# Multiobjective Optimization of Structure and Robustness of a Split Parallel Multicomponent Strain Sensor

Authors: Peng Kong; Xiaoqiang Peng; Zhenzeng Lian
Journal: Wireless Communications and Mobile Computing
 (2022)

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## Abstract

A novel split parallel multicomponent strain sensor structure layout is proposed based on the special requirements of the helicopter rotor airfoil wind tunnel test for measuring aerodynamic sensors. The sensor consists of two splits with the same configuration; the performance of the sensor not only depends on the split structure of the sensor but also depends on the assembly relationship between the splits. Three steps have been performed so as to enhance the technical performance of the sensor. First, the RBF neural network approximate model and the second-generation nondominated sorting genetic algorithm are used to optimize the split of sensor deterministically; secondly, the rotor airfoil wind tunnel test model and the sensor finite element system model are established, and the6σ robustness analysis is carried out; finally, the 6σ robust multiobjective optimization has been carried out considering the sensor split processing errors and the assembly errors. The results show that, compared to initial designed sensors, the sensitivity of the three components of the sensor is increased by 285.46%, 284.95%, and 151.5%, respectively, and the maximum equivalent stress is reduced by 28.4%; the interference to the three components is reduced by 97.82%, 92.83%, and 99.8%, respectively, and the quality is reduced by 25.74%. Meanwhile, the quality level of the sensor was promoted, and the sensitivity of the response to assembly and manufacturing errors were reduced. These results exhibit that the structural layout, optimized path, and method in this strain sensor are suitable for the needs of helicopter rotor airfoil wind tunnel test.


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## Body

## 1. Introduction

Helicopter rotor dynamic stall is a serious unsteady aerodynamic phenomenon with complex mechanisms, especially the airfoil dynamic stall. Hence, in-depth understanding of the rotor airfoil dynamic stall characteristics is of great importance to investigate the ways to improve rotor performance, predict the rotor aerodynamics more accurately, and thereby promote the development of advanced helicopters.The wind tunnel test is the main means to understand the dynamic stall characteristics and flow mechanism of the rotor blade airfoil recently. It is necessary to develop a multicomponent strain-type force sensor to support the model through the left and right sides in parallel and accurately measure the model resistance, lift, and pitch moments during the wind tunnel test of the helicopter rotor airfoil.While in the conventional wind tunnel test, the aircraft model, sensors, and supporting test device are connected in series and connected at a single point, whose precision and accuracy are mainly rely on the performance of the sensor, that is, the sensor’s own sensitivity, stiffness, strength, and mutual interference between components [1–4].Therefore, a novel split parallel multicomponent strain sensor structure layout is proposed consisting of two components, A and B, to meet the needs of the rotor-wing wind tunnel test, on the basis of conventional three-piece beam load cells. A and B are three-component strain sensors with the same configuration, supporting the rotor airfoil wind tunnel test model from both sides in parallel to complete the model aerodynamics and torque measurement. The development of the sensor must consider not only the sensitivity, stiffness, strength, and mutual interference between the components but also the impact of assembly errors between the A and B components on the overall performance of the sensor.The following design and optimization approaches are proposed to improve the sensor split and its overall technical performance. Firstly, a finite element analysis model is established with the sensor split as the object to analyze separately its strain under the action of resistance, lift, and pitch moment cloud map and to determine the location of strain gauges and the way of group bridges; secondly, the RBF neural network approximate model and NSGA-II multiobjective optimization algorithm are utilized to deterministically optimize the sensor split performance and obtain the Pareto optimal solution and excellent monomer performance [5]; thirdly, a finite element system model of the rotor airfoil wind tunnel test model and sensor was established. Based on the RSM response surface approximation model and the Monte Carlo simulation technology, the quality level of the system was tested, and the robustness optimization technology was introduced to improve the robustness of the sensor.


## 2. Materials and Methods

### 2.1. Geometry

The geometry and main parameters of the sensor splits are shown in Figures1 and 2. The left and right ends of the split use single-piece beam-type elastic elements (serial number 1) of the same geometric size to bear resistance FX. The length, width, and height of the single-piece beam-type elastic elements are expressed as L2, B3, and H3; the middle of the split body is a three-beam elastic element; the middle main beam (serial number 2) of the three-beam elastic element bears the lift force Fy; the front and rear side beams (serial number 3) bear the pitching moment MZ; the length, width, and height of the middle main beam are expressed as L1, B1, and H1; the front and rear side beams have the same geometric dimensions, and their length, width, and height are, respectively, L1, B2, and H2; the thickness of the front and rear flange sensors is S2; and the thickness of the middle flange S1 plays the role of connection.Figure 1
The geometric structure of the sensor split.Figure 2
The main geometric parameters of the sensor split.Each measurement of the elastic element of this layout is independent of the load measurement, that is, it is sensitive to the load of the measured component and insensitive to the load of other components, so it is easy to obtain the required sensitivity and less mutual interference.


### 2.2. Key Technical Requirements

The split structure of the sensor requires high sensitivity, sufficient strength, rigidity, and small interference between the components.Sensitivity is an important factor of sensor design which can be improved for the strain-type force sensor by increasing the design strain value of the measuring element. And the design strain value of the general wind tunnel sensor is selected ranging 300~600με [6].Sufficient strength under the maximum external load is necessary to ensure the safety of the wind tunnel test. The rotor airfoil wind tunnel test’s heave motion frequency can reach 5, while the first-order natural frequency of the system composed of strain-type force sensor and rotor airfoil wind tunnel test model must be 10 times than its motion frequency [7].In the structural design, due to mutual interference between the components, it is necessary to allocate the stiffness reasonably to ensure proper deformation in the load direction of the measured component and reduce its deformation in other components. Generally, the amount of interference between the components of the strain sensor should be controlled below 10% [6].


### 2.3. Analysis of Split Finite Element Model

#### 2.3.1. Geometry Simplification

The original structure of the model is simplified, especially some local details without affecting the calculation accuracy of the device. These simplifications will not affect the overall analysis results of the original structure but can significantly improve the speed and quality of the finite element analysis and sometimes improve the accuracy and reliability of calculation results.


#### 2.3.2. Meshing

In order to ensure the accuracy of the calculation results, second-order grid elements are used. In order to reasonably arrange the density of the grid, the dimensional functions proximity and curvature are used. The mesh is refined in the place where the stress gradient is large. The quality of the grid has a greater impact on the calculation accuracy. Through the finite element-preprocessing software, the mesh quality is checked and modified until the finite element model fully meets the high-precision requirements. In actual calculations, the calculation results of two different mesh densities are compared. If the calculation results are very different, you can continue to increase the grid until the calculation results are not much different and the grid size is appropriate.


