To achieve high work performance for compliant mechanisms of motion scope, continuous work condition, and high frequency, we propose a new hybrid algorithm that could be applied to multi-objective optimum design. In this investigation, we use the tools of finite element analysis (FEA) for a magnification mechanism to find out the effects of design variables on the magnification ratio of the mechanism and then select an optimal mechanism that could meet design requirements. A poly-algorithm including the Grey-Taguchi method, fuzzy logic system, and adaptive neuro-fuzzy inference system (ANFIS) algorithm, was utilized mainly in this study. The FEA outcomes indicated that design variables have significantly affected on magnification ratio of the mechanism and verified by analysis of variance and analysis of the signal to noise of grey relational grade. The results are also predicted by employing the tool of ANFIS in MATLAB. In conclusion, the optimal findings obtained: Its magnification is larger than 40 times in comparison with the initial design, the maximum principal stress is 127.89 MPa, and the first modal shape frequency obtained 397.45 Hz. Moreover, we found that the outcomes obtained deviation error compared with predicted results of displacement, stress, and frequency are 8.76%, 3.6%, and 6.92%, respectively.

Recent theoretical development has revealed that the study of the growth of effectively exact positioning-mechanisms has many challenges. As a result of the basic requirement for cutting edge advances in a few enterprises, for example, semiconductor production, where super exact machining and miniature electro-mechanical-frameworks (MEMS) are obligatory. For instance, the size of 0.15-l (130 nm) measurement on 300 mm silicon-wafer created with a 65 nm cycle would be realized early. Other activating systems and control methodologies are fundamental to overwhelm the current restrictions and get an accuracy position in the nanometer dimension. One technique for taking care of this sort of issue is to plan new flexure pivots fueled by piezoelectric actuators. The inalienable highlights of piezoelectric actuators (piezo actuators for short) make them tremendously alluring for driving components in these exactness position applications since they give smooth movements. They are interminable control goals, quick reaction time, and high intransigence. Nonetheless, they have experienced the failure effects of the genuine constraint of a little longitudinal expansion. Ordinary piezo actuators broaden just about 0.1% of their length. To straightforwardly utilize, the piezo actuator to make an ideal scope of movement in various applications and an extended actuator is required. This is unrealistic. To sidestep this restriction and understand the low scope of work, with an accuracy position of a few nanometers, an amplification system utilizing adaptable pivots and driven by a piezo actuator can be used. The magnification mechanism has a compact size, high magnification ratio, high frequency, and lightweight. Therefore, the leaf flexible hinge is selected for the mechanism. To select appropriated dimensions for the mechanism, this investigation proposes a hybrid Taguchi approach based on grey relational analysis and neural network with fuzzy logic and ANFIS algorithms [

The problem with such an implementation is that many flexure hinges are designed for many compliant mechanisms to eliminate the effects of clearance joints. The circular flexure hinge is designed for the 3-degree of freedom (DOF) mechanism, and 3-DOF parallel mechanism [

The analysis and optimization are different from the previous investigation, Gey relational analysis (GRA) based Taguchi method (TM) and ANFIS are applied to predicted displacement amplification ratio of magnification mechanism based on analysis of finite element in ANSYS. Most of the research in this field aims to solve this problem. The Taguchi method is an optimization method for one objective. However, many dimensions are requested for optimal design. Therefore, in this investigation, we utilize grey relational analysis to select one optimum case for a magnification mechanism with three objectives. Then the outcomes are verified by analysis of the signal to noise of the Taguchi method, analysis of variance, analysis of regression, Fuzzy logic, and ANFIS. Designed mechanism set up of the finite element model and boundary condition are presented in Section 2. The Grey-Taguchi, Fuzzy logic system, and ANFIS method are presented in Section 3. The outcomes and arguments will be presented in Section 4. The conclusions will be stated in Section 5.

