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Real-time detection of uncalibrated sensors using Neural
Networks
Luis J. Mu˜noz-Molinaa,c, Ignacio Cazorla-Pi˜nara,
Juan P. Dominguez-Moralesb, Fernando Perez-Pe˜nac
aAltran Innovation Center for Advance Manufacturing
bRobotics and Technology of Computers Lab., Universidad de Sevilla, Seville, 41012,
Spain.
cSchool of Engineering, Universidad de Cadiz, Spain.
Abstract
Nowadays, sensors play a major role in several contexts like science, industry
and daily life which benefit of their use. However, the retrieved information
must be reliable. Anomalies in the behavior of sensors can give rise to critical
consequences such as ruining a scientific project or jeopardizing the quality
of the production in industrial production lines. One of the more subtle
kind of anomalies are uncalibrations. An uncalibration is said to take place
when the sensor is not adjusted or standardized by calibration according
to a ground truth value. In this work, an online machine-learning based
uncalibration detector for temperature, humidity and pressure sensors was
developed. This solution integrates an Artificial Neural Network as main
component which learns from the behavior of the sensors under calibrated
conditions. Then, after trained and deployed, it detects uncalibrations once
they take place. The obtained results show that the proposed solution is able
to detect uncalibrations for deviation values of 0.25º, 1% RH and 1.5 Pa,
respectively. This solution can be adapted to different contexts by means of
transfer learning, whose application allows for the addition of new sensors,
the deployment into new environments and the retraining of the model with
minimum amounts of data.
Keywords: Neural Networks, sensors, uncalibrations, sensor anomalies,
transfer learning
Preprint submitted to Expert Systems with Applications February 3, 2021
arXiv:2102.01565v1 [cs.LG] 2 Feb 2021
1. Introduction
Nowadays, sensors play a major role in the connected world [1, 2, 3, 4].
Science, industry or even day-to-day devices integrate sensors to collect the
information coming from the surrounding environment. Ensuring the reli-
ability and consistency of the information collected is essential in order to
guarantee the proper use of the information. The reliability of the acquired
information depends on the capabilities of the sensor, but also on its cali-
bration status. An uncalibration is said to take place when the sensor is not
adjusted or standardized by calibration according to a ground truth value.
In general, anomalies can appear in several shapes [5], however the uncali-
bration event usually appear in the form of long-term drifts with different
kind of responses such as linear, exponential, logarithmic or, simply, an ir-
regular drift. Furthermore, there are cases where the magnitude to control
is not directly controlled, that is, the set point is unknown. Thus, in the lat-
ter case, the detection of potential uncalibrations can be really challenging.
As it happens with some other kind of anomalies in sensor behaviour [6],
the detection of uncalibrations is a key issue in order to ensure fundamen-
tal aspects such as reliability, safety or cost-effectiveness in crucial assets in
different contexts, for instance, pharma, energy, aeronautics, etc. All these
properties, make the proposed solution a great candidate to be deployed in a
wide variety of context of both scientific and industrial and, more precisely,
in the context of industry 4.0.
The uncalibration detection problem can be tackled from different per-
spectives or paradigms. The available information is a key factor in order
to determine what perspective should be used. On the one hand, the ap-
proaches based on the use of classical techniques can be considered. This is
the case of similarity-based modeling and multivariate analysis [7] or the time
series analysis [8]. A survey of some other classical approaches for anomaly
derection can be seen in [9]. It is important to note that the techniques
mentioned in the previous works were used for the detection of specific kinds
of anomalies, not uncalibrations.
On the other hand, due to the huge development of Machine Learn-
ing (ML) and Artificial Intelligence (AI) experienced during the last years,
the use of techniques and approaches based on them has increased [10, 9]. An
example of this fact is the case of [11], where anomalies, defined as an unusu-
ally different behaviour at a specific time, were detected by means of the use
of Hierarchical Temporal Memory. Another interesting example can be seen
2
in [12], where a solution based on Convolutional Neural Networks (CNN) was
developed in order to detect sensor failures. An example of the application
of Neural networks for anomaly detection in power plants can be found in
[13]. Finally,an overview of Neural Network applications to fault diagnosis
and detection in engineering-related systems can be seen in [14]. As in the
classical approaches, it is important to note that all those developments were
devoted to specific anomalies detection, not uncalibration detection in the
sensor system.
