Optimizing Wireless Sensor Networks with Machine Learning-Based Predictive Maintenance

PdM system focuses on data collection and system operation estimation. It helps users access system conditions, identify faults, predict failures, and estimate the remaining system life. This paper presents a novel PdM model tailored for WSNs. The main contributions of this work include: The integration of FFNNs to predict network conditions based on multivariate time-series QoS data. The implementation of quantization (reducing the number of bits representing data) and encoding (transforming data into processable formats) techniques to minimize computational complexity. A detailed performance evaluation demonstrating the model's efficacy in real-time deployment scenarios.

These contributions aim to enhance the reliability and efficiency of WSNs while addressing resource constraints. The PdM approach maximizes system lifespan, minimizes unplanned downtimes, and reduces maintenance costs, improving overall reliability and production quality. The WSNs and IoT technologies are essential for advancing and refining Predictive Maintenance. These technologies facilitate the collection of vast amounts of data from sensors installed in machinery, within factories, and at various monitoring locations. For PdM to work effectively, an active sensing system is required to gather measurements that accurately represent the condition of the systems being maintained. The selection, quantity, distribution, and reliability of these sensors are critical factors that determine the overall effectiveness and quality of the PdM.

Most researchers and developers in area of PdM utilize WSNs and IoT as fundamental platform for their solutions. In hazardous and challenging industrial environments, the use of WSNs provides an automated method of performing measuring in lieu of manual measurements. Further, PdM systems are easily deployed and configured due to wireless communication through WSNs. However, these systems may be faced with problems including, energy shortages, force majeure threats, bandwidth issues and restricted computing abilities. Similar to this, PdM systems can be enhanced and optimized with the help of IoT, WSN, machine learning, and deep learning. Typically, ML/DL models, which are developed using neural networks, accept input in two or one-dimensional forms and the outputs are categorical for classification models or a continuous value for regression models.

To achieve high performance and fulfil PdM goals, it appears necessary to choose a design technique that best suits the needs of the system and offers accurate prediction and classification. Based on the ML algorithm, a suggested prediction model framework was created in this regard. It calculates the predictive likelihood distribution of the monitored system's operational status by removing redundant data and streamlining the information into a multivariate time series. It predicts the likelihood that the system will remain fully functional in the upcoming M steps and guarantees that this functionality will be maintained with a specified level of dependability.

The suggested model was created using an ML method based on the feed-forward neural network [1, 2]. Prior observations of the QoS parameters—packet loss, delay, throughput, and power consumption expressed as multivariate time series serve as the input for PdM. After M steps forward in time from the current time, the PdM forecasts the output as a vector that gives the WSN's status. In order to meet the criteria of WSNs, the complexity and memory consumption are further reduced through the use of quantization and encoding techniques [3].

The difficulty of applying PdM in WSNs, where energy and computational resource limitations impair the performance of real-time machine learning models, is addressed in this work. Specifically tailored to the resource constraints of WSNs, the objective is to create a low-complexity, high-accuracy PdM model that can forecast network performance and minimize system outages.

The organization of the paper is as follows: The first section gives introduction to the domain followed by related work. The third section is proposed system model, fourth section presents the overall numerical results and performance of the proposed work in different scenarios, finally the proposed work is concluded.

There are two basic parts to the proposed PdM approach:

(i) Forecasting model for the forward probability distribution of the system's operating state under observation. Time-series data is used to display the system information, and the model forecasts how the system will operate over the following M steps to ensure dependable system operation with a specified reliability level parameter.

(ii) To enhance the prediction model, an ML algorithm that has been employed represents the prediction model, that is, a FFNN.

3.1 Estimating future probability distribution

Assume that the system information is represented by time series w(t), which can be derived from direct measurement or processed data. The system status is evaluated as follows:

• If w(t)≤D, then the system is considered faulty and urgent repairs are necessary.

• If w(t)≤D, the system functions normally.

The goal is to estimate likelihood that the system will remain operational over the next N time steps, given past observations w(t−1), w(t−2), …, w(t−L+1). This probability can be represented as:

$\begin{gathered}P(w(t+N) \leq D, w(t+N-1) \leq D, \ldots, w(t) \leq D) \\ (w(t-1)=u, \ldots, w(t-L+1)=v)\end{gathered}$          (1)

More precisely, the objective is to determine whether the system's continued operability over the next N time steps is assured with a specified reliability level, determined by the parameter δ, as shown in:

$\begin{gathered}P(w(t+N) \leq D, w(t+N-1) \leq D, \ldots, w(t) \leq D) \\ (w(t-1)=u, \ldots, w(t-L+1)=v) \geq 1-\delta\end{gathered}$          （2）

Define the following notations for convenience:

