# Hysteresis Curve Fitting Optimization of Magnetic Controlled Shape Memory Alloy Actuator

^{*}

## Abstract

**:**

## 1. Introduction

- (1)
- (2)
- (3)

## 2. Performance Experiment of MSMA Actuator

#### 2.1. Sample and Device of the Experiment

- (1)
- The strain gauge is a series of BX (BX strain gauge refers to phenolic foil type strain gauge) whose properties include the following: the entire structure is sealed, stable performance, good flexibility, and applicability to the general accuracy of the sensor. The strain limit is 1.5%, and usage temperature range is −30 °C–+80 °C.
- (2)
- The strain gauge sampling frequency is 4 Hz.

- (1)
- Turn off the power, place the sample in the cup, and fix the cup on the hydraulic loading device intermediate.
- (2)
- The hydraulic drive loading device is directly placed in the working range. At the same time, the magnetic field is set from 0 to 1.5 T.
- (3)
- Turn on the power, and set up the pre load of the sample.
- (4)
- Turn on the power supply for the temperature loading system, set the temperature parameters, and check whether the outer circulation system makes good contact. When everything is acceptable, turn on the heating power supply and the oil pump power supply, and regulate the flow rate of silicone oil circulation to prevent the silicone oil spilling.
- (5)
- Start the test. The corresponding deformation of MSMA is measured.
- (6)
- After unloading, view and save the experimental data.

#### 2.2. Experimental Results

**H**is parallel to the external load. The operating temperature is 16 °C, and the size of external load is 3.9 kg. In the experimental conditions, the key original experimental data of magnetic field intensity

**H**and magnetic induction intensity

**B**are shown in Table 1.

## 3. Fitting and Results

#### 3.1. Least Squares Method

**P**= [−8.2964, −33.4283, 8.7761, 17.8643, 0.0325]

**B**is maintained at approximately −3.4 T when magnetic field intensity

**H**ranges from −0.25 T to −0.54 T. Shown as curve 1 in Figure 3, magnetic induction intensity

**B**gradually increases from −3.4 T to 6.8 T when magnetic field intensity

**H**ranges from −0.25 T to 0.4 T. However, shown as curve 2 in Figure 3, magnetic induction intensity

**B**gradually decreases from 6.8 T to −3.4 T when magnetic field intensity

**H**ranges from 0.4 T to −2.5 T. Obviously, curve 1 and curve 2 do not coincide. Therefore, as shown in Figure 3, the relation curve between magnetic field intensity

**H**and magnetic induction intensity

**B**is the hysteresis curve of the MSMA.

#### 3.2. BP Artificial Neural Network

**H**and magnetic induction intensity

**B**. The number of input layer nodes and output layer nodes are both 1. Like the least squares method, we apply a BP artificial neural network with MATLAB software to fit the original experimental data. We apply equation calculations combined with programming algorithms to establish a magnetic hysteresis model that is faster and more accurate.

#### 3.3. BP Artificial Neural Network Based on Genetic Algorithm

## 4. Validation

**H**is parallel to the external load; operating temperature is 16 °C; the size of the external load is 4.9 kg; and the range of the magnetic field intensity

**H**is 0–1 T.

^{−5}at the 19th iteration. There is no doubt that a BP artificial neural network based on a genetic algorithm can accelerate the convergence rate and decrease the fitting error.

## 5. Conclusions

- (1)
- The fitting accuracy rate is quite high and can improve the accuracy of MSMA actuators. Because there are fewer undetermined parameters during the hysteresis curve fitting, the fitting speed of least squares method is fast.
- (2)
- Compared with BP artificial neural networks, BP artificial neural networks based on genetic algorithms can accelerate the convergence rate and decrease the fitting error. Therefore, they can improve the accuracy of MSMA actuators and enhance the utilization rate of MSMA actuators in precision positioning.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**Experimental setup: (1) power; (2) loading device; (3) power supply for temperature loading system; (4) computer with data acquisition card, which collects input magnetic field intensity

**H**and output magnetic induction intensity

**B**; and (5) control device for magnetic field.

**Figure 3.**Fitting curve and original experimental data curve. ”Processed 1” represents the fitting curve through least squares method. ”Original data” represents the original experimental data.

**Figure 6.**Fitting curve and original experimental data curve. “Processed 2” represents the fitting curve through the original BP artificial neural network. “Original data” represents the original experimental data curve.

**Figure 10.**Fitting-error-rate curve. “Original” and “improved” represent the fitting-error-rate curve of the BP artificial neural network and BP artificial neural network based on genetic algorithms, respectively.

**Figure 12.**Fitting curve and the original experimental data curve. “Processed 4” represents the fitting curve through the BP neural network based on a genetic algorithm. “Original data” represents the original experimental data.

**Figure 13.**Fitting error rate curve of the BP artificial neural network and the BP artificial neural network based on genetic algorithms.

**Figure 14.**The mean square error curve of the BP artificial neural network based on a genetic algorithm.

Serial Number | H (T) | B (T) | Serial Number | H (T) | B (T) | Serial Number | H (T) | B (T) |
---|---|---|---|---|---|---|---|---|

1 | −0.5258 | −3.4152 | 11 | 0.0301 | 0.2790 | 21 | 0.0707 | 1.9553 |

2 | −0.4640 | −3.3831 | 12 | 0.0503 | 0.8144 | 22 | 0.0446 | 1.2415 |

3 | −0.31118 | −3.4097 | 13 | 0.0966 | 1.4583 | 23 | 0.0070 | 0.6694 |

4 | −0.2506 | −3.4061 | 14 | 0.1284 | 2.0656 | 24 | −0.0133 | 0.0627 |

5 | −0.1235 | −2.7931 | 15 | 0.2066 | 3.2812 | 25 | −0.0857 | −1.2237 |

6 | −0.0887 | −2.0787 | 16 | 0.3252 | 4.9266 | 26 | −0.1088 | −1.6881 |

7 | −0.0569 | −1.6138 | 17 | 0.4439 | 6.7145 | 27 | −0.1754 | −2.7962 |

8 | −0.0395 | −1.1853 | 18 | 0.3741 | 6.7028 | 28 | −0.2188 | −3.3261 |

9 | −0.0134 | −0.7208 | 19 | 0.2126 | 4.4432 | |||

10 | 0.0096 | −0.2920 | 20 | 0.1692 | 3.6708 |

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**MDPI and ACS Style**

Tu, F.; Hu, S.; Zhuang, Y.; Lv, J.; Wang, Y.; Sun, Z.
Hysteresis Curve Fitting Optimization of Magnetic Controlled Shape Memory Alloy Actuator. *Actuators* **2016**, *5*, 25.
https://doi.org/10.3390/act5040025

**AMA Style**

Tu F, Hu S, Zhuang Y, Lv J, Wang Y, Sun Z.
Hysteresis Curve Fitting Optimization of Magnetic Controlled Shape Memory Alloy Actuator. *Actuators*. 2016; 5(4):25.
https://doi.org/10.3390/act5040025

**Chicago/Turabian Style**

Tu, Fuquan, Shengmou Hu, Yuhang Zhuang, Jie Lv, Yunxue Wang, and Zhe Sun.
2016. "Hysteresis Curve Fitting Optimization of Magnetic Controlled Shape Memory Alloy Actuator" *Actuators* 5, no. 4: 25.
https://doi.org/10.3390/act5040025