Battery Life Prediction for Ensuring Robust Operation of IoT Devices in Remote Metering

Abstract

Primary batteries are extensively employed as power sources in Internet of Things (IoT) devices for remote metering. However, primary batteries maintain a relatively consistent discharge voltage curve over a long period before experiencing a full discharge, making it challenging to predict the battery’s life. In this study, we introduce a battery life prediction method to ensure the robust operation of IoT devices in remote metering applications. The robust battery life prediction process is divided into two stages. The first stage involves predicting the state of charge (SOC) to enable real-time remote monitoring of the battery status of metering devices. In the second stage, IoT devices implement a hardware-based alerting mechanism to provide warnings prior to complete discharge, leveraging a custom-designed Multi-Stage Discharge battery architecture. In the first stage, we developed the CNN-Series Decomposition Transformer (C-SDFormer) model, which is capable of accurately predicting the SOC of primary batteries. This model was specifically designed to support the real-time monitoring of battery status in large-scale IoT deployments, enabling proactive maintenance and enhancing system reliability. To validate the performance of the C-SDFormer model, data were collected from smart remote meters installed in households. The model was trained using the collected data and evaluated through a series of experiments. The performance of the C-SDFormer model was compared with existing methods for SOC prediction. The results indicate that the C-SDFormer model outperformed the traditional methods. Specifically, the SOC prediction achieved a mean absolute error (MAE) of less than 4.1%, a root mean square error (RMSE) of less than 5.2%, a symmetric mean absolute percentage error (SMAPE) of less than 7.0%, and a coefficient of determination (R²) exceeding 0.96. These results demonstrate the effectiveness of the C-SDFormer model in accurately predicting the SOC of primary batteries. For the second stage, a Multi-Stage Discharge (MSD) primary battery was developed to ensure a hardware-based low battery alert before the battery is fully discharged. This battery was designed to ensure the reliable operation of IoT devices, especially those whose batteries are not proactively managed through real-time monitoring in the first stage. By providing a low battery alert, the MSD battery reduces the risk of unexpected device shutdowns. This feature enhances the overall reliability of IoT devices, ensuring their continuous operation in remote metering applications.

1. Introduction

Internet of Things (IoT) devices in remote metering applications are typically installed in locations where continuous power supply is challenging, or where human access is limited [1,2]. These devices require a stable and long-lasting power source to operate reliably for several years, and potentially up to a decade [3,4]. Due to these requirements, primary batteries are predominantly used, as they provide the necessary longevity and stability without the need for frequent replacement or maintenance, making them ideal for applications where regular access is restricted [5,6].

However, due to the flat discharge curve characteristics of primary batteries [7], it is difficult to predict the battery life, and this often leads to unexpected fully discharge. Such unexpected power loss can have a significant impact on remote metering devices and cause property damage [8,9,10]. To mitigate this risk, backup batteries [11] are currently used, or batteries are replaced in advance. However, these approaches are expensive and lead to a significant waste of resources, making them unsustainable for wide-ranging or long-term applications.

In this paper, we propose a battery life prediction method to ensure the robust operation of IoT devices in remote metering applications, as shown in Figure 1. The robust battery life prediction process is divided into two stages. As the first stage, we focuses on predicting the state of charge (SOC), facilitating real-time remote monitoring of battery conditions in metering devices. The SOC is estimated using temperature, voltage and communication quantity data. This SOC inference is performed on a server, where the meter device periodically transmits its measured parameters. The high cost of SOC measurement equipment poses a significant challenge in practical IoT devices deployed for remote metering applications. Therefore, we employed alternative parameters for real-time prediction instead of utilizing SOC directly, enabling efficient and cost-effective monitoring. In the second stage, a hardware-based alert system is integrated into IoT devices to issue warnings before complete discharge, leveraging a custom-designed Multi-Stage Discharge battery architecture.

In the first stage, we developed the CNN-Series Decomposition Transformer (C-SDFormer) model, which is capable of accurately predicting the SOC of primary batteries. As mentioned earlier, three inputs are employed for SOC prediction. Among these, instances of communication induce transient voltage fluctuations, which represent significant factors for SOC prediction due to the inherent characteristics of IoT devices in remote metering applications. We incorporated a transformer layer into the model architecture to effectively capture and analyze voltage variations, leveraging its attention mechanism to focus on voltage fluctuation data. In addition, we combined a convolutional neural network (CNN) with series decomposition techniques to enhance the model’s ability to handle complex patterns of battery discharge behavior. This led to the development of the C-SDFormer model, which enables real-time discharge capacity prediction, providing a more accurate and robust approach to battery health monitoring in remote metering applications.

Environmental factors, including the installation location of IoT devices and other external influences, degrade the accuracy of SOC prediction during the first stage [12]. To address these challenges, a Multi-Stage Discharge (MSD) primary battery was developed for the second stage to ensure a hardware-based low battery alert before the battery is fully discharged. Specifically, the MSD primary battery was developed by mixing two electrolytes, which results in two distinct voltage drops during discharge. A low battery alert is triggered within the voltage range corresponding to the first of these voltage drops. This design also enhances the overall robustness against missing or noisy data in the first stage. Even if the C-SDFormer’s real-time SOC estimation is adversely affected by such uncertainties, the voltage drop in the MSD battery still provides a clear hardware-based signal to indicate a low battery state. As a result, the system can reliably detect when the battery is nearing depletion, regardless of model inaccuracies or data gaps. This battery was specifically designed to guarantee the reliable operation of IoT devices, particularly where batteries are not actively monitored in real time during the first stage. By issuing a low battery alert, the MSD battery mitigates the risk of unexpected device shutdowns. Hence, even under noise or missing data conditions, the second stage of the MSD battery architecture ensures continued device reliability and uninterrupted operation in remote metering applications.