$\begin{gathered}Y^{+(t)}:=(y(t+N), y(t+N-1) \ldots \ldots, y(t)) \\ y^{\wedge}-(t):=(y(t-1), \ldots, y(t-L+1))\end{gathered}$       (3)

In this form, the probability can be expressed more compactly, where the set C is defined as:

$C:=\left\{y_i<D, \ldots ., y_{\{N\}} \leq D\right.$ for $\left.1 \leq I \leq N\right\}$

Thus, the probability is given by:

$P\left(y^{+(t)} \in C \mid y^{-(t)}=(u, \ldots, v)\right) \geq 1-\delta$          (4)

Define the following two vectors:

$\begin{aligned} & r(1)=\left(\{r\}_1^{\{(1)\}},\{r\}_2^{\{(1)\}}\right)=(1,0)\{{ indicating }\} y^{+} \in C \\ & \mathit{r(2)}=\left(\{r\}_1^{\{(2)\}},\{r\}_2^{\{(2)\}}\right)=(0,1)\{{ indicating }\} y^{+} \notin C\end{aligned}$           （5）

This allows us to create a training set:

$\begin{gathered}\left.\tau(K)=\left\{\left(y^{\wedge}(t), r(t\right)\right) \mid t=1, \ldots, K\right\}, \\ r(t) \in\{r(1), \backslash r(2)\}\end{gathered}$           （6）

3.2 FFNN algorithm

The proposed task is implemented using the FNN machine learning technique. The basic architecture of FNNs, which consists of several hidden layers, input layers, and output layers, is what defines them. As the number of hidden layers increases, the data flows unidirectional from the input layer to the output layer. Back propagation, a basic and popular technique, is used as the training method in this study. An activation function is used to determine the estimated output, and a loss function is used to calculate the estimation error. Back propagation is used to update the weights according to the gradient of the loss function.

Several factors influence FNN performance, including the size of the training set, the training algorithm, the structure of the hidden layers, the activation function, and a detailed problem description. The primary criterion is user satisfaction with regard to accuracy and complexity because there are no established standards for choosing, contrasting, and assessing solutions.

The training dataset described in Eq. (6) is used to train the FNN, where the mapping of inputs to outputs is given by z=Net(u,v) with v representing the weights to be learned. The weights adjustment/optimized done using back propagation algorithm are as follows:

$v_{\{\{o p t\}\}}=\min _{\{v\} \frac{1}{k} \sum_{\{k=1\}^{\cdot}}^{\{K\}}}\left|t^{\{(k)\}}-\{N e t\}\left(u^{\{(k)\}}, v\right)\right|^2$          (7)

$\frac{1}{k} \sum_{\{k=1\}}^{\{K\}}\left|t^{\{(k)\}}-\{{Net}\}\left(u^{\{(k)\}}, v\right)\right|^2 \rightarrow E|t-\{{Net}\}(u, v)|^2$         (8)

$\begin{gathered}v_{\{\{o p t\}\}}=min_{\{v\} E}|t-\{N e t\}(u, v)|^2 \rightarrow\{N e t\}(u, v)=E(t \mid u)\end{gathered}$           (9)

21.png

Figure 1. Architecture of a FFNN

After training, the output of the FNN provides the estimated conditional probabilities based on the given past observations. If $P\left(w^{+} \in C / u\right) \geq 1-\delta$, then there are at least N steps to failure.

The architecture of a FFNN is depicted in Figure 1, consisting of three hidden layers. The input layer takes in a window of previous observations. These observations are processed through the hidden layers, and the data flows unidirectional from the input layer to output layer. Each hidden layer applies an activation function, and the output layer generates the final prediction or probability estimation.

The architecture includes:

·Input Layer: Accepts a window of past observations (L previous QoS readings).

·Hidden Layers: The network comprises three hidden layers:

·First hidden layer: 128 neurons with ReLU (Rectified Linear Unit) activation function.

·Second hidden layer: 64 neurons with ReLU activation function.

·Third hidden layer: 32 neurons with ReLU activation function. Dropout layers are incorporated after each hidden layer to prevent overfitting, with a dropout rate of 0.3.

·Output Layer: A single neuron with a sigmoid activation function to output the probability of the system’s operational status.

The FFNN uses back propagation as the training algorithm, optimizing weights based on the gradient of the loss function (binary cross-entropy for classification tasks). Batch normalization is applied to stabilize learning and speed up convergence. This architecture effectively balances model complexity and computational efficiency, making it suitable for deployment in resource-constrained WSN environments.

