Rapid Improvement of Fiber Tensile Properties via In Situ Biomimetic Robotic Pulling and Bayesian Optimization

For fiber technology, new approaches such as biomimetic materials, such as silks, are being intensively explored, providing new solutions for a variety of industries, including textiles, composites, and biomedical engineering. New approaches for spinning or these materials are needed. Despite recent advances in enhancing fiber tensile properties, achieving significant improvement in tensile properties remains a tedious and challenging task, suffering from little to no controlled extrusion process and difficult optimization in high‐dimensional parameter spaces. Herein, a novel robotic biomimetic pulling method that can rapidly enhance fiber tensile properties surpassing current methods in both speed and resulting fiber properties is shown. Using a controlled fiber‐pulling device with in situ tensile measurements and adaptive optimization based on Bayesian Optimization, fiber strength exceeding 300% of the traditional full factorial design method within just a few experimental iterations is reached. The rapid experimental method presents a potential avenue for enhancing the performance of artificial fibers across diverse industries and applications.

On the other hand, spider silk has a toughness greater than any synthetic fiber. [29,30]The production of spider silk is a sensor-based mechanically triggered fiberization process.Due to the strain-hardening nature of spider silk, [12] it is well-known that spiders use their sensing to adjust the fiber properties during silk pultrusion.The strongest artificial fiber from spider silk produced using a biomimetic extrusion process is just about one-fifth of the strength and half the toughness of natural spider silk fiber. [31]Nevertheless, the biomimetic extrusion is only part of the pultrusion process of natural spiders where the complex pulling motion of spider claws is not taken into account.Recently, we demonstrated that controlled pulling of silk fibers with regulated pulling forces achieved high strength in comparison to similar extrusion-based methods. [32]Two types of silkone recombinant spider silk (a structural variant of ADF3) and one regenerated silk fibroin were studied-and Dextran was used as a reference material.
This study reports a novel approach for rapidly enhancing the tensile properties of artificial fibers using a robotic fiber-pulling device and BO.The robotic device can pull the fibers precisely with in situ measurement of hardening forces during both pulling and tensile testing.By iteratively optimizing the experimental fiber-pulling process using BO, we rapidly improve the fiber tensile properties by over 300% compared to traditional methods, in just a few iterations.In this study, we use Dextran as the specimen material for its similar rheological behavior to silk protein at high mass concentrations and ease of fabrication.Our results show a new potential path for improving the performance of artificial fibers across diverse industries and applications.

Experimental Setup
The experimental setup, as illustrated in Figure S1, Supporting Information, was devised to enable autonomous fiber pulling and tensile testing in situ, without necessitating fiber removal.This setup was an enhanced version of a previously described configuration. [33]It comprised a syringe mounted on a motorized precision positioner (Physik Instrumente, model M404.4PD) and a blunt glass needle (1 mm diameter) affixed to the syringe.A syringe plunger pusher, secured on another motorized precision positioner (Physik Instrumente, model M-122.2DD),controlled the Dextran level within the glass tube by pushing the syringe plunger.
A force sensor (LCM Systems, model LCM UF1) with a load range of 10 g and accuracy of 0.0082 g was positioned at the top of the device.A pointed tip was attached to the force sensor, aimed toward the needle.The motorized precision positioners were controlled via a controller (Physik Instrumente, model C-884.4CD)using MATLAB/Simulink.The force data was collected using a data acquisition board (National Instrument, model PCIe-6363).
The entire setup was constructed on a vibration isolation table.Two cameras were installed: one camera (FLIR, Model CM3-U3-50S5M-CS) was used to estimate fiber the average fiber diameter from the side, while another camera (FLIR, model GS3-U3-51S5M-C) recorded a side view of the entire experiment.