In this work, an online uncalibration detector for temperature, humidity
and pressure sensors under unknown conditions (set points unknown) has
been developed. The major novelty of the paper is the use of an Artificial
Neural Network (ANN) as an expert on the sensors behaviour, so that the
estimated behaviour by the ANN can be compared to the one measured and
thus, potential uncalibrations can be detected. Different statistical tech-
niques, such as goodness of fit and confidence intervals, are used in order to
check that the estimation of the neural network can be considered as equal
or different from the obtained measures.
The developed architecture detects the ongoing uncalibrations and it ex-
hibits a great flexibility and scalability. Indeed, the obtained results suggest
that the solution can be trained with a generic set of sensors and then be spe-
cialized for more specific contexts with a much lower amount of data. Thus,
for instance, the solution could be trained with a standard set of sensors
and then be specialized for a more specific set devoted to a more concrete
task. Also, including new sensors into the solution is very easy, and fairly
low amount of data is required. Finally, retraining the solution requires data
coming from about one week of data (at a sampling rate of one sample per
minute and per sensor).
The proposed detector has been tested in a real context in the facilities of
a company of the pharmaceutical sector. Thus, it is important to note that
the presented work has been developed under the production conditions of
the aforementioned company.
The rest of the paper is structured as follows: section 2 introduces the
materials used in this work, including the dataset (2.2). The implemented
methods are described in section 3, together with the Neural Network (NN)
model. Then, the results obtained are presented in section 4, which are
divided in two different experiments: first, the performance of a proposed NN
model is evaluated (4.1), and then its scalability and flexibility is evaluated
on (4.2). Section 5 presents the conclusions and the discussion of this work,
3
respectively.
2. Materials
This section describes the sensors used and the dataset obtained from
them.
2.1. Sensors
Three different variables were measured, namely, temperature, humidity
and pressure. Temperature and humidity sensors are integrated within a sin-
gle device, the Novasina nSens-HT-ENS. The humidity measurement range
of this device goes from 0%RH to 100% RH, with a measurement accuracy
of 0.5% RH. Regarding the temperature measurement range, it goes from
-20°to +80°, with a measurement accuracy of 0.1°. The sensor used to mea-
sure the pressure is the Novasina Pascal-ST-ZB. It is a differential pressure
sensor based on static pressure measurement. Regarding its measurement
range, it goes from -50 Pa to 50 Pa, with a measurement accuracy of <0.5%
fs (full scale).
2.2. Dataset
The dataset used to obtain the results presented in this work consists of
temperature, humidity and pressure values coming from the sensors installed
across different clean rooms devoted to drug production. Rooms are located
in two different floors of a building: the second floor and the basement.
More precisely, the data coming from floor 2 is described in Table 1. This
dataset contains data collected during a whole year in different rooms of
the second floor. Each room is endowed with only one sensor per category
(one temperature/humidity sensor and one pressure sensor). Thus, sensor
redundancy is not available. The sensors used are described in 2.1. The data
was collected at a sample per minute rate during the aforementioned period
of time.
A smaller dataset containing data from rooms located in the basement
was also collected. This data is shown in table 1. Conversely to the second
floor, the basement dataset is smaller due to the difficulties to access the
data generated within this floor. This dataset contains, approximately, one
hundred samples per sensor, coming from a total of eleven sensors per cat-
egory. Besides, samples are not equally distributed. The data points (also
called samples) were collected during different periods of the year.
4
Table 1: Dataset summary. Note that -1 floor refers to the basement.
Floor Sensor Type Number of sensors Number of samples
2 Temperature 17 8935200
2 Humidity 17 8935200
2 Pressure 24 12614400
-1 Temperature 11 1100000
-1 Humidity 11 1100000
-1 Pressure 11 1100000
Since the dataset obtained from the second floor is more complete, it
was used as the main dataset. Thus, experiments in subsection 4.1 and
4.2 were conducted taking this dataset for training purposes. However, in
subsection 4.2, the dataset coming from the basement was used for testing
the adaptation of the solution proposed to a different environment.