This assumption is supported by the fact that the model of the magnification mechanism is illustrated in

The magnification mechanism with dimensions as presented in

Material | Young’s modulus (GPa) | Poisson’s ratio | Tensile yield strength (MPa) |
---|---|---|---|

AL-7075 | 72 | 0.33 | 503 |

The TM employed by Minitab 18 software to create an orthogonal array. The optimal output characteristics is obtained like the theoretical model which has to be pointed out first, before the optimal methods are applied. However, the deviations seem to be very big in scale in comparison with the theoretical model. After that, the optimal methods could not be approving. Hence, in this investigation, we applied the Taguchi approach based on grey relational analysis and an artificial neural network, fuzzy logic system, and ANFIS to optimize these output characteristics. Step 1: Choosing optimization combination parameters for the output characteristics. Step 2: Designing the control factors and their levels. Step 3: Laying-out L_{27} orthogonal array. Step 4: Carrying out simulation and collecting data. Step 5: Generating the GRA in comparison of the changes in a system undergoing analysis to estimate the importance of the design variable. The GRA is the approach applied to discretize-sequences. Normalization: Rewrite each sequence between 0 and 1 as follow [

Smaller the better:

Grey relational coefficient (GRC)

Compute grey relational coefficient (GRC).

Here,

Computational GRG

Determination of the total grey-relational-coefficient

Estimation of the normalized coefficient

Determination of the entropy

Here,

Computation of sum of entropy

Determination of the weight

GRG

Step 6: Analysis of Taguchi [^{th} experimental step and n is the quantity of experiment that was recorded from the outcomes of FEA in ANSYS. And then all the data in

Step 7: Analysis of regression equation [

Step 8: {Analysis of variance (ANOVA)} [

Step 9: Analysis of mean and predicted outcomes [

Step 10: Fuzzy logic system [

Regarding the reactive control, the vector of fuzzy inputs includes a couple of parameters. The first one is the displacement desirability and the second one is the frequency desirability. In another word, the output of the second stage is the input of the third stage–operated by the FLS. In this stage, the output data of the multi-characteristic performance index (MCPI) would be computed by the FLS. Its controller compared the input numerical and output numerical data to solve the problem and to employ the expected MPCI. There are many parts in a FLS such as

To execute the FIS framework, the Mandami strategy is utilized in this current study. Thusly, trapezoidal MFs were received for the sources of information and outcomes of the FIS to create the sorts of fuzzy. MFs were in the range from 0 to 1, and MFs could depict how a variable met the sort of fuzzy. Data sources and yields of the fuzzification framework were, after that, changed into etymological variables. The trapezoidal MFs were characterized.

Firstly, we computed the displacement desirability and frequency one. And afterward, we considered both ones as two inputs for the FIS. We consolidated these linguistics inputs to collect the output. We operated the trapezoidal MFs for fuzzification and defuzzification. The accompanying fuzzy principles were quickly portrayed. Fuzzy regulation: If _{1} and _{1} then z_{i} stands for C_{1} else (i runs from 1 to n), where the parameters, ^{th} information sources. Besides, z_{i} stands for the outcomes i^{th}. We define D_{i}, E_{i,} with C_{i} in comparison to MFs (μ_{Di}, μ_{Ei}, and μ_{Ci}), and those boundaries would be viewed as _{o}, known as MCPI:

In light of the hypothesis of the FIS framework, we found the output of MCPI via the Taguchi technique which was considered the most optimal solution for the general reactions with many optimum designing factors [_{i} stands for the i^{th} MCPI; n is known as the number i^{th} experimental value.

We operated a Taguchi-based fuzzy logic to discover optimum competitors in the multi-objectives optimization (MOO) problem yet this methodology was considered as one of the local optimum solutions. It is clear to see that the Taguchi procedure was utilized to limit or expand a solitary wellness work as far as discrete qualities. After that, an actual issue was wanted to look for a globally optimal solution. To defeat that circumstance, ANFIS was then reached out to demonstrating the MCPI, and the MOO design for the mechanisms of one-DOF could be viably understood by utilizing the lightning attachment procedure optimization (LAPO) calculation.

Step 11: ANFIS: We undertook the empirical analysis using data collected in the model of the ANFIS algorithm [_{1} and D_{2} term set, z stands for the outcome. We set a, b, c becoming constant.

It is clear to be seen that the ANFIS algorithm comprises the five-layer feedforward neural network. The first layer has the role of fuzzification which allotted the levels of membership to inputs dependent on the presented MFs. We depicted the first layer outlet as below:
^{th}. _{i}_{i}.