Fiber Pulling
The proposed method for pulling fibers was a multistep process (refer to Figure 1B).The first step entailed inserting the force sensor into the dispenser tube containing the Dextran material.A detailed description of the Dextran fabrication is given in Figure S2, Supporting Information.In the second step, the fiber-pulling process took place, where the Dextran material was extracted from the dispenser tube using the motorized precision positioner, while simultaneously measuring the pulling force.The third step was the hardening phase, during which the motorized precision positioner remained stationary for a specified duration, allowing the fiber to solidify and enabling the measurement of the hardening force.
The fiber-pulling process entails drawing the material from a liquid to a semisolid state, forming a fiber.As the fiber hardens, its chemical and molecular structure undergoes changes, which can impact the tensile properties of fibers and their repeatability.To enhance the repeatability of the fibers' tensile properties, it is crucial to regulate the hardening force or tension force during the fiber-pulling process.This can be accomplished by managing the hardening force during Dextran fiber pulling using impedance control with force tracking, as explored in another study. [34]he objective of impedance control was to regulate the interaction between the precision positioner tip (syringe tip) and the Dextran during fiber hardening by controlling the impedance of the system.This involved specifying and achieving a desired impedance profile through a user-defined relationship between the positions of the syringe and the force sensor tips.This relationship is generally configured as a linear second-order system, allowing control of the relationship between the hardening force and the syringe tip position using a mass-spring-damper system.The mass represents the Dextran fiber mass, the spring characterizes the Dextran fiber stiffness, and the damping describes the Dextran fiber viscosity.In an experimental framework, the force exerted on the Dextran material cannot be detected during dispensing and fiber pulling due to its low viscosity, and it becomes detectable during the hardening phase.It is at this juncture that the impedance controller, in conjunction with an online stiffness estimator, was employed to actively track a predefined force reference.As shown in the illustrative example in Figure 1A, the impedance controller was used to track a force reference of 5 mN with a response time of 6 s without overshooting.The force tracking error was 0.007 mN (0.14%) and the position error was 0.0859 mm (0.29%).The stiffness of the Dextran fiber was continuously estimated during control to be around 0.0835 N m À2 on average.
In the experiments, the force control scheme presented in Figure S2, Supporting Information was implemented with a sampling frequency of 100 Hz without any knowledge of the stiffness of the Dextran before hardening.The control scheme was implemented using the experimental setup presented in Figure S1, Supporting Information.The proportional-integralderivative parameters of the position controller and the target impedance were tuned based on the trial-error method to achieve the desired force performances (time response, accuracy, and overshoot cancelation). [34]igure 1.Overview of the experimental protocol to optimize the tensile properties of artificial fibers using BO.First, the experiments were conducted under random fiber-pulling parameters (pulling velocity, x 1 , hardening force, x 2 , hardening time, x 3 ) to collect the initial data.The tensile properties (toughness, y 1 , strength, y 2 , elongation, y 3 , Young's modulus, y 4 ) were predicted by the GP surrogate, which was used by the acquisition function to determine the fiber-pulling parameters for the next experiment.The experiments were conducted using the proposed parameters, and we added the observed tensile properties to the database.The loop continued until the best fiber-pulling parameters that maximize the tensile properties of the fibers were attained.A) Example of the measured hardening force control and the displacement of the syringe stage during the full experiment.B) a) The experimental setup of the robotic fiber-pulling device, which consists of: 1) a manual positioner for adjusting the force sensor, 2) a force sensor, 3) a pointed tip connected to the force sensor, 4) a precision positioner, 5) a glass needle, 6) a syringe, 7) a plunger, 8) a pusher, 9) a precision positioner to push the plunger.The syringe stage consists of parts 5-9.b) Fiber pulling and tensile testing consists of four steps: (step 1) dispensing sample from the syringe to fill the glass needle and lifting syringe stage until there is contact between the pointed tip of the force sensor and the sample, (step 2) pulling the fiber by lowering the syringe stage until the target fiber length is achieved, (step 3) allowing the fiber to harden, (step 4) releasing tension on the fiber, and then (step 4) performing the tensile test.Illustrations are not drawn to scale.C) Example of a stress-strain curve obtained from a tensile test and calculated using the cross-sectional area.

