(PDF) Data-Driven Midsole: Performance-Oriented Midsole Design Using Computational Multi-Objective Optimization

Runjia Tian* Data-Driven Midsole Graduate School of Design, Harvard University Yujie Wang* Performance-Oriented Midsole Design Using Computational Department of Architecture, Multi-Objective Optimization Massachusetts Institute of Technology Onur Yüce Gün R&D Innovation Studio, New Balance Athletics Inc. *Authors contributed equally to the research. 1 ABSTR ACT With the advancement of additive manufacturing, computational approaches are gaining 1 Midsole design using deep temporal clustering and popularity in midsole design. We develop an experimental understanding of the midsole as computational multi-objective a field and develop designs that are informed by running data. optimization. We streamline two data types, namely underfoot pressure and surface deformation, to generate designs. Unlike typical approaches in which certain types of lattices get distrib- uted across the midsole according to average pressure data, we use ARAMIS data, reflecting the distinct surface deformation characteristics, as our primary design driver. We analyze both pressure and deformation data temporally, and temporal data patterns help us generate and explore a design space to search for optimal designs. First, we define multiple zones across the midsole space using ARAMIS data clustering. Then we develop ways to blend and distribute auxetic and isosurface lattices across the midsole. We hybridize these two structures and blend data-determined zones to enhance visual continuity while applying FEA simulations to ensure structural integrity. This multi-objective optimization approach helps enhance the midsole’s structural performance and visual coherence while introducing a novel approach to 3D-printed footwear design. 188 INTRODUCTION 3D printing has been broadly applied to product prototyping and fabrication. With the advancement of data science and volumetric modeling toolkits, there are opportunities in the footwear industry to employ computationally gener- ated lattice systems in place of conventional components and materials to enhance performance with new design possibilities. As a layer between the upper and the outsole, the midsole of a shoe performs as the main cushioning, stability and pronation control component. Midsole materials, subcom- ponents, and overall composition determine the quality of the running experience, and thus numerous running shoes 2 end up featuring a broad range of midsole components and materials. With the advancement of data science and volumetric modeling toolkits, we see an opportunity in the footwear industry to replace these components and materials through employing computationally generated lattice systems (Nazir et al. 2019) . We develop a data-driven design approach, utilizing multi-objective optimization and performance simulations. In recent years, New Balance partnered with Nervous System to develop 3D-printed midsoles for performance running shoes in which 3D pressure data determined the 3 3D-printed lattice geometry. The authors also experimented with traditional measures 2 Pressure data-driven material 3 Visualization of sequential distribution. pressure data demonstrating to design a midsole using a pressure-data-driven approach. running experience in three In this case, we designed a midsole composed of lattice stages. units whose structural unit angle and member diameter are proportionate to the underfoot pressure data in the midsole (Fig. 1). This can be used to inform lattice distribution and design (Fig. 2). This approach will augment the static pressure-­ Such approaches only take into consideration the instant data-driven approach and bring new opportunities and or averaged sum of underfoot data. Nonetheless, typical insights into computational midsole design. midsole deformations are temporal processes such as running and jogging. The rich temporal information METHODOLOGY: COMPUTATIONAL MULTI- embedded in the change of external force across time OBJECTI VE OPTIMIZ ATION DESIGN is flattened and untapped. The ARAMIS data1 is a set of We develop a computational multi-objective optimization midsole deformation data captured by stereo cameras approach that takes both ARAMIS data and underfoot pres- during a unit duration of the running process on both sides sure data into design and evaluation processes. We apply of the midsole. During each frame, the strain and deforma- a lattice system as a parametric design framework for the tion for each lattice on the midsole were calculated (Fig. 5). midsole design and determine the optimal lattice structure for each group of lattice units using deep-temporal clus- We see an opportunity to add to this data-driven approach tering as a segmentation algorithm. We then evaluate the by taking the temporal implications of running and ARAMIS generated designs through performance-based computa- dataset into consideration: various parts of the midsole tional simulations and determine each segment’s optimal come into effect during various human movement stages. structure combination. We use underfoot pressure data to DATA AND BIAS 189 The first hypothesis is the global-local hypothesis. It assumes that the global system performance corresponds to the case where each local segment’s performance