Evaluating the Influence of Sensor Configuration and Hyperparameter Optimization on Wearable-Based Knee Moment Estimation During Running

L. Höschler; C. Halmich; C. Schranz; A.D. Koelewijn; H. Schwameder

doi:10.2478/ijcss-2025-0014

Figures & Tables

Placement of the wearable sensors. Seven inertial measuring units (IMUs, blue) were placed on the following locations: bilateral dorsal feet, medial shanks, lateral thighs, and sacrum. A pair of pressure insoles (PIs, green) were inserted bilaterally into the footwear at both sides.

Illustration of the baseline model architecture consisting of multiple 1D convolutional layers. First noise is added to the inputs of IMU (blue) and PI (green) before they are processed in individual layers. Outputs are concatenated, then passed through a merging layer (green-blue). Slope information is incorporated as auxiliary input before passing through two auxiliary layers (purple) and two additional layers (yellow) before generating 3D knee moment outputs.

Mean RMSE (across the three dimensions) after cross-validation (n=19) of all 31 configurations using the baseline model settings. Caps indicate the standard deviation. The abbreviation of the configurations corresponds to the combination of sensors used (foot: F, shank: S, thigh: T, pelvis: P, PIs: +). Configurations using the same IMUs with and without PIs are colored similarly and placed side by side.

Mean RMSE (across the three dimension) of all validation runs (n=19) per configuration. The first and second boxes include three configurations each (excluding those with pelvis IMU). The third, fourth, and fifth boxes include six, three and one configurations, respectively. The boxes contain the lower and upper quartiles with median indicated as solid line. The whiskers display the 1.5 times interquartile range. Outliers are indicated by circles, the mean is indicated by a +. ** and *** indicate statistical significance of the fixed effects PI and number of IMUs compared to the intercept (PI: false, 1 IMU) below a p-value of 0.01 and 0.001, respectively.

Number of output channels in 1D convolutional layers at baseline and after hyperparameter optimization. The abbreviation of the optimized configurations corresponds to the combination of sensors used (foot: F, shank: S, thigh: T, pelvis: P).

Test set performance (normalized RMSE) of the baseline and optimized models. Displayed are the results in the three planes of motion and the mean across them. Bar height indicates the mean, caps show the standard deviation. The abbreviation of the configurations corresponds to the combination of sensors used (foot: F, shank: S, thigh: T, pelvis: P). The mean across all configurations is displayed as dashed line. CONT – predictions over the entire sample of 10 seconds, PHSS – predictions during stance phases only.

Test set performance (intra-class correlation, ICC) of the baseline and optimized models. Displayed are the results in the three planes of motion and the mean across them. The abbreviation of the optimized configurations corresponds to the combination of sensors used (foot: F, shank: S, thigh: T, pelvis: P). Bar height indicates the mean, caps show the standard deviation. The mean across all configurations is displayed as dashed line. CONT – predictions over the entire samples of 10 seconds, PHSS – predictions during stance phases only.

Test set performance (RMSE) of the baseline and optimized models. Displayed are the results in the three planes of motion and the mean across them. The abbreviation of the optimized configurations corresponds to the combination of sensors used (foot: F, shank: S, thigh: T, pelvis: P). Bar height indicates the mean, caps show the standard deviation. The mean across all configurations is displayed as dashed line. CONT – predictions over the entire samples of 10 seconds, PHSS – predictions during stance phases only.

Test set performance (intraclass correleation – ICC) of the baseline and optimized models with the respective mean across configurations_ Displayed are the results in the three planes of motion and the mean across them_

ICC		CONT				PHSS
	Sensors	sagittal	frontal	transverse	Mean	sagittal	frontal	transverse	Mean
Baseline	FSTP	0.937	0.655	0.876	0.823	0.921	0.516	0.804	0.747
	FSP	0.952	0.672	0.875	0.833	0.942	0.535	0.801	0.759
	FTP	0.947	0.581	0.842	0.790	0.933	0.459	0.758	0.717
	FS	0.944	0.719	0.878	0.847	0.929	0.596	0.812	0.779
	FT	0.928	0.581	0.836	0.782	0.910	0.475	0.751	0.712
	F	0.932	0.535	0.890	0.786	0.913	0.397	0.825	0.712
	S	0.940	0.733	0.884	0.852	0.924	0.600	0.814	0.779
	Mean	0.940	0.639	0.869	*0.816*	0.924	0.511	0.795	*0.744*
Optimized	FSTP	0.955	0.674	0.880	0.836	0.945	0.555	0.814	0.771
	FSP	0.954	0.733	0.900	0.862	0.942	0.603	0.840	0.795
	FTP	0.939	0.677	0.866	0.827	0.923	0.563	0.797	0.761
	FS	0.952	0.718	0.891	0.853	0.940	0.584	0.824	0.783
	FT	0.928	0.617	0.859	0.801	0.907	0.487	0.781	0.725
	F	0.950	0.657	0.893	0.833	0.937	0.519	0.832	0.763
	S	0.943	0.716	0.868	0.842	0.928	0.584	0.790	0.767
	Mean	0.946	0.684	0.880	*0.837*	0.932	0.556	0.811	*0.766*

