Instrumentation & Measurement Magazine 23-4 - 87

On Nonlinear Methods in
Environmental and Biological
Measurements
Bogdan Dziadak, Adam Jós´ko, and Łukasz Makowski

his paper presents relations between real-world phenomena, sensors and measurement methods that
without applied simplifications are generally nonlinear. The article is built upon real-world examples which
directly affect quality of human life or straightforwardly refer
to life itself. First, the health of a human being is investigated.
Next, attention is moved towards measurements of water and
air quality. We conclude with an observation that commonly
demanded linear characteristics of a measurement system are
feasible with nonlinear methods of signal and data processing.

Introduction to Nonlinear Nature
Real world and natural phenomena are far more complicated
than necessarily constrained computer simulations. With careful observations and meticulous measurements, even a simple
item like a resistor becomes a sophisticated nonlinear component. Apparently, nature is far more complex than elementary
electronics and once it is investigated to a greater extent, it exhibits remarkably convoluted processes. In this paper, we deal
with selected nonlinear methods as they are applied in some
environmental and medical measurements.
Flow of data skyrocketed in recent years due to advancements in electronics and the spread of distributed
measurement systems such as Internet of Things. Furthermore, it is highly infeasible to have an abundance of sensors
working remotely in-situ and keep all of them verified regularly like it is possible with conventional measurement
instruments. Therefore, classic approaches of measurement
and error analysis become harder to apply; hence, different
methods, well rooted in probability theory, are universally
promoted. Such methods are nonlinear in their nature and
some of them will be discussed here, particularly artificial neural networks and Bayesian inference.
In 2002 at the International Meeting on Brain-Computer
Interfaces (BCIs), specialists recommended usage of linear
signal processing [1]. On the other hand, it was also admitted
and proved that nonlinear methods are suitable and perform
significantly better in some areas of research. This addressed
especially problems with complex and/or huge amounts of
June 2020

data that has to be classified. There is one special advantage
of nonlinear approaches over the classical ones which is their
ability to generalize. Quality of generalization depends on several factors such as learning phase. For this reason, a couple
of distinctive nonlinear methods have been in use for many
years.

Complex Biological Systems and
Nonlinear Models
For a human being, two internal organ systems are of major
importance. These are the neural and cardiovascular systems.
Both of them play the fundamental role in human being existence by influencing mental and physical conditions, decision
stages and the complete body action.
The brain acts as a fundamental and primary organ of a
nervous system. It contains tens of billions of neurons (Fig. 1)
which in turn are extensively connected to their neighbors in
the amount of one to a thousand others. The brain plays the
major role not only in human body maintenance including
eyesight, hearing, smell, taste, touch, temperature sense and
control, but also in equilibrioception (sense of balance), nociception (pain sense) and proprioception (body position and
orientation sense). Brain activity can be accomplished thanks
to tiny bio-currents which are generated and flow in the nervous system. As such, the phenomena can be observed even
when employing noninvasive measurement methods like
Electroencephalography-EEG (from the head surface) and
Electrocorticography-ECoG (in lethal cases, when required
from the direct brain surface).
It was observed that the basic and most common components of the brain are neurons which can be modeled using
their computational equivalence. It led to development of artificial neural networks (ANN) (Fig. 2). This is a natural way of
mapping nonlinear processes and activities performed by neurons in the brain.
An artificial neural network is based on a mathematical
model of the neuron, synaptically connected to other neurons
and creating layers of the net. The output signal y from the neuron can be described as follows:

IEEE Instrumentation & Measurement Magazine 87
1094-6969/20/$25.00©2020IEEE

Instrumentation & Measurement Magazine 23-4

Table of Contents for the Digital Edition of Instrumentation & Measurement Magazine 23-4