#### 2.3.3. Definition of Material Properties and Boundary Conditions

The material used in the design is with elastic modulusE=200GPa and yield strength σS=2020MPa. According to the impact factor nc=1.5 and safety factor na=2 selected in [8], the allowable stress can be obtained σ=673MPa.The following loads were applied for static calculations: (1) maximum resistanceFX, (2) maximum lift Fy, (3) maximum pitch moment MZ, (4) maximum lateral force Fz, (5) maximum yaw moment My, (6) maximum roll moment Mx, and (7) maximum load of six components under test conditions.


#### 2.3.4. Static Analysis and Results

Figures3–5 are the strain cloud diagrams of strains under the action of maximum resistance FX, maximum lift Fy, and maximum pitch moment MZ, as well as the distribution diagrams along DC⟶, BA⟶, EF⟶, and HG⟶, respectively. It can be seen from the figure that the maximum strain is close to the endpoint of the elastic measuring element, the best choices for strain gauges, and the maximum strain values at each position are 175.63 με, 249.57 με, and 113.38 με, which cannot meet the sensitivity requirements.Figure 3
Strain cloud diagram and strain distribution of maximum resistance.Figure 4
Strain cloud diagram and strain distribution of maximum lift.Figure 5
Strain cloud diagram and strain distribution of maximum pitching moment.From Figure6, the maximum equivalent stress value of the model is σr=575MPa, which is less than the allowable stress of the material.Figure 6
Strain cloud diagram of maximum load.


#### 2.3.5. Modal Analysis and Results

In terms of resonance, all the modes whose natural frequency is in the range of the external load frequency should be maintained, and it must be calculated to be more than 10 times the operating frequency in this study. Therefore, the first 4 natural frequencies were selected to verify if they are in the resonance zone. The change of the first 4th-order mode shape of splitting is shown in Figure7, and the natural frequency of each order is shown in Table 1.Figure 7
The shape of the first 4th-order splitting mode.Table 1
Result of mode analysis.
Mode1234Frequency202.01670.71761.671197.9


### 2.4. Strain Gauge Position and Group Bridge

According to the strain cloud diagram and strain value distribution diagram [9–11], the installation position of the strain gauge is determined by comprehensively considering the paste technique and sensitivity requirements of the strain gauge. Wheatstone bridge was designed reasonably to achieve the largest possible output for the measured component [8] and the smallest possible output signal for other components, as well as achieve the electrical decomposition of force and torque. The final distribution of strain gauges and bridge formation are shown in Figures 8 and 9.Figure 8
Layout of strain gauges.Figure 9
Wheatstone bridge diagram of each component.


## 2.1. Geometry

The geometry and main parameters of the sensor splits are shown in Figures1 and 2. The left and right ends of the split use single-piece beam-type elastic elements (serial number 1) of the same geometric size to bear resistance FX. The length, width, and height of the single-piece beam-type elastic elements are expressed as L2, B3, and H3; the middle of the split body is a three-beam elastic element; the middle main beam (serial number 2) of the three-beam elastic element bears the lift force Fy; the front and rear side beams (serial number 3) bear the pitching moment MZ; the length, width, and height of the middle main beam are expressed as L1, B1, and H1; the front and rear side beams have the same geometric dimensions, and their length, width, and height are, respectively, L1, B2, and H2; the thickness of the front and rear flange sensors is S2; and the thickness of the middle flange S1 plays the role of connection.Figure 1
The geometric structure of the sensor split.Figure 2
The main geometric parameters of the sensor split.Each measurement of the elastic element of this layout is independent of the load measurement, that is, it is sensitive to the load of the measured component and insensitive to the load of other components, so it is easy to obtain the required sensitivity and less mutual interference.


## 2.2. Key Technical Requirements

The split structure of the sensor requires high sensitivity, sufficient strength, rigidity, and small interference between the components.Sensitivity is an important factor of sensor design which can be improved for the strain-type force sensor by increasing the design strain value of the measuring element. And the design strain value of the general wind tunnel sensor is selected ranging 300~600με [6].Sufficient strength under the maximum external load is necessary to ensure the safety of the wind tunnel test. The rotor airfoil wind tunnel test’s heave motion frequency can reach 5, while the first-order natural frequency of the system composed of strain-type force sensor and rotor airfoil wind tunnel test model must be 10 times than its motion frequency [7].In the structural design, due to mutual interference between the components, it is necessary to allocate the stiffness reasonably to ensure proper deformation in the load direction of the measured component and reduce its deformation in other components. Generally, the amount of interference between the components of the strain sensor should be controlled below 10% [6].


## 2.3. Analysis of Split Finite Element Model

### 2.3.1. Geometry Simplification

The original structure of the model is simplified, especially some local details without affecting the calculation accuracy of the device. These simplifications will not affect the overall analysis results of the original structure but can significantly improve the speed and quality of the finite element analysis and sometimes improve the accuracy and reliability of calculation results.


### 2.3.2. Meshing

In order to ensure the accuracy of the calculation results, second-order grid elements are used. In order to reasonably arrange the density of the grid, the dimensional functions proximity and curvature are used. The mesh is refined in the place where the stress gradient is large. The quality of the grid has a greater impact on the calculation accuracy. Through the finite element-preprocessing software, the mesh quality is checked and modified until the finite element model fully meets the high-precision requirements. In actual calculations, the calculation results of two different mesh densities are compared. If the calculation results are very different, you can continue to increase the grid until the calculation results are not much different and the grid size is appropriate.


### 2.3.3. Definition of Material Properties and Boundary Conditions

The material used in the design is with elastic modulusE=200GPa and yield strength σS=2020MPa. According to the impact factor nc=1.5 and safety factor na=2 selected in [8], the allowable stress can be obtained σ=673MPa.The following loads were applied for static calculations: (1) maximum resistanceFX, (2) maximum lift Fy, (3) maximum pitch moment MZ, (4) maximum lateral force Fz, (5) maximum yaw moment My, (6) maximum roll moment Mx, and (7) maximum load of six components under test conditions.


### 2.3.4. Static Analysis and Results

Figures3–5 are the strain cloud diagrams of strains under the action of maximum resistance FX, maximum lift Fy, and maximum pitch moment MZ, as well as the distribution diagrams along DC⟶, BA⟶, EF⟶, and HG⟶, respectively. It can be seen from the figure that the maximum strain is close to the endpoint of the elastic measuring element, the best choices for strain gauges, and the maximum strain values at each position are 175.63 με, 249.57 με, and 113.38 με, which cannot meet the sensitivity requirements.Figure 3
Strain cloud diagram and strain distribution of maximum resistance.Figure 4
Strain cloud diagram and strain distribution of maximum lift.Figure 5
Strain cloud diagram and strain distribution of maximum pitching moment.From Figure6, the maximum equivalent stress value of the model is σr=575MPa, which is less than the allowable stress of the material.Figure 6
Strain cloud diagram of maximum load.