Optimized hyperparameters, search spaces, and, if applicable, layers, to which the parameter applies, lrmin: minimum learning rate, lrmax: maximum learning rate_

Parameter	Search Space	Applicable Layers
Exists	{True, False}	Merge, Extra 1, Extra 2
Out Channels	{32, 64, 128, 256}	IMU, Aux 1, Conv 1, Extra 1, Extra 2
Kernel Size	{7, 15, 25, 51}	IMU*, Merge, Conv 1, Extra 1, Extra 2, Out
Epochs	{25, 50}, increment of 5	n.a.
Batch Size	{8, 16, 32, 64, 128}	n.a.
lr_min	{10⁻⁴, 10⁻³}	n.a.
lr_max ratio	{1, 10}	n.a.

Results of the stepwise model comparison (ANOVA)_

Model	Df	AIC	BIC	logLik	Test	X²	p-value
Model_0	3	−2987	−2975	1498
Model_1.1	4	−3004	−2987	1508	0 vs 1.1	18.0	< 0.0001
Model_1.2	6	−3001	−2975	1506	1.1 vs.1. 2	1.2	0.54
Model_2	7	−3018	−2988	1516	1.2 vs. 2	18.7	< 0.0001
Model_3	10	−3012	−2969	1516	2 vs. 3	0.3	0.97

Test set performance (normalized root mean squared error – nRMSE) of the baseline and optimized models with the respective mean across configurations_ Displayed are the results in the three planes of motion and the mean across them_

nRMSE		CONT				PHSS
	Sensors	sagittal	frontal	transverse	Mean	sagittal	frontal	transverse	Mean
Baseline	FSTP	0.076	0.153	0.096	0.108	0.117	0.252	0.154	0.174
	FSP	0.067	0.143	0.096	0.102	0.102	0.233	0.155	0.163
	FTP	0.071	0.158	0.104	0.111	0.108	0.258	0.168	0.178
	FS	0.074	0.137	0.098	0.103	0.114	0.223	0.157	0.165
	FT	0.080	0.173	0.110	0.121	0.123	0.285	0.178	0.196
	F	0.085	0.180	0.098	0.121	0.131	0.295	0.156	0.194
	S	0.078	0.137	0.097	0.104	0.121	0.224	0.155	0.167
	Mean	0.076	0.155	0.100	*0.110*	0.117	0.253	0.161	*0.177*
Optimized	FSTP	0.066	0.151	0.094	0.104	0.099	0.247	0.151	0.166
	FSP	0.067	0.131	0.087	0.095	0.102	0.214	0.139	0.151
	FTP	0.073	0.149	0.098	0.107	0.112	0.245	0.157	0.171
	FS	0.069	0.139	0.092	0.100	0.104	0.226	0.147	0.159
	FT	0.081	0.172	0.105	0.119	0.125	0.284	0.169	0.193
	F	0.069	0.150	0.092	0.104	0.104	0.244	0.146	0.165
	S	0.075	0.138	0.099	0.104	0.114	0.225	0.159	0.166
	Mean	0.071	0.147	0.095	*0.105*	0.109	0.241	0.153	*0.167*

Test set performance (root mean squared error – RMSE) of the baseline and optimized models with the respective mean across configurations_ Displayed are the results in the three planes of motion and the mean across them_

RMSE		CONT				PHSS
[Nm/kg]	Sensors	sagittal	frontal	transverse	Mean	sagittal	frontal	transverse	Mean
Baseline	FSTP	0.187	0.139	0.058	0.128	0.290	0.228	0.093	0.204
	FSP	0.166	0.133	0.058	0.119	0.253	0.217	0.093	0.188
	FTP	0.174	0.147	0.063	0.128	0.268	0.240	0.102	0.203
	FS	0.182	0.130	0.059	0.124	0.282	0.211	0.095	0.196
	FT	0.195	0.154	0.067	0.139	0.303	0.252	0.108	0.221
	F	0.204	0.167	0.058	0.143	0.315	0.273	0.092	0.227
	S	0.190	0.127	0.058	0.125	0.293	0.206	0.092	0.197
	Mean	0.185	0.142	0.060	*0.129*	0.286	0.232	0.097	*0.205*
Optimized	FSTP	0.161	0.135	0.057	0.118	0.244	0.221	0.091	0.185
	FSP	0.163	0.122	0.053	0.113	0.249	0.199	0.084	0.177
	FTP	0.179	0.134	0.059	0.124	0.277	0.219	0.095	0.197
	FS	0.168	0.130	0.056	0.118	0.256	0.211	0.089	0.185
	FT	0.198	0.153	0.064	0.138	0.308	0.251	0.102	0.221
	F	0.169	0.141	0.055	0.122	0.258	0.229	0.088	0.192
	S	0.182	0.127	0.059	0.123	0.279	0.206	0.095	0.193
	Mean	0.174	0.135	0.058	*0.122*	0.267	0.219	0.092	*0.193*