Fiber Characterization
In fiber characterization, the tensile properties of the fabricated fiber were evaluated by performing a tensile test.This test involved pulling the same fiber previously fabricated using the same device without removal.Simultaneously, force (N) was recorded and converted into stress (Pa) by dividing it by the cross-sectional area of the fiber.
Determining the cross-sectional area comprising an acquiring an image of the fiber was followed by image segmentation through thresholding and feature extraction using the Canny edge algorithm.To address challenges associated with the conical and nonuniform characteristics of the fibers, the crosssectional area (A) was then computed using the formula A = πd 2 =4, where d is the average diameter of the fiber.The average diameter (d) was obtained by summing all individual diameter measurements along the fiber and dividing by the total number of measurements d ¼ 1 , where N is the total number of measurements along the fiber. [35,36]Figure S3, Supporting Information, provides a visual guide, outlining the step-by-step process involved in estimating the cross-sectional area of the manufactured fiber.
Data for the stress-strain curve (Figure 1C) was obtained from the tensile test step.The experiments were performed at 40.2 AE 5.7 % relative humidity and 20.1 AE 0.9 °C.

BO-Assisted Fiber Pulling
BO was employed to find the fiber-pulling parameters that maximized the tensile properties of the fiber.To perform this optimization, a surrogate Gaussian process (GP) model, f , was learnt to model the relationship between the pulling parameters (X ) and the tensile properties (Y ), building a dataset D ¼ fX , Yg.The tensile properties comprised toughness, y 1 , strength, y 2 , elongation, y 3 , and Young's modulus, y 4 , while the fiber-pulling parameters included pulling velocity, x 1 , hardening force, x 2 , and hardening time, x 3 .To facilitate an effective and efficient optimization process, we first normalized the tensile properties, scaling them between 0 and 1.The output of the surrogate model was then defined as the normalized sum of the tensile properties ðY ¼ to optimize the tensile properties of the Dextran fibers.More details on the GP model can be found in Figure S1, Supporting Information.
To optimize the tensile properties while gathering a small amount of data, and balance the exploration and exploitation, the upper confidence bound (UCB) acquisition function was used in the optimization procedure.The UCB function is described in detail in Figure S1, Supporting Information.
The proposed BO-assisted fiber pulling in Figure 2 was employed for both exploration and exploitation.In the exploration phase, the algorithm selected input parameters that optimized the UCB function and performed experimental evaluations to generate new input-output pairs that were added to the existing dataset D. The surrogate model was then updated using this new data, and the entire process was repeated L times.
In the exploitation phase, the algorithm utilizes the updated surrogate model to determine the next input that maximizes the UCB function.If the resulting output value exceeds the current optimal output value, the optimal input and output pair are updated, and the surrogate model is updated with this new data.This phase can be repeated up to M times.If no improvement is observed for two consecutive iterations, the optimization process is halted, and the algorithm returns the optimal input and its corresponding output value.The pseudocode for BO-assisted fiber pulling is presented in Figure 2.

