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Due to their small size, low weight, low cost and low energy consumption, MEMS accelerometers have achieved great commercial success in recent decades. The aim of this research work is to identify a MEMS accelerometer structure for human body dynamics measurements. Photogrammetry was used in order to measure possible maximum accelerations of human body parts and the bandwidth of the digital acceleration signal. As the primary structure the capacitive accelerometer configuration is chosen in such a way that sensing part measures on all three axes as it is 3D accelerometer and sensitivity on each axis is equal. Hill climbing optimization was used to find the structure parameters. Proof-mass displacements were simulated for all the acceleration range that was given by the optimization problem constraints. The final model was constructed in Comsol Multiphysics. Eigenfrequencies were calculated and model's response was found, when vibration stand displacement data was fed into the model as the base excitation law. Model output comparison with experimental data was conducted for all excitation frequencies used during the experiments.

A new technology usually begins with experimentation. Anything that is ever built must be designed first. This is immediately followed by modeling as one wants to know how well the device works before it is built so that expensive experimentation can be reduced. Modeling techniques and tools enable analysis of an existing design. The design itself is largely dependent on the experience, expertise and the creativity of the designer. Optimal synthesis techniques have the potential to reduce this reliance on the human designer by automatically generating designs matching user-specified requirements [

The availability of a system capable of automatically classifying the physical activity performed by a human subject is extremely attractive for many applications in the field of healthcare monitoring and in developing advanced human-machine interfaces. The information on the human physical activity is valuable in the long-term assessment of biomechanical parameters and physiological variables. Serious estimation errors may occur when wearable sensor systems composed of motion sensors, such as accelerometers, are used without any regard to what the subject is actually doing [

In order to define digital acceleration signal characteristics and guidelines for the hardware selection and safe filtering thresholds to be used, body acceleration signals analysis must be performed in order to identify possible maximum accelerations and signal bandwidth. Such an analysis can only be performed with quantitative analysis methods such as photogrammetry, which allows precise and reliable measurements from images [

Residual analysis was performed for every data set in the given bandwidth of 20 Hz by employing the MATLAB routine that was developed. During residual analysis error _{f}_{i}_{i}

Values of _{f}_{f}

The differentiator filter was applied twice to obtain accelerations for every marker that was tracked. Maximum accelerations observed during experiments are given in

According to Qu

It is common for the MEMS accelerometer to have its sensing part fit into area of ∼1 mm^{2}[^{2}. It is also common to use silicon as the primary material in the manufacturing process [

To investigate the applicability of the optimization technique for identification of MEMS accelerometer structure parameters, the accelerometer (

Requirement of model's sensitivity equality can be defined as follows:

Error function can be defined as:

Here _{m}

Optimization problem that is to be solved in respect of accelerometer beam cross section height and mass density of proof-mass material:
_{m}

Defined optimization problem has following constraints:

These constraints come both from requirements described earlier as well as real world conditions:

^{2} in both directions on any axis because it's common for industrial accelerometers to have measurement range of ±16 g;

^{−4}) : beam cross section height constraint that corresponds to real world manufacturing process;

^{4}) : mass density of proof-mass material constraint.

The width ^{2}.

The problem in

The constraints become:

_{z}_{y}_{z}_{a}^{−5} m, ^{3}. Error function minimum (^{3} also yielding the minimal error function value of 5.06 × 10^{−10} m. The material with nearest value of mass density is copper (Cu), with ^{3}, therefore copper was chosen as proof-mass material. Final model properties are given below in

Material model is isotropic. Silicon (Si) has Young's modulus of 170 GPa, Poisson ration of 0.28 and density of 2,329 kg/m^{3}. Copper (Cu) has Young's modulus of 120 GPa, Poisson ratio of 0.34 and density of 8,960 kg/m^{3}.

The final model (^{2} was applied to the model the displacement in z direction was 50.49 nm (

Displacement in the x direction differs by 0.090% from the displacement in the z direction and by 0.006% from the displacement in the y direction while displacement in the y direction differs by 0.092%. These results clearly show that equal sensitivity on all axes is achieved in the model.

Experimental data that was acquired by monitoring uniaxial vibration stand movement was used to validate the accelerometer model. Vibration stand displacement data was fed into the model as the base excitation law and model's response was observed. Accelerations that were acquired from the model output were compared with vibration stand accelerations during experiment to see how well the model fits real world process.

