A physics-informed intelligent digital twin using multi-task CNN–LSTM for acoustic emission-based fault prognostics in safety-critical systems

Ensuring the structural integrity of pressure vessels is critical across manufacturing, power generation, and aerospace sectors, where even minor failures can lead to catastrophic accidents and severe economic losses (Ono, 2008; Anastasopoulos et al., 2009). Consequently, Structural Health Monitoring (SHM) has emerged as a key strategy for the continuous evaluation of components operating under harsh environments (Montalvao et al., 2006). Among the various SHM approaches, Acoustic Emission (AE) monitoring has gained particular attention due to its ability to detect transient elastic waves associated with crack initiation, fatigue, and corrosion processes (Antonaci et al., 2012; Joseph and Giurgiutiu, 2020). By analyzing these high-frequency signals, AE enables the early detection of degradation, making it highly suitable for safety-critical systems such as pressure vessels, pipelines, and reactors (Cui et al., 2025). Despite these advantages, conventional AE-based prognostic systems face several challenges. They depend on costly experimental setups and dedicated sensor arrays to record AE data under controlled damage conditions (Shamsudin, 2019; Chou, 2024). This dependence increases cost, complexity, and limits scalability and reproducibility. In addition, traditional AE feature extraction relies on manually engineered parameters such as amplitude, counts, and energy, which are sensitive to noise and fail to capture the nonlinear, time-dependent nature of material degradation (Karvelis et al., 2021; Du et al., 2024). These limitations hinder the deployment of AE-based prognostics in real-time industrial applications. In parallel, Finite Element Analysis (FEA)-based digital twins have been explored as alternatives to physical experiments, capable of simulating structural responses under various loading and damage scenarios (Radanliev et al., 2022; Zhong et al., 2023). However, such physics-based twins are computationally intensive, requiring specialized solvers, material models, and extensive calibration, which makes them impractical for real-time health monitoring or online decision-making (Kerkeni et al., 2024). This creates a critical gap between high-fidelity physics-driven twins and adaptive, data-driven prognostic systems. To bridge this gap, recent research has focused on AI-enabled digital twins, wherein machine learning models learn degradation behavior directly from data (Huang et al., 2021; Xu et al., 2023). Deep learning architectures such as Convolutional Neural Networks (CNNs) and Long Short-Term Memory (LSTM) networks have demonstrated exceptional capability in extracting spatial and temporal features for fault diagnostics and Remaining Useful Life (RUL) prediction (Kong et al., 2019; Kim and Sohn, 2021; Marei and Li, 2022). Nevertheless, most existing AI-based digital twins rely on limited or proprietary experimental datasets, constraining their generalization ability. Moreover, the scarcity of open AE databases further restricts validation and benchmarking (Ai et al., 2023). To address these limitations, this study introduces a fully computational, AI-driven digital twin framework for AE-based prognostics of pressure vessels. The approach synthesizes realistic AE waveforms through a physics-inspired signal model, eliminating the need for experimental or FEA datasets. A multi-task CNN–LSTM architecture is developed to simultaneously perform health-state classification (Healthy, Degrading, and Critical) and RUL prediction by learning spatio-temporal AE features. The entire framework is implemented in Python, ensuring computational efficiency, reproducibility, and scalability for intelligent monitoring in Industry 4.0 environments. While this study focuses on synthetic AE validation, it establishes a foundational step toward hybrid digital twins integrating both simulated and experimental AE data in future work.

1. To design a synthetic AE data generation framework that replicates damage evolution in pressure vessel materials.

2. To develop a CNN–LSTM multi-task model capable of joint health-state classification and RUL prediction.

3. To validate the model through accuracy, residual, and visualization analyses (t-SNE and residual heatmaps).

4. To demonstrate the feasibility of building a cost-effective, Python-based digital twin for intelligent monitoring of safety-critical equipment.

Novelty and Contribution Unlike conventional digital twins that depend on finite element simulations or costly experimental AE data, this work introduces a purely AI-driven, physics-inspired digital twin built entirely from computationally generated signals. The integration of multi-task CNN–LSTM learning enables simultaneous classification and lifetime prediction, offering a unified prognostic solution. Additionally, the proposed framework employs interpretability tools such as t-SNE latent mapping and residual analysis to provide physical insight into the degradation process. This combination of synthetic data generation, multi-task deep learning, and visual interpretability forms a novel, resource-efficient approach to digital twin development for AI prognostics within the industry 4.0 ecosystem.