### 2.3.5. Modal Analysis and Results

In terms of resonance, all the modes whose natural frequency is in the range of the external load frequency should be maintained, and it must be calculated to be more than 10 times the operating frequency in this study. Therefore, the first 4 natural frequencies were selected to verify if they are in the resonance zone. The change of the first 4th-order mode shape of splitting is shown in Figure7, and the natural frequency of each order is shown in Table 1.Figure 7
The shape of the first 4th-order splitting mode.Table 1
Result of mode analysis.
Mode1234Frequency202.01670.71761.671197.9


## 2.3.1. Geometry Simplification

The original structure of the model is simplified, especially some local details without affecting the calculation accuracy of the device. These simplifications will not affect the overall analysis results of the original structure but can significantly improve the speed and quality of the finite element analysis and sometimes improve the accuracy and reliability of calculation results.


## 2.3.2. Meshing

In order to ensure the accuracy of the calculation results, second-order grid elements are used. In order to reasonably arrange the density of the grid, the dimensional functions proximity and curvature are used. The mesh is refined in the place where the stress gradient is large. The quality of the grid has a greater impact on the calculation accuracy. Through the finite element-preprocessing software, the mesh quality is checked and modified until the finite element model fully meets the high-precision requirements. In actual calculations, the calculation results of two different mesh densities are compared. If the calculation results are very different, you can continue to increase the grid until the calculation results are not much different and the grid size is appropriate.


## 2.3.3. Definition of Material Properties and Boundary Conditions

The material used in the design is with elastic modulusE=200GPa and yield strength σS=2020MPa. According to the impact factor nc=1.5 and safety factor na=2 selected in [8], the allowable stress can be obtained σ=673MPa.The following loads were applied for static calculations: (1) maximum resistanceFX, (2) maximum lift Fy, (3) maximum pitch moment MZ, (4) maximum lateral force Fz, (5) maximum yaw moment My, (6) maximum roll moment Mx, and (7) maximum load of six components under test conditions.


## 2.3.4. Static Analysis and Results

Figures3–5 are the strain cloud diagrams of strains under the action of maximum resistance FX, maximum lift Fy, and maximum pitch moment MZ, as well as the distribution diagrams along DC⟶, BA⟶, EF⟶, and HG⟶, respectively. It can be seen from the figure that the maximum strain is close to the endpoint of the elastic measuring element, the best choices for strain gauges, and the maximum strain values at each position are 175.63 με, 249.57 με, and 113.38 με, which cannot meet the sensitivity requirements.Figure 3
Strain cloud diagram and strain distribution of maximum resistance.Figure 4
Strain cloud diagram and strain distribution of maximum lift.Figure 5
Strain cloud diagram and strain distribution of maximum pitching moment.From Figure6, the maximum equivalent stress value of the model is σr=575MPa, which is less than the allowable stress of the material.Figure 6
Strain cloud diagram of maximum load.


## 2.3.5. Modal Analysis and Results

In terms of resonance, all the modes whose natural frequency is in the range of the external load frequency should be maintained, and it must be calculated to be more than 10 times the operating frequency in this study. Therefore, the first 4 natural frequencies were selected to verify if they are in the resonance zone. The change of the first 4th-order mode shape of splitting is shown in Figure7, and the natural frequency of each order is shown in Table 1.Figure 7
The shape of the first 4th-order splitting mode.Table 1
Result of mode analysis.
Mode1234Frequency202.01670.71761.671197.9


## 2.4. Strain Gauge Position and Group Bridge

According to the strain cloud diagram and strain value distribution diagram [9–11], the installation position of the strain gauge is determined by comprehensively considering the paste technique and sensitivity requirements of the strain gauge. Wheatstone bridge was designed reasonably to achieve the largest possible output for the measured component [8] and the smallest possible output signal for other components, as well as achieve the electrical decomposition of force and torque. The final distribution of strain gauges and bridge formation are shown in Figures 8 and 9.Figure 8
Layout of strain gauges.Figure 9
Wheatstone bridge diagram of each component.


## 3. Optimized Design of Sensor Split Structure

Parameter optimization is needed as the finite element analysis of the initial design of the sensor split proved that it cannot meet the sensitivity requirements. Appropriate design variables and output responses for experimental design were selected, and a sufficient number of finite element analysis sample points were generated to fit the approximate model; the optimization problem was defined, and the sensor parameters were optimized based on the NSGA-II multiobjective optimization algorithm.


### 3.1. Approximate Model and Verification

The RBF neural network approximate model is used in simulating the input-output relationship of the finite element model to solve the problem of huge time cost during calculation. The establishment of approximate models mainly is as follows:(1)
The input parameters were defined asxi (xi are the geometric parameters B1, B2, B3, H1, H2, H3, L1, L2, S1, S2, and P, 1≤i≤11,i∈N) with a total of 11 input variables whose initial value and range of values are shown in Table 2(2)
The output parameters were defined asyj, with the maximum equivalent stress smax and the maximum deformation displacement value dmax under the maximum load of six components under test conditions, first-order natural frequency freq1; the average strain values (εxx1∼εxx8, εxy1∼εxy8, εxz1∼εxz8, εxmx1∼εxmx8, εxmy1∼εxmy8, and εxmz1∼εxmz8) of strain gauges 1-8 are under maximum resistance FX, maximum lift Fy, maximum lateral force Fz, maximum roll moment Mx, maximum yaw moment My, and maximum pitch moment MZ; average strain values (εyx1∼εyx8, εyy1∼εyy8, εyz1∼εyz8, εymx1∼εymx8, εymy1∼εymy8, and εymz1∼εymz8) of strain gauges 9-16 are under maximum resistance FX, maximum lift Fy, maximum lateral force Fz, maximum roll moment Mx, maximum yaw moment My, and maximum pitch moment MZ; average strain values (εmzx1∼εmzx8, εmzy1∼εmzy8, εmzz1∼εmzz8, εmzmx1∼εmzmx8, εmzmy1∼εmzmy8, are εmzmz1∼εmzmz8) of the serial number 17-24 strain gauges are under maximum resistance FX, maximum lift Fy, maximum lateral force Fz, maximum roll moment Mx, maximum yaw moment My, and maximum pitch moment MZ. A total of 148 output responses are set as output parameters(3)
The optimal Latin hypercube test design method was used to obtain a sufficient number of sample points, and an approximate model of RBF neural network was established(4)
The cross-validation method was used to detect the accuracy of the approximate model. If the accuracy is insufficient, the approximate point is added to increase the approximate model to a sufficient accuracyTable 2
Design parameters and value range.
ParametersLower boundValueUpper boundB151010B2488B351215H1254045H2203040H3506080L1204060L2103040S151515S212.52022.5P303450The credibility indexR2 was utilized as the evaluation index to detect the global and local approximation accuracy of the approximation model with a lower limit of 0.9. The closer the R2 to 1, the more accurate.From the approximate model error calculation results (shown in Table3), it can be seen that the radial basis neural network approximate model exhibits good performance in fitting the sensor split finite element model.Table 3
The error calculation results of an approximate model.
IndexR2IndexR2IndexR2smax0.93εxmy1∼εxmy80.94~0.95εmzx1∼εzx80.97~0.98dmax0.95εxmz1∼εxmz80.93~0.94εmzy1∼εmzy80.91~0.92freq10.988εyx1∼εyx80.97~0.98εmzz1∼εmzz80.97~0.98mass1εyy1∼εyy80.97~0.98εmzmx1∼εmzmx80.97~0.98εxx1∼εxx80.94~0.95εyz1∼εyz80.96~0.97εmzmy1∼εmzmy80.94~0.95εxy1∼εxy80.97~0.98εymx1∼εymx80.94~0.95εmzmz1∼εmzmz80.97~0.98εxz1∼εxz80.94~0.95εymy1∼εymy80.94~0.96εxmx1∼εxmx80.96~0.97εymz1∼εymz80.96~0.97


