. The layered fabrication approach induces d irectional anisotropy and impact s mechanical strength of FDM components significantly . This paper proposes generalized machine learning based parameter optimization framework to determine optimal build orientation f or FDM component s. The algorithm determines ideal build orientation by maximizing the minimum Factor of Safety (FoS) for the component under prescribed loading conditions ensuring its even distribution . An Artificial Neural Network (ANN) coupled with Bayesian algorithm has been employed to accelerate the optimization process . The algorithm begins with an initial sample data collected using brute force approach; uses single layered ANN for approximation and optimization is achieved using Bayesian algorithm. A series of computational experiment s considering five different test components has been devised to evaluate the performance and efficacy of the proposed algorithm. These experiment s demonstrated that the proposed algorithm can determine the optimum build ing orientation effectively with certain limitations . Keywords: 3-D Printing , Building Direction, Finite Element Method , Machine Learning, Optimization DOI:https://doi.org/10.14733/cadaps.YYYY.aaa -bbb 1 INTRODUCTION 3-D Printing also referred as Rapid Prototyping (RP) or Additive manufacturing (AM) is a fundamentally different process from conventional manufacturing techniques. 3 -D Printing integrates Computer Aided Design (CAD), Materials Science and Computer Numerical Control (CNC) to fabricate physical prototypes from virtual models directly by depositing material in the form of layers. The process fabricates 3 -D parts by deposition of layers in 2 -D using three linear motions in the Cartesian axes. Initially , 3-D Printing was confined to polymers but it expanded subsequently to support an increasing array of material such as metals, ceramics , composites and biological material s [10]. Additive manufacturing technique is categorized into six groups as per ASTM classification [13]: Material e xtrusion, Photo polymerization, Material j etting, Sheet Computer -Aided Design & Applications, V(n), YYYY , bbb-ccc © YYYY CAD Solutions, LLC, http://www.cad -journal.net 2 lamination , Powder bed f usion and Directed energy deposition. These process es are unique in terms of m anufacturing science, power source and materials used but operate on the identical philosophy i.e. layer based fabrication . The layer ed fabrication approach has many advantages over conventional processes such as simplified tool -path planning and capabilit y to manufacture complex parts. Nevertheless, it suffers from drawbacks such as stair -casing (aliasing) effect, varying structural properties along different build directions, support structure requirements and inability of building around inserts which li mits its potential as an alternate to conventional manufacturing processes [10]. The layered nature of the process has major impact on characteristics of the resulting part affect ing build time, surface quality, amount of support material required, geometrical accuracy, overall cost and material strength [11].The effects of build orientation and its optimization have been well-researched in the literature . The height of the object for a given build orientation is directly proportional to th e build time and hence cost of the component [2]. The stair casing effect is common due to layered fabrication approach and results into poor surface roughness . It has been observed that the s tair-casing effect is largely depende nt on the component geometry and building orientatio n [5]. The amount of support structure required for building of the component is decided based on the choice of building orientation and thereby influences the total build volume, build time, post -processing time and overall cost . It has been observed that the thermal distortion is affected by the build direction for metal additive m anufacturing [19]. The layered fabrication approach also induces anisotropy in the final part therefore; structural performance of the component is dependent on the choice of build orientation. This intricacy was reported in the past literature but the efforts are not made to explore the best building orientation for the maximum strength . Ahn et al. [1] characterize d anisotropic mechanical properties of A BS parts manufactured using FDM and showed that the components are stronger under tensile load if the orientation and loads are aligned with the fibers. Umetani and Schmidt [28] address ed structural anisotropy of FDM components and showed that the vertical bonds between layers are much weaker than the in - layer bond for pure bending case s. A set of automation techniques were explored by researchers to optimize build orientation that meets user needs. Peng et al. [20 ] presented an algorithm to optimize build orientation for Direct Metal L aser Sintering (DMLS) that minimize s the therma l distortion. The work is limited to metal additive manufacturing since th ermal distortions are not significant in polymer based additive manufacturing process. Thompson and Crawford [26 ] performed set of experiments to generate quantitative measures for various aspects of part quality affected by build orientation . A set of design guidelines was proposed based on these