An automated design methodology for acoustic shells in outdoor concerts Gabriele Mirra InLogicDesign, Computational Designer, Naples (Italy).

Eduardo Pignatelli BuroHappold, Computational Architect, London (UK).

Serafino Di Rosario BDP, Senior Acoustic Consultant, London (UK).

Summary Acoustic shells for outdoor concerts are a specific subclass of passive acoustic systems aimed to amplify and equally distribute sound over an audience area in outdoor conditions. The objective of this paper is to describe an automated design methodology that takes advantages of Computational Morphogenesis to generatively inform an efficient acoustic shape. Numerical predictions combine geometrical acoustic principles, descriptive geometry and Evolutionary Algorithms to explore a multivariate topology and achieve convergence to a series of viable and performing solutions. The case of Resonant String Shells – ReS – is used to show a sample workflow where acoustical, computational and construction problems are addressed under a unique, comprehensive and holistic investigation. The formulation of the problem is general and adaptable to different cases and objectives. The design targets a highly portable structure that results from the aggregation of very simple geometrical elements to support small orchestras over an open-air audience area of up to 400 people. Three acoustic objectives, measured on the audience area, are considered to deliver the project – the maximisation of the sound pressure level, minimisation of the deviation between sound pressure levels and minimization of the sound pressure level difference between different sources. Two technological objectives are pursued in the form of hard constraints of the generative process: the planarity of every reflective panel and adjacency between their edges to realize a watertight enclosed shell. The final, definitive solution is subject to detailed acoustic measurements. PACS no. 43.55. Fw, 43.55. Ka

1. Introduction

The study of the relation between the geometry of architectural spaces and their acoustic performance has always been a topic of major interest for room acoustics. Traditionally, to address the problem of acoustic prediction, designers used to build physical scale models and test them with different techniques. A great step forward in acoustic modelling has been made with the introduction of computer simulation tools in late 1960s [1] . Computer aided design tools allowed the definition of a complex, detailed modelling setup. The benefits of always shorter setting times – compared to physical models - and the high precision of the acoustics results helped this technique become mainstream in solving acoustical simulation problems. However, as Monks asserts in [2] , the growth of direct methods - the set of procedures characterised by having no performance targets, but responsible to just carry out a detailed numerical analysis from a given acoustic environment - failed to enhance the design process itself. The cumbersome, inflexible and

time-consuming nature of these procedures excluded their use in the early stages of design, preventing Acoustics to inform architectural and other sectoral construction aspects. This technological landscape resulted in the isolation of the Acoustic discipline and Acoustic specialists from the early stages of the design process. 2. Automated design to improve early

reflections

Nowadays, to grant the access to acoustic solutions beyond the capabilities of isolated disciplines, the focus shifted from direct methods - embedding complete, detailed acoustic model representations - to performance-based procedures - which inform the design process through simpler, slender and more flexible computational tools. Geometrical acoustics, the branch of acoustic modelling that uses optical geometry to describe sound waves propagation, has become a valued technique to predict early reflections. Its application has proven helpful to support the design decisions

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for both improving the acoustic quality of existing buildings and defining entirely new design solution. Recent studies [3] show that wideband early reflections, which preserve the temporal envelope of sound, contribute to clear and open acoustics with strong bass. Also [4] shows that when sound arrives from the sides of the head, binaural hearing emphasizes the same frequencies produced by higher orchestral-playing dynamics, thus enhancing perceived dynamic range. In particular, this analysis method, based on geometrical acoustics, proved to be highly performing when coupled with optimisation algorithms to automate both the generation of different design solutions and the ranking of their performances. Among these, Genetic Algorithms (GAs) have been widely applied for the design of acoustic reflectors and to find the optimal shape of concert halls [5] and acoustic shells [6] [7] . The main contribution of these studies is the development of bespoke design tools to overcome the limited interoperability between commonly used CAD programs and acoustics, which often translates into an ad-hoc solver, developed and presented for simple scenarios. At the time of writing this paper, two main limits characterise current researches:

a. In most of these applications, the sound source is usually single and placed at the centre of the stage. Not all studies revealed a major interest in the relationship between the position of the sources on stage and the acoustic impact of early reflections.

b. Acoustic design with the aid of machine learning algorithms is seldom accompanied by on field measurements, untying computational processes and real acoustic results.