Regarding the dataset slicing, two approaches were defined depending on
the kind of experiments that were carried out. On the one hand, in subsection
4.1, 60% of the samples of the data coming from the second floor were used
as training set for each type of sensor, 10% were used as validation set and
the remaining 30% were used as testing set. On the other hand, in subsection
4.2, 70% of the samples were used for training the main Neural Network, 10%
as testing set and 20% for the application of the Transfer Learning. In this
last case not only data coming from the second floor was used, but also data
coming from the basement was also included in order to test the transfer
learning application from one floor to another.
The use of the different slices is more detailed in 3.
3. Methodology
In this section, the architecture of the implemented solution, which is
capable for detecting sensor uncalibration, is presented.
The approach is based on ML techniques and it follows the block diagram
shown in Figure 1. The architecture is based on an ANN which, during
the training phase, learns how the sensors behave. Then, in the inference
step, the ANN is able to predict what the measurements should be based on
the input stimuli. Eventually, these predictions are compared with the real
measurements. If there exists any discrepancy between the prediction and
the real measurements, an uncalibration is taking place.
5
Figure 1: Block diagram of the approach presented. Five main stages can be observed:
the measurement stage, the estimation of the set point, the evaluation of the estimated
set point by the NN and the generation of the prediction and, finally, the computation of
the error with respect to the real value.
3.1. Preprocessing
The data used to both train and test the network have to be pre-processed.
This preprocessing, using filtering techniques, is a standard procedure to
detect anomalous values. These values could yield undesired effects on the
performance of the algorithm if they are not properly detected and treated.
Thus, this preprocessing phase can be divided into three stages, namely, a
threshold-based filtering, the Mahalanobis distance [15] and the Savitzky-
Golay filter [16].
The threshold-based filtering is based on the thresholds defined for the
warning and alarm systems in the rooms. This alarm system is designed
to detect extreme values in the incoming measurements. Thus, potential
sudden failures in the sensor systems can be detected. It has been observed
that these extreme values add noise to the input signal and, therefore, worsen
the NN learning. These thresholds were used during this research as a way to
discard all of those extreme values that were already detected by the system
and which could have a deep impact in the NN learning process. Thus, a
6
measured value is dropped whenever one of the aforementioned thresholds is
exceeded. In this way, only calibrated and non-extreme uncalibrated values
remain in the signal.
Next, a filter based on the Mahalanobis distance [17, 15, 18] is applied.
Mahalanobis distance is an outlier detection method specifically designed
for dealing with multidimensional distributions. More precisely, this stage
focuses on determining whether an observation including information from
the whole set of sensors (i.e a vector with as many entries as sensors) can
be considered as an outlier. Thus, in this stage, non-extreme values whose
relative occurrence is low would be classified as outliers.
Finally, the third stage is focused on reducing the noise in the incoming
signal. Different kind of filters such as Butterworth or wavelet filters could
have been applied in this stage. However, the incoming signal presents a
wide variety of different behaviors along the data collection period. Thus, a
more flexible noise filtering process is required. The Savitzky-Golay’s filter
[16], which computes local polynomial regressions providing new values for
each point, is used. This filtering process preserves essential properties of
the signal, such as maximum and minimum values or trends, while noise is
efficiently dropped out.
After the data obtained from the sensors is preprocessed, the average
value of the measurements, at a time, of all the sensors involved is used as
input to a ANN.
3.2. Neural network
The proposed ANN model is a Multi Layer Perceptron (MLP) that con-
sists of an input layer with one neuron, five hidden layers with three hundred
neurons each and an output layer with as many output neurons as sensors in
used. After training the network with the average value of the preprocessed
data from the sensors, the network is able to decompose the input stimulus
into the predicted value for each sensor, which is the expected behavior that
each sensor should have based on that input stimuli.
3.3. Error computation
This is the final step of the proposed approach. In this stage, the dif-
ference between the real measured value obtained from the sensors and the
ones predicted is computed, evaluated and classified as normal or anomalous.
This evaluation is based on the work of [11], where Hierarchical Temporal
7
Memory [19] was used to predict the next measurement. That prediction
was then compared to the real measurement and residuals were computed.
In our approach, goodness of fit tests were applied on the errors obtained
during the training stage. Thus, the underlying distribution of the error could
be used to compute specific confidence intervals with the desired signification
for each sensor. On the one hand, the absolute mean error of the sensors
measurements properly fits a normal distribution. On the other hand, the
mean squared error fits an exponential distribution.