quantitative results. Byun and Lee [6] presented an autom ated approach to determine optimal build orientation for improved surface quality and minimal supports volume. Sood et al. [24] conducted compr ehensive study to examine the impact of build orientation, layer thickness and layer pattern on compressive strength of the part. This was achieved using experimental data and Artificial Neural N etwork (ANN) model to generate processing map for parameter o ptimization and obtain the maximum compressive strength. Zhou et al. [30] adapted the worst -case analysis approach to identify structurally weak er parts from the design . A constrained optimization problem was formulated to obtain the worst loading configuration with orthotropic m aterial assumption s. Thompson and Crawford [26] introduced a n algorithm with loading conditions and material properties using Tsai -Wai failure condition to determine the safer design configuratio ns for a given build or ientation. Ulu et al. [27 ] introduced build orientation optimization algorithm based on maximum -minimum FoS approach under fixed loading condition s. A novel methodology was introduced in the work that utilizes Finite Element Method (FEM) coupled with surrogate optimization to find the best build orientation. Tam and Mueller [25] presented novel approach that synthesizes tool paths along the principal stress lines opening up new possibilities for structurally performative fabrication . In order to determine build orientation for the maximum part strength, it is important to study the mechanical behavior of 3 -D printed material s. The mechanical streng th of the printed part is dependent on multiple factors such as machine, material, pro cess parameters, building direction, environmental conditions etc. However, approximation s based on the previous studies can reduce Computer -Aided Design & Applications, V(n), YYYY , bbb-ccc © YYYY CAD Solutions, LLC, http://www.cad -journal.net 3 number of experiments required for examining material characteristics. Based on the physical experiment s, Ahn al. [1] concluded that the compressive s trength of FDM specimen is approximately twice of the tensile st rength . Barclift and Williams [4] conducted experiments to study and analyze the effect of process parameter s on mechanical properties of components fabricated using jetting technology. It was concluded that the behavior of the 3-D printed material can be considered orthotropic and failure theories such as Tsai -Wu criterion [9] can be used to analyze the components. Tsai-Wu criterion is a special case of the gene ralized Hill Y ield criterion [12] and it is common ly used for orthotropic material s. These theories are useful to assess the design safety where FoS can be considered as a performance indicator of the design. The maximum stress theory is considered as a failure criterion and structural robustness of the part has been quantified using FoS . The evaluation of FoS for each build orientation is practically impossible and robust virtual physics based simulation module is necessary . FEM based simulation s are frequently employed to simulate the part under given loading condition s in design and manufacturing domain . As FEM simulations are computationally expensive , approaches resulting into the minimum number of simulation trials are necessary . Surrogate modeling is suggested in the literature for e ngineering design optimization but it involves costly function evaluation [8], [18], [21 ]. Zhang et al. [29 ] proposed machine learning based algorithm for powder spreading speed optimization for powder bed fusion process . The study employed ANN to interpolate highly nonlinear results obtained from discrete FEM simulations. The purpose of t his paper is to introduce machine learning based optimization framework for parameter optimi zation of 3 -D Printing process . The paper proposes computational framew ork for the build orientation optimization that aims at maximizing resistance to failure under prescribed loading condition s. An objective function has been formulated to determine the optimal build orientation taking into account maximizing the minimum FoS considering the max imum stress failure theory. A n orthotropic material model is used in the computational framework to establish the compliance matrix. As the objective function is dependent on component geometry and loading conditions, its analytical value and gradient cannot be determined. Such problems cannot be solved using conventional optimization methods and requires different approaches. This optimization problem can be considered as blac k box and it can be solved analytically or by using surrogate approximation. The present work employs hybrid approach i.e. analytical algorithm and surrogate approximation algorithm to address this challenge. A single hidden layer ANN is employed to simpli fy computationally expensive black box optimization problem and Bayesian optimization algorithm is implemented to determine the minimum of black -box objective function. The framework proposed in this work utilizes small number of FE M simulation s to acceler ate the optimization process. The major deliverables from the present work are summarized below; 1. The c onceptual framework based on machine learning based algorithm is presented for parameter optimization in 3-D Printing process . 