### 3.2. Multiobjective Optimization

Taking the input parametersxi of the above approximate model as the design variables, the average strain value ε1∼ε24 as the constraint, the minimizing of maximum equivalent stress smax, the maximum displacement value dmax, the maximizing of first-order natural frequency freq1, and the minimizing of interference ηx, ηy, and ηmz of the components of FX, Fy, and MZ are the goal of optimizing. Then, the optimization problem was defined as below [12–15].
(1)Minimize:dmax,MassMinimize:ηx,ηy,ηMzMinimize:sMaxMaximize:freq1s.t300μm≤εj≤600μm,j∈1,24&&j∈NsMax≤673MPaD.v.xiL≤xi≤xiUi∈1,11&&i∈N.According to the principle of Wheatstone bridge, for resistance bridge, whenR≫△R(2)Uo=UiK8ε1+ε2−ε3−ε4+ε5+ε6−ε7−ε8,where Uo is the output voltage of the bridge, Ui is the supply voltage of the bridge, and K is the sensitivity coefficient of the strain gauge.When the sensor is under the maximum load of each component, the output voltage of the resistance bridge is(3)Uoxx=UiK8εxx1+εxx2−εxx3−εxx4+εxx5+εxx6−εxx7−εxx8,Uoxy=UiK8εxy1+εxy2−εxy3−εxy4+εxy5+εxy6−εxy7−εxy8,Uoxz=UiK8εxz1+εxz2−εxz3−εxz4+εxz5+εxz6−εxz7−εxz8,Uoxmx=UiK8εxmx1+εxmx2−εxmx3−εxmx4+εxmx5+εxmx6−εxmx7−εxmx8,Uoxmy=UiK8εxmy1+εxmy2−εxmy3−εxmy4+εxmy5+εxmy6−εxmy7−εxmy8,Uoxmz=UiK8εxmz1+εxmz2−εxmz3−εxmz4+εxmz5+εxmz6−εxmz7−εxmz8,ηxy=absUoxy/Uoxx,ηxz=absUoxz/Uoxx,ηxmx=absUoxmx/Uoxx,ηxmy=absUoxmy/Uoxx,ηxmz=absUoxmz/Uoxx,ηx=ηxy+ηxz+ηxmx+ηxmy+ηxmz.ηyx, ηyz, ηymx, ηymy, ηymz, ηy, ηmzx, ηmzy, ηmzz, ηmzmx, ηmzmy, and ηmz can be obtained based on the same process.Based on the established RBF neural network approximate model, the Pareto optimal solution (shown in Figure10) was obtained by using the NSGA-II optimization algorithm after repeated experiments with a population size of 100, a cross-distribution index of 100, and a cross-probability of 0.9 in 6001 calculation steps.Figure 10
Pareto optimal solution.After sorting the above solution sets, the 1896th is determined to be the optimal solution whose comparative analysis of the results is shown in Table4.Table 4
Optimization results.
Optimization goalInitial value (mm)Optimization value (mm)Percent changedsmax575652.3313.45%dmax0.74130.5399-27.17%freq1 (Hz)202.49212.6285%Mass0.00470.0033828.1%εx81.6302.6271%εy115.1585.19408%εMz167.7548.6222%ηx4.26%0.214%-95.0%ηy0.6125%0.034%-94.4%ηmz5.12%0.098%-98.1%In initial design, the initial interferenceηx on the resistance FX and the interference on the pitching moment MZ are relatively large, reaching 4.26% and 5.12%, respectively; the strain values under the action of the maximum resistance FX, the maximum lift Fy, and the maximum pitching moment MZ are 81.6 με, 115.1 με, and 167.7 με, respectively, which cannot meet the technical requirements of the sensor split. After optimization, the strain values under the action of the maximum resistance FX, the maximum lift Fy, and the maximum pitching moment MZ are increased by 271%, 408%, and 227%, respectively, and the interference of the component is reduced by 95%, 94.4%, and 98.1%; the first-order natural frequency is increased by 5%, and the quality is reduced by 28.1%.