Stress-Stress Behavior of the Dextran
We conducted tensile testing on 16 previously pulled Dextran fibers, using different combinations of fiber-pulling parameters.Figure 3a illustrates the stress-strain curves obtained from these experiments.
Notably, the fibers exhibit similar elastoplastic behavior.Figure 3b further provides a detailed annotation of the distinct phases observed during the tensile test, offering a comprehensive insight into the fiber's response under mechanical stress.
In the initial phase, a linear relationship between stress and deformation is observed, signifying elastic behavior with a return to the original shape upon stress release.The slope of this segment represents Young's modulus.Subsequently, the curve transitions to plastic deformation after a distinct yield point, resulting in increased deformation under applied stress.Notable features include the ultimate tensile strength (commonly referred to as strength), necking indicating localized constriction (see Figure 3c), and the strain at failure, reflecting material elongation before fracture.The area under the curve represents toughness, denoting the material's ability to absorb energy before failure. [37]he hysteresis behavior of the fibers has been investigated; we experimentally subjected the pulled fiber to a cyclic loading and unloading procedure comprising five triangular cycles.Each triangular cycle consisted of two phases: forward loading phase and backward unloading phase.During the forward loading phase, the applied force on the fiber was systematically increased, causing the fiber to undergo stretching and deformation.Subsequently, during the backward unloading phase, the applied force gradually decreased.This phase allowed the fiber to relax and return to its original state, measuring the material's ability to recover from deformation.
The observed hysteresis behavior during cyclic stretching of the fiber reveals a phenomenon known as cyclic stabilization, as shown in Figure 3d.In the initial loading cycle, a substantial hysteresis loop is observed, indicative of significant adjustments or internal reconfigurations within the material.This initial cycle is characterized by a larger energy dissipation.Subsequent cycles, however, show a notable reduction in hysteresis loop size, indicating a trend toward cyclic stabilization.

Effect of Pulling Velocity, Hardening Force, and Hardening Time on the Tensile Properties
To identify limitations or constraints that may exist in the fiberpulling phase, we first studied the acceptable range of the pulling parameters, where the obtained results are shown in Figure S4, Supporting Information.The acceptable range for pulling velocity, which led to successful fiber pulling, was determined to be between 10 and 50 mm s À1 .At velocities lower than 10 mm s À1 , the fiber pulling was unsuccessful.The maximum velocity achievable in our fiber-pulling device was identified as 50 mm s À1 .Similarly, the acceptable range for hardening force was determined to be within 1-9 mN.At forces lower than 1 mN, the fiber pulling was unsuccessful, while forces higher than 9 mN caused the pulled fiber to break.The range for hardening time was also established to be within 0.5-4 min for successful fiber pulling.Hardening times shorter than 0.5 min led to unsuccessful tensile tests, where the fiber continued threading without breaking, as illustrated in the stress-strain curve in Figure S5, Supporting Information, whereas hardening times longer than 4 min did not impact the success rate of fiber pulling; a typical stress-strain curve of a successful tensile test is illustrated in Figure S6, Supporting Information.
To reduce the cross-section stress concentration, we control the pulling process by maintaining a constant velocity, even though the material's response is nonlinear.This helps prevent uneven stretching and stress concentrations in the fiber's cross section.
To investigate the impact of variations in fiber-pulling parameters such as pulling velocity, hardening force, and hardening time, three distinct experiments were conducted.Each experiment focused on altering a single parameter while keeping others constant.The tensile properties of each experiment were assessed through a tensile test.To explore the relationship between the pulling parameters and the tensile properties, Pearson's correlation coefficient was calculated between each pulling parameter and each tensile property.
First, we examined the impact of pulling velocity on fiber properties.Figure 3a1-a4 shows the strength, toughness, Young's modulus, and elongation, respectively, of fibers fabricated at four distinct pulling velocities (10, 20, 30, and 40 mm s À1 ).For each pulling velocity, there are four samples (n = 4) to investigate the repeatability.To compare the means of each property at different velocities, Welch's ANOVA test was conducted, and the corresponding p-values were presented in the same figure.