To evaluate the effectiveness of the proposed C-SDFormer model, we collected data from smart remote meters deployed in households. The model was subsequently trained on this dataset and its performance was validated through a series of experimental analyses. These experiments were designed to demonstrate the model’s capability in accurately predicting SOC and improving battery life management for IoT devices in remote metering. The C-SDFormer model utilizes temperature, voltage, and number of communications as input features for SOC prediction. Furthermore, the efficiency of the C-SDFormer architecture was verified through ablation studies, where the contributions of individual layers to its performance were systematically analyzed. The model also exhibited superior accuracy and robustness compared to existing methods in SOC prediction. Furthermore, the low-battery alert enabled by the MSD primary battery enhanced the robustness of IoT devices in remote metering and ensured their continuous operation.

The rest of this paper is organized as follows. Section 2 introduces the related works on SOC estimation based on deep learning. Section 3 explains the details of the remote metering life prediction method. Section 4 describes the experimental setup. Section 5 demonstrates the SOC estimation and prediction performance in comparison with existing methods and provides a detailed discussion of the experimental results. Finally, Section 6 concludes this paper.

2. Related Work

There has been limited machine learning research focused on estimating the remaining capacity of primary batteries using voltage. This is due to the fact that, as previously discussed, conventional primary batteries exhibit notably flat discharge curves with just a single voltage drop.

Conversely, machine learning–based SOC prediction for secondary batteries has seen active development [13,14,15,16,17,18,19,20,21,22]. Early research employed a deep neural network (DNN) [13] as the foundational model, predicting SOC by considering three main attributes: instantaneous voltage, instantaneous current, and instantaneous temperature. In another study, a long short-term memory (LSTM) [14] architecture was used to examine various features for their correlation with SOC. Parameters such as voltage, current, and environmental factors (temperature, humidity, and wind speed) were compared against SOC. Given that voltage exhibited the strongest correlation, predictions were ultimately based solely on voltage. A convolutional neural network (CNN) [15], commonly applied in computer vision, was then introduced by applying temporal convolutions to relaxation voltage data collected over a 10-s window. Subsequently, a CNN-LSTM-DNN framework [16] was developed, combining the strengths of a DNN, LSTM, and CNN into a single model. In this approach, the CNN extracted temporal features, LSTM handled time series information, and DNN enhanced the estimation accuracy. As a result, the CNN–LSTM–DNN outperformed the basic LSTM, CNN, and CNN-LSTM models in SOC estimation for secondary batteries.

Additionally, some researchers adopted a bidirectional gated recurrent unit (Bi-GRU) [17] to reduce computational overheads while also leveraging bidirectional data analysis. This model processed voltage, current, and temperature inputs. To address gradient loss, the Nesterov Accelerated Gradient (NAG) algorithm was used for estimating the remaining capacity. Building on the Bi-GRU concept, the CNN-bidirectional weighted gated recurrent unit (CNN-BWGRU) [18] was subsequently proposed, integrating a CNN layer to extract input features. It too utilized voltage, current, and temperature data, passing these features through the Bi-GRU for SOC prediction.

Various Transformer-based models [19,20,21,22] have been employed for SoC estimation. The Transformer architecture is renowned for its ability to process more comprehensive information than traditional neural networks. The Transformer with an immersion and invariance adaptive observer [19] utilizes two separate encoders to simultaneously encode information on current temperature and voltage temperature. The outputs are then concatenated and used as input for the decoder to estimate the SoC. Next, TTSNet [20] proposes a sequence-to-sequence network that employs a temporal Transformer, using voltage, current, and temperature as inputs to estimate the SoC. In addition, another Transformer-based online battery life estimation model [21] improves the estimation accuracy by incorporating vehicle speed as an additional input feature. Finally, SGEformer [22] predicts the battery lifespan by leveraging a variety of input data, including the number of charge cycles, voltage, current, and load, combined with a lookback window technique.

Nevertheless, it is essential to note that these studies encompass data from both the charging and discharging processes, rendering them unsuitable for primary batteries, where no charging phase exists. Moreover, the discharge profiles of primary and secondary batteries differ significantly, necessitating distinct models. Consequently, attempting to estimate the SOC of primary batteries using a model trained exclusively on secondary battery data presents formidable challenges. To address these challenges in SOC estimation, we have introduced the MSD primary battery, incorporating machine learning techniques, particularly the C-SDFormer model, for SOC estimation tailored to primary batteries.

3. Remote Metering Life Prediction Method

3.1. Multi-Stage Discharge Primary Battery

As previously mentioned in the introduction, we focus on real-time SOC prediction and on triggering a low battery alert before complete discharge. To achieve this, we developed a Multi-Stage Discharge (MSD) primary battery, as illustrated in Figure 2, which exhibits two distinct voltage drop stages. In Figure 2, the point at which the voltage drop initiates is denoted as the primary point. The primary point represents the final moment at which real-time estimation can be performed. For enhanced life prediction reliability and to allow sufficient time for maintenance, we recommend battery replacement when the battery reaches the primary point rather than waiting for the final drop point. This innovative design incorporates two separate voltage drops rather than the single voltage drop characteristic of conventional primary batteries. The MSD primary battery is produced by blending two electrolytes, $S{O}_{2}C{l}_2$ and $SOC{l}_2$, resulting in two discharge stages governed by the following chemical reactions (see Equations (1) and (2)):

$$\begin{array}{cc}\hfill Firststage:4Li+2S{O}_{2}C{l}_2& \to 4LiCl+2S{O}_2,\hfill \end{array}$$

(1)

$$\begin{array}{cc}\hfill Secondstage:4Li+2SOC{l}_2& \to 4LiCl+S{O}_2+S.\hfill \end{array}$$

(2)

The operation of the MSD primary battery commences with the reaction of $Li$ with $S{O}_{2}C{l}_2$, which leads to a minor voltage drop to a point termed the primary point. This point can be moved to the 10% and 5% points of $SO{C}_{Prim}$, depending on the ratio of the two electrolytes, allowing the MSD primary battery to be used to its full capacity. Subsequently, $Li$ reacts with $SOC{l}_2$, inducing a further reduction in voltage to a lower level, and eventually the battery discharges.