Acoustic Emission (AE) monitoring has long been established as a powerful technique for detecting micro-crack initiation, fatigue progression, and corrosion-related degradation in metallic and composite structures (Ono, 2008; Antonaci et al., 2012). Its capability to capture transient elastic waves generated during damage evolution makes it particularly suitable for real-time Structural Health Monitoring (SHM) of safety-critical systems such as pressure vessels, pipelines, and offshore platforms (Anastasopoulos et al., 2009; Montalvao et al., 2006). Traditional AE analysis has been widely employed to evaluate damage mechanisms in metals and composites (Chou, 2024; Shamsudin, 2019), and recent studies have demonstrated its usefulness for fatigue crack propagation monitoring and microstructural damage identification (Joseph and Giurgiutiu, 2020; Cui et al., 2025). However, most AE-based systems rely on manually engineered features such as energy, amplitude, rise time, and event counts, which are highly sensitive to noise and experimental variability (Karvelis et al., 2021; Suzuki and Shimamoto, 2021). These limitations restrict their use in large-scale or autonomous monitoring systems where high-frequency data streams must be analyzed continuously and accurately. Furthermore, AE-based experimental setups are often costly, time-intensive, and dependent on calibrated sensor networks (Rummel and Matzkanin, 1997), creating a bottleneck for scalable deployment in industrial environments.

The emergence of digital twin technology has revolutionized condition monitoring and predictive maintenance by enabling virtual replicas of physical assets that simulate degradation and operational responses (Zhong et al., 2023; Radanliev et al., 2022). Digital twins have been successfully adopted across manufacturing, oil and gas, and aerospace sectors to enhance reliability and reduce downtime (Wanasinghe et al., 2020; Xu et al., 2023). These twins are typically constructed using high-fidelity finite element or physics-based models that reproduce structural behavior under varying loads and damage conditions (Kerkeni et al., 2024; Wang et al., 2021). However, physics-based digital twins require extensive domain expertise, computational resources, and material model calibration, making them unsuitable for real-time decision-making in dynamic environments (Huang et al., 2021; Lazakis et al., 2022). Consequently, the research focus has shifted toward AI-driven digital twins, which utilize deep learning to directly map input sensor data to structural health states or Remaining Useful Life (RUL) estimates (Ponnusamy et al., 2024; Kim et al., 2023). Such frameworks have been extended to manufacturing and energy systems under Industry 4.0 initiatives (Martinez-Ruedas et al., 2024; Velasco-Gallego and Lazakis, 2023; Ucar et al., 2024).

Deep learning architectures particularly Convolutional Neural Networks (CNNs) and Long Short-Term Memory (LSTM) networks have demonstrated remarkable potential in extracting meaningful features from complex temporal signals (Kong et al., 2019; Kim and Sohn, 2021; Marei and Li, 2022). Hybrid CNN–LSTM frameworks have been applied for fatigue prediction, cutting tool health assessment, and turbofan RUL estimation with high accuracy (Muneer et al., 2021; Khan et al., 2023). Similar approaches have also been utilized for AE-based fault diagnosis, particularly in composites, where CNN–LSTM models were shown to outperform conventional classifiers (Du et al., 2024). Nonetheless, most reported models rely on experimental or finite element AE datasets, which are often limited in size, inaccessible, or specific to certain materials and configurations (Ai et al., 2023; Fabian et al., 2022). Moreover, handcrafted features and high dependency on physical measurements restrict generalization across industries and damage types (Wang et al., 2020; Xi et al., 2018). To enhance transferability, hybrid methods integrating synthetic and experimental data through domain adaptation have recently been proposed (Shukla and Deepa, 2025; Kim et al., 2022), but their implementation for AE-driven digital twins remains scarce.

Recent studies highlight the growing importance of synthetic data generation to overcome the scarcity of real AE datasets for prognostic model training (Fabian et al., 2022; Shukla and Deepa, 2025). Generative approaches and physics-informed neural networks (PINNs) have been employed to simulate signal patterns consistent with underlying material behavior while minimizing experimental dependence (Kim et al., 2022; Ennis and Giurgiutiu, 2024). Moreover, t-SNE and residual heatmap analyses have been leveraged to enhance interpretability and visualize learned feature spaces in fault diagnosis tasks (Liang et al., 2023; Wang et al., 2017; Li et al., 2015). Although these developments have improved data efficiency and model transparency, most synthetic AE frameworks are not yet integrated with multi-task deep learning or digital twin systems capable of performing both classification and life prediction simultaneously. Existing reviews (Ciaburro and Iannace, 2022; Rojas et al., 2025; Shamim et al., 2025) emphasize that a unified, interpretable, and computationally scalable digital twin using physics-inspired synthetic AE data remains an unresolved challenge.

From the reviewed literature, it is evident that:

1. Traditional AE systems are constrained by dependence on costly experiments and manual feature extraction (Antonaci et al., 2012; Karvelis et al., 2021).

2. Physics-based digital twins provide accuracy but lack computational efficiency and adaptability for real-time prognostics (Zhong et al., 2023; Kerkeni et al., 2024).

3. AI-driven prognostic models excel in pattern learning but rely heavily on scarce experimental AE datasets and are limited in interpretability (Du et al., 2024; Khan et al., 2023).

4. Synthetic AE modeling and physics-informed neural networks have been explored separately but not unified into a deployable, interpretable digital twin (Fabian et al., 2022; Kim et al., 2022).

Hence, the novelty of this work lies in the integration of all these domains into a single, computationally driven digital twin framework.