is optimal. Therefore, the midsole’s optimal global perfor- mance of impact absorption is achieved where each segment deformation is at its local minima. Similarly, each segmentation archives its best performance metrics when each lattice unit resists its local temporal strain effect to its best. The second hypothesis proposes a blending hypothesis. In this case, the designer assumes that the strain is interpo- 4 lated along the major axis of midsole and that the aesthetics metric is optimal when the lattice units between the center of two segments are smooth volumetric interpolation of lattice units on the two poles. Data-Driven Approach The performance-based midsole design starts with ideating how available data types affect the running experience. There are two types of footwear data available in this project: the under-foot pressure data2 and ARAMIS data. Both are sequential, making it possible to track the midsole’s behavior over a specific period. The under-foot pressure data reflects the load distribu- tion of midsole upper surface in the running process, but it cannot be used for temporal analysis due to its limited frame counts. There have been many explorations of using under-foot 5 pressure data as a primary form factor for additive manu- 4 Holistic computational multi-­ 5 ARAMIS data overview. facturing (Brennan-Craddock, Wildman, and Hague 2012) objective optimization workflow. and midsole designs (Dong, Tessier, and Zhao 2019). The approach we present challenged this conventional foot- determine the optimal form factor and material distribu- wear data usage by proposing a new design agenda that tion for each lattice unit. Meanwhile, we research ways to treats ARAMIS data as the primary factor and pressure implement aesthetic decisions into the design. data as the secondary factor. A holistic approach is critical in this method as we intend to The ARAMIS data set (Fig. 5) includes measurements of the unify and synthesize the performance and aesthetic goals surface deformation of the inner and outer side-surface for and computation and human agency in the design process. midsole, and is created by New Balance Inc. using digi- The approach is composed of three steps: ideation, data- tal-image-correlation (DIC) systems (Chu et al. 1985). The driven approach, and multi-objective optimization. data set includes more than 200 instantaneous frames of optically measured position data and surface strains for Ideation midsole deformations. We used the midsole side surface The synthetic workflow starts with an ideation phase driven data, which is composed of a grid of 152 × 18 data points. by human designers. In this phase, the designers define Each data point in the data set contains the unique x and y high-level shape grammars and hypotheses for perfor- index for the point, the coordinate of the point on that frame, mance space (Fig. 4). the displacement of the point in x and y direction compared to the calibration status, the strain in x, y, and z direction, 190 Data-Driven Midsole Tian, Wang, Gün 6 6 ARAMIS data sample and deep temporal clustering algorithm. and the x, y, and z directions of minor and major strain. in the ARAMIS data set. K-shape uses a normalized Here we use the primary strain vector and the displace- version of the cross-correlation measure algorithm ment vector as major features for temporal clustering. that compares the time series’s shape (Paparrizos and Gravano 2015). Data clustering allows us to understand different zones • Obtain optimal segmentation: In the deep temporal of the midsole’s behavior and come up with different data clustering approach above, we have a hyperparam- interpretations to inform various types of designs. Applying eter—cluster number—that we need to determine the deep temporal clustering (Madiraju et al. 2018) and using validation. We first select a reasonable range of K-Shape clustering (Paparrizos and Gravano 2015) algo- cluster numbers (between 4 and 8) that do not convey rithms to the ARAMIS data, we can discover a reasonable too overwhelming visual variation while maintaining the range of segments with the available frames of displace- design’s shape diversity (Paparrizos and Gravano 2015). ment and strains. We select the optimal clustering number with validation where the number of clusters is maximum while all • Deep temporal autoencoder: We first extract time series segments maintain a reasonable number of data points. data for each data point in the ARAMIS data set based We maximize the number of segments in the midsole on the deformation pattern for the strain and displace- to obtain a diversity of unit structures to reflect the ment. Then we use a long-short term memory (LSTM) midsole deformation process’s temporal pattern. (Hochreiter and Jürgen 1997) autoencoder composed of multiple LSTM layers to learn a latent representation Then we segment the whole midsole into optimal zones with of the temporal data for all data points in the data set. optimal lattice units to be distributed in each segment. The The strain data and displacement data are concatenated pressure data is then utilized to affect material distribution as input vectors to the neural network. We minimize the in terms of the lattice units’ member diameter. mean-squared error (MSE) and Kullback–Leibler (KL) divergence as the loss function