In our implementation, the MSD primary battery demonstrates a total capacity of approximately $17.40\mathrm{Ah}$. During the first discharge stage, where the average operating voltage typically stabilizes at around $3.78\mathrm{V}$, the battery constitutes about $14.82\mathrm{Ah}$ of its total capacity. We also observed that this first-stage voltage may vary with temperature: at 60 °C, the battery maintains around $3.60\mathrm{V}$, whereas at −20 °C, it drops to about $3.30\mathrm{V}$, and at ambient temperature (20 °C), it averages approximately $3.75\mathrm{V}$. After passing the primary point, the voltage transitions to the second stage, averaging around $3.47\mathrm{V}$. Considering that the remote metering device consumes approximately $11.8\mathrm{mAh}$ per day, the battery sustains operation for about four years before reaching complete discharge.

Figure 2. Discharge curve of the MSD primary battery. Batteries produced through electrolyte mixing exhibit a primary point at 15% of $SO{C}_{Prim}$. $DO{D}_{Prim}$ represents the depth of discharge at the primary point, while $SO{C}_{Prim}$ denotes the state of charge at the primary point.

Figure 2. Discharge curve of the MSD primary battery. Batteries produced through electrolyte mixing exhibit a primary point at 15% of $SO{C}_{Prim}$. $DO{D}_{Prim}$ represents the depth of discharge at the primary point, while $SO{C}_{Prim}$ denotes the state of charge at the primary point.

3.2. Data Collection and Preprocessing

To analyze the discharge characteristics of MSD primary batteries in a real-world setting, we implemented the printed circuit board (PCB) embedded within the remote gas meter for collecting data (refer to Figure 3a). Figure 3b shows the MSD Primary battery installed in the remote gas meter. Figure 3c shows that the rear part of the board is equipped with a PMIC for overseeing voltage and current, a Cortex-M0 microcontroller’s temperature sensor to measure temperature, and an SX1276 Long Range Radio (LoRa) module for wireless data transmission. We deployed 50 remote gas meters within households (as illustrated in Figure 3d) and harnessed a power management integrated circuit (PMIC) embedded in each remote gas meter to capture the data. The collected data include timestamps, discharge capacity, temperature, voltage, and the communication count, as outlined in

Table 1. Data collected from smart gas meters.

Collected Data	Detail
Timestamp [Second]	Timestamp of data collection
Discharge Capacity [mAh]	Battery usage using Coulomb Counter (Used as the ground truth for SOC prediction)
Temperature [°C]	Battery operating temperature
Voltage [V]	Present voltage
Communication Count [count]	Number of communications attempts per 10 min

. We utilized temperature, voltage, and communication count as input data for the C-SDFormer model, while discharge capacity was employed as the ground truth for prediction. This approach was adopted because, in real-world scenarios, measuring discharge capacity requires expensive equipment, making it impractical for widespread applications such as smart metering. The data were recorded at 10 min intervals and subsequently transmitted to the server for storage at hourly intervals.

For clarity,

Table 2. Sample of input data.

Timestamp	Voltage [V]	Temperature [°C]	Communication Count [Count]
1658103487	3.814	32.81	0
1658104087	3.814	32.76	0
1658104687	3.785	32.86	3
1658105287	3.811	32.71	0
1658105887	3.811	32.69	0
1658106487	3.813	32.74	0

presents a sample excerpt of the collected data over a one-hour period, showing representative values for timestamps, voltage, temperature, and communication count. This sample illustrates the typical range of input values observed during operation and highlights how communication events affect voltage changes. Additionally,

Table 3. Summary statistics of input data.

Input Variables	Mean	Std	Min	Max
Temperature [°C]	25.2	4.37	3.02	37.1
Voltage [V]	3.59	0.08	3.34	3.83
Communication Count [count]	0.55	1.56	0.00	41.0

presents summary statistics (mean, standard deviation (Std), minimum (Min), and maximum (Max)) for the measured input variables, providing an overview of the range of operating conditions observed in our dataset. These statistics illustrate the diversity in temperature, voltage, and communication count values, which helps the model capture variations in operating conditions and improve the accuracy of discharge capacity predictions.

Raw data acquired from remote gas meters frequently contain missing values and noise, which may hinder the performance of machine learning models. To address these challenges and improve model performance, we implemented a four-step data preprocessing procedure including missing value interpolation, noise reduction, primary point identification, and normalization. First, missing values in voltage, temperature, and communication count were addressed using Algorithm 1, while discharge capacity was handled through linear interpolation. To ensure the reliability of this process, missing values were analyzed across multiple test sets, and different interpolation techniques were compared to minimize bias in data imputation. Second, convolution-based smoothing [23] was employed to reduce noise in the discharge capacity and voltage data. This technique was selected based on empirical analysis comparing various denoising methods, ensuring that essential signal patterns were preserved while removing irrelevant fluctuations. Third, the primary point for triggering alerts was mathematically determined based on the first voltage drop. Lastly, min–max normalization was applied to enhance model performance.