Hence, the proposed study moves from two issues:

1. The effects of an over-simplified representation play a critical role in the analysis of outdoor acoustic shells. Here, in absence of a reverberant tail, the sound source position greatly contributes to the distribution of sound pressure levels (SPL) over the audience, therefore affecting the results of the optimisation process.

2. The quality of the acoustic model is given by the acoustic solver utilised. In most common software implementations, a hybrid approach, combining image source with ray-tracing, is chosen. In most optimisation applications, raytracing is preferred due to its high computational efficiency. However, for the purpose of this work, image-source algorithms

are preferred because of their ability to accurately model early reflections that assume a key role in assessing the acoustic quality of outdoor spaces [8] .

3. Resonant String Shell

Resonant String Shell (ReS) is an acoustic shell developed to improve the acoustic experience of concertgoers attending outdoor music performances [9] . From 2011, The ReS research group worked on three different topics: a. structural and technological design of the shell; b. development of computational tools for acoustic prediction and design; c. methods for acoustic measurements; addressing a specific objective for each of them:

- Development of a simple structural system made entirely by recyclable materials. This system should consist of modular elements, easy to assemble and stiff enough to bear the high loads of the acoustic reflectors.

- Define the most efficient design solution according to specific performance criteria

- Improvement of the IR measurement methodology with focus on the specific case of shells for outdoor concerts.

The initial architectural concept was based on old gramophone horns shape and it has been kept until the latest development of the design, taking into account the fact that these shapes are based on impedance matching mechanisms that do not apply to acoustic sources. For the purposes of this paper we will discuss just the latest achievements of this research project by introducing ReS 4.1 (2015), which configured a key step in the development of this methodology, proceeding with a detailed description of ReS 6.0 (2017) for which the presented methodology has been actually applied.

3.1 ReS 4.1 (2015) ReS 4.1 were designed with a novel computational approach exhaustively described in [8] . The geometry was generated parametrically by the loft of a series of polylines lying on the planes of the structural arches. To ensure the planarity of the resulting surfaces, the polylines shared the same shape (defined as main profile) and only allowed to be scaled on their respective planes. All candidate solutions were generated by combining a large set of parameters which allowed to change, inter alia: the number of surfaces, the shape of the main profile, the scaling factor of each polyline, depth and height of the shell.

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Figure 1: iterative shape generation for ReS 4.1.

The acoustic simulation was performed by means of a custom coded Image Source algorithm (called Aeolus) used to analyse the shell capability to reflect sound up to the 2nd reflection order. A set of six omnidirectional sources was chosen to represent a sextet orchestral configuration while, a series of target points, describing the audience, was arranged in a regular grid 14 m x 19 m placed in front of the proscenium. The SPLs carried by direct and reflected rays were summed at each target location using the following equation:

𝑆𝑃𝐿 = 10!"!!"!"#!" (!!)!!!

!"!!!! (1)

Where: SPL is the Sound Pressure Level on a specific target; N is the number of incoming rays; Lw is the sound power of the source; li is the length of the ith reflection path.

Then a synthetic performance measure was computed by summing all the SPL values recorded at the target points, plus a penalty function. The resulting formulation was:

𝑓(𝑧) = − 𝑥!!!!1 − 𝑘𝑋∗ (2) Where: z is the set of parameters controlling the shape of each candidate solution; N is the number of targets; xi is the SPL referred to ith target calculated using (1); k is the weight of the penalty function; X* is the number of SPL values under the threshold x*.

The search process was carried out through a Genetic Algorithm to find the set of parameters z corresponding to the fittest design solution, i.e. the one that minimise f(z). The optimisation process converged after 70 generations. Results are shown

in Figure 2. The same geometry has been used for ReS 5.0 which acoustic performance, despite stage and shell height was raised up to 50 cm, is substantially equal to that of ReS 4.1.