The present study introduces:

1. A physics-inspired synthetic AE signal generation model, eliminating the dependency on experimental or FEA datasets.

2. A multi-task CNN–LSTM architecture capable of performing both health-state classification and RUL regression simultaneously.

3. A fully Python-implemented digital twin, ensuring lightweight, scalable, and reproducible deployment.

4. The use of t-SNE and residual visualization for physically interpretable feature-space analysis, linking deep learning representations to real degradation phenomena.

This unique combination establishes a data-efficient, interpretable, and physics-consistent AI framework for the prognostics of safety-critical equipment, addressing long-standing challenges in SHM, predictive maintenance, and Industry 4.0 integration (Radanliev et al., 2022; Ponnusamy et al., 2024; Nagy et al., 2025; Garcia et al., 2025). Representative summary of existing studies on AE-based prognostics and digital twin frameworks is shown in Table 1.

This section presents the workflow adopted to construct and validate the proposed AI-driven digital twin framework for acoustic emission (AE)-based prognostics of pressure vessels. The overall pipeline involves four major stages: (1) generation of synthetic AE waveforms for different health states, (2) dataset formation and preprocessing, (3) model architecture design using a multi-task CNN–LSTM structure, and (4) model training and performance evaluation. The methodology ensures that the digital twin can be developed and validated entirely within a computational environment without requiring experimental data or finite element simulations.

To emulate realistic Acoustic Emission (AE) activity corresponding to varying levels of structural degradation, synthetic AE waveforms were generated using a physics-inspired burst model. Each signal represents a transient waveform comprising one or more burst-type AE events that decay over time due to material damping and propagation losses. This modeling approach enables the controlled simulation of AE responses associated with micro-crack initiation, crack coalescence, and final fracture events under progressive damage conditions.

The individual AE burst waveform was formulated as a damped sinusoidal function with additive stochastic noise, expressed as:

where:

$A$ is the burst amplitude, proportional to the instantaneous stress energy release; $α$ is the exponential decay constant governing material damping and signal attenuation; $f$ represents the dominant frequency of the burst; $ϕ$ is a random phase term introducing variability among events; and

$η(t)$ denotes Gaussian white noise simulating sensor and environmental interference.

The proposed damped-sinusoidal formulation is physically consistent with the mechanics of stress-wave propagation and acoustic-emission generation in solids. When a micro-crack initiates or grows, a sudden release of elastic strain energy generates transient stress waves that travel through the material. The exponential decay term, $e−αt$⁠, represents the attenuation of wave amplitude caused by internal friction, microstructural scattering, and boundary reflections, while the sinusoidal component captures the dominant resonant frequency governed by the material's local stiffness and density. The burst amplitude $A$ is directly related to the instantaneous energy-release rate $G˙$⁠, yielding a proportionality of $EAE∝G˙/f$⁠. In this way, the model establishes a clear physical link between material damping, wave-energy loss, and acoustic-emission intensity, offering a physics-aware yet computationally efficient representation of progressive degradation. Distinct parameter ranges were assigned to each health state to represent the evolving acoustic behavior during degradation. The Healthy state consisted of sparse, low-amplitude bursts with strong damping (large $α$⁠), while the Degrading state showed moderate event density and energy. The Critical state contained multiple overlapping, high-energy bursts with weaker damping and higher event frequency. These variations reflect the experimentally observed increase in AE event density and signal energy associated with fatigue and crack propagation (Ono, 2008; Antonaci et al., 2012; Cui et al., 2025). Although this single-mode formulation does not capture the full multimodal and dispersive nature of real AE wave propagation, it provides an efficient first-order approximation for studying degradation trends and validating the proposed AI-driven framework. Future work will extend the model using multi-frequency wavelets and propagation physics to improve its fidelity. Overall, most existing AE-based prognostic frameworks rely heavily on costly experiments and often lack physical interpretability. The present study addresses these limitations by introducing a synthetic-data-driven, interpretable, and unified digital-twin framework that couple's physics-inspired AE modeling with deep-learning-based prognostic intelligence. While simplified, the damped-sinusoidal model successfully captures the essential temporal-decay and frequency-modulation features observed in typical AE bursts. It should therefore be regarded as a parameterized, physics-consistent representation rather than a high-fidelity acoustic-wave simulation. This work focuses on validating the learning capability of the digital twin under controlled conditions, while future extensions will incorporate dispersion effects, multimode propagation, and boundary reflections. Representative synthetic AE signals for the three health conditions Healthy, Degrading, and Critical are shown in Figure 1, illustrating their characteristic amplitude, frequency, and damping variations corresponding to realistic degradation behavior.

The synthetic AE waveforms in Figure 1 clearly illustrate how acoustic activity intensifies as material damage advances. The Healthy state displays low-intensity, strongly damped bursts that indicate stable microstructural behavior. The Degrading state shows moderate energy levels with partially overlapping transients, typical of gradual crack initiation and growth. The Critical state presents high-amplitude, slowly decaying oscillations associated with rapid energy release and impending failure. This progressive transition confirms that the proposed physics-inspired signal-generation framework effectively emulates AE responses across different degradation severities. The corresponding AE-signal generation parameters are summarized in Table 2.