During the data collection process, missing values in discharge capacity, temperature, voltage, and communication count can occur due to communication interruptions between the smart gas meter and the server. Algorithm 1 presents the pseudocode for imputing missing voltage values through interpolation, maintaining the voltage variation patterns attributed to LoRa communication, as observed in the measured data. Here, T represents a time series with N empty values, $T^{\ast }$ is the imputed version of T, X signifies the previous data point for T, and Y stands for the subsequent data point for T. Line 3 assigns X to T, and lines 4 and 5 calculate the average of X and Y, respectively. Line 6 finds the bias, and lines 7 and 8 update T by subtracting the bias from each element of T. Line 9 allocates the updated T to $T^{\ast }$. The same procedure is applied to the temperature and the communication count for the same reasons. Missing values for discharge capacity were imputed through linear interpolation. Figure 4 illustrates the change in voltage data after implementing Algorithm 1.

Algorithm 1 Voltage Interpolation

Input: time series $T=[t_{m+1},t_{m+2},\cdots ,t_{m+n}]$, with empty value of length N Output: filled time series $T^{\ast }$ 1:      Let $X=[t_{m-n+1},t_{m-n},\cdots ,t_m]$, Length N 2:      Let $Y=[t_{m+n+1},t_{m+n+2},\cdots ,t_{m+2n}]$, Length N 3:      $T\leftarrow X$ 4:      $x_{average}={\displaystyle \frac{1}{n}}{\sum }_{i=m-n+1}^m{t}_i$ 5:      $y_{average}={\displaystyle \frac{1}{n}}{\sum }_{i=m+n+1}^{m+2n}{t}_i$ 6:      $Bias={\displaystyle \frac{x_{average}-y_{average}}{2}}$ 7: for each t in T do 8:      Update t as $t\leftarrow t-Bias$ 9: $T^{\ast }\leftarrow T$

During data collection, noise can significantly affect the training process. To address this, we applied a convolution-based smoothing technique commonly used in signal processing, as defined in Equation (3).

$$\begin{array}{c}\hfill h\left(t\right)=f\left(t\right)\ast g\left(t\right)=\sum _{k=0}^{N}f\left(k\right)g(t-k),\end{array}$$

(3)

where $g\left(t\right)$ is the input filter, N is the length of the data collected for $f\left(t\right)$, t is the time parameter, and $h\left(t\right)$ is the denoised data obtained by the convolution of $g\left(t\right)$ and $f\left(t\right)$. Figure 5 shows a clear and noticeable reduction in noise after the data passes through the filter.

The process of determining the primary point utilized the second derivative of the daily voltage data, as shown in Figure 6a. These second derivative values capture significant changes in the voltage slope between consecutive days. A negative second derivative indicates a decreasing voltage slope, marking the onset of a voltage drop, whereas a positive second derivative reflects an increasing voltage slope, signifying the end of the voltage drop. The primary point was identified as the point with the smallest second derivative value (as defined by Equation (4)).

$$\begin{array}{c}\hfill Primarypoint=Minimum({\displaystyle \frac{\mathrm{d}}{{\mathrm{d}}^{2}t}}V\left(t\right)),\end{array}$$

(4)

where $V\left(t\right)$ represents the voltage discharge curve over time. Figure 6b visually illustrates the placement of the primary point on the discharge curve, while Figure 6c showcases the extracted data for learning, using the primary point as a reference.

For the final step, we applied a machine learning technique, normalization. This method aims to standardize the scales of input features, ensuring equitable significance during model training. To address the scale disparities within our collected data, encompassing discharge capacity, temperature, voltage, and the communication count, we opted for min–max normalization. This process scaled the original data to fall within the range of 0 to 1, as per Equation (5).

$$\begin{array}{c}\hfill Y\left(t\right)={\displaystyle \frac{y\left(t\right)-y_{min}}{y_{max}-y_{min}}},\end{array}$$

(5)

In Equation (5), where t represents time, $y\left(t\right)$ signifies the data before normalization, $y_{min}$ denotes the minimum value of $y\left(t\right)$, $y_{max}$ represents the maximum value of $y\left(t\right)$, and $Y\left(t\right)$ is the normalized data.

3.3. C-SDFormer Model for Predicting the Discharge Capacity of MSD Primary Battery

Our objective is to predict the discharge capacity in real-time using deep learning techniques, with input parameters including voltage, temperature, and communication count. To achieve this, we employed a transformer-based model, which represents an evolution of the seq2seq model [24], featuring an encoder–decoder architecture. Diverging from traditional recurrent architectures [25,26,27], the transformer model relies on a neural network with an attention mechanism to analyze the relationships between outputs based on the voltage drop characteristics occurring during communication. While transformer models are predominantly used in natural language processing [28], they also find utility in analyzing time series data [29,30,31,32].

To predict the discharge capacity during the first discharge stage, we introduce the C-SDFormer model, which builds upon the encoder architecture of the Transformer [33]. Unlike conventional Transformer models, C-SDFormer is specifically designed to handle the unique challenges posed by transient voltage fluctuations in remote metering environments. Traditional models struggle to effectively capture these variations, particularly those induced by communication events. To address this, C-SDFormer integrates mechanisms to differentiate between short-term fluctuations and long-term discharge trends, making it more suitable for battery discharge prediction in practical applications.

Prior research has utilized traditional convolutional neural networks (CNNs [15]) for local feature extraction, as well as long short-term memory networks (LSTMs [14]) and gated recurrent units (GRUs [17]) for time series forecasting. However, these models exhibit limitations in capturing long-range dependencies and tend to suffer from vanishing gradients when processing extended sequences. Transformer-based models have emerged as a powerful alternative due to their capability to model long-term dependencies through self-attention mechanisms. Informer [29], Autoformer [30], and Fedformer [31] are notable Transformer-based architectures designed for time series forecasting. While these models improve efficiency and accuracy compared to RNN-based approaches, they are not explicitly optimized for battery discharge prediction in remote metering environments.