of the autoencoder. With Computational Optimization Approach the LSTM autoencoder, we reduce the dimensionality of Predefined and tested metrics help evaluate design itera- input data from a high-dimensional signal to a one-di- tions across design spaces in computational optimizations mensional signal, which allows us to further use the (Ma, Wu, and Matusik 2020). In this project, we set up K-shape algorithm for further clustering the temporal two optimization goals for lattice units. The primary goal pattern (Fig. 6). is to create a rigid and protective structure to resist the • K-shape clustering: Then we use the K-shape algorithm load (Alderson et al. 2019). We achieve this by selecting for clustering the latent time series for each data point lattice units with a smaller vertical displacement under DATA AND BIAS 191 7 pressure in proportion to the overall unit height (shifting • Segment blending: Segment blending creates a smooth ratio). The secondary goal is to achieve a smaller overall transition between segments by tuning material density material-to-volume ratio, which yields lighter solutions for and blending the unit cell structure. The blending similarly performing designs. factors are associated with the characteristics of adjacent segments. Parameters of lattice unit structure • Design space exploration: We make iterations with in adjacent segments are tuned to achieve coherent selected design variables for design space exploration aesthetics through gradient transition. (Gün 2010). We control the lattice system’s form factors and focus on the performance of the lattice unit with two RESULTS AND DISCUSSION variables as the internal form factor: the scale ratio for A Performance-Based Midsole Design Using compactness and the member diameter for manufac- Computational Multi-Objective Optimization turing feasibility. The authors designed and prototyped a midsole that func- • Performance simulation: We set up multiple optimization tioned as part of the sneaker with a lattice system as a objectives and search for optimal unit cell design. The experiment for the proposed workflow.3 simulation results are then evaluated according to two metrics: the shifting ratio (reflecting rigidity to deforma- A multi-objective optimization system was designed to tion) and the volume ratio (reflecting material efficiency). evaluate the performance of designs. First, a family of unit Finite element analysis (FEA), which subdivides a large structures was selected based on heuristic speculations. complex system into smaller, simpler solvable parts Within this family, each unit was tested with simulation through discretization in the space dimensions, is imple- in accordance with each temporal cluster. The unit with mented here to quantify the displacement of members optimal performance was matched to the respective of the lattice units when being applied to the same load cluster. by treating auxetic units as beam-like structures (Wang 2018) and gyroid units as shell-like structures (Yang et Lattice System Design al. 2019). The midsole design used a lattice system as a flexible • Prototyping and fabrication: We made a 1:1 partial structure, as this system could be easily deformed and prototype with resin 3D printing thanks to New Balance remapped. We tested various lattice units, starting from an Sports Research Lab. This experiment helped under- auxetic structure that provides cushioning and bouncing to stand the actual material performance and behavior a solid minimal surface structure that provides resistance through physical impressions and simple material tests in the pronation process (Wang 2018). to understand how the segments respond to pressure and deformation. We apply a uniformly distributed lattice system of 18 × 20 × 6 in x, y, and z dimensions. The lattice system’s size is 192 Data-Driven Midsole Tian, Wang, Gün 7 Principle component analysis visualization of the latent space of temporal data clustering and K-shape analysis. 8 Lattice unit segmentation based on deep temporal clustering. 8 constrained by the fabrication precision and the consis- similar, therefore overfitting the clustering task. Therefore, tency with the data grid size in the ARAMIS data. we determined that cluster number 6 would be used as the optimal hyperparameter (Fig. 8). Temporal Clustering and Midsole Segmentation Our deep temporal clustering network comprises a mixture Design Space Exploration of Unit Structure of one-dimensional convolutional layers, max-pooling A multi-objective optimization system was designed to layers, and multiple gated recurring unit (GRU) layers. The evaluate the performance of the designs. First, a family of decoder is composed of a similar structure of deconvolu- unit structures was selected to test metamaterial proper- tional layers, unspooling layers, and GRU layers. ties. Within this family, each unit was tested via simulation in accordance with each temporal cluster. The unit with Then we train the deep temporal autoencoder on the optimal performance was matched to the respective feature-engineered ARAMIS data set with MSE and KL cluster. divergence. The training process converged after 2,000 epochs on both the training set and validation set to prevent With controlled form factors of the lattice system, we overfitting. generated lattice unit iterations