling language specification techniques[END_REF]. One possible approach is to ensure that a common modeling language is used across domains, like the semantic web ontology (OWL) language. However, UML models are often used by domain experts [START_REF] De Paepe | Automated UML-Based Ontology Generation in OSLO[END_REF] to conceive and represent information models instead of semantic web technologies like OWL, RDFS etc. Another possible approach is to build ontologies from existing standards, i.e., transforming models conceived using different modeling languages to a semantic web ontology. Researchers are currently exploring how to make the most of the familiar modeling languages like UML [START_REF] De Paepe | Automated UML-Based Ontology Generation in OSLO[END_REF] and automatically generate ontologies in OWL from these models. Works like [START_REF] Bohring | Mapping XML to OWL ontologies[END_REF][START_REF] Kramer | Software Tools for XML to OWL Translation[END_REF][START_REF] Usmani | AUTOMATIC ONTOLOGY GENERATION OF BIM AND GIS DATA[END_REF] use similar approaches based on XML Schema as a model towards OWL ontologies.

Another possible solution to this problem is if a standards body releases the ontologies for their conceived models. Take for example, the GML 3.2 geometries ontology2 made available by the OGC. Currently, an official ontology for CityGML 2.0 is missing from the standards body. Nevertheless, it is important to state some works like [START_REF] Brink | Linking spatial data: automated conversion of geo-information models and GML data to RDF[END_REF][START_REF] Métral | EXTENSION AND CONTEXTUALISATION FOR LINKED SEMANTIC 3D GEODATA[END_REF] proposed ontologies for CityGML 2.0. Additionally, there is a semantic web working group looking for ensuring the release of OWL for future releases of CityGML.

As discussed above, we are looking for integrating heterogeneous data from multiple sources by proposing an approach that preserves the semantics of a 3D urban model when converting it to semantic web representations.

Hence, it is important to have standard procedures or guidelines for ensuring the mapping between different models so that it can be easily reproduced by other users. Our approach is to take into consideration the conceptual model of information related to cities and transform the model using these standard procedures so that the data converted is conformance to the original model and can also be reproduced by other users following these guidelines.

Proposed approach illustrated with the CityGML 2.0 Conceptual Model

As previously stated, the information produced by cities and the urban lifecycle can be broken down into hierarchies of concrete and abstract subdomains of information -such as energy, transportation, infrastructure, and many others -and be represented and visualized by 3D urban data models. CityGML is an international OGC standard that is commonly used for this purpose. Taking the CityGML conceptual model as an example, we see frameworks for describing the spatial and thematic information of the more 'material' subdomains within CityGML's modules, e.g. water, buildings, terrain, etc. More immaterial subdomains such as education or public administration are not currently represented by these modules but as a first step the existing conceptual model is more than sufficient to begin transforming open urban data into semantic web formats.

To efficiently take advantage of the benefits of semantic web formats, a direct transformation of CityGML instances is not enough, the CityGML conceptual model itself must also be transformed and be used to 'guide' instance transformations. This results in meaningful RDF graphs that respect the resulting urban data conceptual model. Resources for reproducing the approach proposed here is discussed in Section 6: Data and code availability statement.

Proposed Approach Design

In order to transform the CityGML conceptual model and CityGML instances into semantic web representations, our proposal uses several XSLT-based transformations based on previous works on XML to RDF, RDFS, and OWL conversion [START_REF] Bedini | Transforming XML Schema to OWL Using Patterns[END_REF][START_REF] Bohring | Mapping XML to OWL ontologies[END_REF][START_REF] Brink | Linking spatial data: automated conversion of geo-information models and GML data to RDF[END_REF][START_REF] Kramer | Software Tools for XML to OWL Translation[END_REF][START_REF] Métral | EXTENSION AND CONTEXTUALISATION FOR LINKED SEMANTIC 3D GEODATA[END_REF][START_REF] Vinasco-Alvarez | From CityGML to OWL[END_REF]. The general proposed pipeline is described in Figure 1, which can be broken down into 3 main activities:

-Creation of an urban data model ontology from the CityGML conceptual model (as described by its application schema) -Generation of a CityGML instance to RDF transformation stylesheet from the CityGML conceptual model (as described by its application schema) -Transformation of CityGML instances to RDF graphs using the stylesheet generated in step 2.