C-SDFormer distinguishes itself from existing Transformer-based time series models through its series decomposition module, which separates trend and seasonal components to better capture transient voltage variations caused by communication activities. Additionally, the CNN-based feature extraction module enhances the representation of voltage changes by identifying spatial patterns in time-series data, making it particularly effective in detecting sudden voltage drops induced by communication events. Furthermore, the self-attention mechanism in the Transformer encoder dynamically weighs the importance of different time steps and refines the extracted features from the series decomposition and CNN modules. This allows the model to focus on the most relevant temporal dependencies and spatial patterns, enhancing its ability to capture both short-term fluctuations and long-term battery discharge trends. This hybrid approach ensures that both short-term and long-term voltage dynamics are modelled accurately, leading to improved battery discharge prediction.

The architecture of C-SDFormer consists of several key components, including a CNN-based input embedding layer, a positional encoding layer, an encoder layer, a series decomposition, and a linear output layer. Figure 7 illustrates the detailed structure of C-SDFormer. Initially, the voltage, communication count, and temperature are obtained through a sliding window and stacked together. They then pass through the input embedding layer, which consists of a CNN and facilitates the feature extraction process within the encoder layer, mapping them to a 128-dimensional vector. The C-SDFormer model lacks a recursive architecture, necessitating the inclusion of position tokens to indicate the position of each element in the sequence. This aids the model in comprehending the sequence’s item order and retaining this order. Various techniques exist for incorporating positional information into sequences, but in this study, we employ sine and cosine functions, as defined in Equations (6) and (7).

$$\begin{array}{cc}\hfill P{E}_{(pos,2i)}& =sin({\displaystyle \frac{pos}{{10,000}^{(2i/d_{model})}}}),\hfill \end{array}$$

(6)

$$\begin{array}{cc}\hfill P{E}_{(pos,2i+1)}& =cos({\displaystyle \frac{pos}{{10,000}^{(2i/d_{model})}}}),\hfill \end{array}$$

(7)

where $pos$ is the position of the embedding vector in the sequence and i is the index for each dimension of the embedding vector. If the index is even, we use the sine function. If the index is odd, we use the cosine function.

Subsequently, the input, now encompassing positional information, proceeds to the encoder block. This encoder block comprises multiple layers, including a multi-head self-attention layer, a series decomposition layer, a feed-forward network (FFN), residual connections (Add), and layer normalization (LayerNorm). Residual connections serve to mitigate the risk of gradient vanishing, while layer normalization aids in convergence learning and enhances the model’s resilience to data variations. The self-attention mechanism, a potent tool for learning dependencies within sequence components, enables the model to focus on the most pertinent information in the sequence. It operates by generating three matrices: Query (Q), Key (K), and Value (V) for the input sequence. These matrices are computed using distinct weight matrices, $W^q$, $W^k$, and $W^v$, learned during training. The Q and K matrices are multiplied and scaled by $\sqrt{d_k}$, and then converted into a probability distribution using the softmax function. Subsequently, the V matrix is multiplied by this probability distribution to yield the attention value, which provides the model with more detailed insights into the elements deserving of focus. The calculation of the attention value can be summarized by Equation (8).

$$\begin{array}{c}\hfill Attention(Q,K,V)=softmax({\displaystyle \frac{Q{K}^T}{\sqrt{d_k}}})V,\end{array}$$

(8)

where $d_k$ is the dimension of the K vector. Our model also incorporates multi-head self-attention, an enhancement of the self-attention mechanism. Multi-head self-attention simultaneously applies multiple self-attention mechanisms to model the relationships among input data from various perspectives and extracts comprehensive information. This approach empowers the model to distinguish between distinct features within the input sequence, thereby enhancing its learning capacity. After passing through Add&LayerNorm, the model employs a series decomposition layer to segregate the data into seasonal and trend components. This separation streamlines the identification of seasonal and trend information in isolation, with only the seasonal features undergoing processing through the FFN. This step allows for more detailed information extraction and pattern learning from the seasonal features.

Ultimately, following transit through the series of N encoder blocks, the discharge capacity is predicted utilizing M convolution layers and a dense layer. For specific model hyperparameters, please refer to Section 4 for detailed information.

3.4. SOC and Remaining Time Calculation Using the Predicted Discharge Capacity

The SOC indicates the remaining battery capacity relative to the rated capacity. The SOC value ranges from 0% to 100%, with 100% representing a fully charged battery and 0% representing a fully discharged battery. To estimate the SOC of the MSD primary battery, we use the discharge capacity predicted by the C-SDFormer. Equation (9) shows the $SO{C}_t$ calculation process.

$$SO{C}_t=100\%-{\displaystyle \frac{C_{released}}{C_{rated}}}\times 100\%,$$

(9)

where $SO{C}_t$ is the SOC at time t, $C_{released}$ is the discharge capacity, and $C_{rated}$ is the rated capacity as specified by the manufacturer.

In addition, to enhance the practical relevance of our approach, we converted the predicted SOC into an estimated remaining time until complete battery discharge. Measuring current in real-world settings is challenging. Therefore, we defined $I_{avg}$ as the daily average current consumption derived from the predicted SOC based on the device’s power consumption profile data. This profile was estimated in real time because it varies with each device’s operating conditions, such as the number of retransmissions determined by the communication environment and the ambient temperature. The estimated remaining time, $T_{remaining}$, is then calculated using:

$$T_{remaining}={\displaystyle \frac{C_{rated}-C_{released}}{I_{avg}}},$$

(10)

where $T_{remaining}$ represents the estimated remaining operational time until full discharge, measured in days, and $I_{avg}$ is the daily average of $C_{released}$. This transformation enables the model to provide users with a practical, time-based prediction of battery life, thereby further improving the applicability of our battery management strategy.