2. A build orientation optimum algorithm is presented for FDM process that maximizes the minimum factor of safety under defined boundary and geometrical constraints. 3. A hybrid optimization approach using machine learning coupled with stochastic op timization algorithm is proposed and implemented . Further, the p aper is structured as follows; a generalized machine learning based framework is proposed for parameter optimization initially . Based on proposed framework, a build orientation optimization is developed for maximum resistance to mechanical forces. A set of computation al and physical experiment consisting of five test cases are devised for validating the algorithm and results are presented subsequently . 2 METHODOLOGY This section summarizes generalized machine learning based parameter optimization framework proposed in this paper. The framework is inspired from the three -step approach presented by Computer -Aided Design & Applications, V(n), YYYY , bbb-ccc © YYYY CAD Solutions, LLC, http://www.cad -journal.net 4 Zhang et al. [ 29] to determine optimal powder spreading pattern in AM. The proposed algorithm aims at determining the optimal building direction for FDM components maximizing the minimum FoS under defined boundary and geometrical constraints . Figure 1 shows t he framework proposed in this paper consisting of four stage s: Physical Experimentation, Virtual Simulation, Ma chine learning and Optimization. Figure 1 : Machine learning based optimization framework . The first step involves characterization of the FDM printed material with the change of parameter of interest ( building direction in the present work) and other process paramet ers maintained at constant level . The data obtained fro m characterization is necessary to calibrate the physics based virtual simulation model. This involves validating the virtual simulation results by compar ing com putational results and physical experiments . The r ecalibration may be necessary if results are not comparable. Once calibration is achieved , virtual physics -based model is simulated over the entire design space generated using various method s e.g. ANOVA, 2-factorial design, brute force , FEM etc. The present study uses a hybrid approach combining brute force and FEM for this purpose. The data generated by a series of virtual simulation s can be used further to approximate physics -based model using linear or non -linear regression techniques , machine learning etc. The present work approximate s the physics -based model using ANN based machine learning algorithm . The final step is to optimize the approximated model -using gradient based or stochastic based optimization methods depending on the complexity of approximated model. The Bayesian optimization algorithm has been used in the study to determine optimal process parameter ( building direction in the present work) . The proposed framework is generic and it can be executed to perform parameter optimization for any AM process and associated parameters. The algorithm has been implemented to determine optimal build orientation for maximizing the strength of FDM printed compon ents in the present work . Figure 2 summarizes the overall computational framework developed in the present work. Figure 2 : Flowchart of build orientation optimization algorithm . Step 1Physical Experiments •Material Characterization •Calibration •Validation Step 2Virtual Simulation •Stochastic Methods •Anova •Brute force •2nfactorial design •Training Set Step 3Machine Learning •Linear Regression •Non-linear regression •Artificial Neural Network •Convolutional Neural Network Step 4Optimization •Gradient based approach •Stochastic approach •Process maps Computer -Aided Design & Applications, V(n), YYYY , bbb-ccc © YYYY CAD Solutions, LLC, http://www.cad -journal.net 5 2.1 Physical Experiments: Material Characterization The first step of the framework requires determination of the material behavior in physical environment. The given problem statement requires determination of the mechanical properties of components printed using FDM . It is well established that t he mechanical propertie s of 3 -D printed components are dependent on large number of variables such as machine parameters, process parameters, material used for printing, and post -process operations . A set of experiments are conducted to determine mechanical properties of compone nts in different build orientations maintaining other parameters at constant level. As per ASTM D638 , nine different build orientation s are possible however, three principle direction s have major impact o n the part strength considering an in-layer isotropy. Figure 3 shows these three principle directions used for building of the components for physical experiments . The orthotropic material model enables properties to be determined with a minimal number of tests using well-established techni ques such as tensile, compressive and shear strength tests. An orthotropic material model requires determination of nine parameters experimentally viz. Young’s Modulus, S hear modulus and Poisso n’s ratio for the three princip le directions. Additionally, tensile and compressive y ield s trength s along with s hear strength for each principal direction are necessary to compute the FoS . Figure 3 : Build orientations for physical experiments. A set of standard tensile test specimen s (ASTM D638) are built along three principle building directions using ABS (ABSplus P430) as specimen material and material extrusion process based FDM printer uPrint (Stratasys Inc. ). Three specimens are printed at a 100% infill for each building direction to ensure repeatability of the test results. The t ensile test is conducted on Floyd UTM instrument at an extension rate of 0.5mm/min and constant load of 50N. Table 1 summarizes physical properties of 3-D print ed components extracted from the stress -strain curve obtained from the tensile test . The Young ’s modulus and tensile yield strength were obtained using 0.2% strain offset method. The corresponding compressive strength is assumed to be double of the tensile yield strength [1] and shear strength is assumed to be half of the lowest yield strength according to the maximum shear theory [23]. Principal Axes Average Yield Strength (MPa) Average Young ’s Modulus (GPa) Shear Strength (MPa) Shear Modulus (GPa) Poisson’s Ratio X 31.722 1.360 4.50 0.51 0.11 Y 26.392 0.975 4.37 0.28 0.39 Z 19.530 0.930 4.31 0.30 0.31 Table 1 : Mechanical properties obtained from stress -strain curve 2.2 Virtual Simulation: FE Infrastructure The s econd step of the proposed framework is to establish physics -based model for virtual simulation of the 3-D printed components . FEM is commonly employed for simulating the effect of static and dynamic loading on engineering components. The present work employs ANSYS X Y Z Building direction Computer -Aided Design & Applications, V(n), YYYY , bbb-ccc © YYYY CAD Solutions, LLC, http://www.cad -journal.net 6 Parametric Design L anguage (APDL) [3] to establish a FEM infrastructure for virtual simulation s. APDL is preferred for parametric simulation s as it can be controlled using a script generated by an external program e.g. MATLAB or Python . The FEM based virtual model is simulated over entire design space generated using brute force sweeping approach. A total of 320 evaluations are performed using brute force approach. The number represents uniform grid of 45° increments for each design variable i.e. build orientation . Figure 4 represent the complete process of obtaining data from FE M model in the form of a process flow chart. In general, FEM simulation is required to perform three steps; pre -processing, solver and p ost-processing. The pre -processing step is required to define geometry , material properties , loading conditions and boundary conditions. Once pre-processing is accomplished, the user needs to specify the solution steps . Finally, the post - proces sing step is required to visualize and record results for further discovery. FEA script performing each of these steps is developed using APDL for given geometry, boundary and loading condition s. The model is also validated by comparing values of maximum s tress and highest stress concentration point in FEM along with breaking point in a tensile test. Figure 4: Flowchart of the virtual simulation module To simulate the effect of build orientation change using FEM, geometric coordinate frame is adjusted operating on fixed geometry, mesh and boundary conditions . Since geometric coordinate frame is different from material coordinate frame, each FEM simulation will be unique and res ult in a different stress value . A new local (a⊥b⊥c) and gl obal (x⊥y⊥z) coordinate system is defined for each build orientation angle for a given geometry and boundary conditions. A new local coordinate system is defined using LOCAL command, which contains three variables . The local coordinate system is assigned as geometric coordinate sy stem using CSYS command and global coor dinate system is assigned as material coordinate system using ESYS comm and. APDL accepts variables from another external script instead of changing the ma in FE M script every time. An input file “parameters.inp” containing build orienta tion angles is generated using MATLAB. After completing solver step in APDL , the stress values of each element are being stored in a file. This file is subsequently read by MATLAB and stress tensor is evaluated for each element. Since computed stress tensor is in geometry coordinate frame, stress transformation is necessary to evaluate stress es in the material coordinate system and determining mechanical properties. The Stress tensor for each element is transformed using Cauchy’s relation for 3 -D stress transformation [22]. Cauchy’s relation can be expressed i n the primed coordinate frame as [σ′]=a [σ]aT. Here a is another transformation matrix that serves to transform the vector components in the original coordinate system to those in the primed system. The final axes are visualized as being achieved in three steps: Firstly, rotation of original x -y-z axes by Ψ about the z -axis to obtain new frame termed as x'-y'-z. Secondly, rotation of the new frame by θ about the x' axis to obtain another frame termed as x'-y''-z'. Finally, rotation of this frame by ϕ about y'' axis to obtain the final frame x''-y'''-z'. These three transformations correspond to the transformation matrix given using a as Equation (2.1) which is used for the transformation from geometry to material coordinate frame. 