FIGURE 1. Overview of proposed pipeline applied to the CityGML conceptual model and instances

During each transformation, the resulting information must be logically consistent and maintain its interoperability from CityGML and GML. To ensure this, several challenges need to be overcome. For instance, the generated RDF graphs and types must conform to the model described by the ontology. How can mappings be created to ensure this? The CityGML application schema often implements elements that do not have a direct equivalent in OWL or RDFS; how should these elements be represented to best describe CityGML with semantic web formats? In addition, CityGML schema often draws from elements, types, functionality from external schema such as xLinks and xAL addresses. How should these imported elements be addressed to preserve their original functionality? Finally, how can we make use of existing semantic web standards to make geospatial queries? These issues are addressed in sections 4.2 and 4.3.

In addition, to create holistic transformations, the CityGML conceptual model must be assimilated or imported in its entirety into our pipeline. Because the model is divided into several modules which are sometimes interdependent and dependent on the GML standard, the complete model is defined by 43 different XML schema documents: 29 to define the GML 3.1 standard3 and 14 to define the CityGML 2.0 standard4 (not including xAL). Schema cannot be processed in isolation or we risk certain loss of data in the transformation (for example in distinguishing when to generate an owl:ObjectProperty from an owl:Datatype property when the XML element type in question is declared outside the current schema).

Our proposed approach chooses to consolidate these components in a composite XML schema, created from the definitions within each relevant schema in the conceptual model. This prerequisite step also requires that all definitions in the composite schema use normalized namespace prefixes to differentiate between references to one module or another. Once this is complete, the composite schema can be passed into the transformation pipelines.

Creating a 3D Urban Data Ontology

As an initial approach, we consider that the conceptual model can be expressed by XML schema and in a general simplification, XML schema can use xs:elements, xs:complexTypes, and xs:simpleTypes to define the concepts and semantics of domain specific urban. In addition, when creating the transformation from the CityGML conceptual model into an OWL ontology, it is important to reuse as many existing concepts as possible in the semantic web to enrich and render the model interoperable. Using the mapping transformations proposed in the previously mentioned works [START_REF] Bedini | Transforming XML Schema to OWL Using Patterns[END_REF][START_REF] Bohring | Mapping XML to OWL ontologies[END_REF][START_REF] Kramer | Software Tools for XML to OWL Translation[END_REF][START_REF] Vinasco-Alvarez | From CityGML to OWL[END_REF], this can be efficiently achieved.

Once the XML schema is transformed into a domain ontology, we can integrate the GeoSPARQL standard5 . In GeoSPARQL, the geo:SpatialObject class represents any real world object with thematic and geospatial properties. Geometric properties of these classes are represented by geo:Geometry, a subclass of geo:SpatialObject, and can be serialized by geo:gmlLiterals. It is disjoint with the geo:Feature class, which represents the thematic properties of a geo:SpatialObject and can be linked to related geometric classes via the geo:hasGeometry property. As suggested in [START_REF] Battle | Enabling the geospatial Semantic Web with Parliament and GeoSPARQL[END_REF], to integrate the thematic classes of our generated ontology with GeoSPARQL, we must declare our classes as a subclass of the geo:Feature class. Since our ontology is partially generated from the GML schema, any class which is derived from the gml:_Feature type is implicitly declared an rdfs:subClassOf geo:Feature. This also means that all of the geometry class declarations defined from the GML schema can be removed from the ontology as they are already defined in the GeoSPARQL standard and by ISO 19136:2007 6 and references to these classes can be changed to http://www.opengis.net/ont/gml. These proposed transformation strategies to create OWL ontologies from XML schema are an amalgam of previous transformation approaches with several specializations for the CityGML application schema. However, they are largely generalized and can be applied to schema outside of the main GML and CityGML schema, such as the external xAL addressing schema used by CityGML.

