Hammerstein–Wiener Multimodel Approach for Fast and Efficient Muscle Force Estimation from EMG Signals
Abstract
:1. Introduction
2. Related Studies
3. Methods
EMGm1 and EMGm2: | Inputs of the multimodel bi-forces estimator. |
Fm1 and Fm2: | Outputs of the multimodel bi-forces estimator. |
EMGN: | Input of sub-model (i). |
Fi: | Output of sub-model (i). |
Fi1 and Fi2: | Output of sub-model (i) obtained by applying multimodel inputs, EMGm1 and EMGm2, respectively. |
erri1 and erri2: | Errors of sub-model (i) computed between its real output, Fi, and outputs, Fi1 and Fi2 |
μi1 and μi2: | Validities of sub-model (i) according to Fm1 and Fm2, respectively. |
- Step 1_Elaboration of sub-models: Definition of sub-models of the library: Sub-model (i): model defined for the measurements couple (EMGi, Fi).
- Step 2_Normalised residues estimation: Computation of the normalised error of each sub-model (i): err’i1 and err’i2.
- Step 3_Validity Computing: Computation of the weight, also named validity, of each sub-model: μi1 and μi2.
- Step 4_Outputs Computing: Computation of outputs Fm1 and Fm2.
ɸ(k) | : Observation vector, also named regression vector, contains inputs and outputs data of previous instants. ɸ(k)= ɸ(uk–1 , fk–1) |
θ(k) | : Parameter vector θ = [θ1, θ2, …, θp] p is the number of parameters to be estimated. |
3.1. Experimental Approach
3.2. Data Analysis
- Scenario1: Predict force profiles from sub-models characterising the same kind of desired forces. For example, predicting a step from another instance of the step profile.
- Scenario2: Predict profiles of arbitrary forces from sub-models characterising 02 known forces. For example, using step and circle to estimate free profiles (vol).
- Scenario3: Predict profiles of arbitrary forces from sub-models characterising 03 known forces. This is the same as scenario 2, but with three standard profiles. For the different scenarios, we note that inputs/outputs of the multimodel approach are considered unknown, and any sub-model of the library does not represent them. Three performance measures: coefficient of determination (R2), root mean squared error (RMSE), and computational time (CT), were used to assess the proposed approach. For each performance metric, a two-way repeated measure analysis of variance (ANOVA, IBM SPSS Statistics 26) with factors methods (multimodel vs. ANN) and scenarios (1,2 and 3) was used to assess the performance of the proposed approach. Table 1 present the computational environment used in this paper.
Number of feed-forward network layers: | 2 |
Number of hidden layers: | 1 |
Number of neurons in the hidden layer: | 7 |
Type of activation function: | Tangent Sigmoid |
Batch training method: | Levenberg–Marquardt |
Number of output neurons: | 4 |
4. Results
5. Discussion
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Experimental Environment | Proprieties |
---|---|
Operating system | Windows 10 Professionnel |
Processor | Intel(R) Core(TM) i7-8565U CPU @ 1.80 GHz 1.99 GHz |
Processor generation | 8th Gen |
Installed RAM | 8.00 Go, (7.88 Go usable) |
System Type | 64 bits operating system, x64-based process |
Graphics card | NVIDIA GeForce MX110 |
Software | Matlab 2017 |
Scenario-1 | Scenario-2 | Scenario-3 | ||||
---|---|---|---|---|---|---|
mm | ANN | mm | ANN | mm | ANN | |
Sub-1 | 0.9592 | 0.6374 | 0.9742 | 0.7479 | 0.7922 | 0.5060 |
Sub-2 | 0.8923 | 0.8443 | 0.8979 | 0.8987 | 0.6568 | 0.5625 |
Sub-3 | 0.8878 | 0.8620 | 0.9466 | 0.9329 | 0.7997 | 0.5780 |
Sub-4 | 0.9754 | 0.8258 | 0.8299 | 0.8855 | 0.6015 | 0.6054 |