3.2 Problems and observations Genetic Algorithms have been used to maximize the total amount of energy arriving at the target points. Sound rays that propagate from sound sources placed underneath the shell transport this energy. However, by using equation (2) to represent the acoustic performance of the shell, a significant amount of information is lost. Indeed, considering the use of six sound sources, a single value seems to be inadequate to convey the relative contribution to SPL values of each sound source. By analysing the maps in Figure , representing the SPLs registered at different distances from the proscenium, one can notice relevant differences among SPL values distribution over the audience for each pair of sound sources. These are grouped according to their distance from the bottom panel of the shell and named back, middle and front sources. The graph shows that at 2 m the SPL of front sources is the highest one, this is because the contribution of direct sound has clearly a major influence on the SPLs related to the sources closest to the audience. However, already at 4 m the situation changes: the high slope of the front sources SPL curve makes the levels recorded for the back sources prevail. Back sources seem to have a major influence on the total reflected energy, in fact, because of their position, they can easily exploit all the reflective surfaces and obtain an excellent projection up to 20 m. At the same distance, the worst condition is represented by the front sources that take advantage just from the utmost array of panels.

Figure 2: SPL maps for back, middle and front sources; SPL decay curves along the longitudinal axis.

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3.3 ReS 4.1 on site measurements In this section, we present measurements results from ReS 4.1, which has been built in 2015 in the Villa Pennisi’s garden. Results are presented in terms of Strength (G [dB]).

Every measurement has been performed with a dodecahedron loudspeaker which acoustic performance is in accordance with EN ISO 140-4. 10s Logarithmic Sweep sine with 1s of silence has been used as excitation signal and only one measurement per point has been considered due to the length of the employed signal [10] . The loudspeaker’s emission level has been measured with a Type-A Sound Level Meter in a quasi-free-field condition and both recording and reproduction chain have been digitally calibrated. The recording device used for the measurements is a DBX RTA microphone. Figure 3 (Top) and (Bottom) show locations of emitters and receivers for ReS 4.1. Comparing the graphs at the centre of Figure 3 one can notice that along the central positions of the audience there is a substantial difference between

the G values recorded from different emitters positions, with more than 10 dB reduction below 500 Hz. However, along the right side of the audience this large difference cannot be seen. Emitter position in Figure 3 (Bottom) corresponds to the typical position of the second violin in a sextet configuration, while emitter position in Figure 3 (Top) could be considered a soloist in an octet or larger configuration. This reduction in performance has also been confirmed by a subjective assessment through questionnaires handed to a selected audience (musicians mainly) during the general rehearsals. 80% of the questionnaires indicated that instruments closer to the bottom and central axis of the shell have been regarded as prominent in the performance. Considering that violas or cellos usually occupy those locations, they also offer a masking effect to the violins that sits lateral by the front of the shell.

Figure 3: (Top) sound strength (G) measured at the central and side receivers’ locations with central emitter. (Bottom) sound strength (G) measured at the central and side receivers’ locations with side emitter.

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3.4 ReS 6.0 In view of these results a question arises: is it possible to find a design solution which optimise at the same time SPL values associated with different emitter positions? To achieve this goal, the problem formulation switched from a single-objective optimisation problem to a multi-objective optimisation. The aim of the new implementation is to explore which kind of variations of the shell geometry can effectively maximise at the same time the reflected energy for each pair of sound sources. The new design space starts from the geometry of ReS 5.0 and is constructed to maximise the compatibility between any new design solution and its structural system, which was supposed to be reused for the new version. Hereby, unlike the form finding performed for the design of ReS 4.1, the new parametric model allows just a limited set of variations that are directly informed by specific geometrical constraints. This configures the design problem as a form-improvement one. The structural system of ReS 6.0 consists of a set of arches discretized by polylines and made by timber trusses joined together to form a 3D spatial frame. The acoustic reflectors were anchored to steel L-shaped profiles linked to the structure by means of differently sized spacers. Hereby, all the possible variations of the main profile must be contained in the area subtended by the intrados of the first arch (Figure 4a). The new parametric model allows adjusting the main profile shape by varying the spacers’ size up to 50 cm. Geometrically, this is translated into a set of vectors applied to the vertices of the ReS 6.0 first arch intrados. The number of vertices is 7, however, to preserve the symmetry condition