for performance simula- tions focusing on two internal unit form factors as input We obtain a low-dimensional latent representation that variables: the scale ratio for compactness and member captures each data point’s essential temporal pattern with diameter for material manufacturability. the deep temporal clustering. Then we use the K-shape clustering to further visualize the temporal pattern for the The form factor was further determined with a pressure latent signal representation for each data point across all data set about the material grading. The structure perfor- time stamps (Fig. 7). mance was then validated with simulation for testing. We experiment with cluster numbers 4–8 to observe After six iterations of design and performance simulation, the result for temporal clustering. Then we visualize we concluded that Schoen Gyroid surfaces, shell-based the clustering result for various cluster numbers in the Schoen Gyroid surfaces, Schwarz P surfaces, and Schoen latent space with principal component analysis. All cluster I-WP surfaces would produce reasonable shape blending numbers seemed reasonable. effects as well as balanced deformation characteristics of minimal surface structures (Fig. 9). From this visualization, we observe that cluster number 5 does not differentiate temporal patterns between clusters, Multi-Objective Optimization of Cluster Performance underfitting the clustering task, and in the case of cluster Various lattice units were tested, starting from an number 7, two clusters have temporal patterns that are too auxetic structure that provides cushioning (Wang 2018) DATA AND BIAS 193 9 Finite element analysis (FEA) performance simulation of lattice units. 9 and bouncing, to a solid minimal surface structure that provides resistance in the pronation process (Yang et al. 2019). According to two metrics, the simulation results are eval- uated: the shifting ratio (reflecting rigidity to deformation) and the volume ratio (reflecting material efficiency). The shifting ratio is the vertical displacement in proportion to the overall unit height responding to the same vertical load applied to the unit surface area. It reflects the rigidity of the unit to deformation by measuring how geometry responds to the same load. The volume ratio is the lattice unit’s mate- rial volume in proportion to the uniform unit cell volume. It reflects the material efficiency of the lattice unit in the additive manufacturing process. We aim to select unit cells 10 with a lower shifting ratio (higher rigidity) and lower volume ratio (higher material efficiency) and hybridize them into segments responding to optimal ARAMIS data segmenta- tion through iterative performance simulations (Fig. 10). Finite element analysis (FEA) conducted with Kiwi!3D (str. ucture 2020), a plugin for Rhino and Grasshopper enabling the integration of isogeometric analysis (IGA) into the CAD environment, is implemented to quantify the displacement of members of the lattice units when applied to the same load on the unit surface area. Auxetic units are treated as beam-like structures (Wang 2018), and gyroid units are treated as shell-like structures (Yang et al. 2019) in the simulations. Material properties of additive manufacturing are also applied in the simulation. Prototyping and Fabrication 11 Partial prototypes of the segment samples were 3D printed 10 Design space exploration with 11 Partial prototype and defor- with photopolymer/rebound resin powder by a selective lattice unit clusters. mation experiments with laser sintering (SLS) printer to test physical properties and thermoplastic powders via SLS printing. material performance (Fig. 11). Further material testing in a rigorous lab environment would be an ideal next step.4 194 Data-Driven Midsole Tian, Wang, Gün 12 12 Volumetric blending of lattice units and resulting lattice structure. Volumetric Blending and Optimal Selection Our approach demonstrated how to use deep temporal With the blending hypothesis, we decided to interpolate the clustering to analyze the sequential pattern of running lattice units volumetrically in adjacent segments to create experience and segmentation of midsole areas. We devel- a midsole design that could reflect a delicate balance of oped a multi-objective computational system for midsole local and global temporal strain patterns. We tested with design optimization. Furthermore, we employed computa- various lattice unit structure set choices and discovered tional simulations to make informed decisions to iterate our the optimal unit set that allows reasonable material density designs. We developed a method for blending lattice units after the blending process. with different topological configurations. We implemented the blending algorithm using the Dendro As computational optimization tools become central in for Rhinoceros 3D Library. Dendro is a volumetric modeling decision-making processes, human interventions become library for Rhino/Grasshopper built on top of the OpenVDB even more crucial for setting and running such systems library (ecrlabs 2020). We perform a trilinear volumetric efficiently and intuitively. interpolation between the optimal structural units to popu- late the lattice units between structure segment centers. Our holistic approach could be applied to a scenario This blending process