Sub-5 | 0.9330 | 0.7038 | 0.8867 | 0.8452 | 0.8517 | 0.6014 |
Sub-6 | 0.8963 | 0.8919 | 0.9038 | 0.8619 | 0.9090 | 0.6830 |
Sub-7 | 0.8285 | 0.5417 | 0.8087 | 0.8317 | 0.8972 | 0.5419 |
Sub-8 | 0.9584 | 0.8092 | 0.9684 | 0.8858 | 0.9062 | 0.8354 |
Sub-9 | 0.9539 | 0.7776 | 0.9033 | 0.5931 | 0.8454 | 0.7360 |
Sub-10 | 0.9326 | 0.6403 | 0.8026 | 0.8326 | 0.8912 | 0.6434 |
mean | 0.8927 | 0.7127 | 0.8427 | 0.6485 | 0.7559 | 0.3810 |
Max | 0.9754 | 0.8970 | 0.9742 | 0.9329 | 0.9090 | 0.8354 |
STD | 0.0043 | 0.0180 | 0.0099 | 0.0884 | 0.0210 | 0.1480 |
Scenario-1 | Scenario-2 | Scenario-3 | ||||
---|---|---|---|---|---|---|
mm | ANN | mm | ANN | mm | ANN | |
Sub-1 | 0.0186 | 0.0554 | 0.0201 | 0.0190 | 0.0353 | 0.0671 |
Sub-2 | 0.0348 | 0.0348 | 0.0123 | 0.0215 | 0.0471 | 0.0434 |
Sub-3 | 0.0211 | 0.0227 | 0.0230 | 0.0255 | 0.0232 | 0.0360 |
Sub-4 | 0.0173 | 0.0460 | 0.0352 | 0.0288 | 0.0477 | 0.0658 |
Sub-5 | 0.0249 | 0.0524 | 0.0217 | 0.0389 | 0.0261 | 0.3050 |
Sub-6 | 0.0300 | 0.0249 | 0.0146 | 0.0194 | 0.0193 | 0.0323 |
Sub-7 | 0.0242 | 0.0395 | 0.0227 | 0.0213 | 0.0207 | 0.0437 |
Sub-8 | 0.0167 | 0.0358 | 0.0244 | 0.0465 | 0.0275 | 0.0383 |
Sub-9 | 0.0210 | 0.0481 | 0.0107 | 0.0219 | 0.0356 | 0.0440 |
Sub-10 | 0.0261 | 0.0602 | 0.0549 | 0.0508 | 0.0308 | 0.0557 |
mean | 0.0304 | 0.0498 | 0.0318 | 0.0387 | 0.0396 | 0.0868 |
min | 0.0167 | 0.0227 | 0.0107 | 0.0190 | 0.0193 | 0.0323 |
STD | 1.7450 e-04 | 2.2470 e-04 | 0.0003 | 0.00035 | 0.00025 | 0.0091 |
Scenario-1 | Scenario-2 | Scenario-3 | ||||
---|---|---|---|---|---|---|
mm | ANN | mm | ANN | mm | ANN | |
Sub-1 | 0.1114 | 0.3606 | 0.0859 | 0.2210 | 0.0859 | 0.2210 |
Sub-2 | 0.1014 | 0.6231 | 0.1191 | 0.8610 | 0.0977 | 1.1734 |
Sub-3 | 0.0989 | 0.8061 | 0.0986 | 0.6714 | 0.0884 | 0.8842 |
Sub-4 | 0.0911 | 0.5401 | 0.1067 | 0.7296 | 0.1245 | 0.8619 |
Sub-5 | 0.0872 | 0.4602 | 0.1155 | 0.4712 | 0.0839 | 0.2351 |
Sub-6 | 0.0952 | 0.4128 | 0.1061 | 0.5638 | 0.1028 | 0.5850 |
Sub-7 | 0.0936 | 1.7428 | 0.0930 | 0.8783 | 0.1219 | 1.9918 |
Sub-8 | 0.1006 | 0.9940 | 0.1589 | 1.1822 | 0.1477 | 2.1794 |
Sub-9 | 0.1858 | 0.5114 | 0.1545 | 1.4397 | 0.1822 | 0.9611 |
Sub-10 | 0.1089 | 0.7438 | 0.1041 | 0.7531 | 0.0833 | 0.7904 |
Mean | 0.1074 | 0.7195 | 0.1142 | 0.7771 | 0.1118 | 0.9783 |
Max | 0.1858 | 1.7428 | 0.1589 | 1.1822 | 0.1822 | 2.1794 |
Min | 0.0872 | 0.3606 | 0.0859 | 0.2210 | 0.0833 | 0.2210 |
mm | ANN | |
---|---|---|
Maximum Possible Array Bytes | 2.8949 × 109 | 3.3673 × 109 |
Memory Available All Arrays | 2.8949 × 109 | 3.3673 × 109 |
Memory Used MATLAB | 3.9115 × 109 | 4.9214 × 109 |
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Chihi, I.; Sidhom, L.; Kamavuako, E.N. Hammerstein–Wiener Multimodel Approach for Fast and Efficient Muscle Force Estimation from EMG Signals. Biosensors 2022, 12, 117. https://doi.org/10.3390/bios12020117
Chihi I, Sidhom L, Kamavuako EN. Hammerstein–Wiener Multimodel Approach for Fast and Efficient Muscle Force Estimation from EMG Signals. Biosensors. 2022; 12(2):117. https://doi.org/10.3390/bios12020117
Chicago/Turabian StyleChihi, Ines, Lilia Sidhom, and Ernest Nlandu Kamavuako. 2022. "Hammerstein–Wiener Multimodel Approach for Fast and Efficient Muscle Force Estimation from EMG Signals" Biosensors 12, no. 2: 117. https://doi.org/10.3390/bios12020117
APA StyleChihi, I., Sidhom, L., & Kamavuako, E. N. (2022). Hammerstein–Wiener Multimodel Approach for Fast and Efficient Muscle Force Estimation from EMG Signals. Biosensors, 12(2), 117. https://doi.org/10.3390/bios12020117