Baseline hyperparameters of the 1D convolutional layers_

Parameter	IMU	PI	Merge	Aux 1	Aux 2	Conv 1	Out
In channels	n_IMUs × 6	9	64	66	64	64	64
Out channels	32	32	64	64	64	64	3
Kernel size	51*	51	27	1	1	15	7
Stride	4	1	1	1	1	1	1
Groups	1	1	4	1	1	4	1

Model architecture at baseline and after hyperparameter optimization of the 1D convolutional layers_ Additionally, the median and mean of the optimized configurations are shown_

Layer	Parameter	*Baseline*	FSTP	FSP	FTP	FS	FT	F	S	Median	Mean
IMU	In Channels	24	24	18	18	12	12	6	6	12	14
	Out Channels	32	64	64	128	128	32	128	128	128	96
	Kernel Size*	51	51	15	51	51	27	51	15	51	37
Merge	In Channels	32	64	n.a.	128	n.a.	32	n.a.	128	96	88
	Out Channels	32	64	n.a.	128	n.a.	32	n.a.	128	96	88
	Kernel Size	27	27	n.a.	7	n.a.	15	n.a.	15	15	16
Aux 1	In Channels	34	66	66	130	130	34	130	130	130	98
	Out Channels	64	256	64	32	32	32	256	32	32	101
Aux 2	In Channels	64	256	64	32	32	32	256	32	32	101
	Out Channels	64	64	64	128	128	32	128	128	128	96
Conv 1	In Channels	64	64	64	128	128	32	128	128	128	96
	Out Channels	64	128	64	64	256	128	128	256	128	146
	Kernel Size	15	7	27	7	15	51	7	51	15	24
Extra 1	In Channels	n.a.	128	64	64	256	128	n.a.	256	128	149
	Out Channels	n.a.	64	256	256	128	64	n.a.	64	96	139
	Kernel Size	n.a.	51	51	27	27	27	n.a.	27	27	35
Extra 2	In Channels	n.a.	64	n.a.	256	128	n.a.	n.a.	64	96	128
	Out Channels	n.a.	128	n.a.	128	256	n.a.	n.a.	128	128	160
	Kernel Size	n.a.	15	n.a.	27	51	n.a.	n.a.	15	21	27
Output	In Channels	64	128	256	128	256	64	128	128	128	155
	Out Channels	3	3	3	3	3	3	3	3	3	3
	Kernel Size	7	15	15	15	27	27	51	7	15	22

Training parameters of the baseline model and the optimized configurations_ Additionally, the median and mean of the optimized configurations are shown_

Parameter	*Baseline*	FSTP	FSP	FTP	FS	FT	F	S	Median	Mean
Epochs	20	35	25	25	25	25	35	50	25	31
Batch Size	64	8	8	8	8	8	16	16	8	10
lr_min	1×10⁻³	2.27×10⁻⁴	1.56×10⁻⁴	1.60×10⁻⁴	4.42×10⁻⁴	2.31×10⁻⁴	7.96×10⁻⁴	3.78×10⁻⁴	2.31×10⁻⁴	3.41×10⁻⁴
lr_min	4×10⁻³	7.26×10⁻⁴	7.89×10⁻⁴	6.49×10⁻⁴	4.84×10⁻⁴	1.14×10⁻³	2.01×10⁻³	1.78×10⁻³	7.89×10⁻⁴	1.08×10⁻³

Evaluating the Influence of Sensor Configuration and Hyperparameter Optimization on Wearable-Based Knee Moment Estimation During Running

Figures & Tables

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Figure A2.

Test set performance (intraclass correleation – ICC) of the baseline and optimized models with the respective mean across configurations_ Displayed are the results in the three planes of motion and the mean across them_

Optimized hyperparameters, search spaces, and, if applicable, layers, to which the parameter applies, lrmin: minimum learning rate, lrmax: maximum learning rate_

Results of the stepwise model comparison (ANOVA)_

Test set performance (normalized root mean squared error – nRMSE) of the baseline and optimized models with the respective mean across configurations_ Displayed are the results in the three planes of motion and the mean across them_

Test set performance (root mean squared error – RMSE) of the baseline and optimized models with the respective mean across configurations_ Displayed are the results in the three planes of motion and the mean across them_

Baseline hyperparameters of the 1D convolutional layers_

Model architecture at baseline and after hyperparameter optimization of the 1D convolutional layers_ Additionally, the median and mean of the optimized configurations are shown_

Training parameters of the baseline model and the optimized configurations_ Additionally, the median and mean of the optimized configurations are shown_

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