The structure of macrobending fiber optics is an ideal structure for constructing fiber optic sensors. This study presents a new design and implementation of U-shaped fiber optics. The basic geometric parameters of U-shaped fiber optics, such as dimension size or curve radius, are analyzed. The Taguchi method was used to optimize the effects of the control and noise factors with respect to dimension size, loop, wavelength, and core size. The control factors were varied at different levels to achieve a novel sensitivity response optimization of the wavelength and core size. The quality characteristics of the signal-to-noise ratio (larger-the-better characteristics) were used to determine the effect of the control parameters in the data analysis. The data of the sensitivity response was analyzed to predict the performance of the U-shaped fiber optics. Results indicate that, by using the Taguchi method, the best control factor setting involves 2.5 cm × 1.5 cm (dimension size) and 1550 nm (wavelength). The percentage contribution of wavelength is the highest at 67.17%, followed by dimension size (13.31%) and number of loops (11.72%) for the fiber optic core size of 50–9–50 μm. For the 9 μm single-mode fiber optics, the corresponding percentages are 61.48%, 16.64%, and 12.81% for wavelength, dimension size, and number of loops, respectively. The Taguchi methodology is suitable for designing sensor geometry.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Fiber optics are known to be innovative wires owing to their unique advantages of immunity to electromagnetic interference and high temperature capability [1,2]. Although the size of fiber optics is smaller than that of a traditional wire, it can perform better with its environment. A fiber optics’ dimension allows it to be used as a sensor. Nowadays, many types of fiber optic sensors can be used to measure pressure, temperature, and strain in a variety of industrial environments, including power transformers and civil structures [1,3–6]. Besides, fiber optics have potential applications in the healthcare field, in which the most recent technology is for personal healthcare, also known as wearable healthcare [7,8]. With such developments, researchers have also attempted to enhance the performance of fiber optic sensors. Currently, the three types or structures of fiber optic sensors used for textiles are the Bragg grating (wavelength-modulated) [1,2,9], microbending , and macrobending [10–12] sensors. Wavelength-modulated sensors use changes in the wavelength of light for detection . However, Bragg grating fibers require complicated operation, and they are difficult to develop and costly to manufacture. Therefore, majority of researchers have utilized microbending and macrobending to determine the capability of fiber optics in terms of sensitivity. Microbending and macrobending focus on mechanical defects affecting the changes in light intensity. Similarly, light intensity is modulated by body vibration (mechanical defects). Macrobending and microbending sensors are essentially similar except for their sensor geometries and bending scales. Macrobending structures can be created in a loop, wave, 8-shaped, serpent, double-loop, double-wave, mirror-wave, or single-serpent structure. Both microbending and macrobending sensors can prevent fiber breakage and are capable of becoming a potential candidate for wearable application.
Between the abovementioned two types of sensors, researchers have focused more on macrobending sensors because they are easy to build, control, and less expensive. Although previous studies have analyzed the performance of macrobending fiber optics embedded in textiles, none of the researchers have attempted to optimize the best performance parameter. Several aspects regarding the effect of bending should be considered. Consequently, theoretical and experimental studies on the bending effect have been conducted, such as those that focus on the curvature radius, turn number, and bend structure . Previous researchers have also attempted to eliminate performance loss to improve the efficiency of fiber optics, but none of them centered on optimization via the Taguchi method. In this study, the U-shaped structure of fiber optics was selected for performance analysis. The loop, wavelength, core size, and dimension size of the U-shaped fiber optics were analyzed, and then the best parameter was considered for optimization in the development of a fiber optic sensor. The performance and accuracy of measurement were both strongly dependent on the geometric parameters. The optimization of the sensor’s geometry determined on the basis of a series of experiments was used to select the parametric setting for the design of the targeted high-performance sensor.
The principal tools in the parametric design are orthogonal array (OA) and signal-to-noise ratio (SNR). By selecting the appropriate OA to arrange the experiment times, each factor that may influence the target characteristics can be identified using an even fewer number of experiments. Each matrix in the OA represents a set of experimental data, and a change in each matrix parameter represents a change in the its setting value. In actual scenarios, the parameters are referred as the influence factors, while the setting values correspond to the levels. Then, the optimum combination conditions and the significance of each process factor can be determined according to experimental results, followed by SNR analysis and analysis of variance (ANOVA). In this study, the described method was initially adopted to analyze the control factors that could influence the quality of the U-shaped fiber optics. Different quality evaluation parameters were selected, and then the corresponding combinations of the process factors were determined. Finally, the optimum combination of the process factors was selected to design the optimal U-shaped fiber optics sensor.