serves both aesthetic and functional in which the design resides in a context with an explicit purposes (Fig. 12). temporal pattern. The shape-blending approach reveals the material response to external force and strain and will Various lattice units were tested both individually and serve as a generic aesthetic quality that could be used in hybrid to search for the optimal midsole design. We tested various scenarios in performance optimization. with six combinations of the same primitive lattice units and selected the optimal design based on both the evaluation Computational optimization requires quantitative metrics metrics derived by computational optimization and the form to run, and thus, subjective decision-making, such as visual density evaluation metrics that influence aesthetic quality choices, cannot easily be quantified (Gün 2017). However, (Fig. 13). such decisions remain significant for design space explora- tion. While computational optimization tools remain central CONCLUSION in decision-making processes, human interaction becomes Unlike the standard approach in which certain types of even more crucial for setting and running such systems lattices get distributed across the midsole according to an in efficient and intuitive ways. Revisiting the challenges averaged pressure data, in this project we use ARAMIS of blending visual and performative design goals in this data reflecting the distinct surface deformation charac- project, we aim to develop systems to enhance human input teristics as our primary design driver (instead of averaged into our optimization system through more holistic compu- pressure data). We proposed a data-driven workflow for tational design approaches in the future. midsole design. DATA AND BIAS 195 13 13 Various iterations of midsole designs. ACKNOWLEDGMENTS Dong, Guoying, Daniel Tessier, and Yaoyao Fiona Zhao. 2019. We want to express our gratitude to Onur Yüce Gün, the MIT “Design of Shoe Soles Using Lattice Structures Fabricated by Department of Architecture, and NEW Balance R&D Innovation Additive Manufacturing.” In Proceedings of the Design Society: Studio for their generous support. International Conference on Engineering Design, 719–728. Cambridge University Press. NOTES 1. The ARAMIS data set is proprietary information created by New ecrlabs. 2020. Dendro for Grasshopper. V. 0.9.0. PC. Balance Inc. 2. Data source available through New Balance Sports Research Gün, Onur Yüce. 2010. “Geometric Gestures” In Elements of Lab. Parametric Design, edited by Robert Woodbury, 171–184. USA & 3. We developed the proposed workflow in a computational design Canada: Routledge. class 4.s56 Special Subject: Shape Grammars — Superseding Parts, Computing Wholes, taught by Onur Yüce Gün PhD at Gün, Onur Yüce. 2017. “Computing with Watercolor Shapes.” In Massachusetts Institute of Technology in 2020. The course’s Computer-Aided Architectural Design: Future Trajectories objective was to “employ computational design with a critical [Proceedings of the 17th International Conference, CAAD Futures inquiry of conventional part-to-whole relationships.” 2017], Istanbul, Turkey, 12–14 July 2017, edited by Gülen Çağdaş, 4. This experiment has been postponed due to COVID-19. 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Trained as an architect, Onur holds a PhD and a Masters in Design and Computation, both earned at MIT. Onur Paparrizos, John, and Luis Gravano. 2015. “K-Shape: Efficient and instituted the Computational Geometry Group at KPF NY in 2006. Accurate Clustering of Time Series” In SIGMOD '15 [Proceedings of His computational architecture work has been published in the 2015 ACM SIGMOD International Conference on Management Elements of Parametric Design (Gün 2010). In 2009, he developed of Data], Melbourne, Australia, 31 May–4 June 2015, edited by the curriculum and directed İstanbul Bilgi University’s under- Timos Sellis, 1855–1870. Association for Computing Machinery. graduate program in architecture. He has taught at MIT, RISD and Adolfo Ibáñez University in Chile. He is currently the Creative str.ucture. 2020. KIWI!3D. V. BETA 0.5.0. PC. 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He investigates the future of design through the synergetic engagement of creative computation, extended reality, multimodal media, and machine perceptions. His more recent research focuses on the enactive cocreation between human designers and artificial intelligence. Runjia has authored/ coauthored several peer-reviewed publications on architecture, urban design, and technology. He is the cofounder of AiRCAD, with research and working experience at MIT CSAIL and at Autodesk. Yujie Wang is a master of architecture student at Massachusetts Institute of Technology. As an interaction design architect and creative technologist working across intelligent systems, sensory experiences, tangible products, and intangible services, Yujie investigates the future of social and technological systems by mediating human and machine perception and transforming how people interact with media such as mixed reality, brain-computer interface, self-driving vehicles, and adaptive built environment. He is the cofounder of Muser and AiRCAD, with research experience at Media Lab and Harvard Medical School and professional experi- ence at Philips Healthcare. DATA AND BIAS 197