Input:
-Initial dataset of specimens -: maximum number of exploration iterations -: maximum number of exploitation iterations -a: UCB acquisition function -: surrogate model Output: input the optimal output The statistical analysis revealed no significant differences in strength and toughness among fibers pulled at different velocities (p-values of 0.08 and 0.19, respectively).However, there was a general trend of increased pulling velocity, leading to decreased strength and toughness, as indicated by the moderate negative linear correlations between pulling velocity and these properties (Pearson's coefficients of À0.42 and À0.46, respectively).The relationships between pulling velocity, elongation, and Young's modulus were also investigated, and Welch's ANOVA test yielded p-values of 0.25 and 0.56, respectively, indicating no significant differences in these properties among fibers pulled at different velocities.The correlations between pulling velocity and elongation or Young's modulus were weakly negative (Pearson's coefficient of À0.26) and weakly positive (Pearson's coefficient of 0.028), respectively.Thus, the data suggest that changes in pulling velocity have a lesser effect on elongation and Young's modulus than on strength and toughness.It has also been observed that the repeatability of fiber behavior manifests variability corresponding to distinct values of the pulling velocity.Secon, we studied the effect of hardening force on the fiber tensile properties.Figure 4b1-b4 represents the strength, toughness, Young's modulus, and elongation, respectively, of fibers fabricated at four distinct hardening forces (2, 4, 6, 8 mN).For each hardening force, there are four samples (n = 4) to investigate the repeatability.The p-values of Welch's ANOVA test show that the relationship between hardening force and the four tensile properties appears to be highly predictable and less dispersed, where p-values of 3.4 Â 10 À6 , 0.0007, 0.0033, and 0.023 are obtained for strength, toughness, Young's modulus, and elongation respectively.Additionally, our observations indicate that increased hardening force is typically associated with higher levels of strength, and this relationship exhibits a strong positive linear correlation, as indicated by a Pearson's coefficient of 0.88.Similarly, we found that toughness also tends to increase as the hardening force is increased, with a strong linear correlation represented by a Pearson's coefficient of 0.78.We observed a similar upward trend in both elongation and Young's modulus with increasing hardening force, and these relationships were found to be highly linear, with Pearson's coefficients of 0.71 and 0.75 respectively.It has also been observed that the repeatability of fiber behavior manifests variability corresponding to distinct values of the hardening force.
Finally, the third experiment was conducted to investigate the influence of the hardening time on the tensile properties of fibers, including strength, toughness, Young's modulus, and elongation.Figure 4c1-c4 shows the strength, toughness, Young's modulus, and elongation, respectively, of fibers fabricated at four distinct hardening times (1.5, 2.5, 3.5, 4.5 min).For each hardening time, there are four samples (n = 4) to investigate the repeatability.The results show that there is also a highly predictable relationship between hardening time and the four tensile properties, where Welch's ANOVA test results yielded p-values of 0.0028, 6.7 Â 10 À5 , 0.049, and 0.0082 for strength, toughness, Young's modulus, and elongation, respectively.Moreover, our observations suggest that increased hardening time is typically linked with higher strength, toughness, and Young's modulus, displaying a moderate positive linear correlation with Pearson's coefficients of 0.58, 0.48, and 0.49, respectively.Although the relationship between elongation and hardening time was weakly linear, with a Pearson's coefficient of 0.21, a similar upward trend was noted with increasing hardening time.It has also been observed that the repeatability of fiber behavior manifests variability corresponding to distinct values of the hardening time.