the actual number of parameters controlling the vectors, magnitude is 4 (Figure 4a). Then, if vertices are not assigned vectors with both extreme magnitudes (0 and 50 cm) at the same time, each profile can be scaled on its plane by a factor defined by the residual minimum and maximum allowable displacements (Figure 4b). This way a global transformation is included (Figure 4c), increasing the range of possibilities within the design space. By adding a new variable for each profile, the total number of parameters controlling the design space becomes 8. In order to estimate the relative contribution of each pair of sound sources to SPL values, calculation of SPL is performed three times - for back, middle and front sources - using equation 1 for the whole array of targets. Then for each collection of SPL values, the Standard Deviation (SD) is computed and used as objective function to be minimised for the multi-objective optimisation algorithm. This yields three different objectives, described by the following fitness function:

𝑆𝐷! 𝑑, 𝑠 = !! 𝑥! − 𝑥 !!

!!! (3)

subject to: 𝑑 = 𝑑!,𝑑…,𝑑!𝜖 0,50 , 𝑠 = 𝑠!, 𝑠…, 𝑠!𝜖 0,1

Where: i is the identifier of the source pair used for the SPL calculation; N is the total number of targets; xj is the SPL value on the jth target; 𝑥 is the arithmetical mean of xj; d is the array of magnitudes assigned to the displacement vectors; s is the array of scale factors applied to the shell profiles.

Figure 4: ReS 6.0 genome and phenotype. (a) Position and direction of the displacement vectors; (b) min and max allowable displacements as extremes of the scale factors domain; (c) solution generated by random parameters.

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Figure 5: ReS 6.0 optimisation results. Set of the Pareto Optimal solutions according to the three objectives; perspective view and profile of the three selected solutions.

Figure 6: SPL maps for back, middle and front sources; SPL decay curves along the longitudinal axis.

3.5 ReS 6.0 optimisation results Optimisation has been performed using Octopus, an implementation of the Hype multi-objective optimization algorithm within Grasshopper (Rhinoceros). The graph in Figure 5 shows different design solutions, represented as coloured dots, resulting from the optimisation process after 30 generations. Each dot belongs to the class of non-dominated solutions and lies on the theoretical Pareto Optimal surface. Colours represent the genetic diversity of the design solutions and give a measure of the relative difference among their genomes (or set of

parameters (d,s)). The graph shows that the design solutions tend to cluster into three groups, populating specific regions of the objectives space, in particular: towards the planes SDm-SDb at the min and max SDf values and in between the two. Interestingly, these clusters roughly correspond to the different distributions of the generic diversity values. Three solutions named A, B and C have been selected from these clusters. Solution A represent the one which minimise objective SDf, solution C minimise SDb, while

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Figure 7: sound strength (G) measured at the central and lateral receivers’ locations with central emitter.

Figure 8: comparison between measured and predicted SPL values for ReS 4.1 and ReS 6.0.

solution B, being closer to the axis origin, represent a trade-off between the three objectives. Their phenotypes are shown in the rightmost column in Figure 5. Solution B has been selected as the final design due to its good response to all the objectives and because of the continuity of its profile that makes the shape architecturally more appealing. It is worth noting that the section of solution B is slightly convex, making the new design of ReS 6.0 considerably different from that of ReS 4.1 characterized instead by a concave profile (Figure ). Comparing the maps in Figure 6 with the ones in Figure , it is straightforward to notice the improvements in terms of SPL distributions and the similarity among the maps relative to the three sources positions. The success of the optimisation process is even more evident if we compare the graphs of the SPL decay curves. The SPL values coherently decay the same way regardless the sources position. Furthermore, an average gain of 3.5dB has been recorded at the maximum distance of 20m.

3.6 ReS 6.0 on site measurements In this section we present measurements results from ReS 6.0, built during the 2017 edition of the classical music festival in the Villa Pennisi historical garden. The employed equipment is the same used in 2015 (3.3) except for the dodecahedron of a different brand that has been calibrated in the anechoic chamber of Milan Polytechnic University. The sound source has also been calibrated on site using the same procedure described previously. The graph in Figure 7 (middle) shows a good response in terms of Strength (G) along the full length of the audience, although from 8m onwards the frequency response shows dips at 250 Hz and at 1 kHz (8m only). This is possibly due to the audience seats and to the new construction of the main shell panels made of timber sticks tightened together. Figure 7 (right) also shows measurements made on the left and right side of the audience in order to demonstrate the even coverage provided by the acoustic shell. Comparing Figure 7 with Figure 3,

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it can be easily seen that the latest version provide a more even distribution of sound energy with distance and a more even frequency response but it still needs improvements on the global frequency response.

