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

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

International Journal of Computer Science in Sport

Volume 24 (2025): Issue 2 (June 2025)

By: L. Höschler, C. Halmich, C. Schranz, A.D. Koelewijn and H. Schwameder

Open Access

|Sep 2025

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.

Table 1.

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

n_IMUs – number of IMUs in the respective configurations.

* IMU kernel size is multiplied by 4 due to higher sampling rate.

Table 2.

Optimized hyperparameters, search spaces, and, if applicable, layers, to which the parameter applies, lr_min: minimum learning rate, lr_max: 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.

* only if layer exists,

** IMU kernel size is multiplied by 4 due to higher sampling rate,

n.a.: not applicable (for the general training parameters).

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.

Table A1.

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

[i] Lower AIC and BIC indicate a better model fit. Df: degrees of freedom, AIC: Akaike Information Criterion, BIC: Bayesian Information Criterion, logLik: log likelihood, X²; Chi-squarred.

Table A2.

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

The abbreviation of the optimized configurations corresponds to the combination of sensors used (foot: F, shank: S, thigh: T, pelvis: P).

* IMU kernel size is multiplied by 4 due to higher sampling rate, n.a.: not applicable, layer does not exist.

Table A3.

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

[i] The abbreviation of the optimized configurations corresponds to the combination of sensors used (foot: F, shank: S, thigh: T, pelvis: P), lr_min: minimum learning rate, lr_max: maximum learning rate.

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.

Table A4.

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*

[i] The abbreviation of the optimized configurations corresponds to the combination of sensors used (foot: F, shank: S, thigh: T, pelvis: P). CONT – predictions over the entire samples of 10 seconds, PHSS – predictions during stance phases only.

Table A5.

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*

Table A6.

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*

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DOI: https://doi.org/10.2478/ijcss-2025-0014 | Journal eISSN: 1684-4769

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Language: English

Page range: 80 - 106

Published on: Sep 14, 2025

Published by: International Association of Computer Science in Sport

In partnership with: Paradigm Publishing Services

Keywords:

IMU,

Related subjects:

Databases and data mining,

Computer sciences, other,

Sports and recreation,

Physical education,

Sports and recreation, other

© 2025 L. Höschler, C. Halmich, C. Schranz, A.D. Koelewijn, H. Schwameder, published by International Association of Computer Science in Sport
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 24 (2025): Issue 2 (June 2025)

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

Figures & Tables

Figure 1.

Figure 2.

Table 1.

Table 2.

Figure 3.

Figure 4.

Figure 5.

Figure 6.

Table A1.

Table A2.

Table A3.

Figure A1.

Figure A2.

Table A4.

Table A5.

Table A6.

Paradigm

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