BO-Driven Parameter Selection for Fiber Pulling
We developed a BO-assisted fiber-pulling method to guide experiments by suggesting the next set of fiber-pulling parameters in real time, aiming to maximize the tensile properties of the fibers.The pulling velocity, x 1 , ranges from 10 to 50 mm s À1 , with a step size of 1 mm s À1 , resulting in 41 values in total.The hardening force, x 2 , ranges from 1 to 9 mN, with a step size of 1 mN, totaling 9 values.The hardening time, x 3 , ranges from The study investigated the effects of fiber pulling velocity on the tensile properties of fibers, including strength, toughness, Young's modulus, and elongation.Four distinct pulling velocities (10, 20, 30, 40 mm s À1 ) were used to fabricate four fibers each, and the resulting properties were represented using boxplots.b1Àb4) The study also examined the effects of hardening force on the tensile mechanical properties of fibers.Four distinct hardening forces (2, 4, 6, 8 mN) were applied to create four fibers each, and the resulting properties were represented using boxplots.c1Àc4) The study explored the effects of hardening time on the tensile mechanical properties of fibers.Four distinct hardening times (1.5, 2.5, 3.5, 4.5 min) were used to create four fibers each, and the resulting properties were represented using boxplots.0.5 to 4 min, with a step size of 0.5 min, yielding 8 values in total.These parameters create a 3D search space with 2952 process parameter combinations.
Initially, we conducted a three-level factorial design [26,38] before applying the BO.The evaluation process involved analyzing 27 specimens, each produced with different pulling velocities, hardening forces, and hardening times to uniformly cover the design space, as shown in Figure S7, Supporting Information.Subsequently, the tensile properties of the fibers were assessed via tensile testing on the pulling device, without removing the fibers.These 27 generated samples served as the starting set for the BO.In each optimization cycle, the GP model is updated, and new experimental parameters are suggested.This process continues until the maximum tensile properties are achieved, as illustrated in Figure 1.
Figure 5A depicts the experimental samples obtained.The first 27 samples, shaded in blue, were generated using a three-level factorial design sampling.Following that, four samples, shaded in brown, were acquired during the exploration phase using BO.Finally, the last three samples, shaded in yellow, were obtained during the exploitation phase using BO.In Figure S8, Supporting Information, stress-strain curves for the 27 specimens are presented in blue, with curves corresponding to the pulling parameters tested during the exploration phase using Bayesian optimization (BO) depicted in brown.Additionally, the stress-strain curves for the tested pulling parameters during the exploitation phase using BO are highlighted in yellow.
We stopped the optimization process after three iterations.The stopping criterion was defined as the repetition of the same input parameters without any observed improvement in the output.The choice of λ values in the exploration and exploitation phases of the BO was guided by experimental tests.In the exploration phase, we selected λ = 10 to prioritize exploration and gather diverse information about the search space.For the exploitation phase, we determined that λ = 0.5 yielded the best performance in terms of convergence and solution quality.These λ values were chosen based on iterative experimentation and evaluation of performance metrics.
All tested experimental sets are displayed in Figure 5B, which is a parallel coordinate plot capable of encompassing all data sets and outcomes from an n-dimensional experimental space.The vertical axes on the graph represent each pulling parameter, with the parameter name listed below the axis and all the allowed values of that parameter shown along the axis.Each colored line running longitudinally and connecting a point on each axis represents a single experiment.The point at which the colored line intersects each axis reflects the parameter value for that experiment.Additionally, the color gradient used for the colored lines indicates the quality of the output.In our case, the output variable was the sum of the normalized tensile properties (Y ).The line color represents the weight output, with blue lines representing lower values and yellow lines signifying higher values, as shown on the color scale located on the right of the graph.The brightest yellow line represents the fiber-pulling parameters that yield the highest tensile properties.
The results obtained from the experiments revealed that the optimal pulling parameters differed between the three-level factorial design and the BO.For the three-level factorial design, the optimal parameters were found to be a pulling velocity of 30 mm s À1 , a hardening force of 7 mN, and a hardening time of 1 min.In contrast, the BO suggested that the optimal pulling parameters were a pulling velocity of 27 mm s À1 , a hardening force of 7 mN, and a hardening time of 0.5 min.