The third layer is a standardized layer utilized to assess a proportion of terminating quality of an offered rule to an aggregate of terminating qualities all things considered. Every single node was named a cycle one. Inside that layer, NFS was labeled to the rule standardized terminating quality and characterized as shown in

The 4^{th} layer stands for the defuzzification cycle and the ^{th}

The 5^{th} layer is a general outlet, he whole all things considered, which is characterized as.

In this investigation, the trapezoidal MFs were received for the ANFIS framework too.

The three-length dimension was selected as three design variables with changed dimensions and presented in

Parameters | Unit | Design levels | ||
---|---|---|---|---|

1 | 2 | 3 | ||

Length A | mm | 0 | 1.0 | |

Length B | mm | 20 | 23 | 26 |

Length C | mm | 60 | 63 | 66 |

Trial No. | A | B | C | Displacement (mm) | Stress (MPa) | Frequency (Hz) |
---|---|---|---|---|---|---|

1 | 0 | 20 | 60 | 0.364 | 98.577 | 264.260 |

2 | 0 | 20 | 63 | 0.338 | 103.830 | 265.730 |

3 | 0 | 20 | 66 | 0.311 | 108.210 | 261.930 |

4 | 0 | 23 | 60 | 0.439 | 119.310 | 331.270 |

5 | 0 | 23 | 63 | 0.428 | 132.790 | 319.200 |

6 | 0 | 23 | 66 | 0.403 | 142.920 | 307.240 |

7 | 0 | 26 | 60 | 0.400 | 131.510 | 400.180 |

8 | 0 | 26 | 63 | 0.421 | 124.940 | 377.440 |

9 | 0 | 26 | 66 | 0.386 | 137.210 | 351.450 |

10 | 1 | 20 | 60 | 0.231 | 106.450 | 340.820 |

11 | 1 | 20 | 63 | 0.188 | 106.950 | 350.320 |

12 | 1 | 20 | 66 | 0.151 | 103.540 | 361.630 |

13 | 1 | 23 | 60 | 0.31 | 129.650 | 393.980 |

14 | 1 | 23 | 63 | 0.271 | 113.230 | 387.390 |

15 | 1 | 23 | 66 | 0.220 | 119.590 | 386.400 |

16 | 1 | 26 | 60 | 0.313 | 132.180 | 431.740 |

17 | 1 | 26 | 63 | 0.288 | 122.870 | 427.860 |

18 | 1 | 26 | 66 | 0.239 | 131.500 | 411.580 |

Another promising finding in _{oi}(1), Δ_{oi}(2) and Δ_{oi}(3) were obtained by

No. | Δ_{oi}(1) |
Δ_{oi}(2) |
Δ_{oi}(3) |
|||
---|---|---|---|---|---|---|

1 | 0.739 | 1.000 | 0.014 | 0.261 | 0.000 | 0.986 |

2 | 0.649 | 0.882 | 0.022 | 0.351 | 0.119 | 0.978 |

3 | 0.553 | 0.783 | 0.000 | 0.447 | 0.217 | 1.000 |

4 | 1.000 | 0.532 | 0.408 | 0.000 | 0.468 | 0.593 |

5 | 0.962 | 0.228 | 0.337 | 0.038 | 0.772 | 0.663 |

6 | 0.875 | 0.000 | 0.267 | 0.125 | 1.000 | 0.733 |

7 | 0.934 | 0.556 | 0.814 | 0.066 | 0.444 | 0.186 |

8 | 0.938 | 0.405 | 0.680 | 0.062 | 0.595 | 0.319 |

9 | 0.815 | 0.129 | 0.527 | 0.185 | 0.871 | 0.473 |

10 | 0.275 | 0.823 | 0.465 | 0.724 | 0.178 | 0.535 |

11 | 0.128 | 0.811 | 0.521 | 0.872 | 0.188 | 0.479 |

12 | 0.000 | 0.888 | 0.587 | 1.000 | 0.112 | 0.413 |

13 | 0.562 | 0.299 | 0.777 | 0.438 | 0.701 | 0.222 |

14 | 0.414 | 0.669 | 0.738 | 0.586 | 0.330 | 0.261 |

15 | 0.238 | 0.526 | 0.733 | 0.762 | 0.474 | 0.267 |

16 | 0.562 | 0.242 | 1.000 | 0.439 | 0.758 | 0.000 |