The current Remaining Useful Life (RUL) formulation is intentionally empirical and is used as a surrogate degradation indicator rather than a direct crack-length prediction model. Nevertheless, the adopted acoustic-emission (AE) energy–based mapping is physically consistent with classical fatigue mechanics. Increased AE energy corresponds to higher stress-intensity fluctuations and accelerated damage accumulation, analogous to Paris' crack growth law, while cumulative AE activity aligns with Miner's linear damage accumulation principle. Accordingly, the proposed formulation establishes a physically meaningful connection between AE signal characteristics and degradation progression. Future work will explicitly integrate Paris–Forman fatigue relations into the digital twin framework to enable fully physics-driven life prediction calibrated to material-specific fracture behavior. A total of 1800 synthetic AE signals were generated, comprising 600 samples per health state (Healthy, Degrading, and Critical). Each signal contained 1,024 time-domain samples and was normalized to unit variance. The dataset was divided into training and testing subsets using an 80:20 split. StandardScaler normalization was applied to standardize amplitude distributions and improve model convergence. To associate each AE signal with a degradation indicator, an RUL value was synthetically assigned based on signal energy and envelope amplitude following an empirical degradation rule inspired by energy-based fatigue models:

where $E=∑s(t)2$ represents the total signal energy, $Aenv$ is the maximum amplitude of the signal envelope, $β$ is the base life constant (set to 100 for the Healthy state), $k1$ and $k2$ are scaling coefficients reflecting material sensitivity, and $ε$ is a Gaussian noise term representing measurement uncertainty. This formulation ensures that increasing signal energy and envelope amplitude indicative of progressive damage and higher energy dissipation lead to a monotonic reduction in RUL, thereby generating a realistic degradation trajectory for training the prognostic model. Although the RUL estimation is empirical, its monotonic relationship between AE energy and life reduction mirrors fatigue-damage behavior described by Paris' crack growth law $(da/dN=C(ΔK)m)$ and Miner's cumulative damage rule. As a result, the generated RUL values serve as physically meaningful relative indicators of structural health, enabling the digital twin to learn degradation patterns that closely resemble realistic fatigue evolution. The parameters used to synthesize AE waveforms for different health states are summarized in Table 3.

The proposed digital twin integrates a multi-task Convolutional Neural Network–Long Short-Term Memory (CNN–LSTM) architecture to jointly perform health-state classification and Remaining Useful Life (RUL) prediction from synthetic AE signals. The design rationale is grounded in the distinct physical characteristics of AE data where each burst exhibits localized frequency energy patterns that evolve temporally as structural degradation progresses. Accordingly, the CNN component captures spatial-frequency representations of AE bursts, while the LSTM component models temporal correlations reflecting cumulative damage evolution. The network architecture, illustrated schematically in Figure 2, comprises the following key elements:

1. Three 1D convolutional blocks (Conv1D → Batch Normalization → MaxPooling) to extract hierarchical spectral–energy features while suppressing high-frequency noise components.

2. A Global Average Pooling (GAP) layer to condense feature maps into a compact latent embedding, reducing overfitting and ensuring translational invariance of frequency patterns.

3. A single LSTM layer (64 units) to encode sequential dependencies among AE bursts, capturing the nonlinear degradation trajectory over time.

4. A shared Dense layer (64 neurons, ReLU activation, Dropout = 0.25) forming a unified latent representation that preserves the physical continuity between spatial and temporal features.

5. Two parallel output heads:

   • A Softmax classification head predicting health states (Healthy, Degrading, Critical).

   • A Linear regression head estimating the RUL in normalized time units.

This dual-task design encourages the model to learn shared physical representations where features relevant for class discrimination also support degradation trend estimation. The multi-task learning strategy enhances generalization by enforcing consistency between short-term AE event characteristics and long-term life prediction patterns. All model components were implemented in Python (TensorFlow/Keras) for transparency and reproducibility. The architecture was optimized for computational efficiency, enabling rapid training and potential real-time inference within edge or cloud-based industrial monitoring systems. Importantly, this structure maintains physical interpretability: convolutional filters correspond to dominant AE frequency bands linked to material microcracking, while LSTM activations reflect temporal evolution of these features over successive degradation stages. This correlation between network behavior and physical processes strengthens the credibility of the digital twin framework, ensuring that the model's predictions are both data-driven and physics-consistent.

Training was conducted using a batch size of 32, a learning rate of 0.001, and a maximum of 50 epochs. Early stopping and learning rate reduction callbacks were applied to prevent overfitting and accelerate convergence.

The total loss $Ltotal$ minimized during training was defined as:

where $Lclass$ is the categorical cross-entropy loss, $LRUL$ is the mean squared error loss, and $λ1$⁠, $λ2$ are weighting coefficients (set to 1.0 for balanced optimization).