Tensile Properties of the Pulled Fibers Using BO
The comparison between the stress-strain curves of fibers produced using the three-level factorial design and the BO, under the same environmental conditions (temperature of 22 °C and humidity of 22.5%), is shown in Figure 5C.The corresponding tensile properties (toughness, strength, Young's modulus, and elongation) and the average diameter for each stress-strain curve are displayed in Figure 5D.
Compared to the three-level factorial design, the toughness obtained using the BO represents a 3.66-fold increase, the strength a 3.06-fold increase, the Young's modulus a 2.37-fold increase, and the elongation a 1.27-fold increase.These significant improvements demonstrate the effectiveness of the BO in enhancing the tensile properties of the fibers.
Furthermore, the stress-strain curve noticeably improved after implementing the BO, without involving any postdrawing during the fabrication process.This result highlights the remarkable potential of the BO in optimizing the properties of the fibers, leading to enhanced performance.The comparison between the three-level factorial design and the results obtained from the BO provides scientific evidence of the algorithm's effectiveness and its ability to produce superior tensile properties in the fibers.
The tensile mechanical properties in relation to the average diameter of dextran fibers are depicted in Figure S9, Supporting Information.The results indicate that the strength, toughness, and Young's modulus exhibit an exponential correlation with the average diameter of the fibers, indicating that thinner fibers generally possess higher strength, toughness, and Young's modulus.Conversely, the relationship with elongation appears more stochastic.Notably, fibers with diameters ranging from 20 to 140 μm demonstrate comparable strengths and toughness.

Conclusion
Our study has demonstrated the potential for significant advancements in fiber manufacturing, a critical aspect across various industries such as textiles, composites, and biomedical engineering.Currently, at the industrial scale, laser-based methods are frequently deployed for quality, size, and morphology studies.This study shifts the focus from traditional industrial fiber optimization methods to explore biomimetic approaches.We particularly investigate biomimetic fiber spinning, customized for producing novel silk fibers.The traditional challenges associated with enhancing fiber tensile properties, which included issues with uncontrolled extrusion processes and the complexities of optimizing parameters in high-dimensional spaces, have been successfully addressed through the introduction of our novel robotic pulling method.This method not only accelerates the process but also yields superior fiber properties when compared to existing methods.
Using a controlled fiber-pulling device equipped with in situ tensile measurements and harnessing adaptive optimization through BO, we have achieved remarkable results.In just a few experimental iterations, our method has enabled us to achieve fiber strength levels exceeding 300% of what is attainable using the traditional full factorial design method.This breakthrough in rapid experimentation opens up promising avenues for enhancing the performance of artificial fibers, offering substantial benefits to a wide range of industries and applications.

Figure 3 .
Figure 3. Stress-stress behavior of the Dextran fibers: a) The stress-strain curve of the pulled fibers.b) Detailed annotation of the distinct phases of fiber behavior observed during the tensile test.c) SEM image of the fracture point of the fiber.d) Cyclic pulling curves to a cyclic loading and unloading procedure comprising five cycles.

Figure 4 .
Figure 4. a1-a4)The study investigated the effects of fiber pulling velocity on the tensile properties of fibers, including strength, toughness, Young's modulus, and elongation.Four distinct pulling velocities (10, 20, 30, 40 mm s À1 ) were used to fabricate four fibers each, and the resulting properties were represented using boxplots.b1Àb4) The study also examined the effects of hardening force on the tensile mechanical properties of fibers.Four distinct hardening forces (2, 4, 6, 8 mN) were applied to create four fibers each, and the resulting properties were represented using boxplots.c1Àc4) The study explored the effects of hardening time on the tensile mechanical properties of fibers.Four distinct hardening times (1.5, 2.5, 3.5, 4.5 min) were used to create four fibers each, and the resulting properties were represented using boxplots.

Figure 5 .
Figure 5.A) The values of the toughness, strength, Young's modulus, elongation, and average diameter for the 27 specimens in blue shading.The values of the toughness, strength, Young's modulus, elongation, and average diameter of the tested pulling parameters during the exploration phase using BO are represented with brown shading.The values of the toughness, strength, Young's modulus, elongation, and average diameter of the tested pulling parameters during the exploitation phase using BO are represented with yellow shading.B) Suggested parameters for each fiber-pulling experiment (Y is the sum of the normalized tensile properties).C) Representative strain-stress curves with three-level factorial design and using BO.Both fiber groups were fabricated without post-treatment.D) Representative tensile properties (toughness, strength, Young's modulus, and elongation) with three-level factorial design and using BO.