17 | 0.473 | 0.452 | 0.977 | 0.527 | 0.548 | 0.023 |

18 | 0.303 | 0.258 | 0.881 | 0.697 | 0.743 | 0.119 |

No. | γ_{i}(1) |
γ_{i}(2) |
γ_{i}(3) |
ψ_{i} |
Rank |
---|---|---|---|---|---|

1 | 0.657 | 1.000 | 0.336 | 0.742 | 2 |

2 | 0.588 | 0.808 | 0.338 | 0.646 | 8 |

3 | 0.528 | 0.697 | 0.333 | 0.580 | 17 |

4 | 1.000 | 0.517 | 0.458 | 0.735 | 3 |

5 | 0.929 | 0.393 | 0.430 | 0.653 | 7 |

6 | 0.799 | 0.333 | 0.405 | 0.573 | 18 |

7 | 0.883 | 0.529 | 0.730 | 0.797 | 1 |

8 | 0.889 | 0.457 | 0.610 | 0.728 | 4 |

9 | 0.729 | 0.365 | 0.514 | 0.599 | 14 |

10 | 0.408 | 0.738 | 0.483 | 0.606 | 12 |

11 | 0.365 | 0.726 | 0.511 | 0.596 | 15 |

12 | 0.333 | 0.817 | 0.548 | 0.632 | 10 |

13 | 0.533 | 0.416 | 0.692 | 0.611 | 11 |

14 | 0.461 | 0.602 | 0.657 | 0.640 | 9 |

15 | 0.396 | 0.513 | 0.652 | 0.581 | 16 |

16 | 0.533 | 0.398 | 1.000 | 0.719 | 5 |

17 | 0.487 | 0.477 | 0.956 | 0.715 | 6 |

18 | 0.418 | 0.402 | 0.808 | 0.606 | 13 |

From these results, it is clear that the regression-equation (RE) of GRG was gained through Minitab 18 as presented in

We found that the results agree well with the other single methods. The graph of GRG was painted in

Overall, our proposed approach is obtained the most robust results. The surface plot of GRG as shown in

From these results, it is clear that the graph of S/N of GRG was painted from the values in _{1}, B_{3}, C_{1}, respectively, to the seventh case in

Level | A | B | C |
---|---|---|---|

1 | −3.501 | −6.990 | −3.120 |

2 | −3.979 | −4.013 | −3.590 |

3 | −3.218 | −4.511 | |

Delta | 0.478 | 0.795 | 1.391 |

Rank | 3 | 2 | 1 |

Source | DF | Seq SS | Contribution | Adj SS | Adj MS | F-Value | |
---|---|---|---|---|---|---|---|

A | 1 | 0.006643 | 8.39% | 0.006643 | 0.006643 | 19.84 | 0.004 |

B | 2 | 0.014899 | 18.83% | 0.014899 | 0.007450 | 22.24 | 0.002 |

C | 2 | 0.034893 | 44.09% | 0.034893 | 0.017446 | 52.09 | 0.000 |

A × C | 2 | 0.014152 | 17.88% | 0.014152 | 0.007076 | 21.13 | 0.002 |

B × C | 4 | 0.006546 | 8.27% | 0.006546 | 0.001636 | 4.89 | 0.043 |

Error | 6 | 0.002009 | 2.54% | 0.002009 | 0.000335 | ||

Total | 17 | 0.079143 | 100.00% |

The finding in this investigation is equal to or better than an outcome that is presently accepted. The outcome of the mean analysis of GRG is illustrated in

Level | A | B | C |
---|---|---|---|

1 | 0.6726 | 0.6338 | 0.7018 |

2 | 0.6341 | 0.6322 | 0.6630 |

3 | 0.6940 | 0.5953 | |

Delta | 0.0384 | 0.0618 | 0.1066 |

Rank | 3 | 2 | 1 |

It is significant to pay attention that the current outcome relies on the mean analysis of displacement as illustrated in _{1}, B_{3}, C_{1}. The value of variable A is 0.3901 mm, the variable B is 0.3444 mm and the value of variable C is 0.3466 mm, respectively. Together, the present findings confirm that the outcome of the mean analysis of maximum principal stress as illustrated in