2.1 Experimental principle and procedure
For the periodic macrobending, the specimens were designed as single-mode (9–9–9 μm) and hetero-core (50–9–50 μm) fiber optics with periodic “U” turns or sinusoidal shapes (Fig. 1). 9 μm refer to sensor part is maintained at both design. The bending radius of the fibers formed with U turns called the loop amplitude (denoted by A) and the bending periodicity called the loop period (denoted by T) were adjusted at different lengths (Table 1). The loop period and loop amplitude were used to represent the dimension size (loop amplitude (A) × loop period (T)). The experimental configuration is illustrated in Fig. 1, and the details of A and T are given in Table 1. The length of the fiber was 3 m, including the hetero-core portion measured from the light source to the input of the power meter operating at the wavelengths of 850, 1310, and 1550 nm. The hetero-core portion was mounted onto a supporting piece with different vertices (1.0, 1.5, and 2.0) and turned by up to eight times to cause the light to propagate in the cladding region and allow the radiation modes to be generated.
3.2 Taguchi method
The Taguchi method was utilized to optimize the control and noise factor variations on the U-shaped fiber optics. The control factor and its level are both listed in Table 2. According to the Taguchi method [15,16], the suitable OA for two factors is the mixed level, as depicted in Table 3. Therefore, the OA consisting of 16 experiments was used to investigate the impact of dimension size and number of loops, which could contribute to the sensitivity performance of the U-shaped fiber optics. SNR is the performance parameter of the Taguchi method that can result from various optimization experiments. As a parameter, SNR can be operated under the following two conditions: a smaller-the-better or a larger-the-better SNR. In this study, the aim of the 16-row experiment is to optimize the best dimension size of the U-shaped fiber optics by using the larger-the-better SNR. The larger-the-better SNR, denoted by ɳL, and the smaller-the-better SNR are given by Eqs. (1) and (2), respectively [17,18].
Subsequently, ANOVA test (a common statistical technique) was conducted to investigate which among the control factors had significantly affected the performance characteristics. The insignificant control factor was assumed to be pooled and negligible. Then, for the dimension size, the various significant factor effects were compared. The higher percentages in terms of level were selected and combined as the best setting. Only a single confirmation run would be performed. In addition, the larger-the-better SNR was utilized to optimize the sensitivity of the U-shape fiber optics based on the output power with the noise factor, core size (single or hetero-core fibers), wavelength in the range of 850–1550 nm, and 1–8 loops. In this manner, the sensitivity of the U-shaped fiber optic sensor could be optimized simultaneously using the Taguchi method. The Taguchi method requires at least five steps , namely, planning, factor selection, conduct of experiment, data analysis, and confirmation experiment. A previous research  applied the Taguchi method for optimization design via the process development approach (i.e., system design, parameter design, and tolerance design). In this study, the step in which the output results need to be obtained from the experimental data was modified. In particular, simulation experiments were not applied; rather, the analysis and optimization of the best parameter for the macrobending fiber optics were based on the experimental data.
3. Results and discussion
The effects of dimension size, number of loops, wavelength, and different core diameters were investigated to explore the essential characteristics of bending loss performance. Then, the Taguchi method was used to analyze and optimize the best parameter of the U-shaped fiber optics.
3.1 Loss due to dimension size, number of loops, wavelength, and core size based on the experimental data
The experimental results are presented as a power intensity versus loop number plot in Fig. 2. This study explored the relationship between bending loss and LN (number of loops), where N is simplified as a linear equation, for both fiber configurations [10,14]. The 50–9–50 hetero-core fiber is more sensitive than the 9 μm standard single-mode fiber optic. In the case of the 2.5 cm × 1.5 cm hetero-core and 2.5 cm × 1.5 cm single-mode fiber, the output intensity of 52 μW dB and 125 μW was measured at N = 1, respectively. The light loss can be attributed to the mode coupling and its impact at the splice region resulting from the different core diameters of the fibers. Then, the bending loss of the hetero-core fiber optics was measured using the three wavelengths of 850, 1310, and 1550 nm (Fig. 3). The bending loss is clearly much larger at 1550 nm compared with that at 850 nm, which aligns with the findings of a previous research . The longer wavelength can induce much more bending loss exponentially between 850 and 1550 nm.
