# PrognosEase: A data generator for health deterioration prognosis

Tarek Berghout, Mohamed Benbouzid

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## To cite this version:

Tarek Berghout, Mohamed Benbouzid. PrognosEase: A data generator for health deterioration prognosis. SoftwareX, 2023, 23, pp.101461. 10.1016/j.softx.2023.101461. hal-05339419

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Distributed under a Creative Commons Attribution 4.0 International License
Original software publication

# PrognosEase: A data generator for health deterioration prognosis☆

Tarek Berghout<sup>a</sup>, Mohamed Benbouzid<sup>b,c,*</sup>

<figure><img src="image_3.png" /></figure>

## ARTICLE INFO

**Article history:**

Received 1 November 2022

Received in revised form 9 May 2023

Accepted 23 June 2023

**Keywords:**

Data generator

Dataset

Deep learning

Health index

Machine learning

Prognosis and health management

Remaining useful life

## ABSTRACT

This paper presents PrognosEase; a software that provides an easier way to produce different types of run-to-failure data mimicking real-world conditions to simplify prognosis studies in terms of data collection and improvement in machine learning degradation modeling process. Different types of degradation types made available to meet different types of applications. Besides, some primary machine learning experiments were performed to ensure that complexity patterns of real systems could be observed in the training/testing predictions attitude. This paper also presents the impacts, limitations and potential improvements of the data generator.

© 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license

(http://creativecommons.org/licenses/by/4.0/).

## Code metadata

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Permanent link to code/repository used for this code version

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Legal code license

Code versioning system used

Software code languages, tools and services used

Compilation requirements, operating environments and dependencies

If available, link to developer documentation/manual

Support email for questions

v1.0.0

https://github.com/ElsevierSoftwareX/SOFTX-D-22-00354

none

University of Batna 2 and University of Brest

none

MATLAB

MATLAB ≥ r2018b

none

berghouttarek@gmail.com

## 1. Motivation and significance

Prognosis and health management (PHM) is a discipline dedicated to study health deteriorations of systems under operating conditions [1-3]. Thus, it plays a crucial role in scheduling Condition-Based Maintenance (CBM) tasks while reducing downtime through early failure detection. Remaining Useful Life (RUL) is the primary health indicator, upon which the prognosis process

depends to assess the spread of damage during system operating conditions. Indeed, this is the time between the current state of health (SoH) (i.e. the health state prediction time) and the time when the failure could occur.

Similar to how it dominates other fields, machine learning (ML) is becoming nowadays one of the prominent tools in PHM [4]. ML modeling requires both health signatures presented by run-to-failure sensor measurements reflecting actual conditions of the studied system and RUL labels [5]. Logically, for accurate modeling, these run-to-failure RUL labels need to be obtained from real-world degradation cycles of systems. However, for some systems such as safety critical systems (e.g., aircraft engines) or for long-term degradations such as of bearing, it is impossible to achieve such conditions as a higher level of criticality and damage could be achieved, including financial, loss of reputation and loss of life [6]. As an alternative, accelerated aging experiments and simulation models (i.e., physics-based

<figure><img src="image_4.png" /></figure>

PROGNOSEase

<footnote><sup>a</sup> University of Batna 2, Laboratory of Automation and Manufacturing Engineering, 05000 Batna, Algeria</footnote>

<footnote><sup>b</sup> University of Brest, UMR CNRS 6027 IRDL, 29238 Brest, France</footnote>

<footnote><sup>c</sup> Shanghai Maritime University, Logistics Engineering College, Shanghai 201306, China</footnote>

<footnote>* Corresponding author at: University of Brest, UMR CNRS 6027 IRDL, 29238 Brest, France.</footnote>

<footnote>E-mail addresses: t.berghout@univ-batna2.dz (Tarek Berghout),
mohamed.benbouzid@univ-brest.fr (Mohamed Benbouzid).</footnote>
models) are the only available data source used to build such ML methods [6,7]. In this case, acceleration and simulation will not maintain RUL synchronization as in real conditions (i.e., degradation time does not reflect reality due to accelerated aging). Accordingly, other health indicators such as Health Index (HI) and Health Stage (HS) should be used to identify the system SoH [1,2]. The HI index whose deterioration function is expressed in different trends (e.g., linear and exponential) could also provide important information on the current performance of the system. HS indicates the health level of the system at the time of SoH assessment based on some specific divisions (e.g., healthy, critical, and unhealthy SoH) defined by ML developers. Data obtained from accelerated aging experiments suffer from missing patterns and labels, as well as a higher level of non-stationary due to the harsh conditions imposed by the experiment [8]. Moreover, simulation models lack real data patterns. In addition to lacking authenticity at some point, the most significant drawback of both data collection is the time-consuming and financial costs that make replication difficult.