Level | A | B | C |
---|---|---|---|

1 | 0.3879 | 0.2638 | 0.3433 |

2 | 0.2459 | 0.3457 | 0.3224 |

3 | 0.3411 | 0.2849 | |

Delta | 0.1442 | 0.0819 | 0.0617 |

Rank | 1 | 2 | 3 |

Level | A | B | C |
---|---|---|---|

1 | 319.3 | 307.4 | 359.5 |

2 | 388.0 | 354.2 | 354.7 |

3 | 399.2 | 346.7 | |

Delta | 68.7 | 91.8 | 12.8 |

Rank | 2 | 1 | 3 |

Level | A | B | C |
---|---|---|---|

1 | 120.7 | 104.6 | 117.4 |

2 | 118.4 | 126.2 | 117.4 |

3 | 127.8 | 123.8 | |

Delta | 2.2 | 23.2 | 6.4 |

Rank | 3 | 1 | 2 |

As listed in _{0.05}(1, 6) = 5.9874 [

Type mesh | Fine | ||
---|---|---|---|

Size element | Displacement (mm) | Maximum principle stress (MPa) | Frequency(Hz) |

0.2 | 0.40536 | 135.81 | 398.52 |

0.5 | 0.40345 | 131.51 | 400.18 |

0.8 | 0.4049 | 133.22 | 402.3 |

Type mesh | 0.5 mm | ||
---|---|---|---|

Size element | Displacement (mm) | Maximum principle stress (MPa) | Frequency(Hz) |

Coarse | 0.40213 | 128.7 | 398.50 |

Fine | 0.40232 | 128.7 | 398.53 |

We showed that, whereby, the predicted values of GRG, DI, ST, frequency are 0.7616, 0.4385 mm, 126.7882 MPa and 372.4756 Hz, respectively. The GREY relational analysis outcome gained one optimization case and then use this case to simulate and obtained optimization outcomes of GRG, DI, ST and Fre are 0.7973, 0.4001 mm, 131.51 MPa and 400.18 Hz as shown in

Hybrid optimization | GRG | DI (mm) | ST (MPa) | Frequency (Hz) | |
---|---|---|---|---|---|

Predicted values (i) | A1B3C1 | 0.7616 | 0.4385 | 126.7882 | 372.4756 |

Optimization without Fuzzy logic ANFIS (ii) | 0.7973 | 0.4001 | 131.51 | 400.18 | |

Our proposed approach (iii) | 0.8212 | 0.4521 | 127.894 | 397.45 | |

Error (%) between (i) |
4.48 | 8.76 | 3.6 | 6.92 | |

Error (%) between (ii) |
2.91 | 11.50 | 2.83 | 0.69 |

The findings are equal to or better than those of previous studies that are currently agreed upon. From these results, it is clear that after choosing the mechanism with combination variables at optimal values, the static structural and modal shape were used to obtain the optimum value of displacement, maximum principal stress, and the first modal shape of frequency which are 0.4521 mm, 127.894 MPa, and 397.45 Hz as depicted in

This conclusion follows from the fact that the influences of three variables (A, B, C) on displacement, maximum principal stress, and frequency of the first modeling shape case were analyzed through using FEA. Our findings identified that these variables have strongly affected three outputs as proved by S/N analysis, ANOVA, regression analysis, prediction of the artificial neural network, statistical analysis, Fuzzy logic system, and ANFIS. Besides, these findings provided additional information about the simulation, optimization, prediction results which are good to agree with and better than the previous publication as presented and discussed. The magnification ratio, maximum principal stress, and the first modal shape frequency were obtained larger than 40.35 times, 127.894 MPa, and 397.45 Hz, respectively. Nevertheless, we found that the optimal method was permitted to utilize optimization analysis for variables of the compliant mechanism because the outcomes of the research have errors that are less than 9%. From the obtained outputs pointed out that the Taguchi method based on grey relational analysis and ANFIS are the robust optimization methods. The methods proposed to apply for optimal problem in the fields technique, industry, life and society.

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