3.2 Optimization of dimension size of U-shaped fiber optics
Minitab was employed as the software in the statistical analysis. The experiment was run on the basis of the OA (Table 3), and the SNR was calculated for the different experiments. Then, on the basis of the SNR analysis, the impact of the control factor on the U-shaped fiber optics was investigated. As for dimension size, its impact was investigated to determine the best sensitive control factor before continuing to the next Taguchi method. The wavelength values in Table 4 had been purposely inserted to correspond to the various experiments and different parameter values previously shown in Table 3. The larger is the SNR value, the higher is the impact of the parameter as a response, and vice versa. Figure 4 shows a smooth performance trend of the L16 OA. The experimental was run four times along with the change in the number of loops (1–2, 3–4, 5–6, and 7–8 loops). After 16 experimental runs and repeat runs for four more times, the most significant control factor affecting the U-shaped fiber optic sensor’s response was determined. The average SNR of the dimension factor and their levels were calculated (Fig. 4). The best factor combination for the wavelength was 2.5 cm × 1.5 cm for all 1–8 loops. In other words, this dimension is already optimized for the best number of loops (i.e., 1–8 loops) and wavelength (850, 1310, and 1550 nm). These results obey the relationship formula between loop period and loop amplitude, as discussed in a previous work . It also can be justified by the theoretical bending loss explanation from  in which the loss happened on the slab waveguide due to the increment of incident angle. Increasing the incident angle at a curved interface, increases the critical angle. Therefore, light radiates away, and dimension size influence the loss. Moreover,  found that 1.5 cm length of loop amplitude is the most sensitive sensor, which agree with bend theory. Therefore, the best three dimensions are finally selected to generate a new control factor. According to the optimization results, the top three dimension sizes are 2.5 cm × 1.5 cm, 2.0 cm × 1.5 cm, and 1.5 cm × 1.5 cm for the larger-the-better SNR.
3.3 Optimization of wavelength of U-shaped fiber optics
In Section 3.1, the three best dimension sizes had been selected. Usually, the wavelengths of 1310 and 1550 nm are suitable for single-mode fiber optics. However, knowing which wavelength is more effective cannot be easily determined for a type of particular fiber optics. Therefore, wavelength was used as one of the control factors for the U-shaped fiber optics. The Taguchi method was similarly utilized to optimize the control factor. The control factors and their levels are listed in Table 5. According to the Taguchi method, the suitable OA is L9 for three control factors, as shown in Table 6. Therefore, the OA of L9, which entails nine experiments, was used to investigate the impact of the three control factors for the core size of the fiber optics (assumed as a noise factor in this study) as they could also contribute to sensitivity performance. The aim of this nine-row experiment is to obtain a sufficiently large core size value and ensure optimization by using the Taguchi method’s larger-the-better SNR in Eq. (1). This experiment was repeated two times by using 4–6 and 6–8 loops (Table 7).
After nine experimental runs, the most significant control factor affecting the U-shaped fiber optic’s response was determined. The average SNR of each control factor and the corresponding levels were calculated. Figure 5(a) shows the 1–3 loops, Fig. 5(b) shows the 4–6 loops, and Fig. 5(c) shows the 6–8 loops. As depicted in Fig. 5(a), the best factor combination for both 9 μm and 50–9–50 μm fiber optics involves 2.5 cm × 1.5 cm, 3 loops, and 1550 nm. Meanwhile, as shown in both Figs. 5(b) and 5(c), the best combination involves 2.5 cm × 1.5 cm and 1550 nm, but they differ in the number of loops (5 and 7 loops, respectively). These findings confirm that 2.5 cm × 1.5 cm and 1550 nm are the best factors. The determination of 1550 nm can be related to mode fields. Single mode fiber has a larger mode field diameter at 1550 nm than other wavelengths, therefore, it is more sensitive to losses incurred by bends . As for the number of loops, the best ones are 3, 5, and 7 loops.