In summary, based on the previous analysis, three distinct methods exist for collecting run-to-failure data in order to satisfy the requirements of ML modeling. However, there remain research gaps and open challenges that can be summarized as follows.

* Real degradation: not readily available due to safety-critical maintenance schedule or long-term degradation requiring massive computational resources (time, hardware, software);

* Accelerated degradation: result in massive financial losses, lack of real labeled deterioration patterns due to imposed artificial conditions;

* Physics-based simulation: lacks authenticity, generating data real-alike labeled degradation patterns.

As a result, accelerated aging and simulation are the most recommended solutions in this case. However, they still suffer from a scarcity of data. In such a situation, ML models need to be assisted in providing further knowledge either by (i) generative modeling bringing more data, or via (ii) transfer learning that overcomes the lack of patterns by providing additional knowledge [9,10].

In this context, it is important to provide an easy way to collect massive data needed to produce and assist ML algorithms for faster and more accurate training as easily as possible. Accordingly, PrognosEase is introduced in this paper with the aim of overcoming the shortcomings of accelerated aging and simulation models, simplifying ML studies and speeding up data generation process. More simply, the main advantage over traditional data generation methods (i.e., simulation and accelerated aging) is the simplicity of generating synthetic, real-alike data that assists ML modeling directly or indirectly (i.e., generative modeling and training or transfer learning via fine tuning). In summary, the developed software contributions can be outlined as follows.

* Solve the problem of data scarcity generating a wide range of run-to-failure measurements imitating real-world degradation scenarios;

* Reduce the cost of expensive simulations and accelerated aging.

* Provide primary data to develop and evaluate ML models at first glance.

The philosophy of PrognosEase depends on the generation of complete life cycles based on specific measurement types and the corresponding HI. These measurements are equivalent to sensor measurements in real applications and show a variety of trends, for example, linear degradation trends like in fuel cells [11], exponential like in turbofan engines [12,13], sinusoidal with exponential growth as in bearings [14], cyclic linear degradation trends as for Li-ion batteries [15,16]. Since the signals are generated according to some specific patterns, hence they lack RUL timings. In this case, HI and HS can be used. HI from

PrognosEase comes with two different types, namely exponential and linear deterioration trends. Non-stationary and changing working conditions are generated as noise and distortion in a kind of randomly injected pulses in the generated measurements. Accordingly, this paper is dedicated to presenting all these signals in relation to sensor and HI measurements. Also, it is dedicated to presenting some ML experiments indicating the training attitude and providing similar conclusions to accelerated aging and simulation experiments. In addition, it presents the impact of PrognosEase in the field of PHM, the limitations and potential improvements.

This paper is organized as follows. Besides, the introduction in Section 1, Section 2 describes PrognosEase and its main features. Section 3 is devoted to some ML experiments conducted using data generated by PrognosEase. Section 4 is devoted to the study of the impact of PrognosEase in the field of PHM. Section 5 presents limitations and potential improvements. Finally, Section 5 concludes this work.

## 2. Software description

This section is dedicated to introducing different aforementioned types of measurements in life cycles generated by PrognosEase in two different subsections, both sensor measurements generation and also types of HI trends.

### 2.1. Generating sensors measurements

As mentioned earlier, the measurement trends are generated according to some specific variations inspired by some well-known works in the literature, including linear, exponential and exponentially growing sinusoidal, cyclic with linear and exponential trends. Additional features such as noise and distortions have been added to emulate real-world conditions affecting the system.

**Linear:** Sensor measurements describing a linear trend $L$ are generated according to a linearly growing function with the slope $a$ and initial value $b$ for an input time unites $x$ as in one (1). A random noise $\mu$ is generated from a specific type of probability distribution $P(x)$ defined according to user experience as addressed by (2). After that, the noise $\mu$ and the degradation trend $L$ are summed up while the noise is penalized with some specific noise rate $\vartheta$ to construct the signal $S_N^*$ as in (3). Next, $S_N^*$ will be scaled in range [0, 1] using min-max normalization as in (4) to obtain $S_L^*$. Finally, $S_L^*$ will subject to some random distortion $\rho$ with random number of pulses $n\rho$ controlled according specific amplitude $w$, and normalization factors $(\alpha_\rho, \beta_\rho)$, to generate the final measurements $S_L$ as in (6) while, the pulses are periodically generated according to the discreet function as in (5).