## 3.1. Approximate Model and Verification

The RBF neural network approximate model is used in simulating the input-output relationship of the finite element model to solve the problem of huge time cost during calculation. The establishment of approximate models mainly is as follows:(1)
The input parameters were defined asxi (xi are the geometric parameters B1, B2, B3, H1, H2, H3, L1, L2, S1, S2, and P, 1≤i≤11,i∈N) with a total of 11 input variables whose initial value and range of values are shown in Table 2(2)
The output parameters were defined asyj, with the maximum equivalent stress smax and the maximum deformation displacement value dmax under the maximum load of six components under test conditions, first-order natural frequency freq1; the average strain values (εxx1∼εxx8, εxy1∼εxy8, εxz1∼εxz8, εxmx1∼εxmx8, εxmy1∼εxmy8, and εxmz1∼εxmz8) of strain gauges 1-8 are under maximum resistance FX, maximum lift Fy, maximum lateral force Fz, maximum roll moment Mx, maximum yaw moment My, and maximum pitch moment MZ; average strain values (εyx1∼εyx8, εyy1∼εyy8, εyz1∼εyz8, εymx1∼εymx8, εymy1∼εymy8, and εymz1∼εymz8) of strain gauges 9-16 are under maximum resistance FX, maximum lift Fy, maximum lateral force Fz, maximum roll moment Mx, maximum yaw moment My, and maximum pitch moment MZ; average strain values (εmzx1∼εmzx8, εmzy1∼εmzy8, εmzz1∼εmzz8, εmzmx1∼εmzmx8, εmzmy1∼εmzmy8, are εmzmz1∼εmzmz8) of the serial number 17-24 strain gauges are under maximum resistance FX, maximum lift Fy, maximum lateral force Fz, maximum roll moment Mx, maximum yaw moment My, and maximum pitch moment MZ. A total of 148 output responses are set as output parameters(3)
The optimal Latin hypercube test design method was used to obtain a sufficient number of sample points, and an approximate model of RBF neural network was established(4)
The cross-validation method was used to detect the accuracy of the approximate model. If the accuracy is insufficient, the approximate point is added to increase the approximate model to a sufficient accuracyTable 2
Design parameters and value range.
ParametersLower boundValueUpper boundB151010B2488B351215H1254045H2203040H3506080L1204060L2103040S151515S212.52022.5P303450The credibility indexR2 was utilized as the evaluation index to detect the global and local approximation accuracy of the approximation model with a lower limit of 0.9. The closer the R2 to 1, the more accurate.From the approximate model error calculation results (shown in Table3), it can be seen that the radial basis neural network approximate model exhibits good performance in fitting the sensor split finite element model.Table 3
The error calculation results of an approximate model.
IndexR2IndexR2IndexR2smax0.93εxmy1∼εxmy80.94~0.95εmzx1∼εzx80.97~0.98dmax0.95εxmz1∼εxmz80.93~0.94εmzy1∼εmzy80.91~0.92freq10.988εyx1∼εyx80.97~0.98εmzz1∼εmzz80.97~0.98mass1εyy1∼εyy80.97~0.98εmzmx1∼εmzmx80.97~0.98εxx1∼εxx80.94~0.95εyz1∼εyz80.96~0.97εmzmy1∼εmzmy80.94~0.95εxy1∼εxy80.97~0.98εymx1∼εymx80.94~0.95εmzmz1∼εmzmz80.97~0.98εxz1∼εxz80.94~0.95εymy1∼εymy80.94~0.96εxmx1∼εxmx80.96~0.97εymz1∼εymz80.96~0.97


## 3.2. Multiobjective Optimization

Taking the input parametersxi of the above approximate model as the design variables, the average strain value ε1∼ε24 as the constraint, the minimizing of maximum equivalent stress smax, the maximum displacement value dmax, the maximizing of first-order natural frequency freq1, and the minimizing of interference ηx, ηy, and ηmz of the components of FX, Fy, and MZ are the goal of optimizing. Then, the optimization problem was defined as below [12–15].
(1)Minimize:dmax,MassMinimize:ηx,ηy,ηMzMinimize:sMaxMaximize:freq1s.t300μm≤εj≤600μm,j∈1,24&&j∈NsMax≤673MPaD.v.xiL≤xi≤xiUi∈1,11&&i∈N.According to the principle of Wheatstone bridge, for resistance bridge, whenR≫△R(2)Uo=UiK8ε1+ε2−ε3−ε4+ε5+ε6−ε7−ε8,where Uo is the output voltage of the bridge, Ui is the supply voltage of the bridge, and K is the sensitivity coefficient of the strain gauge.When the sensor is under the maximum load of each component, the output voltage of the resistance bridge is(3)Uoxx=UiK8εxx1+εxx2−εxx3−εxx4+εxx5+εxx6−εxx7−εxx8,Uoxy=UiK8εxy1+εxy2−εxy3−εxy4+εxy5+εxy6−εxy7−εxy8,Uoxz=UiK8εxz1+εxz2−εxz3−εxz4+εxz5+εxz6−εxz7−εxz8,Uoxmx=UiK8εxmx1+εxmx2−εxmx3−εxmx4+εxmx5+εxmx6−εxmx7−εxmx8,Uoxmy=UiK8εxmy1+εxmy2−εxmy3−εxmy4+εxmy5+εxmy6−εxmy7−εxmy8,Uoxmz=UiK8εxmz1+εxmz2−εxmz3−εxmz4+εxmz5+εxmz6−εxmz7−εxmz8,ηxy=absUoxy/Uoxx,ηxz=absUoxz/Uoxx,ηxmx=absUoxmx/Uoxx,ηxmy=absUoxmy/Uoxx,ηxmz=absUoxmz/Uoxx,ηx=ηxy+ηxz+ηxmx+ηxmy+ηxmz.ηyx, ηyz, ηymx, ηymy, ηymz, ηy, ηmzx, ηmzy, ηmzz, ηmzmx, ηmzmy, and ηmz can be obtained based on the same process.Based on the established RBF neural network approximate model, the Pareto optimal solution (shown in Figure10) was obtained by using the NSGA-II optimization algorithm after repeated experiments with a population size of 100, a cross-distribution index of 100, and a cross-probability of 0.9 in 6001 calculation steps.Figure 10
Pareto optimal solution.After sorting the above solution sets, the 1896th is determined to be the optimal solution whose comparative analysis of the results is shown in Table4.Table 4
Optimization results.
Optimization goalInitial value (mm)Optimization value (mm)Percent changedsmax575652.3313.45%dmax0.74130.5399-27.17%freq1 (Hz)202.49212.6285%Mass0.00470.0033828.1%εx81.6302.6271%εy115.1585.19408%εMz167.7548.6222%ηx4.26%0.214%-95.0%ηy0.6125%0.034%-94.4%ηmz5.12%0.098%-98.1%In initial design, the initial interferenceηx on the resistance FX and the interference on the pitching moment MZ are relatively large, reaching 4.26% and 5.12%, respectively; the strain values under the action of the maximum resistance FX, the maximum lift Fy, and the maximum pitching moment MZ are 81.6 με, 115.1 με, and 167.7 με, respectively, which cannot meet the technical requirements of the sensor split. After optimization, the strain values under the action of the maximum resistance FX, the maximum lift Fy, and the maximum pitching moment MZ are increased by 271%, 408%, and 227%, respectively, and the interference of the component is reduced by 95%, 94.4%, and 98.1%; the first-order natural frequency is increased by 5%, and the quality is reduced by 28.1%.


## 4. Robustness Analysis and Optimization

Some uncertain factors, such as the processing error of the sensor split and the assembly error between the sensor splits, are inevitable to encounter during the execution of the actual rotor blade wind tunnel test project. Without considering the influence of these uncertain factors in the deterministic optimization of the sensor split, the optimization result may present lower reliability or robustness and greater technical risks in practice [16, 17].Therefore, it is necessary to further perform robust analysis and even optimization on the split parallel multicomponent strain sensor considering the interference of uncertain factors.