The ANOVA test was similarly conducted to identify the control factors that could significantly influence the performance of the U-shaped fiber optic sensor. The combined factor effects based on the ANOVA results for the 9 μm and 50–9–50 μm fiber optics are presented in Table 8. The value of the factor effect from both responses were compared to determine the best setting. The higher factor effect percentage from either the 9 μm or 50–9–50 μm tabulation in Table 8 was selected as the best setting for the U-shaped fiber optic sensor. For the first factor on A (dimension size), 14.18% of A1 factor level corresponding to 2.5 cm × 1.5 cm can affect the sensitivity of the U-shaped fiber optics. Therefore, the sensitivity response from loss due to core size can be combined as one of the best settings, i.e., A1B3C3, A1B2C3, and A1B2C3 for 1–3, 4–6, and 6–8 loop, respectively. The item on BX presents an inconsistent value for the factor effect with respect to the different loop numbers. Therefore, the Taguchi method would be needed for analysis (see Section 3.4) to confirm the influence of number of loops on performance loss. The trends in Table 8 depict a higher percentage contribution of wavelength compared with those of dimension size and number of loops. The percentages of 62.44%, 76.19%, 80.95%, 66.79%, 86.24%, and 87.59% were obtained for 1–3, 4–6, and 6–8 loops for each core size of the fiber optics.
3.4 Confirmation run of the influence factor with respect to sensitivity response
The confirmation run is the closing procedure in the design of the experimental process, and it is performed to verify the results. After the optimal level was selected, the final experimental run was conducted by utilizing the final best level setting of the control factors, which were obtained on the basis of the Taguchi method (Table 9). As discussed in the previous section, the influence of loop number was inconsistent for each analysis. The 4–8 loops (i.e., number of loops) exhibited the least influence, as signified by the lowest percentage contribution in the development of the U-shaped fiber optics, followed by 1–3 loops. Consequently, the confirmation run was performed to determine the exact factor that would contribute to this study. According to the previous experimental run, only the best numbers of loops (3, 5, and 7 loops) were considered for each experiment. The remaining factors were all considered on all three levels. The factors in the selection process and their levels are shown in Table 9. The total degrees of freedom were computed in the selection of the appropriate OA. According to the Taguchi method, the best OA corresponds to L9, and only nine-group trails would be needed to derive the optimum factors. Table 10 illustrates the selected OAs for L9.
The evaluation standard requires an obtainment of the importance of each process factor, in which the SNR can help to determine the robustness of the system, i.e., the sensitivity of the system to noise . Consequently, the larger-the-better SNR based on Eq. (2) was used again in this study. The configurations consisting of two core sizes were measured and then plotted (Fig. 6). The findings indicate that the best setting parameter is A1B3C3, which corresponds to 2.5 cm × 1.5 cm (dimension size), 7 loops (number of loops), and 1550 nm (wavelength). Then, an ANOVA and significance test was performed to further investigate the effect of each factor. The results are summarized in Table 11. The contribution of each process factor to quality in the development of the U-shaped fiber optics is in the order of C > A > B.
Table 11 shows dimension size as the factor with the second highest contribution to the development of U-shaped fiber optics. Wavelength contributes the highest percentage, with 61.48% and 67.17% for the single-core and hetero-core fibers, respectively. The contribution of loop number as a factor is inconsistent; that is, it has the second highest contribution for 1–3 loops, whereas it has the least contribution for 4–8 loops. This trend can be compared to the experimental data in Fig. 2, in which the intensity sharply decreases between 1 and 3 loops and then slowly decreases until 8 loops are reached. This trend can help to explain why the contribution of loop number differs among the 1–3, 4–6, and 6–8 loops. Then, a repeat experiment was conducted using the best loop for each tabulated result (Fig. 5). As a factor, number of loops has the least contribution to the development of U-shaped fiber optics.
The larger-the-better SNR was used in this study for the optimized sensitivity and best sensitivity configuration of U-shaped fiber optics. The optimum parameters that could help to realize the sensitivity response design were successfully achieved using the Taguchi method. The best setting of the control factors was identified to be 1550 nm (wavelength) and 2.5 cm × 1.5 cm (dimension size). Wavelength could highly influence the development of U-shaped fiber optics, followed by dimension size and number of loops. Using the Taguchi method, it confirmed the previous study on macrobend structure and obeyed the theoretical of fiber optics bend. In future, nanomaterial-coated fiber optics, particularly macrobending fiber optics, can be developed based on this study’s findings depicting the best setting and the most effective control factor.
Ministry of Higher Education, Malaysia ; Universiti Malaysia Sarawak.
Authors are sincerely thankful to Prof. Dr. Sahbudin Shaari and Najmiah Radiah Mohamad for proper guidance and supportive discussion. The authors are also thankful to Nanohotonics Lab, Institute of Microengineering and Nanoelectronics (IMEN), UKM for providing facilities.
The authors declare no conflicts of interest.
The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy.
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