Model performance was evaluated using:

1. Classification metrics: Accuracy, Precision, Recall, and F1-score.

2. Regression metrics: Root Mean Square Error (RMSE) and Coefficient of Determination (R²).

3. Residual Analysis: Distribution of RUL prediction errors per class.

4. Visualization Tools: Training/validation curves, t-SNE latent space mapping, and residual heatmaps to assess interpretability and robustness. This methodological framework integrates physics-inspired AE signal generation, multi-task deep learning, and interpretable validation to construct a fully computational digital twin. The proposed workflow allows accurate prediction of both health states and remaining life without reliance on physical experiments, demonstrating a scalable and efficient pathway for AI-driven prognostics in safety-critical systems.

The proposed CNN–LSTM digital twin was designed with computational efficiency as a core objective to support real-time industrial monitoring applications. The final trained model contains approximately 0.8 million trainable parameters, corresponding to a compact memory footprint of approximately 3.2 MB when stored using 32-bit floating-point precision. On a standard CPU-based workstation, the average inference time per acoustic emission signal was observed to be below 8 ms, which is well within typical AE data acquisition intervals. The shallow convolutional depth and single LSTM layer result in relatively low computational complexity, indicating suitability for deployment on embedded edge devices such as industrial gateways or ARM-based processors. While detailed hardware-level energy profiling was beyond the scope of this study, the lightweight architecture suggests favorable computational and energy efficiency for real-time condition-based maintenance applications in safety-critical systems.

This section presents the classification and regression results of the proposed CNN–LSTM digital twin framework for AE-based pressure vessel prognostics. The results are organized to illustrate the model's accuracy, convergence behavior, interpretability, and generalization through cross-validation.

The proposed multi-task CNN–LSTM digital twin effectively accomplished both health-state classification and Remaining Useful Life (RUL) prediction using physics-inspired synthetic AE signals. The confusion matrix presented in Figure 3 demonstrates clear class separation among the three health states Healthy, Degrading, and Critical with negligible overlap. Occasional misclassifications were primarily observed between adjacent states, which is physically consistent with the gradual and continuous nature of material degradation rather than abrupt transitions. Quantitatively, the model achieved an overall classification accuracy of 99.0%, confirming its ability to discern degradation stages from subtle variations in AE waveform characteristics. In the regression task, the model yielded a Root Mean Square Error (RMSE) of 4.8 and a coefficient of determination (R²) of 0.95, as summarized in Table 4. These results indicate a strong correlation between predicted and assigned RUL values, reflecting the model's capacity to learn meaningful temporal degradation trends from synthetic data. The combination of CNN-based spatial feature extraction and LSTM-based temporal encoding proved effective in capturing the underlying physics of AE evolution specifically, the increase in burst amplitude and event density with damage progression. The minimal residual dispersion observed in RUL predictions further demonstrates stable convergence and consistent generalization across all simulated degradation scenarios. While the reported metrics reflect idealized synthetic conditions, the framework's robustness and interpretability establish a promising foundation for subsequent validation using experimental or hybrid datasets. Such cross-domain testing will further confirm its real-world applicability to pressure vessel monitoring and intelligent prognostic systems.

Table 4 shows the summary of the classification and regression performance of the proposed CNN–LSTM digital twin model. The network achieved 99% overall accuracy for health-state classification and an RMSE of 4.8 in RUL prediction, corresponding to a strong linear correlation (R² = 0.95) between predicted and true lifetimes. These results confirm the model's ability to simultaneously perform accurate condition recognition and quantitative prognostics from synthetic AE signals.

The training process exhibited smooth and stable convergence, as illustrated in Figures 4 and 5, which depict the evolution of model accuracy and loss over successive epochs. The CNN–LSTM architecture demonstrated rapid feature learning, achieving over 95% classification accuracy within the first 10 epochs, attributed to effective gradient propagation across both convolutional and recurrent layers. The incorporation of adaptive learning rate scheduling further facilitated stable optimization and prevented oscillations during training. Throughout the process, validation accuracy closely tracked training accuracy, with the two curves remaining nearly parallel. The validation loss consistently decreased without late-stage divergence, confirming that the model maintained strong generalization capability and minimal overfitting despite its relatively deep structure. The smooth monotonic convergence of both loss functions reflects well-conditioned learning dynamics and efficient parameter tuning under the chosen batch normalization and dropout configurations. Overall, the convergence behavior substantiates the robustness and stability of the proposed hybrid architecture, indicating that the model effectively captures the dominant degradation patterns embedded in the AE data while preserving predictive consistency across training and validation subsets.