### 4.1. System Finite Element Model Analysis

#### 4.1.1. Geometric Model

The scheme of analysis system is shown in Figure11, consisting of main components such as front and rear beams, longitudinal beams, and skin with a total length of 1950 mm and a chord length of 300 mm. The binary model of OA309 airfoil is used in characterizing cross-section.Figure 11
Three-dimensional diagram of the system. (a) Test model skin. (b) Test model front beam. (c) Test model rear beam. (d) Test model longitudinal beam. (e) Sensor split.


#### 4.1.2. Pretreatment

Firstly, the model is simplified as below without affecting the calculation accuracy of the device.(1)
The fine process holes for nonconnections with little effect on the overall performance of the structure are ignored(2)
Small chamfers and rounded corners are removed(3)
The quality unit is used for the parts that do not participate in the analysis(4)
Quadrilateral shell elements are used to divide the grid after extracting the corresponding shellSecondly, 4-node quadrilateral elements divided each component and were combined with the aforementioned sensor split grid to form an assembly (Figure12) so as to ensure the accuracy and efficiency of the calculation, using the wind tunnel test model.Figure 12
Grid division diagram.Finally, the material properties and boundary conditions are defined. The material of the front beam of the test model is 7075, and the rest of the test model is made of T800 carbon fiber-reinforced composite material. The material properties are shown in Tables5 and 6. The applied loads and constraints are mainly composed of three aspects that are inertial load and aerodynamic load, the last one is one sensor split that is fixedly connected through the screw hole, and the other is applied with 6 degrees of freedom through the screw hole assembly error (Δx, Δy, Δz, Δα, Δβ, and Δγ).Table 5
Mechanical parameters of T800 carbon fiber-reinforced composites.
Elastic modulus, GPaShear modulus, GPaPoisson’s ratioE1E2E3G12G13G23ν12ν13ν231958.588.584.64.62.90.330.330.48Tensile strength, MPaCompression strength, MPaShear strength, MPaXTYTZTXCYCZCS12S13S23307188881747271271143143143Table 6
Material properties.
MaterialModulus (GPa)Poisson’s ratioDensity (kg m-3)7075720.332810


#### 4.1.3. Finite Element Static Analysis and Results

The von Mises stress is employed for strength evaluation according to the fourth strength theory. In Figure13, the maximum equivalent stress value of the sensor σr=600.9 MPa is smaller than the allowable stress of the material. Hence, the model is applicable.Figure 13
Stress contours of the model.


#### 4.1.4. Modal Analysis and Results

The first-order natural frequency of the system must be greater than 50 Hz. Figure14 shows the first-order vibration mode of the system with natural frequency of 54.17 Hz.Figure 14
The first-order natural frequency of the system.


### 4.2. System Approximate Model

The optimal Latin hypercube test design method is used to obtain a certain number of sample points, and a fourth-order polynomial response surface (RSM) approximate model is established. Input parameters and output parameters are shown in Table7.Table 7
Input parameters and value range.
Input parametersLower boundUpper boundOutput parametersB158smaxB248freq1B3515massH12545H22040H35080L12060L21040S1515S212.522.5P3050Δx00.3Δy00.5Δz00.2Δα00.15Δβ00.15Δγ00.15Credibility indicators (R2) are taken as evaluation indicators. It can be seen from the calculation results of the approximate model error (Table 8) that the approximate model has good performance in fitting the system.Table 8
The error calculation results of an approximate model.
IndexR2smax0.985freq10.964mass0.992


### 4.3. Robustness Analysis

The 6σ robustness analysis, the basis of the robustness optimization, is to evaluate the quality level of the deterministic optimization plan by disturbing the current design point, generating a set of sample points around its average value, and then estimating the quality level reliability failure rate and million defective rate of the output response index at a single design point through statistical analysis. At the same time, the average and standard deviation of each output response index are counted. The 6σ robustness analysis assumes that the product performance distribution is a normal distribution, and the distance between the mean value of the performance index and the quality constraint is ±6σ.
(4)Minimize:μMass+6σMinimize:μηx,ηy,ηMz+6σs.tμηx,ηy,ηMz+6σ≤0.01μεj−6σ≥300μεμεj+6σ≤600μεμsMax+6σ≤673MPaμfreq1−6σ≤50Hzj∈1,24&&j∈Nj∈1,24&&j∈ND.v.xiL≤xi≤xiUi∈1,17&&i∈N.Based on the results of the deterministic optimization of the above sensor splits and the assembly errors between the splits, the sensor split approximate model and the system approximate model are combined. The Monte Carlo sampling is used to evaluate the quality level of the deterministic optimization plan, and 11 design variables and assembly error variables (the relative displacement and angular error between the two sensor splits: three displacement errors,Δx, Δy, and Δz, and three angular errors, Δα, Δβ, and Δγ) are selected as the noise factor (Tables 9 and 10). Based on the combined approximation model, the sample points were collected by descriptive sampling method with 100 sampling times to obtain the quality level of the deterministic optimization plan. As shown in Table 11, the quality levels of maximum equivalent stress smax, first-order natural frequency freq1, and the strain εx and εMz, under the action of the maximum resistance FX, and the maximum pitching moment MZ are 1.414 σ, 1.636 σ, and 1.31 σ, which cannot reach the level of robustness quality, and robustness optimization is required. The robustness optimization of the split-parallel multicomponent strain-type force sensor is still based on the approximation model established above. The descriptive sampling method is used to collect sample points. The value ranges of design variables and noise factors are shown in Tables 9, 10, and 12. Algorithm NSGA-II is used for robust optimization. Through robust multiobjective optimization, the sensor output parameters can reach a quality level above 6 sigma (Table 11). By comparing the parameters before and after the robustness optimization (Table 13), it is found that the sensitivity of the three components increases by 14.73%, 21.2%, and 29.3%, respectively, when the quality of the sensor increases slightly and the amount of interference changes little.Table 9
Random noise variables and values of probability density function (distribution type, average, and coefficient of variation).
Input parameterDistribution typeAverageCoefficient of variationB1Normal5.761%B2Normal5.291%B3Normal7.591%H1Normal33.560.1%H2Normal29.380.1%H3Normal65.180.1%L1Normal43.330.1%L2Normal12.620.5%S1Normal13.590.5%S2Normal15.940.5%PNormal40.180.1%Table 10
Random noise variables and values of probability density function (distribution type and range).
Input parameterDistribution typeRangeΔxUniform[0,0.3]ΔyUniform[0,0.5]ΔzUniform[0,0.2]ΔαUniform[0, 0.1°]ΔβUniform[0, 0.1°]ΔγUniform[0, 0.1°]Table 11
Comparison of robustness before and after optimization.
Input parameterDeterministic optimization valueRobust optimization valueSolution6σ analysisSolutionQuality levelB15.7685.978B25.2985.868B37.5987.358H133.56833.788H229.38834.308H365.18864.788L143.33841.608L212.62815.048S113.59812.678S215.94814.858P40.18835.498Δx0808Δy0808Δz0808Δα0808Δβ0808Δγ0808εx302.651.516314.548εy585.198443.088εMz548.621.31421.798ηx0.214%80.093%8ηy0.034%80.0439%8ηmz0.098%80.008%8smax600.91.414419.30358freq154.7131.63653.278mass0.003380.00349Table 12
Design variables and value ranges.
Input parameterLower boundUpper boundB158B248B3515H12545H22040H35080L12060L21040S1515S212.522.5P3050Table 13
Comparison of results before and after two optimizations.
Optimization goalInitial valueOptimization valuePercent changedMass0.00470.00349-25.74%εx81.6314.54285.46%εy115.1443.08284.95%εMz167.7421.79151.5%ηx4.26%0.093%-97.82%ηy0.6125%0.0439%-92.83%ηmz5.12%0.008%-99.8%