Therefore, the confidence intervals were generated by using the normal
distribution associated to the error of each sensor. This choice was based
on the fact that the absolute mean error was approximately equal to the
uncalibration that was taking place.
Finally, a rejection takes place whenever the value exceeds the bounds of
the confidence interval. The density of rejections is computed as the rolling
ratio between the number of rejections for a window of a fixed time length
(with 1440 minutes as default value, which corresponds to the number of
minutes in a day) and the length of the window.
The rejection density is the variable that triggered the uncalibration warn-
ing. A uncalibration is said to take place whenever a threshold is overcome
during a specified amount of time.
It should be considered that the proposed architecture does not really
know what being calibrated means. The expected behaviour is that the
NN detects small differences between the current measurement and the one
from which it learnt. Thus, in the eventuality of a maintenance task in any
sensor, the architecture proposed might detect this new event as a potential
uncalibration. This uncalibration event will remain active until this new
condition of the sensor is re-learnt as ‘calibrated’ by the model.
The standard procedure to overcome this issue is to re-train the model
under these new conditions. Thus, this process would require a very high
temporal cost, since collecting data during almost a whole year would be
necessary. Because of this reason, transfer learning arises as a feasible solu-
tion. Using transfer learning, a small amount of data is needed to teach the
new condition to the NN.
3.4. Transfer learning
Transfer learning [20] is a ML technique aimed at specializing ML models
with a minimum amount of data. This technique consists of two main steps.
The first step is training a model for a more general task conceptually related
8
with the target or specialized task. For instance, the target task could be
identifying a specific face in a picture and, in that case, the general task
would be training a model for general face identification. The second step,
would be to re-train a subset of layers of the model with a training dataset
made out of elements corresponding to the specialized task (a specific face
in the example presented).
In the case of this work, multiple scenarios can benefit from transfer
learning. These scenarios can be summarized as it follows: changing the
ground truth value for all sensors or for a subset of them, including new
sensors and adapting to some other environments with, possibly, lack of
information.
As it was presented in subsection 2.2, a different slicing of the dataset
was used for transfer learning. Transfer learning is applied by dividing the
original dataset into three smaller subsets, namely, a training subset for the
original model, which will be called model A, a re-training subset for the
application of transfer learning (model A will be renamed to model B after
this process) and, finally, a testing subset for both models. Regarding the
training subset, it contains 70% of the datapoints. This stage corresponds to
the training for the general task. Regarding the subset devoted to be used
for re-training the model and, thus, for the application of transfer learning, it
contains the 20% of the datapoints. The amount of required datapoints can
be reduced to up to 2.5% of the total (10000 datapoints per sensor) in the
case of temperature and humidity. Finally, the testing subset includes 10%
of the datapoints. This subset was used to test the performance of the neural
network, both before and after the application of the transfer learning. A
constant offset was added in the last part of the test set in order to simulate
the recalibration due to a maintenance task. It is important to note that this
offset is not applied to the whole test set in order to properly see the change
of conditions and the associated evaluation by both, model A and model B.
As mentioned, one of the main purposes of the application of transfer
learning is the reduced amount of necessary samples for training a model.
This amount is directly associated to the number of parameters to retrain,
which, at the same time, is intimately related to the number of layers to
retrain. The nature of the target task, i.e., how abstract it is, and where
(in which layers) the concepts learnt are located within the NN, are crucial
factors which will determine the amount of required data. During the current
research, transfer learning has been applied on the very last hidden layer
of the NN, i.e., only the weighs connecting the last hidden layer with the
9
output layer has been retrained. The obtained results suggest that training
this subset of weights was enough for the existing requirements.
4. Results
This section shows the results obtained using the methods presented in
section 3. Two different experiments were conducted: (1) to evaluate the
capability for the detection of uncalibrations of the current approach through,
which has been called, performance evaluation experiments; (2) to test the
flexibility and scalability of the solution, which have been called transfer
learning experiments.
4.1. Performance evaluation experiments
These experiments were conducted to test the detection of uncalibrated
sensors using architecture presented. The dataset used is the one shown in
2.2. Uncalibrations were introduced in the testing set as drifts of different
nature (e.g linear, exponential or logarithmic) across time and in different
temporal frames (for instance, at the beginning, in the middle and at the end
of the year).