Creating Meaningful Transformations of Urban Data Instances

When generating the CityGML instance to RDF transformation, it is important that the patterns created are general enough to be reused and can take advantage of the OWL/RDFS and GeoSPARQL vocabulary whenever possible. Several techniques suggested in [START_REF] Brink | Linking spatial data: automated conversion of geo-information models and GML data to RDF[END_REF] are implemented to achieve this. In addition, this process uses the general structure of the approaches proposed in [START_REF] Bohring | Mapping XML to OWL ontologies[END_REF][START_REF] Kramer | Software Tools for XML to OWL Translation[END_REF][START_REF] Vinasco-Alvarez | From CityGML to OWL[END_REF] with consideration taken so that these mappings work with the ontology to be generated alongside the RDF data.

In general, the following mappings in table 1 are applied to the composite schema to generate the CityGML to RDF transformation stylesheet. The generated CityGML to RDF template also uses gml:id attributes as rdf:ID or rdf:about whenever possible, as proposed in [START_REF] Brink | Linking spatial data: automated conversion of geo-information models and GML data to RDF[END_REF]. If no gml:id is available, a unique id is generated and appended to the local name of the element. Also as suggested in [START_REF] Brink | Linking spatial data: automated conversion of geo-information models and GML data to RDF[END_REF], the rdf:type of each individual should be generated from its local name in order to reference the generated ontology from section 4.2, or the official GML ontology in the case of geometric elements. These transformations also map the geometry of a CityGML feature to an RDF triple using GeoSPARQL's geo:asGML datatype property. This is applied whenever a branch of GML elements is detected which has a CityGML parent and is composed of only GML nodes. Such a branch represents a valid geo:gmlLiteral if all of its nodes are in the substitution group gml:_Geometry. This is ensured by placing the geo:gmlLiteral transformation within the template for gml:AbstractGeometryType, as any element within the same substitution group as this type can be serialized as a GML literal.

This script also scans the transformed instances for malformed RDF triples and fully qualifies any RDF attributes that contain namespace prefixes such as rdf:resources, rdf:type, and rdf:about. These transformations follow the "garbage in, garbage out" concept that poorly formed data input into a program, will produce nonsensical results, and thus assume that the GML and CityGML instance documents provided are well structured and conform to their application schema. If this assumption is met, the resulting data should conform to the ontology transformation discussed in the previous section.

Leveraging the GeoSPARQL Standard

Once the dataset was generated, a GeoSPARQL endpoint was installed to perform geospatial queries. The Parliament triple-store7 was used for this purpose as proposed in [START_REF] Battle | Enabling the geospatial Semantic Web with Parliament and GeoSPARQL[END_REF] since it contains a SPARQL endpoint with GeoSPARQL support based on the Apache-Jena libraries8 . We noted that if a particular coordinate reference system (CRS) is used, it must be declared in the literal value as a gml:srsName attribute in order for Parliament to parse and index the coordinates and geometry as the default reference system is <http://www.opengis.net/def/crs/OGC/ 1.3/CRS84>. Thus any GML data that uses a different reference system must include it in the GML instances themselves during transformation or manually add it to the output geo:gmlLiterals after transformation. This implementation adds these CRS declarations to the data through a Python script after the transformation since they are not declared in the source CityGML data. Through these practices, the geometry of CityGML instances can effectively be generated, stored, and queried through GeoSPARQL.

Discussion

The CityGML conceptual model is a useful starting point for creating a 3D urban data ontology as a city information model. Its domain specific, modular structure provides a solid base for describing several hard domains of the urban ecosystem, which can be easily extended and integrated once in ontological form [START_REF] Métral | EXTENSION AND CONTEXTUALISATION FOR LINKED SEMANTIC 3D GEODATA[END_REF]. Even ADE extensions of CityGML could be applied to this approach to describe existing sub-domains of information if an XML schema is provided -such as the NoiseADE9 provided by the OGC. Another benefit of this modular approach is that the ontology can easily be pruned into domain specific sub-ontologies as each domain can be referenced by a unique URI namespace. In addition, enriching the ontology after transformation with existing geospatial standards is straightforward.