4. Experimental Setup

In this section, we delve into a comprehensive exploration of the experimental components crucial to our study. We provide detailed insights into our experimental setup, encompassing hyperparameters, implementation specifics, and the evaluation metrics.

4.1. Hyperparameters of C-SDFormer

The hyperparameters of the C-SDFormer model are comprehensively outlined in

Table 4. Hyperparameters of the C-SDFormer.

Stage	Order	Layers	Layers Parameters
Input Embedding	1	Xavier Initialization	gain = 1.0
	2	Conv1D	Number of filters = 32, Kernel size = 7
	3	BatchNorm1D	-
	4	Activation Function	Tanh
	5	Conv 1D	Number of filters = 64, Kernel size = 5
	6	BatchNorm 1D	-
	7	Activation Function	Tanh
	8	Conv 1D	Number of filters = 128, Kernel size = 3
	9	BatchNorm 1D	-
	10	Activation Function	Tanh
	11	Conv 1D	Number of filters = 128, kernel size = 1
	12	BatchNorm 1D	-
	13	Activation Function	Tanh
Encoder	1	Encoder layer	Self-attention heads = 4, Encoder blocks = 8
Feed Forward	1	Linear	Hidden units = 32, Activation = Gelu
	2	Drop out	Rate = 0.05
	3	Linear	Hidden units = 128
Outputs	1	Xavier Initialization	gain = 1.0
	2	Conv1D	Number of filters = 64, Kernel size = 3
	3	Activation Function	Tanh
	4	Conv1D	Number of filters = 32, Kernel size = 3
	5	Linear	Hidden units = 1

. Here, the encoder block, input dimension of the encoder, number of attention heads, and feed-forward network dimension were set based on the optimal parameter values obtained from grid search. In the input embedding stage, we adopted an optimal CNN structure, determined through rigorous experimentation. This choice allows us to more effectively extract local patterns for voltage, temperature, and the communication count than a linear layer. We incorporated zero padding and the tanh activation function, notably omitting a pooling layer to preserve the temporal order of the time series data. Additionally, we employed Batch Normalization (BatchNorm) 1D to maintain the model’s training stability.

The encoder stage integrated four self-attention heads and eight encoder blocks to adeptly learn features and patterns. The feed-forward stage enhanced the model’s capability to represent various types of information through the inclusion of two linear layers, one dropout layer, and the GELU activation function. The output stage utilized two CNN layers and one linear layer to yield the final results. Only the values corresponding to the first vector in the output of the second CNN layer are used as input to the subsequent linear layer.

4.2. Implementation Details

For the prediction of discharge capacity using the C-SDFormer model, we established a standardized dataset for network training, represented as $D=\left\{\right(X\left(1\right),C\left(1\right)),(X\left(2\right),C\left(2\right)),\cdots ,(X\left(\tau \right),C\left(\tau \right))\}$, where $C\left(t\right)$ denotes the discharge capacity value, and $X\left(t\right)$ signifies the input vector or scalar at time step t. The input $X\left(t\right)$ is $X_{VNT}\left(t\right)=[V\left(t\right),N\left(t\right),T\left(t\right)]$, where $V\left(t\right)$, $N\left(t\right)$, and $T\left(t\right)$ correspond to voltage, the communication count, and temperature at time step t. To enable the model to grasp the temporal relationships among the input variables, we employed a sliding window algorithm with a window size of 24 h on the input data, with the subsequent 10 min being predicted as the output.

Data that did not reach the primary point, contained numerous missing values, or exhibited excessive noise were not used in the discharge profile data. Moreover, we excluded three test sets from the training process for model evaluation. The remaining data were divided into a training set (80%) and a validation set (20%). We implemented early stopping to combat overfitting, terminating training when the validation loss exhibited no improvement for 10 epochs, with a maximum limit of 100 epochs. The model was trained using the Adam optimizer and the mean absolute error (MAE) loss function, employing a batch size of 64 and a learning rate of 0.0001.

The C-SDFormer model was implemented in Python (version 3.8.11) using the PyTorch deep learning framework (version 2.2.1). Our experiments were conducted on a Linux-based system (Ubuntu 20.04) equipped with CUDA 12.1 and an NVIDIA GeForce RTX 3090.

4.3. Evaluation Metrics

To evaluate our model’s performance, we utilized four metrics: mean absolute error (MAE), root mean square error (RMSE), symmetric mean absolute percentage error (SMAPE), and the coefficient of determination (R²). The MAE, as the most intuitive metric, represents the average of the absolute differences between the predicted and actual values, making it effective for evaluating overall prediction accuracy. RMSE, the square root of the mean squared error, transforms the error metrics into the same units as the actual values and is particularly sensitive to larger errors, highlighting significant deviations. SMAPE evaluates the percentage difference between the predicted and actual values, considering their magnitude, and is less sensitive to outliers, making it suitable for assessing relative errors in balanced datasets. R² serves as a measure of the extent to which the dependent variable can be explained by the independent variable, serving as a key indicator of the model’s goodness of fit.

5. Experimental Results and Discussion

In this section, we conducted experiments on the SOC estimation capability up to the primary point and the prediction of the primary point using three MSD primary battery test sets (#1, #2, and #3). Specifically, we evaluated the efficiency of the C-SDFormer model through ablation studies. Additionally, we trained existing battery SOC estimation methods on MSD primary battery data and compared their performance on the same test set.