An uncalibration is considered to be detected once the rejection density
value has overcome a predefined threshold, which depends on the sensor,
and whose average value is 0.8. Besides, this threshold has to be overcome
during a predefined period of time, which also depends on the sensor, and
can be defined as two weeks, since it is enough time for all sensors and it is a
reasonably low period of time for uncalibration detection. An example of the
application of this technique can be seen in figure 2 where rejection density
for both the upper and lower bound of the confidence interval are shown.
The second and third plots show the rejection density values. It can be
seen that these values keep low whenever a uncalibration is not taking place.
Conversely, when a uncalibration takes place, the rejection density reaches
values close to one.
Regarding the performance of the approach, uncalibrations were detected
for all different types of sensors. However, two different scenarios can be dis-
tinguished, namely, a first optimistic scenario, where the uncalibration is
detected within the tolerance ranges defined by the quality requirements of
the pharma industry (i.e. ±0.5°,±3% and ±0.5P in temperature, humidity
and pressure respectively), and a non-optimistic scenario, where the uncal-
ibration is detected over the tolerance range. For all those sensors that are
10
Figure 2: Uncalibration detection through rejection density. In the upper subplot, the
blue trace shows the error corresponding to a linear uncalibration and the red dashed line
stands for the error zero value. In the middle subplot, the value of the rejection density
for error values exceeding the lower bounds of the confidence interval is shown. As it
can be seen, the maximum value for this rejection is, approximately, 0.3. In the lower
subplot, the value of the rejection density for error values exceeding the upper bounds of
the confidence interval is shown. As it can be seen, this density reaches the maximum
possible value from a critical point and during the whole uncalibration phenomenon.
11
in the optimistic scenario, an estimation of the remaining time until the
tolerance range gets exceeded can be provided.
Thus, for the case of the temperature sensors, the proposed approach was
tested on the available data coming from temperature sensors over 17 rooms.
All uncalibrations were detected for all sensors. In the best scenario, the
architecture detected uncalibrations associated to deviations of 0.25°C (tol-
erance 0.5°C). This accuracy was reached for 16 rooms out of 17 of the second
floor. In the worst scenario, the uncalibration was detected for deviations of,
approximately, 0.5°C.
For the humidity sensors case, the proposed method was tested on the
available data coming from humidity sensors over 17 clean rooms. All uncal-
ibrations were detected for all sensors. In the best scenario, the algorithm
detects uncalibrations associated to deviations of 2% (tolerance 3%). This
accuracy was reached for 14 rooms out of 17 of the second floor. In the worst
scenario, the uncalibration was detected for deviations close to 3%.
Finally, for the pressure sensors case, the proposed method was tested on
the available data coming from over 24 pressure sensors. All uncalibrations
were detected for all sensors. In the best scenario, the algorithm detected
uncalibrations associated to deviations under 0.5 Pascals (tolerance 0.5 Pas-
cals). This accuracy was reached for 6 out of 20 rooms of the second floor.
In the worst scenario, the uncalibration was detected for deviations close to
1.5 Pascals.
Some other ANN architectures were tested during the development of the
present research. More precisely, the same experiments were conducted using
a Wide & Deep Neural Network for temperature and humidity sensors and
Recursive Neural Networks (RNN) for the pressure sensors. The architecture
of the Wide & Deep Neural Network was based on the MLP used on the
implemented approach, but also includes an input layer per sensor, so that
the precise information coming separately from each sensor can be included.
This can be seen in figure 3.
Wide and Deep architecture yielded better results for most of the rooms.
However, for two of them, the uncalibrations were not detected. It has been
observed that, for these two rooms, how the sensor is supposed to behave
under a specific condition is not learnt by the neural network, and the identity
function is approximated instead. Thus, when an anomaly of any kind was
introduced on the input signal, this same value was retrieved by the NN and,
therefore, the uncalibration was not detected. It has been observed that
the worst results were obtained for these two rooms independently of the
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Figure 3: Wide and Deep model diagram. In this figure, the tested architecture of the
wide and deep model is shown. It can be seen n+ 1 different input layers; an input
layer with one single neuron, which is connected to a hidden block of five hidden layers
with three hundred neurons each. This input layer takes the estimated global set point
as input. Next, ninput layers with one single neuron each. Each input layer takes the
measurements coming from the different associated sensors as input. Finally, these input
layers are concatenated to the output of the hidden block and connected to the output
layer, which has a neuron per sensor.
architecture. This fact suggests that the local conditions inside these rooms
had a deep impact on the learning capabilities of the different models.