To evaluate the regression component of the proposed digital twin, comprehensive post-training validation analyses were performed. The parity plot in Figure 6 shows a strong linear relationship between predicted and true Remaining Useful Life (RUL) values, with most data points closely aligned along the 45° reference line. This indicates consistent model estimation and high predictive fidelity across all degradation conditions, yielding an overall coefficient of determination (R²) of 0.95 and a Root Mean Square Error (RMSE) of approximately 4.8. The residual distribution, illustrated in Figure 7, follows an approximately Gaussian profile cantered near zero, confirming that the model's RUL predictions are statistically unbiased. The narrow spread of residuals highlights the framework's ability to generalize effectively across diverse acoustic-emission (AE) signal patterns without systematic over- or underestimation. Furthermore, the residual heatmap in Figure 8 visualizes the mean and standard deviation of RUL prediction errors across the three health states. As anticipated, the Critical class exhibits slightly higher variance, attributed to the increased nonlinearity and stochastic nature of AE signals at advanced damage stages behavior that is physically consistent with near-failure acoustic activity. The approximately Gaussian residual distribution and the relatively low variance observed across health states provide an implicit measure of epistemic uncertainty in the proposed prognostic framework. Accordingly, the residual heatmaps serve as practical prediction-uncertainty indicators, supporting risk-informed maintenance decisions by highlighting confidence bounds associated with different degradation stages. Collectively, these results demonstrate that the proposed multi-task CNN–LSTM model achieves robust and unbiased regression performance, maintaining high accuracy even under high-degradation variability. This validates the digital twin's suitability for real-time prognostic decision-making and establishes its reliability for intelligent condition monitoring of pressure vessels. Future work will extend this uncertainty analysis using Bayesian inference and Monte Carlo dropout techniques to provide explicit confidence intervals for RUL predictions.

The latent feature representations extracted by the proposed CNN–LSTM architecture were analyzed using t-distributed Stochastic Neighbor Embedding (t-SNE) to evaluate class separability and interpretability within the learned feature space. As illustrated in Figure 9, the embeddings form three well-defined clusters corresponding to the Healthy, Degrading, and Critical conditions, with minimal overlap between neighboring classes. This distinct spatial organization demonstrates that the model successfully learns discriminative and physically consistent representations of AE behavior. Samples in the Healthy cluster exhibit compact grouping, consistent with low variability in AE signal amplitude and frequency. The Degrading cluster appears moderately dispersed, reflecting the onset of microcrack activity and increasing signal heterogeneity, while the Critical cluster displays a wider spread due to the stochastic and nonlinear nature of high-energy AE events in advanced damage states. Such clustering behavior confirms that the CNN layers effectively encode localized frequency–energy features, while the LSTM component captures the temporal evolution of degradation. This alignment between latent-space structure and physical degradation progression enhances the transparency and trustworthiness of the digital twin framework. From an explainable AI perspective, the t-SNE visualization validates that the model's internal feature hierarchy is not arbitrary but corresponds to meaningful physical phenomena, thereby strengthening its interpretability and applicability for intelligent prognostic decision-making in safety-critical systems.

To ensure statistical robustness and model reliability, a 10-fold cross-validation procedure was conducted on the synthetic AE dataset. The resulting performance metrics, summarized in Table 5 and illustrated in Figure 10, exhibit remarkable consistency across all folds. The model achieved an average classification accuracy of 0.991 ± 0.003 and an RMSE of 4.9 ± 0.4, indicating low dispersion and high repeatability of predictive outcomes. The narrow standard deviation across folds confirms that the CNN–LSTM architecture maintains stable convergence behavior and strong generalization capability, independent of data partitioning or initialization variance. This robustness is particularly important in prognostic applications, where data imbalance and stochastic variability can significantly affect reliability. These findings validate that the proposed multi-task framework consistently captures the underlying degradation dynamics rather than memorizing specific signal patterns. Consequently, the model demonstrates industrial-grade reliability, satisfying the essential requirement of prediction consistency under varying operational data distributions a prerequisite for dependable real-time deployment within digital twin ecosystems.

Table 5 shows the statistical summary of 10-fold cross-validation performance for the proposed CNN–LSTM digital twin model. The consistently high mean accuracy (0.991) and low RMSE (4.9 ± 0.4) demonstrate the model's strong generalization capability and stable predictive behavior across varying data partitions. These results confirm the robustness and reproducibility of the digital twin framework for AE-based prognostic modeling.

To further evaluate the stability and generalization capability of the proposed CNN–LSTM digital twin, a robustness test was performed by systematically increasing the Gaussian noise level (η) applied to the synthetic acoustic emission (AE) signals. This analysis emulates realistic sensor and environmental disturbances that commonly occur in industrial monitoring systems. For each noise configuration, the model was retrained using identical hyperparameters to isolate the effect of noise on predictive performance. s summarized in Table 6, the proposed framework demonstrates remarkable resilience to noise perturbation. When the noise variance was doubled from η = 0.01 to η = 0.02, the classification accuracy decreased by only 1.2%, and the RMSE for Remaining Useful Life (RUL) prediction increased marginally from 4.8 to 5.3. Even under fourfold noise amplification (η = 0.04), the model retained an accuracy above 94% and an R² value close to 0.9. These results confirm that the learned spatio-temporal representations are not overly sensitive to random signal fluctuations and that the digital twin maintains high predictive fidelity under realistic sensing conditions.

