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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).

References

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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.