Regarding the RNN, Long-Short Term Memory (LSTM) neurons were
used. In this case, uncalibrations were not detected either. This was probably
caused due to the long-term nature of uncalibrations. Uncalibrations are long
term phenomenons, thus, the deviation associated to an uncalibration will be
observed during long periods of time. Hence, the deviation will be included
13
as relevant by LSTM neurons during the information inclusion stage, that
is, when the input gate evaluates what information is relevant and what
information is not. In this case, the learning of this long-term phenomenons
by the NN provoke the worst results.
4.2. Transfer learning experiments
These experiments were conducted to test the capability of the architec-
ture for learning a new condition with the less temporal cost. Thus, these
experiments were split in three categories, namely, change in global or spe-
cific conditions, adding new sensors and adapting to some other environments
with lack of information. To evaluate transfer learning, the error obtained
for the main model (model A) and the retrained model (model B) under the
specific new condition were compared.
4.2.1. Change of conditions
These experiments were conducted to test the capability of the architec-
ture proposed for learning a new condition as the current calibration status
for one or more sensors.
In the case of the individual offset, in figure 4 two different phases of the
error obtained from model A can be observed. The first one corresponds to
the model evaluation under normal conditions. The second one corresponds
to the model evaluation under the generation of a specific offset. It can be
seen how the error is displaced, approximately, three units which is the same
amount of the generated offset.
However, regarding model B, it can be seen how the error returns to
the same range of values as previously. This behaviour suggests that the
expected results have been obtained. This experiment was reproduced for
different rooms and the different types of sensors, obtaining similar results.
It can be observed in figure 5.
It should be noted that the minimum number of datapoints to properly
use transfer learning is around ten thousand samples. This number of samples
corresponds, approximately, to one week of data collection.
Regarding the generation of an offset for the whole set of sensors, the
model did not detect any change in its behavior. It suggests that, if the
behaviour of the whole set of sensors is equally changed, then, no effect
on the joint behaviour can be detected. Thus, no uncalibration is taking
place from the point of view of the model. This fact proposes an interesting
question regarding how the joint behaviour could be learnt.
14
Figure 4: In this figure, the error associated to a scheduled recalibration can be seen.
The blue trace shows the error and the red dashed line stands for the error zero value.
The recalibration takes place at the mid point of the figure. Since transfer learning is not
applied, once the recalibration takes place, the error immediately increases.
Figure 5: In this figure, the blue trace shows the error associated to a scheduled recal-
ibration and the red dashed line stands for the error zero value. In this case, transfer
learning is applied, thus, once the recalibration takes place, the error immediately de-
creases. It is important to note that this model is not applied in the previous moments to
the recalibration task.
4.2.2. Adding new sensors to the model
These experiments were conducted to determine the time that the archi-
tecture takes to learn and include the behaviour of new sensors in the loop.
These tests were made using the humidity and temperature sensors.
A first dataset with data coming from 13 sensors out of seventeen was
taken as main set. For this set of sensors, o1= 322677 datapoints were
available. In this case, model A was trained with this dataset. Next, model
B was re-trained with data coming from both the initial set of thirteen sensors
and a set of four new sensors. The obtained results show that uncalibrations
on the new set of sensors can be properly detected by model B. Figure 6
15
shows how uncalibrations are detected in the new sensors that were included
for the temperature case.
16
Figure 6: Uncalibration detection for new included sensors. In this figure, we can see
the results of the application of transfer learning in order to include new sensors in the
solution. The detection of an uncalibration for one of those sensors is shown. In the upper
subplot,the error corresponding to a linear uncalibration can be seen. The red dashed line
stands for the error zero value. In the middle subplot, the value of the rejection density
for error values exceeding the lower bounds of the confidence interval is presented. In this
case, the maximum value for this rejection is approximately zero. In the lower subplot, the
value of the rejection density for error values exceeding the upper bounds of the confidence
interval is presented. As it can be seen, this density reaches the maximum possible value
from a critical point and during the whole uncalibration phenomenon.