𝑎=[cos (Ψ) sin (Ψ)0 −sin (Ψ)cos (Ψ)0 0 0 1][1 0 0 0 cos (θ) sin (θ) 0−sin (θ)cos (θ)][cos (ϕ) 1sin (ϕ) 0 1 0 −sin (ϕ)0cos (ϕ)] (2.1) Build Orientation Angles generated using MATLABParameters .inpFE Script with Input Parameters FE SimulationResults as Stress TensorStress TransformObjective Function Evaluation Build Orientation AnglesElement TypeMaterial PropertiesMeshingBoundary ConditionsLoading ConditionsSolve Computer -Aided Design & Applications, V(n), YYYY , bbb-ccc © YYYY CAD Solutions, LLC, http://www.cad -journal.net 7 The structu ral robustness of component is quantified using FoS criterion as per the maximum stress theory . The primary objective of the proposed algorithm is to select a build orientation that maximizes FoS for the component . This is achieved by evaluating s tress tensor for each element which consist s of 6 components 𝜎𝑥,𝜎𝑦, 𝜎𝑧, 𝜎𝑥𝑦,𝜎𝑦𝑧,𝜎𝑥𝑧. An approach to determine FoS for a given element requires computation of 6 independent values based on maximum stress theory and assigning minimum value as an output . The normalized objective function is defined as a function of build orientation angles (𝛼,𝛽,𝛾) using Equation (2.2). min 𝑓(𝑥)= ∑[∑1 (𝐹(𝑥𝑘𝑖))𝑟6 𝑘=1]𝑛 𝑖=1 where, 𝑥=[𝛼,𝛽,𝛾] subject to 𝛼,𝛾=[ −𝜋,𝜋] 𝑎𝑛𝑑 𝛽=[0,𝜋] (2.2) 2.3 Machine Learning The o bjective function described using Equation 2.2 is computed using FEM results and stress tensor for each orientation considering f ixed geometry and boundary condition s. The determination of optimum building orientation using conventional methods such as brute force approach is computationally expensive due to large number of FEM simulations . Also, the computation al effort will increase with geometric complexity of the components as large number of element level calculations is necessary. Therefore, it is important to minimize the number of function evaluation s. Such problem is well suited for implementation of machine learning techniques to regre ss between the data obtained using brute force sweeping approach in the previous step . The approxima ted function can be used to determine the minimum of objective function and optimum angles using a suitable optimization method. Levenberg Backpropagation algorithm [15] with Bayesian regularization ANN is implemented for an unbiased fit over the dataset . The Backpropagation algorithm is commonly employed for regression problems in ANN due to its efficiency. The Backpropagation with Bayesian regularization ensur es optimum weight distribution and does not over fit the network [14]. ANNs are derived from biological systems and can be expressed as mathematical model s of biological neuron s in simpler terms . ANN has three categories of layer s in the network: i nput layer, hidden layers and output layer. The input layer is a vector of input variable s, which are build orientation angles (𝛼,𝛽,𝛾) in the present work . Similarly, output layer is a v ector of output variable i.e. objective function. The h idden layers conn ect the input with output layer and it is responsible for regression of the dataset. There can be one or few hidden layer s with multiple nodes in the network depending on complexity of the problem . A non-linear activation function is used to capture complex relationships involved for the problem under consideration. The network is trained by minimizing a loss function described us ing Equation (2.3). Here, 𝑁 is the total number of training data sets; 𝑌𝑖 is the actual output vector for 𝑖𝑡ℎ training data; 𝑂𝑖 is the target output vector for 𝑖𝑡ℎ training data, 𝜆 is the regula rization control parameter and 𝑊 is the weight. 𝐿=1 𝑁∑‖𝑌𝑖−𝑂𝑖‖2𝑁 𝑖=1+𝜆 ‖𝑊‖ (2.3) The o ver-fitting of the data is one of the major challenges during training of ANN. This happens when the data is quite complex and high er magnitude s of weights are assigned. The r egularization term in Equation (2.3) helps in preventing over-fitting of the data by ensuring low er magnitude of weights. The weights are initially generated randomly and corresponding output values are evaluated. The value of loss function is calculated subsequently and it is used to update weights using Equatio n (2.4). Here, 𝛼 is the learning rate that controls the step size of gradient descent for the iteration . Computer -Aided Design & Applications, V(n), YYYY , bbb-ccc © YYYY CAD Solutions, LLC, http://www.cad -journal.net 8 𝑊𝑛+1=𝑊𝑛+𝛼𝛿𝐿 𝛿𝑊 (2.4) The present work uses machine learning toolbox of MATLAB s oftware to develop ANN model [17]. The input data is split into two dataset for training (70%) and testing (30%) purposes. A network of one hidden layer with variable number of nodes is developed . The n umber of nodes in a hidden layer is selected based on the performance of neural network. As a general thumb rule, more number of hidden nodes is required for the complex systems to improve t he performance of ANN. Table 2 summarizes network parameters used in the development of ANN model . ANN Parameters Associated Value Number of i nput data set 320 Number of hidden l ayers 1 Number of nodes in i nput layer 3 Number of nodes in hidden l ayer 150 Number of nodes in o utput layer 1 Activation Function of hidden layer Tansigmoid Training f unction Bayesian regularization Learning rate 0.0001 Regularization control parameter 0.1 Table 2 : ANN Parame ters 2.4 Optimization Algorithm The development of an analytical expression between input and output of