## 4.1. System Finite Element Model Analysis

### 4.1.1. Geometric Model

The scheme of analysis system is shown in Figure11, consisting of main components such as front and rear beams, longitudinal beams, and skin with a total length of 1950 mm and a chord length of 300 mm. The binary model of OA309 airfoil is used in characterizing cross-section.Figure 11
Three-dimensional diagram of the system. (a) Test model skin. (b) Test model front beam. (c) Test model rear beam. (d) Test model longitudinal beam. (e) Sensor split.


### 4.1.2. Pretreatment

Firstly, the model is simplified as below without affecting the calculation accuracy of the device.(1)
The fine process holes for nonconnections with little effect on the overall performance of the structure are ignored(2)
Small chamfers and rounded corners are removed(3)
The quality unit is used for the parts that do not participate in the analysis(4)
Quadrilateral shell elements are used to divide the grid after extracting the corresponding shellSecondly, 4-node quadrilateral elements divided each component and were combined with the aforementioned sensor split grid to form an assembly (Figure12) so as to ensure the accuracy and efficiency of the calculation, using the wind tunnel test model.Figure 12
Grid division diagram.Finally, the material properties and boundary conditions are defined. The material of the front beam of the test model is 7075, and the rest of the test model is made of T800 carbon fiber-reinforced composite material. The material properties are shown in Tables5 and 6. The applied loads and constraints are mainly composed of three aspects that are inertial load and aerodynamic load, the last one is one sensor split that is fixedly connected through the screw hole, and the other is applied with 6 degrees of freedom through the screw hole assembly error (Δx, Δy, Δz, Δα, Δβ, and Δγ).Table 5
Mechanical parameters of T800 carbon fiber-reinforced composites.
Elastic modulus, GPaShear modulus, GPaPoisson’s ratioE1E2E3G12G13G23ν12ν13ν231958.588.584.64.62.90.330.330.48Tensile strength, MPaCompression strength, MPaShear strength, MPaXTYTZTXCYCZCS12S13S23307188881747271271143143143Table 6
Material properties.
MaterialModulus (GPa)Poisson’s ratioDensity (kg m-3)7075720.332810


### 4.1.3. Finite Element Static Analysis and Results

The von Mises stress is employed for strength evaluation according to the fourth strength theory. In Figure13, the maximum equivalent stress value of the sensor σr=600.9 MPa is smaller than the allowable stress of the material. Hence, the model is applicable.Figure 13
Stress contours of the model.


### 4.1.4. Modal Analysis and Results

The first-order natural frequency of the system must be greater than 50 Hz. Figure14 shows the first-order vibration mode of the system with natural frequency of 54.17 Hz.Figure 14
The first-order natural frequency of the system.


## 4.1.1. Geometric Model

The scheme of analysis system is shown in Figure11, consisting of main components such as front and rear beams, longitudinal beams, and skin with a total length of 1950 mm and a chord length of 300 mm. The binary model of OA309 airfoil is used in characterizing cross-section.Figure 11
Three-dimensional diagram of the system. (a) Test model skin. (b) Test model front beam. (c) Test model rear beam. (d) Test model longitudinal beam. (e) Sensor split.


## 4.1.2. Pretreatment

Firstly, the model is simplified as below without affecting the calculation accuracy of the device.(1)
The fine process holes for nonconnections with little effect on the overall performance of the structure are ignored(2)
Small chamfers and rounded corners are removed(3)
The quality unit is used for the parts that do not participate in the analysis(4)
Quadrilateral shell elements are used to divide the grid after extracting the corresponding shellSecondly, 4-node quadrilateral elements divided each component and were combined with the aforementioned sensor split grid to form an assembly (Figure12) so as to ensure the accuracy and efficiency of the calculation, using the wind tunnel test model.Figure 12
Grid division diagram.Finally, the material properties and boundary conditions are defined. The material of the front beam of the test model is 7075, and the rest of the test model is made of T800 carbon fiber-reinforced composite material. The material properties are shown in Tables5 and 6. The applied loads and constraints are mainly composed of three aspects that are inertial load and aerodynamic load, the last one is one sensor split that is fixedly connected through the screw hole, and the other is applied with 6 degrees of freedom through the screw hole assembly error (Δx, Δy, Δz, Δα, Δβ, and Δγ).Table 5
Mechanical parameters of T800 carbon fiber-reinforced composites.
Elastic modulus, GPaShear modulus, GPaPoisson’s ratioE1E2E3G12G13G23ν12ν13ν231958.588.584.64.62.90.330.330.48Tensile strength, MPaCompression strength, MPaShear strength, MPaXTYTZTXCYCZCS12S13S23307188881747271271143143143Table 6
Material properties.
MaterialModulus (GPa)Poisson’s ratioDensity (kg m-3)7075720.332810


## 4.1.3. Finite Element Static Analysis and Results

The von Mises stress is employed for strength evaluation according to the fourth strength theory. In Figure13, the maximum equivalent stress value of the sensor σr=600.9 MPa is smaller than the allowable stress of the material. Hence, the model is applicable.Figure 13
Stress contours of the model.


## 4.1.4. Modal Analysis and Results

The first-order natural frequency of the system must be greater than 50 Hz. Figure14 shows the first-order vibration mode of the system with natural frequency of 54.17 Hz.Figure 14
The first-order natural frequency of the system.