3.3 Customized PdM for WSNs

The proposed paradigm is covered in this part as a PdM strategy for WSNs. A WSN is made up of one or more base stations and several tiny nodes that work together to collect data. The nodes use a wireless radio transceiver to connect with the base station and with each other. Small-scale processing units and sensors to measure or track physical phenomena are included with these nodes. WSN nodes are frequently installed in complicated situations and typically run on batteries with a limited power source. Restricted memory, low processing power, limited communication bandwidth, and inadequate power backup are some of the constraints that WSN designers and operators must take into account. Notwithstanding these limitations, the system's functionality must satisfy specific QoS standards. Dependability, energy efficiency, security, accuracy, and low latency are some of the QoS requirements for WSNs. In order to enhance WSN performance, the maintenance action may entail selecting new cluster heads, rearranging clusters, installing new sensors, controlling ON/OFF schedules, and other tactics. A low-complexity PdM model is required due to the restricted resources of WSNs.

3.4 Quantized FFNN

The energy, memory, and computing capability of WSNs are limited. A quantization approach that speeds up training and lowers the model's complexity is used to make sure the PdM model performs effectively under these limitations. Quantization speeds up training and makes the model simpler, but it may also decrease accuracy, necessitating a trade-off between precision and complexity. The quantization function converts variables and weights from their typical floating-point representations into integers, which are fixed-point representations of numbers. This conversion improves memory efficiency and computation speed.

The quantization level $q$ of the actual value v is determined by a deterministic quantization function in the manner described below:

$q(v)=\{{sign}\}(v) \cdot \Delta(\{|v|\} /\{\Delta\}+\{1\} /\{2\})$            (10)

where, $\Delta$ is the resolution or the quantization step size.

We refer to these functions as equidistant quantization. Each quantization level has an equal portion of the quantization range. Data that is uniformly distributed is ideal for these functions. Non-equidistant quantization works better for distributions that are not uniform.

This algorithm minimizes mean square quantization error $\sigma$ by taking the probability distribution function (PDF) of the samples into account.

The optimal quantized level $q_i(v)$ of a sample v is found iteratively:

$q_{j(v)}=\frac{\left\{\int_{\left\{d_j\right\}}^{\left\{d_{\{j+1\}}\right\}} v \cdot h(v), d v\right\}}{\left\{\int_{\left\{d_j\right\}}^{\left\{d_{\{j+1\}}\right\},} h(v) d v\right\}}$         (11)

The PDF of the sample distribution is denoted by $h(v)$, whereas $d_j$ and $d_{j+1}$ stand for the limits of the suggested quantization level $q_j$.

The goal is to minimize the mean square quantization error $\tau$, expressed as:

$\tau=\int_{\left\{d_j\right\}}^{\left\{d_{\{j+1\}}\right\}}\left(v-q_j\right)^2 h(v) d v$          (12)

By using this approach, the quantization error is minimized while considering the underlying distribution of the data. Quantization and encoding techniques have a significant impact on the model’s performance and complexity. Quantization reduces the model’s memory footprint, making it suitable for deployment on devices with limited resources. Fixed-point operations resulting from quantization are computationally faster than floating-point operations, reducing inference time. While quantization may introduce minor inaccuracies, these are offset by the model’s robustness, which is particularly beneficial in applications where precision is not critical. Furthermore, dropout layers and encoding techniques enhance the model’s ability to generalize, ensuring reliable predictions even with noisy or incomplete data.

Quantization reduces the model's memory and computational requirements by mapping floating-point parameters to fixed-point representations. While this optimization enables deployment on resource-constrained devices, it introduces trade-offs. Specifically, lower precision may slightly degrade model accuracy. However, these inaccuracies are typically negligible in WSN applications where computational efficiency and energy savings are paramount. The benefits include reduced memory footprint, faster inference times, and improved suitability for real-time processing in WSN environments.

3.5 Sparsity of FFNN

The main issue with using FFNNs on WSNs is memory limitations. A number of techniques are used to advance ML/DL algorithms' memory efficiency. While some strategies target memory demands during training, others concentrate on reducing the amount of memory needed for inference. Sparse FFNNs are one popular and effective method for enhancing DL/ML algorithms.

A sparse vector, with the majority of its entries being zeros, is used to represent input characteristics in a sparse FFNN. As a result, less memory and computational load are required. Sparsity can have a detrimental effect on the FFNN's accuracy even while it lowers computational complexity and increases memory economy. As a result, the degree of sparsity and the model's accuracy need to be balanced. We use a straightforward encoding system in this work, which was motivated by the approach described in the previous study. The quantization approach, which encodes each quantized level into an orthonormal vector, is enhanced by this encoding technique:

$q_m \rightarrow t_q^m: t_q^m(j)=\left\{\frac{1 \text { if } j=m}{0 \text { otherwise }}, j=\{1,2 \ldots \ldots T\}\right\}$       (13)

By applying this encoding, Eq. (3) becomes:

$\begin{gathered}z^{+}(n):=\left(t_q(n+P), t_q(n+P-1), \ldots t_q(n)\right), \\ z^{-}(n):=\left(t_q(n-1), \ldots t_q(n-K+1)\right)\end{gathered}$         (14)

3.6 Dataset setup

In order to gather data, two TelosB nodes were connected via an IEEE 802.15.4 link that was constructed on TinyOS. Every node was fitted with a 250 kbps TI CC2420 radio transceiver. They tracked packet delivery performance based on several predefined parameters associated with the physical, MAC, and application layers. A table of 10,000 observations was generated. Each row in the table summarizes the average values of 300 packets.