Proof-mass displacements were analyzed for all acceleration ranges given by the optimization problem constraints (4). Results show that dependence between displacement and acceleration is linear, it means that acceleration conversion into digital signal is possible by measuring the capacitance between two plates where one is on the bounding box and other is on the proof mass. Electrical capacity between two plates is inversely related to the distance between plates and linearly depends on the area of overlap between these plates. Model output comparison with experimental data was conducted for all excitation frequencies that were used during experiment.

The given results show that the model fits the experimental data quite well. Although relative errors go a little over 9% of the acceleration amplitude, absolute errors does not exceed 0.12 m/s^{2}. This shows that the model is valid and stable throughout the bandwidth of 20 Hz.

An accelerometer model was identified and validated. Silicon was used for L-shaped beams, copper for proof-mass. Overall top size was 1.23 mm^{2}. L-shaped beam cross section size was 4 × 8.25 μm, proof mass size was 100 × 100 × 100 μm. It was shown that the model has first resonant frequencies (over 2,200 Hz) far from the bandwidth of interest (20 Hz). The model achieves equal sensitivity in all directions. Displacement in the x direction differed by 0.090% from displacement in the z direction and by 0.006% from displacement in the y direction when an acceleration of 10 m/s^{2} was applied to the accelerometer. Displacement in the y direction differed by 0.092% from displacement in the z direction. Validation of the model showed that in a frequency range up to 20 Hz modeled accelerations were up to 10% different from measured values with the absolute error being less than 0.12 m/s^{2}.

High technology project funded by Lithuanian Agency for Science, Innovation and Technology “Development of the Sensor System Technology to Monitor Human Physiological Data Employing MEMS, IT and Smart Textiles Technologies”.

The authors declare no conflicts of interest.

Set of locations to be tracked on the human body during experiments.

Computational scheme of MEMS accelerometer.

Final accelerometer model geometry.

Displacements field in the z direction when 10 m/s^{2} acceleration is applied along the z axis.

Displacement field in y direction when 10 m/s^{2} acceleration is applied along the y axis.

Displacement field in x direction when 10 m/s^{2} acceleration is applied along the x axis.

Residual analysis results for walking/running task data samples.

Chest | 10 |

Back | 10 |

Right biceps | 11 |

Left biceps | 11 |

Left hip | 11 |

Right hip | 10 |

Left wrist | 10 |

Right wrist | 10 |

Left thigh | 16 |

Right thigh | 16 |

Left tarsus | 16 |

Right tarsus | 16 |

Maximum accelerations observed in three directions.

_{x}|), m/s^{2} |
_{y}|), m/s^{2} |
_{z}|), m/s^{2} | |
---|---|---|---|

Chest | 15.879 | 38.277 | 35.708 |

Back | 22.437 | 38.587 | 18.750 |

Biceps | 23.812 | 19.476 | 39.375 |

Hip | 28.145 | 37.636 | 45.645 |

Wrist | 31.656 | 32.347 | 71.700 |

Thigh | 35.736 | 36.232 | 39.749 |

Tarsus | 66.873 | 24.016 | 56.383 |

Initial accelerometer model properties.

Material | Si |

Overall size (top) | 1 mm^{2} |

L-shaped beam cross section size | 50 × 50 μm |

Proof mass size | 100 × 100 μm |

Final accelerometer model properties.

L-shaped beam material | Si |

Proof mass material | Cu |

Overall size (top) | 1.23 mm^{2} |

L-shaped beam cross section size | 4 × 8.25 μm |

Proof mass size | 100 × 100 × 100 μm |

Accelerometer model eigenfrequencies.

In x direction | 2,238.81 |

In y direction | 2,239.11 |

In z direction | 2,244.52 |

Accelerometer's model output comparison with vibration stand accelerations.

^{2} |
^{2} |
^{2}| | |||
---|---|---|---|---|---|

1 | 0.8813 | 0.3480 | 0.3169 | 9.82% | 0.0311 |

4 | 0.9517 | 0.6772 | 0.6296 | 7.56% | 0.0476 |

7 | 0.9510 | 1.8397 | 1.7461 | 5.36% | 0.0936 |

10 | 1.0822 | 4.2725 | 4.1853 | 2.08% | 0.0872 |

14 | 1.0335 | 7.9967 | 7.8770 | 1.52% | 0.1197 |

17 | 0.9891 | 11.2849 | 11.1665 | 1.06% | 0.1184 |

20 | 0.9241 | 14.5920 | 14.4876 | 0.72% | 0.1044 |