To evaluate the effectiveness of the proposed framework, its performance was benchmarked against representative AE-based prognostic and digital-twin models reported in recent literature. Table 6 summarizes the comparative results in terms of classification accuracy and Remaining Useful Life (RUL) prediction error (RMSE). Du et al. (2024) developed a CNN–LSTM architecture for acoustic-emission-based structural health monitoring of composite materials using experimental AE datasets (Engineering Fracture Mechanics, Vol. 309, 110,447). Their model achieved a classification accuracy of 95.2% with an RMSE of 6.8 but was limited to single-task classification and relied on extensive laboratory AE measurements. Ai et al. (2023) implemented an LSTM-based transfer-learning model with domain adaptation using finite-element AE simulations (Mechanical Systems and Signal Processing, Vol. 192, 110,216). Although they achieved 96.4% accuracy and an RMSE of 5.9, their approach focused primarily on zonal localization and lacked physical interpretability. Karvelis et al. (2021) adopted a Support Vector Machine (SVM) classifier using handcrafted AE statistical features (Ships and Offshore Structures, Vol. 16 No. 4, pp. 440–448), attaining 93% accuracy with an RMSE of 7.2; however, their model depended heavily on manually engineered descriptors and showed limited temporal learning capability. In contrast, the proposed multi-task CNN–LSTM digital twin achieved a classification accuracy of 99% and an RMSE of 4.8 using entirely physics-inspired synthetic AE data. This performance is comparable to, or better than, results obtained from experimental or finite-element-based approaches, demonstrating that a purely computational dataset when guided by physics-informed modeling can effectively reproduce degradation patterns essential for reliable prognostics. The unified dual-task structure allows simultaneous health-state classification and RUL prediction within a single interpretable framework, reinforced by t-SNE-based feature visualization and residual analysis. Unlike previous approaches that depend on costly experiments or computationally intensive simulations, the present framework delivers high predictive reliability with minimal resource requirements, making it scalable and reproducible across diverse industrial systems. To further assess generalization, the trained CNN–LSTM model was evaluated using an independent acoustic-emission dataset from the NASA Prognostics Center of Excellence (PCoE). This dataset, containing fatigue-crack-propagation signals from metallic specimens, represents a substantially different signal domain compared with the synthetic AE data used for training. Without any retraining or fine-tuning, the model achieved a classification accuracy of 89.3% and an RMSE of 7.5 versus 99% and 4.8 on the synthetic dataset. Although performance decreased slightly due to the higher stochastic noise and multimodal nature of experimental AE signals, the latent-space clustering remained consistent across both domains. This confirms that the learned spatio-temporal features are physically meaningful rather than data-specific artifacts, demonstrating strong cross-domain robustness and predictive integrity under realistic signal variability. In addition to these benchmark models, several recent studies have introduced advanced hybrid deep-learning architectures for AE-based prognostics. Ma et al. (2022) proposed a CNN–Transformer network for acoustic-emission fault diagnosis, achieving 97.2% classification accuracy with an RMSE of 5.2 (Applied sciences12(5), 2759). Zhou et al. (2025) developed a hybrid GRU–CNN framework for Fatigue-life prediction of metallic structures, reporting 90.1%–95% accuracy (Eng 7.1 (2025): 9). These studies highlight the increasing trend of combining temporal and spectral feature learning to enhance prognostic precision. However, most of these models remain dependent on large experimental datasets and lack the physics coupling that ensures interpretability and transferability. The comparative performance of the proposed CNN–LSTM digital twin and other state-of-the-art AE-based prognostic frameworks is summarized in Table 7.

Although the synthetic acoustic emission (AE) signals in this study were generated using a generalized physics-inspired damage model, validation on the NASA Prognostics Center of Excellence (PCoE) dataset demonstrates the material-agnostic nature of the learned spatio-temporal representations. Acoustic emission wave propagation is governed primarily by elastic-wave mechanics and energy dissipation rather than material-specific chemistry. Consequently, the extracted CNN–LSTM features are inherently transferable across pressure-vessel steels, pipeline steels, and composite tanks, subject to appropriate signal scaling and domain calibration. This confirms that the proposed digital twin learns physically meaningful degradation patterns rather than data-specific artifacts, supporting its applicability across diverse safety-critical materials. To further examine generalization capability, the trained CNN–LSTM model was evaluated on an independent AE dataset from the NASA PCoE repository without any retraining or hyperparameter adjustment. This dataset contains fatigue crack growth signals from metallic specimens and exhibits higher stochastic noise, frequency dispersion, and sensor variability compared with the controlled synthetic data. The model achieved a classification accuracy of 89.3% and an RUL prediction RMSE of 7.5, compared to 99.0% accuracy and an RMSE of 4.8 on the synthetic dataset. While a modest performance reduction is expected due to increased signal complexity, the latent feature clusters remained clearly separable, indicating that the model captures physically consistent and transferable degradation representations. These results confirm the cross-domain robustness of the proposed digital twin and highlight its potential as a pre-training foundation for hybrid frameworks integrating synthetic, finite element, and experimental AE data for industrial-scale prognostics and health management applications.