## 4.2. System Approximate Model

The optimal Latin hypercube test design method is used to obtain a certain number of sample points, and a fourth-order polynomial response surface (RSM) approximate model is established. Input parameters and output parameters are shown in Table7.Table 7
Input parameters and value range.
Input parametersLower boundUpper boundOutput parametersB158smaxB248freq1B3515massH12545H22040H35080L12060L21040S1515S212.522.5P3050Δx00.3Δy00.5Δz00.2Δα00.15Δβ00.15Δγ00.15Credibility indicators (R2) are taken as evaluation indicators. It can be seen from the calculation results of the approximate model error (Table 8) that the approximate model has good performance in fitting the system.Table 8
The error calculation results of an approximate model.
IndexR2smax0.985freq10.964mass0.992


## 4.3. Robustness Analysis

The 6σ robustness analysis, the basis of the robustness optimization, is to evaluate the quality level of the deterministic optimization plan by disturbing the current design point, generating a set of sample points around its average value, and then estimating the quality level reliability failure rate and million defective rate of the output response index at a single design point through statistical analysis. At the same time, the average and standard deviation of each output response index are counted. The 6σ robustness analysis assumes that the product performance distribution is a normal distribution, and the distance between the mean value of the performance index and the quality constraint is ±6σ.
(4)Minimize:μMass+6σMinimize:μηx,ηy,ηMz+6σs.tμηx,ηy,ηMz+6σ≤0.01μεj−6σ≥300μεμεj+6σ≤600μεμsMax+6σ≤673MPaμfreq1−6σ≤50Hzj∈1,24&&j∈Nj∈1,24&&j∈ND.v.xiL≤xi≤xiUi∈1,17&&i∈N.Based on the results of the deterministic optimization of the above sensor splits and the assembly errors between the splits, the sensor split approximate model and the system approximate model are combined. The Monte Carlo sampling is used to evaluate the quality level of the deterministic optimization plan, and 11 design variables and assembly error variables (the relative displacement and angular error between the two sensor splits: three displacement errors,Δx, Δy, and Δz, and three angular errors, Δα, Δβ, and Δγ) are selected as the noise factor (Tables 9 and 10). Based on the combined approximation model, the sample points were collected by descriptive sampling method with 100 sampling times to obtain the quality level of the deterministic optimization plan. As shown in Table 11, the quality levels of maximum equivalent stress smax, first-order natural frequency freq1, and the strain εx and εMz, under the action of the maximum resistance FX, and the maximum pitching moment MZ are 1.414 σ, 1.636 σ, and 1.31 σ, which cannot reach the level of robustness quality, and robustness optimization is required. The robustness optimization of the split-parallel multicomponent strain-type force sensor is still based on the approximation model established above. The descriptive sampling method is used to collect sample points. The value ranges of design variables and noise factors are shown in Tables 9, 10, and 12. Algorithm NSGA-II is used for robust optimization. Through robust multiobjective optimization, the sensor output parameters can reach a quality level above 6 sigma (Table 11). By comparing the parameters before and after the robustness optimization (Table 13), it is found that the sensitivity of the three components increases by 14.73%, 21.2%, and 29.3%, respectively, when the quality of the sensor increases slightly and the amount of interference changes little.Table 9
Random noise variables and values of probability density function (distribution type, average, and coefficient of variation).
Input parameterDistribution typeAverageCoefficient of variationB1Normal5.761%B2Normal5.291%B3Normal7.591%H1Normal33.560.1%H2Normal29.380.1%H3Normal65.180.1%L1Normal43.330.1%L2Normal12.620.5%S1Normal13.590.5%S2Normal15.940.5%PNormal40.180.1%Table 10
Random noise variables and values of probability density function (distribution type and range).
Input parameterDistribution typeRangeΔxUniform[0,0.3]ΔyUniform[0,0.5]ΔzUniform[0,0.2]ΔαUniform[0, 0.1°]ΔβUniform[0, 0.1°]ΔγUniform[0, 0.1°]Table 11
Comparison of robustness before and after optimization.
Input parameterDeterministic optimization valueRobust optimization valueSolution6σ analysisSolutionQuality levelB15.7685.978B25.2985.868B37.5987.358H133.56833.788H229.38834.308H365.18864.788L143.33841.608L212.62815.048S113.59812.678S215.94814.858P40.18835.498Δx0808Δy0808Δz0808Δα0808Δβ0808Δγ0808εx302.651.516314.548εy585.198443.088εMz548.621.31421.798ηx0.214%80.093%8ηy0.034%80.0439%8ηmz0.098%80.008%8smax600.91.414419.30358freq154.7131.63653.278mass0.003380.00349Table 12
Design variables and value ranges.
Input parameterLower boundUpper boundB158B248B3515H12545H22040H35080L12060L21040S1515S212.522.5P3050Table 13
Comparison of results before and after two optimizations.
Optimization goalInitial valueOptimization valuePercent changedMass0.00470.00349-25.74%εx81.6314.54285.46%εy115.1443.08284.95%εMz167.7421.79151.5%ηx4.26%0.093%-97.82%ηy0.6125%0.0439%-92.83%ηmz5.12%0.008%-99.8%


## 5. Conclusions

(1)
A split parallel multicomponent strain sensor structure layout is proposed to satisfy the special requirements for the measurement of aerodynamic sensors by the helicopter rotor airfoil wind tunnel test(2)
A finite element analysis model is established with the sensor split as the object to analyze separately its strain under the action of resistance, lift, and pitch moment cloud map and to determine the location of strain gauges and the way of group bridges(3)
The RBF neural network approximate model and NSGA-II multiobjective optimization algorithm are utilized to deterministically optimize the sensor split performance and obtain excellent monomer performance. Satisfying the strength and rigidity, the strain values under the action of the maximum resistanceFX, the maximum lift Fy, and the maximum pitching moment MZ of the sensor split structure are increased by 271%, 408%, and 227%, respectively, and the interference of the component is reduced by 95%, 94.4%, and 98.1%; the first-order natural frequency is increased by 5%, and the quality is reduced by 28.1%(4)
Based on the above deterministic optimization, the split manufacturing error and the assembly error between the splits are introduced, and the sensor and rotor airfoil test model-integrated finite element system model and RSM approximate model are successively established by using the Monte Carlo sampling method to check the quality level of the system and6σ robustness optimization to improve the robustness of the sensor and reduce the sensitivity of the response to assembly and manufacturing errors(5)
Through6σ robustness analysis based on deterministic optimization, the robustness of the sensor was improved, and the sensitivity of the response to assembly and manufacturing errors were reduces(6)
After these two optimizations, satisfying the strength and rigidity and considering the random noise effect of the split manufacturing error and the assembly error between the splits, the strain value of the maximum resistanceFX, the maximum lift Fy, and the maximum pitching moment MZ of the sensor were increased by 285.46%, 284.95%, and 151.5%, respectively, the interference to the three components was reduced by 97.82%, 92.83%, and 99.8%, respectively, and the quality was reduced by 25.74%. At the same time, the sensor quality level reached 6σ



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*Source: 6387919-2022-03-07.xml*