To assess the contributions of individual components in the C-SDFormer model, we conducted an ablation study, evaluating four modifications: (i) without the CNN embedding layer (which effectively replaces it with a linear layer), (ii) without the CNN output layer, (iii) without the transformer layer, and (iv) without the series decomposition layer. The experimental results, summarized in

Table 5. Ablation study of C-SDFormer.

Ablated Layer	MAE (%)				RMSE (%)				SMAPE (%)				R2
	#1	#2	#3	Average	#1	#2	#3	Average	#1	#2	#3	Average	#1	#2	#3	Average
w/o CNN Embedding	4.764	6.822	7.907	6.497	6.177	8.628	9.525	8.110	7.977	12.92	12.86	11.21	0.947	0.871	0.882	0.900
w/o CNN Output	4.524	4.634	7.064	5.407	5.597	6.447	7.064	6.369	7.235	8.431	11.49	9.052	0.954	0.933	0.915	0.934
w/o Transformer	5.273	6.816	5.644	5.911	6.178	8.338	6.777	7.097	10.33	10.89	9.117	10.11	0.928	0.854	0.928	0.903
w/o Series Decomposition	4.641	4.966	4.500	4.702	6.236	6.652	5.973	6.287	6.714	9.790	6.323	7.609	0.949	0.944	0.958	0.950
C-SDFormer (Ours)	3.408	5.123	3.534	4.021	4.602	6.391	4.567	5.186	5.070	11.60	4.547	7.072	0.972	0.950	0.974	0.965

Note: Bold values indicate the best performance among the ablated layers.

, indicate that the complete C-SDFormer architecture outperforms all of these modified configurations across all evaluation metrics. Specifically, our ablation study reveals that the CNN embedding layer is the critical component: its removal resulted in the largest performance drop across MAE, RMSE, and R² metrics. This finding underscores its essential role in extracting robust, informative features from the raw input data. Without this layer, the model’s ability to capture subtle variations in voltage, temperature, and communication count is markedly diminished, leading to poorer SOC estimation. Similarly, when the CNN output layer was omitted, we observed a notable decline in prediction accuracy. This layer is responsible for refining and consolidating the extracted features before they are passed to subsequent processing stages, and its absence reduces the model’s capacity to form a cohesive representation of the input signal. Moreover, a configuration of the model that entirely excluded the transformer component—relying solely on CNN layers—showed significantly reduced performance across all evaluated metrics. This result demonstrates that the self-attention mechanism inherent to the transformer is indispensable for capturing the temporal dependencies and transient voltage fluctuations induced by communication. These transient events, although brief, are crucial for accurately predicting the discharge capacity, and the transformer effectively highlights these features through its attention weights. Finally, the removal of the series decomposition layer led to a considerable performance reduction (over 0.6% increase in MAE, 1% increase in RMSE, 0.5% increase in SMAPE, and a decrease of 0.01 in R²). This layer plays a pivotal role in segregating seasonal patterns from trend components, enabling the model to address the nonlinear dynamics present in the data more effectively. Its exclusion confirms that without this separation, the model struggles to differentiate between long-term trends and periodic variations, thereby compromising prediction accuracy. Collectively, these results highlight the complementary roles of each component in the C-SDFormer architecture. The ablation study not only validates the design choices made in our model but also demonstrates how each module contributes significantly to the overall robustness and accuracy of SOC prediction in real-world conditions.

The previous experiments show that the structure of the proposed C-SDFormer model can successfully learn the characteristics of an MSD primary battery. Here, we performed a performance comparison with existing battery SoC estimation methods on the same dataset under identical conditions, and found that C-SDFormer was superior.

Table 6. Performance comparison of SOC estimation between C-SDFormer and other methods.

Method	MAE (%)				RMSE (%)				SMAPE (%)				R2
	#1	#2	#3	Average	#1	#2	#3	Average	#1	#2	#3	Average	#1	#2	#3	Average
DNN [13]	4.799	7.643	6.366	6.269	6.207	9.802	8.018	8.009	8.131	11.54	8.708	9.459	0.949	0.854	0.920	0.907
LSTM [14]	3.745	6.921	4.360	5.008	4.406	8.037	5.558	6.000	7.471	10.23	6.744	8.148	0.974	0.903	0.960	0.945
CNN [15]	3.793	5.337	6.169	5.099	4.840	6.763	7.035	6.212	7.366	8.144	9.441	8.317	0.964	0.921	0.928	0.937
CNN-LSTM-DNN [16]	4.228	5.120	6.241	5.196	5.716	6.448	7.729	6.631	7.260	11.03	9.226	9.172	0.954	0.943	0.920	0.939
Bi-GRU [17]	3.810	7.492	6.565	5.955	4.844	9.250	8.417	7.503	6.714	12.32	8.789	9.274	0.968	0.889	0.904	0.920
CNN-BWGRU [18]	3.777	6.586	4.995	5.119	4.704	8.353	6.192	6.416	6.834	12.48	6.898	8.737	0.970	0.904	0.948	0.940
C-SDFormer (Ours)	3.408	5.123	3.534	4.021	4.602	6.391	4.567	5.186	5.070	11.60	4.547	7.072	0.972	0.950	0.974	0.965

Note: Bold values indicate the best performance among the compared methods.

