Smart Sensor Calibration with Auto-Rotating Perceptrons

Abstract

Sensor calibration is vital to have valid measurements of physical activities. Herein we deal with adjusting the signal from a wearable force sensor against a reference scale. By using a few samples and data augmentation, we trained a neural-based regression model to correct the wearable output. For this task, we tested the novel Auto-Rotating Perceptrons (ARP). We found that a neural ARP model with sigmoid activations can outperform an identical neural network based on classic per-ceptrons with sigmoid and even ReLU activation.

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Smart Sensor Calibration with Auto-Rotating Perceptrons
Daniel Saromo 1 2 Leonardo Bravo 2Elizabeth Villota 2
Abstract
Sensor calibration is vital to have valid measure-
ments of physical activities. Herein we deal with
adjusting the signal from a wearable force sensor
against a reference scale. By using a few samples
and data augmentation, we trained a neural-based
regression model to correct the wearable output.
For this task, we tested the novel Auto-Rotating
Perceptrons (ARP). We found that a neural ARP
model with sigmoid activations can outperform
an identical neural network based on classic per-
ceptrons with sigmoid and even ReLU activation.
1. Introduction
In recent years, wearable technology has seen an increase
in sports applications. Unlike conventional motion capture
systems, wearables can gather data outside the laboratory
environments (Adesida et al.,2019). Sensing of ground re-
action forces (GRF) in particular is of great interest for per-
formance evaluation in sports (Evans et al.,2018). Wearable
technology for GRF sensing mainly consists of insole-type
wearables that measure plantar pressure distribution (Naga-
mune & Yamada,2018). Calibration of these devices has
been performed with classical statistical approaches (Eguchi
& Takahashi,2018) and also using neural networks (Eng
et al.,2018). For instance, an LMBP-ANN model served to
predict validated load signals from a nonlinear pressure sen-
sor (Almassri et al.,2018), a WNN model predicted GRFs
using plantar information from insole pressure sensors (Sim
et al.,2015), and an LSTM model predicted the strain state
from a stretch sensor (Oldfrey et al.,2019).
This paper presents the calibration of an insole-type GRF
sensor using the recently developed Auto-Rotating Percep-
trons (ARP) for artificial neural networks. We aim to im-
plement and train a feedforward network model in order
1
PUCP Artificial Intelligence Research Group
2
PUCP Biome-
chanics and Applied Robotics Research Laboratory. Correspon-
dence to: Daniel Saromo
<
daniel.saromo@pucp.pe
>
, Leonardo
Bravo
<
leonardo.bravot@pucp.pe
>
, Elizabeth Villota
<
evil-
lota@pucp.edu.pe>.
LXAI Workshop at
37 th
International Conference on Machine
Learning, Vienna, Austria, PMLR 108, 2020. Copyright 2020 by
the author(s).
to have a valid posterior measurement without requiring
reference signals.
2. Problem definition
A WEarable VErtical GRF Sensor system (WEVES) com-
posed of an insole with piezoelectric sensors and an elec-
tronic housing -to be attached to the leg- was developed,
see Figure 1(a). WEVES was designed to measure forces
up to
2600 N
. A 65-
kg
male amateur athlete wore WEVES
and performed a standardized movement on an AMTI force
plate (OPT400600 model), see Figure 1(b). AMTI and
WEVES signals were recorded for
30 s
, which we show in
Figure 1(c). Even though AMTI and WEVES signals are
quite similar in shape, there exists a difference in scale, and
this is recurrent in all sample pairs recorded. Let
K
be the
scaling factor between AMTI and WEVES measurements.
Then, WEVES calibration consists in finding that factor,
which varies across the signal pairs.
(a) (b) (c)
Figure 1.
(a) WEVES mechatronic system: electronic box and
insole. (b) Stand-up straight position test with AMTI (red) and
WEVES (green) sensors. (c) Force measurements (
N
): AMTI
(red), uncalibrated WEVES (green), and scaled WEVES (blue).
3. Methodology
WEVES calibration was performed employing a neural re-
gression model that predicts the
K
factor. We compared
four model types with the same architecture, half of them
had classic perceptrons, and the others used the novel ARP
units (Saromo et al.,2019). ARP and classical perceptrons
were tested for both sigmoid and ReLU activation func-
tions. Previous ARP implementations have reported that
this neural unit can lead to better performance in image
classification tasks, provided that the sigmoid is the network
activation function (Saromo et al.,2019).