ANN is not possible due to non -linear activation function and complex relationship between nodes . Additionally, ANN is dependent on FEM results and development of an expression will not be an efficient approach. ANN treats the process as black box and similar optimization algorithm is necessary to get the optimum output value [7]. As ANN can reduce computational time to few milliseconds, optimization process can be accelerated . Bayesian optimization [14] is an efficient way to deal with this problem and it is popular for solving global optimization problems with non -convex or black-box functions without using the gradient. As the objective function is not known, Bayesian strategy treat s it as a random function and place prior over it which capture s the behavior . The prior will update automatically after each iteration and forms posterior distribution over the objective function. The posterior distribution can be used to construct an acquisition function th at determines the next query point. The maximum of the acquisition function is found by resorting to discretization or by auxiliary optimization. Bayesian optimization with exponent convergence is implemented in the present work for solving the optimization problem [16]. As Bayesian optimization method is used to find the maximum of bl ack box function , objective function is modified by adding a negative sign, i.e.𝑓(𝑥)= −𝑔(𝑥). Figure 5 shows number of ANN evaluations along with process map and Bayesian algorithm. It can be seen from Figure 5(b) that the number of function evaluations are reduced significantly using the proposed approach. A visual representation can also be generated in order to evaluate the effect of the build orientations on FoS distribution using Figure 5(a). The process map approach allows selection of build orientation as per the user needs and desired FoS . However, it is not precise and requires human interpretation of the visual representatio n. Computer -Aided Design & Applications, V(n), YYYY , bbb-ccc © YYYY CAD Solutions, LLC, http://www.cad -journal.net 9 Figure 5 : ANN evaluations: (a) Process Map (b) Bayesian O ptimization 3 COMPUTATIONAL EXPERIM ENTS The proposed algorithm s are implemented in the form of an integrated computational tool developed using MATLAB, APDL, ANN toolbox and Bayesian optimization routine. To examine the efficacy of proposed framework, five different cases were conceptualized with varying level of complexity of geomet ry, loading and boundary conditions. Figure 6 shows schematic CAD representation of these test cases. The first test case represent ASTM D638 sample subjected to tensile load of 5 0N with fixed supports at bottom ed ges (Figure 6(a)). The motivation for this test case is the ease of fabrication, physical validation and intuitive optimal build orientation. This helps in quick benchmarking of the proposed algorithm with relative ease. The s econd test case shown in Figure 6 (b) is modified version of the first case but the component complex ity is relatively higher . The component is subjected to tensile load of 50 N and fixed at the bottom edges. This can also be fabricated easily and physically tested on UTM for validation . In the third c ase, the component geometry is ideal as second case but it is subjected to bending loading condition in place of tensile pull of the previous case . This test case is conceived to evaluate the effect of the loading condition s on the optimum build orientation. Figure 6 (c) shows t he fourth test case i.e. door handle subjected to bending loading condition as commonly employed in the practice . The last test case is a wheel hub shown in Figure 6(d) and it is subjected to both radial and bending load as in practice. Figure 6: CAD model s for test cases :(a) ASTM D638 (b) Modified ASTM D638 (c) Doo r handle (d) Wheel h ub. Computer -Aided Design & Applications, V(n), YYYY , bbb-ccc © YYYY CAD Solutions, LLC, http://www.cad -journal.net 10 3.1 Algorithm Implementation To demonstrate the effectiveness of proposed framework is determining optimal building direction, second test case shown in Figure 6 (b) is discussed in this section. The optimal build orientations for other components are determined computationally using the proposed framework and results are discussed in the subsequent subsection. The second test case is chosen in the present study as it is easy to fabricate using FDM 3 -D printer and subsequently testing on UTM for val idation. The first step of the algorithm is to determi ne mechanical properties of the 3 -D printed material which are identical as derived in Section 2.1 and are summarized in Table 1 . The s econd step is to develop FEM architecture for the component. The st udy uses tetrahedron element s for discretizing the component followed by input related to material properties . The boundary and loading condition s are defined by fixing the bottom surface and a pplication of 50 N tensile pull at the top. Figure 7 shows FEM model of the component along with application of boundary conditions and pull load. Total 320 FEM simulations were executed for training of the ANN model based on parameters outlined in Table 2. Based o n these simulations, the optimum orientation is determined using Bayesian optimization considering ANN based objective function . The optimum build orientation