17
4.2.3. Adapting to some other environment with lack of information
These experiments were conducted to test if the architecture could be
trained with data coming from one specific location and then be implemented
on a different location after a transfer learning process.
In this case, model A was trained with data coming from the second
floor with 17 sensors of both types, temperature and humidity. Then, model
B was re-trained with a small amount of data coming from the basement.
Approximately, 80000 datapoints were used. The obtained results show that
uncalibrations are indeed detected by model B in this new environment.
Furthermore, the problem of the lack of data was solved by applying this
method. Figure 7 shows an example of how uncalibrations were detected by
model B in this specific context.
18
Figure 7: Uncalibration detection in the basement. In this figure, the detection of an
uncalibration taking place in the basement is shown. In this case, transfer learning has
been applied in order to re-train a model with a small quantity of data coming from the
basement. The model was previously trained with data coming from the second floor. In
the upper subplot, the error corresponding to a linear uncalibration is shown in blue. The
red dashed line stands for the error zero value. In the middle subplot, the value of the
rejection density for error values exceeding the lower bounds of the confidence interval is
shown. In this case, the maximum value for this rejection is 0.3. In the lower subplot, the
value of the rejection density for error values exceeding the upper bounds of the confidence
interval is shown. As it can be seen, this density reaches the maximum value starting from
a critical point and remains during the whole uncalibration phenomenon.
19
The obtained results suggest that transfer learning is a valid technique
for the adaptation of the solution to some other locations.
5. Discussion and Conclusions
Regarding the performance of the solution, it can be firstly concluded
that uncalibrations can indeed be detected even for values smaller than the
defined tolerance ranges for most cases in temperature and humidity sensors.
Secondly, it can be concluded that the application of transfer learning
yielded results that were coherent with the expected ones. Besides, these
results empowered the flexibility and scalability of the solution, enabling the
use of the model in a wide variety of contexts such as sensor addition, inte-
gration within new environments and partially solving problems associated
to the lack of data.
Furthermore, transfer learning retrieved good results for very low amounts
of data. The minimum amount of data required is about 10000 samples
which is the data coming from one week of observations at a sampling rate
of one sample per minute. Indeed, the fact that only the last weight matrix
was needed to re-train means that the information associated to all these
modifications were learned on a very abstract level in the NN [21]. This
fact suggest, on the one hand, that offsets have a low impact on the joint
dynamics of sensors. Thus, the joint behavior of the whole set of sensors
is ruled by much deeper relationships than the addition of specific values.
On the other hand, the results obtained for pressure sensors, despite they
are not under a common constant condition, may be explained by this fact.
The sudden changes in pressure values could be then understood as an offset,
what implies that the model has a deep knowledge of the sensor behavior,
although these offsets reduce the accuracy on the detection of uncalibrations.
As a remarkable aspect of this research, it is important to note that the
solution has been trained and tested in a real context, with data coming
directly from production. Indeed, the solution presented in this work is cur-
rently deployed in Azure [22], where the solution performs the uncalibration
detection directly from the information of the sensors from a digital twin of
the building. This digital twin contains the current status of the physical
sensors.
To the best of our knowledge, this is the first time that potential un-
calibrations of a set of sensors are online detected whenever the set point is
20
unknown. Furthermore, the proposed architecture can be extended by means
of transfer learning to a wide range of different fields.
Regarding the future work, different targets are considered: (1) extend-
ing the results obtained after the application of transfer learning. Thus, we
are interested in training the solution with a generic set of sensors of one
type (such as temperature sensors) and then, testing the performance of the
solution on sensor systems of a different kind, for instance, engine sensor
systems, smart-city sensors systems and power plants sensor systems, among
others; (2) obtaining information about the learning of the solution through
the application of Explainable Artificial Intelligence (XAI). This could pro-
vide useful information about the potential scalability and flexibility of the
solution and the different models to which it could be applied.
Acknowledgement
This work was partially supported by the Altran Innovation Center for
Advance Manufacturing, the EU H2020 project Virtual IoT Maintenance
System (VIMS Grant ID: 878757), the Spanish grant (with support from the
European Regional Development Fund) MIND-ROB (PID2019-105556GB-
C33) and by the EU H2020 project CHIST-ERA SMALL (PCI2019-111841-
2).
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