$$L = ax + b \quad (1)$$

$$\mu = P(x) \quad (2)$$

$$S_N^* = (\vartheta L) \mu + L \quad (3)$$

$$S_N^{**} = \frac{S_N^* - \min(S_N^*)}{\max(S_N^*) - \min(S_N^*)} \quad (4)$$

$$\rho = \{w e^{\pm \ln(\alpha_{\rho}) x^{(i)/\beta_{\rho}}}\}_{i=1}^{n_{\rho}} \quad (5)$$

$$S_L = S_N^{**} + \rho^L \quad (6)$$

Fig. 1 showcases an example constructing a linear sensor measurements trend with $P(x)$ a Gaussian noise, $\vartheta = 0.9$, $n\rho = 2$, $w = 0.1$.

**Exponential:** Sensors measurements describing an exponential trend $E$ are generated according to formula (7) with the base of exponentiation $e$ and exponentiation parameter $\alpha_E$. The measurements of $E$ follow similar steps of corruptions by adding
<figure><img src="image_5.png" /><figcaption>Fig. 1. An example of sensor measurements generated according to a linear degradation trend.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 2. An example of sensor measurements generated according to an exponential degradation trend.</figcaption></figure>

the noise and distortions pulses while, scaling is also necessary (i.e. Eqs. (3)-(5)) to finally attend the $S_E$ as in (8).

$$E = e^{(\alpha_E x)} \qquad (7)$$

$$S_E = S_N^{**} + \rho \qquad (8)$$

Fig. 2 is an example constructing sensor measurements according to an exponential trend with $P(x)$ a Gaussian noise, $\vartheta = 0.03$, $n\rho = 2$, $w = 0.1$, and $\alpha_E = 0.01$.

**Sinusoidal with exponential growth:** This type of measurements of sinusoidal with exponential growth $SE$ are generated according to formula (9) with an exponentiation parameter $\alpha_{SE}$ and angular frequency $\omega$ while being subject to distortion by noise and randomly injected pulses until the final shape $S_{SE}$

reached using formula (10).

$$SE = e^{(\alpha_{SE} x)} \cos(\omega x) \qquad (9)$$

$$S_{SE} = S_N^{**} + \rho \qquad (10)$$

Fig. 3 is an example constructing sensor measurements according to a sinusoidal with an exponential growth trend with $P(x)$ a Gaussian noise, $\vartheta = 0.1$, $n\rho = 2$, $w = 0.1$, $\alpha_{SE} = 0.02$, and $\omega = 0.2$.

**Cyclic degradation:** The cyclic degradation $S_C$ comes up with two types (i.e., linear and exponential trends). The pulses are similarly generated according to Eq. (5) but periodically with a distance between pulses $D$ dynamically changes at each cycle with a specific user ratio $\vartheta_C$ as in formula (11) while (12) is
<figure><img src="image_7.png" /><figcaption>Fig. 3. An example of sensor measurements generated according to a sinusoidal with an exponential growth trend.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Fig. 4. Example of generated sensor measurements according to a cyclic degradation trend: (a) Exponential cyclic degradation; (b) Linear cyclic degradation.</figcaption></figure>

describing the final output signal.

$$ \rho = \{we^{\frac{\pm \ln(\alpha_{\rho})x(i)}{\beta_{\rho}}} + \vartheta_{C}D\}_{i=1}^{n_{\rho}} \quad (11) $$

$$ S_C = S_N^{**} + \rho \quad (12) $$

Fig. 4 is an example that showcases both types of cyclic degradation that PrognosEase is programmed to do.

## 2.2. Generating RUL measurements

In PrognosEase, RUL degradation function is actually a HI generated according to two main trends either exponential or linear following formula (1) and (7) respectively with different parameters values from the sensors measurements. These parameters are user-defined ones depends on accuracy of predictions

and also user experience. The example in Fig. 5 illustrates both types of HIs.