4. Aeolus - On site measurements comparison

In order to validate the predictions performed by Aeolus, Figure 8 shows a comparison of SPL distribution along the central axis of the audience with on-site measurements for ReS 4.1 (left) and ReS 6.0 (right). SPL values are shown for 125Hz only because the model and the built structure are slightly different. The acoustic shell is provided on site with an additional QRD diffuser on the back wall and an array of reflectors above the musicians that has not be considered in the simulations due to the application of geometrical acoustics only. Analysing only SPL distribution at 125Hz reduces the influence of these additional elements on the measured values but still comply with the frequency response of the dodecahedron source used. Results shows that there is very good agreement between Aeolus and measurements from 8m onwards but that between 1 m and 4 m there is a difference up to 5dB, which can be reported to different factors including emerging resonances under the shell or to the effect of the panel array. We can consider these results as an initial validation of the Aeolus approach to simulate the particular case of an acoustic shell and the improvement of early reflection on an audience area by means of computational design optimisation. 5. Conclusions and future work

This paper takes advantage of the experience of Resonant Strings Shell (ReS) – the acoustic background of Villa Pennisi in Musica Festival - to report on the automated design of early reflectors for outdoor acoustic shells. It describes the development of a performance-based approach to enable acoustics inform early stages of the design process. GAs are used to approximate a performing acoustics setup. Future research will focus on the modelling of perturbations in the optimisation process, involving both source directivity mutations during performance and reflective geometry defects, to target a solutions landscape with a higher robustness value.

6. Acknowledgements

The project involved several institutions, associations and key accounts without whose help it would never come to be. We are grateful to VPM festival (vpmusica.com) for funding the experimental phase and providing a playground for experimentation and testing; to Prof. Livio Mazzarella, Politecnico di Milano, who has allowed us to use the University’s facilities and to rent the equipment for acoustic testing.

7. References

[1] A. Krokstad, S. Strom, and S. Sorsdal. Calculating the acoustical room response by the use of a ray tracing technique. Journal of Sound Vibration, 8(1):118–125, 1968.

[2] Monks, M., Oh, B.M. and Dorsey, J., 2000. Audioptimization: goal-based acoustic design. IEEE computer graphics and applications, 20(3), pp.76-90.

[3] Lokki T., Why is it so hard to design a concert hall with excellent acoustics?. Dim, 1, pp.73-13.

[4] Lokki, T., Pätynen, J., Tervo, S., Siltanen, S. and Savioja, L., 2011. Engaging concert hall acoustics is made up of temporal envelope preserving reflections. The Journal of the Acoustical Society of America, 129(6), pp.EL223-EL228.

[5] T.Mendez Echenagucia, A. Astolfi, A. van der Harten, 2013. Interactive design methods for complex curved reflectors in concert halls. International Symposium on Room Acoustics.

[6] W. Boning, A. Bassuet, 2015. A room without walls: optimizing an outdoor music shell to maintain views and maximize reflections. Proceedings of the Institute of Acoustics, Vol.37 Pt.3

[7] M.Palma, A. Astolfi, 2013. Sound strength driven parametric design of an acoustic shell in a free field environment. International Symposium on Room Acoustics.

[8] Mirra G., Pignatelli E. and Pone S., 2016. Computational morphogenesis and construction of an acoustic shell for outdoor chamber music. IASS Annual Symposium.

[9] Pignatelli E., Colabella S., Di Rosario S. and Pone S., 2015. A wooden acoustic shell for open-air chamber music concert. Future Visions: Proceedings of the International Association for Shell and Spatial Structures Symposium.

[10] Di Rosario S., Vetter K., 2011. Expochirp Toolbox: A Pure Data Implementation of Exponential Sweep Sine (ESS) Impulse Response Measurement. Proceedings of the Institute of Acoustics, Vol.33 Pt.6.

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