presents the performance comparison of SOC estimation for the test sets between the C-SDFormer and other methods. Transformer-based advanced models [19,20,21,22] utilize various features such as current and SOC as input to specific layers during training to improve SOC estimation. However, these models were not applicable to our study because our dataset does not include these features as training inputs. In Table 6, the C-SDFormer outperforms the other models on all performance metrics, generally, with RMSE being the best performer for all test sets. The average MAE of C-SDFormer is 4.021, showing that on average, the SOC estimates are closest to the actual values. The average RMSE is 5.186, indicating that large errors occur less frequently. The average SMAPE is 7.072, highlighting the model’s reduced sensitivity to relative differences, which underscores its robustness. The average R² is 0.965, demonstrating the model’s ability to accurately capture the patterns and variability in the data. Specifically, the average MAE and RMSE values demonstrate over 1% better performance compared to existing models, with the average RMSE showing a difference of approximately 1%, and the average R² value exhibiting a difference of over 0.02. In addition, C-SDFormer shows competitive results, with an MAE difference of only 0.003 compared to CNN-LSTM-DNN [16] for #2, and an R² difference of 0.02 compared to LSTM [14] for #1. These results highlight the effectiveness of the C-SDFormer model in enabling real-time SOC estimation and providing accurate and robust predictions without relying on discharge capacity as an input. The proposed battery life prediction method is particularly suitable for practical applications such as remote metering. It addresses critical considerations, including minimizing hardware costs and ensuring robust operation. The model demonstrates high prediction accuracy while processing data such as voltage, temperature, and communication count. This capability highlights its potential for deployment in real-world scenarios. Additional performance evaluations and extended analyses are provided in

Table A1. Performance comparison of SOC estimation between C-SDFormer and other methods (MAPE and MSE).

Method	MAPE				MSE (%)
	#1	#2	#3	Average	#1	#2	#3	Average
DNN [13]	14.65	25.86	19.93	20.14	0.385	0.960	0.642	0.662
LSTM [14]	12.57	17.84	15.43	15.28	0.220	0.581	0.311	0.370
CNN [15]	12.50	16.70	18.93	16.04	0.234	0.457	0.495	0.395
CNN-LSTM-DNN [16]	13.84	14.92	16.01	14.92	0.326	0.415	0.597	0.446
Bi-GRU [17]	11.89	23.60	15.50	16.99	0.326	0.415	0.597	0.446
CNN-BWGRU [18]	12.07	18.55	13.17	14.59	0.221	0.697	0.383	0.433
C-SDFormer (Ours)	9.840	16.63	12.01	12.82	0.211	0.408	0.208	0.275

Note: Bold values indicate the best performance among the compared models.

in the appendix, offering further insights into the model’s robustness and superiority.

We recommend replacing the battery as soon as it reaches the primary point, ensuring a sufficient maintenance margin for life prediction stability. To validate this approach, we evaluated the SOC estimation error at the primary point. Figure 8 illustrates the SOC estimation error rates at the primary point for the C-SDFormer model compared to other methods. Our results show that the C-SDFormer model achieves the lowest error rates, with values of 0.27, 0.25, and 0.01, respectively. These findings demonstrate the superior predictive accuracy and robustness of the C-SDFormer model in estimating battery SOC. The ability to accurately predict the primary point before a sharp voltage drop occurs ensures that a hardware-based low battery alert is triggered in time. Moreover, even when unexpected SOC estimation errors result in missing SOC states, the voltage drop still effectively activates the low battery alert. This capability substantially mitigates the risk of unexpected power loss and supports proactive battery management, thereby enhancing the overall reliability and operational stability of our system in real-world applications.

6. Conclusions

In this paper, we propose a battery life prediction method to ensure the robust operation of IoT devices in remote metering applications. The robust battery life prediction process proposed in this paper is structured in two stages. The first stage focuses on predicting the SOC, enabling the real-time remote monitoring of battery conditions in metering devices. In the second stage, a hardware-based alerting mechanism is integrated into IoT devices to issue warnings prior to complete discharge. This mechanism utilizes a custom-designed MSD primary battery architecture to enhance the reliability and operational efficiency of IoT devices in remote metering applications. These two stages collectively contribute to improving battery life management and ensuring the robust operation of IoT systems.

For the real-time prediction of SOC, we developed the C-SDFormer model. C-SDFormer uses a self-attention mechanism to process sequences of voltage, temperature, and communication count data for SOC prediction. Specifically, the model uses transformer layers to effectively extract features from input and output sequences, and series decomposition is integrated into the transformer to mitigate noise. The effectiveness of this model architecture was validated through an ablation study.

To evaluate the SOC estimation, we deployed smart gas meters equipped with the MSD primary battery in households and collected discharge characteristic data. The collected temperature, voltage, and communication count data were used as model inputs, while the discharge capacity was used as the ground truth for SOC estimation. As a result, C-SDFormer demonstrated superior performance compared to existing SOC prediction methods, achieving an average MAE of 4.021%, an average RMSE of 5.186%, an average SMAPE of 7.072%, and an average R² of 0.965. In addition, C-SDFormer produced results closer to the ground truth in primary point estimation than other methods. These results confirm the C-SDFormer model’s robustness and accuracy in SOC estimation and primary point prediction for MSD primary batteries, offering a promising solution for real-world applications.

In the second stage of the proposed method, a Multi-Stage Discharge (MSD) primary battery was developed to enable a hardware-based low battery alert before the battery is fully discharged. This design ensures the reliable operation of IoT devices, particularly those not actively managed through real-time SOC monitoring in the first stage. By providing timely low battery alerts, the MSD battery minimizes the risk of unexpected device shutdowns, thereby enhancing the overall reliability and operational continuity of IoT devices in remote metering scenarios. These contributions collectively address critical challenges in battery management and pave the way for more robust IoT applications in real-world environments.Furthermore, our proposed method demonstrates significant potential for practical deployment, as it effectively reduces the reliance on expensive SOC measurement equipment while maintaining robust performance, even in challenging environments. However, challenges remain in integrating the model into resource-constrained devices and ensuring consistent accuracy across diverse operational conditions. Future work will focus on optimizing system integration and enhancing adaptability to further improve the scalability and reliability of the proposed approach in real-world applications.