## 3. Illustrative examples

In this study, PrognosEase is used to generate a dataset that combines a mixture of sensor measurements types with a higher level of complexity, similar to the work done in the literature in terms of data generation. 10 features, 5 lifecycles for training and 2 cycles for testing are generated with cycles that are 300 samples long. Fig. 6 depicts an example of a single run-to-failure life cycle, wherein PrognosEase successfully generates a mixture of data representing non-linearity and reflecting real-alike run-to-failure measurements. Such data visualization also shows that the constructed feature space includes different types of complex samples with high-level of non-stationarity. In fact, these samples
<figure><img src="image_9.png" /><figcaption>**Fig. 5.** An example of HI degradation functions: (a) A linear degradation; (b) An exponential degradation.</figcaption></figure>

are supposed to be flown from the same devices under different conditions. This means that all data generation parameters are fixed when reconstructing the data set while retaining only the noise generation and distortion that changes the conditions. This is done with the aim of reaching a certain level by mimicking real-world conditions. HI is set in this case by default to the exponential deterioration function due to the existence of an exponential deterioration phenomenon in the collected measurements. Since the typical features types in Fig. 6 are randomly generated, it was difficult to track each generated feature by type and create a legend for it. Therefore, the most important thing is that the different measurements are completely different in terms of features and measurements representing different degradation cycles.

An ML model, namely a long-sort term memory neural network, is tested for its potential capabilities using a grid search mechanism to adjust its parameters for a better approximation. An example of a curve fitting results for a life cycle from testing set is shown in Fig. 7. The learning model shows that it attempts to mimic the shape of the decay trend in the training process as it is logically difficult to do for new unseen samples to the model. Thus, improving ML models will consist of enhancing the curve fitting as much as possible in the testing phase while taking into account real-world conditions and training constraints such as centralized, decentralized, and federated learning, etc., with all types of learning paradigms such as online, offline and reinforcement learning, etc.

It should be mentioned, the main goal of this study is to demonstrate the visual capabilities of PrognosEase in generating meaningful data that can be used for prognosis studies. The primary focus is on presenting the software and its design, while further machine learning modeling studies will be conducted to evaluate and compare the effects of parameters such as noise and numerical distortions in different scenarios. A previous study, similar to this one, used PrognosEase software to explain an experiment and perform a numerical evaluation [17]. The impact of PrognosEase parameters on model performance will also be investigated in future studies.

<figure><img src="image_10.png" /><figcaption>**Fig. 6.** Visualizing feature spaces of a dataset generated by PrognosEase.</figcaption></figure>

## 4. Impact

PrognosEase actually introduced an effective and a simple way to study ML models for deterioration analysis. Its simplicity remains in following items:

* Easily generating many types of degradation samples with any preferred number of training and testing cycles making useful for many types of many applications.

* PrognosEase simplifies centralized learning for both offline and online learning.

* PrognosEase also allows experiments to be done according to decentralized and federated learning [18].

* PrognosEase provides a feature space accessing times series experiments for both cyclic and non-cyclic degradation.

* PrognosEase provides features achieving great experiments on direct HI predictions experiments.
<figure><img src="image_11.png" /><figcaption>Fig. 7. Visualizing curve fit results with a deep learning network on a life cycle of the testing set.</figcaption></figure>

* PrognosEase does not follow supervised direct HI and time series predictions; in fact, it can be used for unsupervised HS assessment with clustering methods also.

* PrognosEase allows experiments not only be limited to improving ML methods. In fact, it can also be used for studying data quality and preprocessing tools also.

## 5. Limits and potential improvements

PrognosEase has limits in addressing reality in context of following items:

* Similar to simulation and accelerated aging, PrognosEase does not have the capability of estimating actual RUL timing. Rather than that, it provides HIs instead.

* PrognosEase comes up with Gaussian noise only, so potential improvement will consist of adding more types of noises to approach reality when emulating real conditions.

* Only single type of pulses generation when distorting generated measurements. Accordingly, more efforts can be made on generating other pulses types mimicking distortions in real applications.

* For cyclic degradations better formulas could be released to better control cycles dynamic changes as in real systems such as for batteries for instance.

## 6. Conclusions

This paper presented PrognosEase; a software for generating run-to-failure data for Data-driven prognosis studies. PrognosEase mimics real conditions of different systems by generating similar measurements to their real degradation trends and working conditions. Data visualization for feature spaces generated by PrognosEase and Some ML experiments shows that the software is able to address prediction complexity for unseen samples as in real samples. This paper also presented impact of PrognosEase in PHM filed besides to some future prospects on its potential improvements.

## CRediT authorship contribution statement

**Tarek Berghout:** Conceptualization, Methodology, Software simulations, Data analysis, Writing – original draft. **Mohamed Benbouzid:** Conceptualization, Data analysis, Supervision, Writing – review & editing.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Data availability

Data will be made available on request.

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