The transmission power was fixed at -19 dBm, while other parameters were varied according to the combinations listed in Table 1.

In addition to these configured parameters, the table also records a number of performance metrics related to packet delivery for each parameter combination, as presented in Table 2. A trial of the observation is provided in Table 3. The table provides shows configured parameters for a system, along with their acronyms, possible values, and comments. Here’s a breakdown:

Table 1. Parameters configuration

Table 2. Performance metrics

Table 3. Observation values

We calculated the QoS requirements of the WSN based on both pre-set and observed parameters, focusing on energy efficiency, throughput, delay, and packet loss.

The reliability of the system is reflected in the packet error rate (PER), which is affected by the nodes' queuing behavior and the quality of connection metrics like LQI, RSSI and NF.

PER is calculated as:

$P E R=\frac{\left\{N_{\{p\}}-A\right\}}{\left\{N_{\{p\}}\right\}}$       （15）

Energy efficiency (E_eff): This measures the energy required to transmit a useful bit. It is influenced by PER, transmission power level, packet payload, header length, and transmission rate:

$E_{\{e f f\}}=\frac{\left\{P_{\{t x\}} \times\left(H_{\{L\}}+P_{\{L\}}\right) \times T_{\{s\}}\right\}}{\left\{P_{\{L\}(1-\{P E R\})}\right\}}$        （16）

where, T_s is the transmission time, which is 0.004 ms at a rate of 250 kb/s, and H_L is the header length, which can vary between 11 and 31 bytes in IEEE 802.15.4.

Throughput (T_p) refers to the number of useful bits received per unit time. It determined by on packet payload (P_L), PER, and transmission service time (T_srv):

$\begin{gathered}{Throughput }\left(T_p\right)=\frac{\left\{P_{\{L\}(1-\{P E R\})}\right\}}{\left\{T_{\{s r v\}}\right\}} \\ \left(T_{\text {srv }}\right)=K+T_{\{s\}}+\left(N_{\{p\}} \times D_{\{R\}}\right) \\ { Transmission\ Service\ Time }\left(T_{ {srv }}\right)\end{gathered}$     （17）

where, K is a constant depending on the protocol and radio system specifications. In this case, it is approximately 13.5 ms based on the experimental setup.

Delay refers to the time from packet creation to its successful reception. It is influenced by the link quality indicator (LQI) and node queuing characteristics. Often, a queuing model is used to represent delay in WSNs. We use system utilization (u) as a metric for delay, where u=T_srv/TBA, and as u→1 delay increases.

The computed QoS metrics (PER, E_eff, T_p, and u) are organized into a 10,000×4 input feature table, where each row corresponds to an entry in the observations table. As a fifth input feature, the time of packet arrival (TPA) is converted into a time series and added. The QoS metrics frequently depend on one another; for example, by increasing energy efficiency, throughput may decrease, or dependability may increase. For the user, these metrics must be balanced. The following ranges are established for each statistic in order to specify the WSN's operating conditions:

$\begin{gathered}\alpha^{\{+\}} \leq\{P E R\}<\alpha^{\{-\}}, \beta^{\{+\}} \leq E_{\{e f f\}}<\beta^{\{-\}}, \gamma^{\{+\}} \leq T_{\{p\}}<\gamma^{\{-\}}, \delta^{\{+\}} \leq u<\delta^{\{-\}}\end{gathered}$           （18）

This paper introduces a machine learning-driven approach to PdM tailored for WSNs. Using a FFNN, the model forecasts future network conditions by analyzing QoS metrics. By incorporating quantization and encoding, the model reduces complexity, making it suitable for real-time deployment in resource-limited WSNs. Findings reveal that longer prediction steps (M) can increase complexity and error, while a larger historical data window (L) improves accuracy. Overall, the PdM model achieves a practical balance between prediction precision and resource limitations, supporting reliable network performance with efficient energy use and minimized packet loss. The limitations include its reliance on a fixed data window size and FFNN, which may not generalize well to other network types or capture long-term dependencies.

Deploying the model in real-world WSNs involves addressing challenges like resource constraints, environmental variability, and network latency. Quantization and encoding techniques ensure efficient operation on resource-limited devices, while edge computing mitigates latency by enabling local data processing. For diverse applications, the model can be optimized by tailoring input features and retraining with domain-specific datasets.