was found to be [-179, 2, 178]. Two identical components corresponding to the second test case are fabricated using material extrusion based 3-D printer uPrint, Stratasys Inc. The first variant was fabricated as per default build orientation meanwhile the second variant was fabricated as per optimal bu ilding direction determined using proposed framework. Both these components were tested using Floyd UTM instrument at an extension rate of 0.5mm/min and constant load of 50 N. The test set up and experimental results in the form of stress -strain curves are shown in Figure 8(a) and 8(b). The tensile strength showed improvement of 126% with optimal b uilding direction in comparison to the initial design configuration. The results are summarized in Table 3. Figure 7: FEM infrastructure for test case 2 Figure 8 : Algorithm implementation on test case 2: (a) UTM set up (b) Stress -strain curve 0123 0.001 0.002 0.004 0.005 0.007 0.008 0.010 0.011 0.013 0.014 0.016 0.017 0.019 0.020Stress Strain Optimum Initial Computer -Aided Design & Applications, V(n), YYYY , bbb-ccc © YYYY CAD Solutions, LLC, http://www.cad -journal.net 11 3.2 Test Cases The proposed framework has been extended to other test cases shown in Figure 6 to determine optimal build orientation for given loading and boundary conditions. Table 3 summarizes optimal building orientation of components determined using propo sed framework for given boundary and loading conditions. The optimal building direction is shown schematically as well as numerically along with FoS in the original and optimum conditions. It can be seen that the build orientation has significant effect on mechanical properties of 3 -D printed components. The results show significant improvement in the FoS when component is built along optimal build direction in each case. The results corresponding to the first test case corroborate with intuitive findings i.e. the best properties when loading is along build direction. The other t est case s i.e. door handle and Wheel hub also show improvement in the FoS with the optimum build orientation. It can also be observed that the strength of comp onent is changed from unsafe (Fo S<1) to safer (FoS>1) condi tions under given loading and boundary conditions by changing build orientation and without any modification of any geom etrical attributes. This is one of the major advantages of 3 -D printing process, which can be explored, with the support of such computational tools . Table 3 : Summary of computational experiment results Computer -Aided Design & Applications, V(n), YYYY , bbb-ccc © YYYY CAD Solutions, LLC, http://www.cad -journal.net 12 The results corresponding to test case 2 considering modified ASTM sample with tensile loading condition s result in horizontal build orientation . Meanwhile, the same sample with bending loading condition results into completely different build orientation. Based on these results , it can be inferr ed that the loading condition s influence the optimum build orientation significantly and proposed framework captures this phenomenon very well . An important point to note here is that the other factor s associated with 3 -D printing process such as surface roughness, support material requirement etc. are not considered in the proposed framework . Although the proposed algor ithm successfully finds ideal build orientation fo r a given component and loading conditions, there are few limitations associated with th e proposed method . The mechanical strength is not the sole criterion in most cases and it is necessary to consider o ther factors such as surface roughness or support structure requirements . This necessitates formulation of multi-objective optimization problem instead of focusing on mechanical strength of components only. FEM consumes considerable amount of time in the optimization process limiting its applicability to simpler components. The computational time can be improved by developing a simple design guidelines based computational tool. A single layer ANN is able to approximate such expens ive function but it still requ ires a large training data to achieve prediction accuracy . A deep neural network can be implemented to produce accurate ANN model wit h lesser training data . 4 CONCLUSION S The present work proposed an integrated approach to determine optimal building direction that enhances mechanical strength of 3 -D printed components. The first step of the algorithm is to determine anisotropic properties of a 3 -D printed component by performing strength testing experiments on UTM. The material properties derived from the experiments are used subsequently in FE M simulations and machine learning based optimization algorithm to determine optimal building dir ection. The proposed methodology has been implemented in the form of an integrated computational model that determines optimal building direction for known loading and boundary conditions. A set of computational and experimental studies are conducted for s ample components to determine optimal building direction using proposed algorithm. It has been observed that the optimal building direction has significant impact on load withstanding abili ties of 3 -D printed components. Manoj Malviya , https://orcid.org/0000 -0003-0151-6239 K. A. Desai , https://orcid.org/0000 -0001-5103-9480