Smart Sensor Calibration with Auto-Rotating Perceptrons
Dataset preparation:
In order to find the target
K
, we need
to quantify the similarity between AMTI platform signal and
filtered WEVES outputs. These signals are represented by
the vectors
p
and
w
, respectively. We define the root mean
square error (RMSE) as the loss function, so that finding the
Kfactor can be posed as an optimality problem:
K= arg min
K
{RMSE (p, Kw)},K > 0.
Several algorithms find the best solution for such an op-
timization problem (Karaboga,2005;Wang et al.,2018;
Kumari & Kaur,2019). We have implemented the Artificial
Bee Colony (ABC) and the Particle Swarm Optimization
(PSO) algorithms to obtain
K
values for each signal pair
(
p
,
w
). The
K
factor chosen corresponds to the lowest cost
function value found. Descriptive statistics and information
related to these experiments are shown in Table A1.
WEVES signals were obtained at
100 Hz
and then interpo-
lated to reach
1 MHz
, which is the frequency of the AMTI
output data. We generated the
K
values and then downsam-
pled both signals by a factor of 15. Hence, we reduced the
input data dimension to 2000. We then filtered WEVES
signals by using a 4th-order low-pass Butterworth filter with
a normalized cutoff frequency of 0.15, as implemented in
literature for these signal types (Pandit et al.,2018). Data
was then circularly shifted, retaining important information
-the signal’s middle part, see Figure 1(c). By this artifice, the
number of pair samples increased from 12 to 8787. Result-
ing signals were further scaled to the range
[0,1]
. The final
dataset was divided into three groups: 7029 for training, 879
for validation, and the remaining 829 for testing.
Architecture definition:
Aiming for a real-time implemen-
tation, we chose a feedforward neural network with only one
hidden layer and the following architecture: 2000-256-1.
The scalar output is the scaling factor
K
that the regression
neural network needs to predict. We assigned the same
initial weights and biases to the four network types before
each execution. For the experiments, the ARP hyperparam-
eters are defined as:
xQ= 2.6
, since the maximum input
value is
1< xQ
; and
L= 3
, because the unipolar sigmoid
derivative σ0(z)is not very small for |z| ≤ 3.
4. Experiments: Classic perceptrons vs ARP
Figure 2shows the loss evolution throughout the epochs.
We observe that the networks with vanilla units activated
by sigmoids rapidly stagnate in a constant loss value. This
undesired premature convergence happens for both the train
and validation losses. By far, this is the worst-performing
model type. The other model family, which uses classic
perceptrons with ReLU, presents a loss decay consistent
over time and performs better than the first model type. The
following two model groups had ARP in their hidden layer
neurons. The ReLU-activated ARP model family exhibit
an initial better performance than the other ReLU network
type with classical perceptrons, but then is overtaken. The
remaining two curves show information of the last model set,
an ARP network with sigmoid activations. This model type
has the best performance, reaching the lowest loss values,
even when compared to the ReLU networks. Notably, with
ARP, the test loss of the sigmoid networks was reduced by
a factor of 15 at the cost of increasing the execution time by
∼12% (for details see Figure A1).
Figure 2.
Loss function of the four model types. Central bold
lines are median curves, and shades represent interquartile ranges.
Number of executions per model type: 50. Epochs per iteration:
100. Batch size: 64. Optimizer: Nadam (lr = 0.003).
5. Conclusions
In this work, we employed the ARP neural unit aiming to
calibrate a wearable GRF sensor. We compared the ARP
performance against models with classic perceptrons using
two different activation functions. The results show that
in a neural network with sigmoid activations, changing the
classic perceptrons to ARP can lead to a better performance,
even beating the same neural model with vanilla perceptrons
and ReLU activations. Also, even though the ARP units
were designed to be employed with saturated functions, we
can see that ARP can improve the model performance for
the early epochs, when using them with a non-saturated
function like ReLU. A more in-depth analysis needs to be
performed to explain this behavior appropriately.
The calibration pipeline herein presented could be extrapo-
lated to other cases where it is required to calibrate a sensor
output to make it close to a reference scaled signal.

Smart Sensor Calibration with Auto-Rotating Perceptrons
Acknowledgments
This work is funded by CONCYTEC-FONDECYT Peru
(contract number E041-01/058-2018-FONDECYT-BM-
IADT-AV).
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A. Supplementary Material
Table A1.
Comparison of the algorithms used to calculate
K
. Both
algorithms ran 100 times with 50 elements (food sources and
particles for the ABC and PSO algorithms, respectively).
ALGORITHM ABC PSO
FINA L
RMSE
MEA N 32.712 29.440
STD . DE V. 7.458 7.159
EXECUTION
TI ME [s]
MEA N 31.908 3.121
STD . DE V. 0.206 0.059
Figure A1.
Best test loss value (left vertical axis) and correspond-
ing processing time (right vertical axis) per execution. Each one
of the executions has 100 epochs. The loss function is the loga-
rithm of the hyperbolic cosine of the network prediction error. The
bars represent the median value obtained after 50 executions. The
vertical lines at the top of the bars represent the interquartile range.