However, a limitation of this approach is its reliance on the semantic limitations of XML Schema. For example, the recently declared ISO 19150-2 standardizes guidelines for UML to OWL transformation of geographic information standards. For GML, [START_REF] Brink | Linking spatial data: automated conversion of geo-information models and GML data to RDF[END_REF] proposes using Shapechange10 , which takes advantage of this standard, to generate ontological models and acknowledges that ontology generation from UML and XML schema conceptual models are not semantically equivalent. When comparing the resulting ontologies between Shapechange and this proposed approach, still focusing on CityGML, initial explorations indicate that the ISO 19150-2:201511 ontology mappings are more expressive and direct than XML Schema to OWL. For example, an aggregation in UML can be converted into an OWL object property, while XML Schema expresses these entities as complex types which may be converted into extraneous OWL classes and properties to represent the same semantic information. Yet, Shapechange does not facilitate the transformation of CityGML or XML data into graph formats, and thus can only improve the city information model generated by our approach without supplemental transformations.

Conclusion

In this article, we proposed a model centric approach towards semantic 3D urban data representations, where we consider that any data transformation from one data format to another format must conform to the equivalent underlying conceptual model. We implemented this proposed approach to convert the CityGML 2.0 conceptual model into an OWL ontology and to convert CityGML 2.0 data to RDF based on the conceptual model. Subsequently, geospatial queries were made on the resulting data using a GeoSPARQL endpoint. This open-source solution is available

Table 1 .

 1 General XSD to 'XML to RDF XSLT' mapping transformations

	XML Schema Concept	Resulting XML to RDF XSLT
	global xs:element elements based	xsl:template for generating
	on a xs:complexType	owl:NamedIndividuals of type xs:element
		that calls the template for its xs:complexType
	xs:elements which are children of	xsl:templates for owl:ObjectProperties or
	xs:complexTypes or xs:groups	owl:DatatypeProperties based on the type of
		the xs:element
	xs:attributes of xs:complexTypes	xsl:templates for owl:DatatypeProperties
	or xs:attributeGroups
	xs:complexType,	xsl:template that calls relevant templates for
	xs:attributeGroup, and xs:group	every possible property or text the element
		could have

https://www.ogc.org/standards/citygml

http://schemas.opengis.net/gml/3.2.1/gml_32_geometries.rdf

http://schemas.opengis.net/gml/3.1.1/

http://schemas.opengis.net/citygml/

https://www.ogc.org/standards/geosparql

https://def.isotc211.org/ontologies/iso19136/

https://github.com/SemWebCentral/parliament

https://jena.apache.org

http://schemas.opengis.net/citygml/examples/2.0/ade/noise-ade/CityGML-Noise ADE.xsd

https://shapechange.net/

Geographic information -Ontology -Part 2: Rules for developing ontologies in the Web Ontology Language (OWL), https://www.iso.org/standard/57466.html, Publication date: 2015-07

Acknowledgements

The authors would like to thank University Lumière Lyon 2 for funding the PhD Thesis of Diego Vinasco-Alvarez and the LIRIS UMR 5205 Laboratory for funding his internship as part of a transversal effort with the GOAL team. This work has been done within the Vcity project (https://projet.liris.cnrs.fr/vcity/). Special thanks to Eric Boix for fruitful discussions and kind help.

Data and code availability statement

Detailed notes and the code for reproducing the results of section 4.2 can be found at: https://github.com/VCityTeam/UD-Graph/tree/master/CityGML_Transformati ons/XSD-to-OWL. Detailed notes and the code for reproducing the results of sections 4.3 can be found at: https://github.com/VCityTeam/UD-Graph/tree/maste r/CityGML_Transformations/XML-to-RDF.

online 12 and has been tested with the data from the 1st borough of Lyon (see the data and code availability statement below). Our future works will explore integrating other information sources -taking into consideration their conceptual models -and integrating a UML based approach. This approach will lead us to facilitate integration of 3D data in city information models and building information models. We are working to test this approach on CityGML 3.0. This will also demonstrate the application of this approach across different versions of standards.