The proposed AI-driven digital twin framework establishes a new paradigm for acoustic emission (AE)-based prognostics of pressure vessel integrity. Unlike conventional data-driven or finite element–based approaches, the present method integrates physics-inspired signal synthesis with multi-task deep learning, effectively bridging the gap between synthetic data modeling and real-world prognostic accuracy.

The study's key novelty lies in three aspects:

1. Synthetic AE Signal Generation — The framework generates realistic AE bursts through a damped sinusoidal model that emulates the physical emission mechanisms associated with crack initiation and growth. This enables model training and validation without reliance on costly experimental setups.

2. Multi-Task CNN–LSTM Digital Twin — The integration of convolutional and recurrent layers allows simultaneous health-state classification and Remaining Useful Life (RUL) prediction, enhancing both diagnostic interpretability and temporal consistency.

3. Physics-Interpretable Learning — Visualization techniques such as t-SNE and residual heatmaps reveal physically meaningful feature clustering and degradation trends, making the digital twin not just predictive but explainable.

Together, these features make the framework computationally efficient, scalable, and easily transferable across industrial assets. The model's ability to achieve 99% classification accuracy and low RUL error (RMSE ≈ 4.8) entirely from synthetic AE data demonstrates that AI-driven digital twins can achieve experimental-grade performance with minimal physical data requirements.

Furthermore, the framework lays a foundation for autonomous condition-based maintenance (CBM) systems, where structural health can be continuously monitored, predicted, and optimized in real time through intelligent edge or cloud-based deployments.

While the proposed framework demonstrates the feasibility and effectiveness of a physics-inspired digital twin for acoustic emission (AE)–based prognostics, several clear avenues remain for further development to enhance realism, adaptability, and industrial applicability.

A primary direction for future research is hybrid data integration, in which physics-inspired synthetic AE data are combined with limited real-world sensor measurements using transfer-learning and domain-adaptation strategies. This approach is expected to improve robustness and generalization across different materials, geometries, and operating conditions while retaining the data efficiency of the current framework.

In addition, broader validation using diverse datasets will be pursued by incorporating experimental and service-condition AE data obtained from a wider range of materials and loading scenarios. Such validation will strengthen confidence in the model's reliability and support its deployment in practical industrial environments.

Another important extension involves the integration of physics-informed neural network (PINN) concepts, where governing equations of stress-wave propagation and damage evolution are embedded directly within the learning architecture. This enhancement will further improve physical consistency, interpretability, and extrapolation capability beyond the conditions represented in the training data.

Future work will also focus on edge deployment and real-time analytics, building on the lightweight CNN–LSTM design to enable implementation on embedded processors and IoT-edge platforms. This will facilitate continuous, low-latency monitoring of safety-critical assets such as pressure vessels, pipelines, and reactors, enabling timely, on-site decision-making and predictive maintenance.

Finally, the proposed digital twin can be extended into a multi-sensor framework by fusing AE data with complementary sensing modalities such as vibration, temperature, and strain measurements. Multi-modal data fusion is expected to provide a more comprehensive representation of structural health and improve resilience to sensor noise and uncertainty in complex Industry 4.0 environments.

Overall, these future developments will progressively transform the current simulation-based prototype into a hybrid, scalable, and real-time digital twin capable of autonomous monitoring and intelligent maintenance. Such advancements will further strengthen the practical relevance of the framework and support its adoption in smart industrial ecosystems.

To demonstrate practical relevance, the proposed framework can be applied across multiple real-world scenarios involving safety-critical components and predictive maintenance operations:

In petrochemical processing units, pressure vessels operate under high temperature and cyclic pressure, leading to gradual material fatigue. Implementing the proposed digital twin enables continuous AE-based monitoring, allowing operators to detect early-stage crack formation and predict failure onset. This facilitates predictive shutdowns, reducing unscheduled downtime and improving plant safety margins.

In aerospace systems, composite pressure tanks and structural panels experience progressive delamination and micro-cracking. The synthetic AE framework can be adapted to model composite acoustic behavior, with the CNN–LSTM twin trained to predict delamination severity and RUL. This case extends the framework's relevance beyond metals, demonstrating adaptability to multi-material environments and weight-critical applications.

Long-distance transport pipelines and nuclear reactor vessels are prone to stress corrosion cracking. Using synthetic AE modeling combined with field data, the proposed digital twin can serve as a predictive layer for existing SCADA systems. It can alert maintenance teams about localized damage zones and estimate the remaining life of segments under cyclic thermal stress.

In conclusion, the study introduces a novel, data-efficient, and physics-informed digital twin that eliminates the dependency on experimental AE data, without compromising predictive performance. Its hybrid CNN–LSTM architecture, supported by interpretable learning visualizations, paves the way for the next generation of AI-based prognostic systems. The framework's versatility, low computational cost, and strong physical correlation make it a practical and scalable solution for industrial health monitoring and digital manufacturing ecosystems.

Although the proposed physics-informed digital twin demonstrates strong predictive performance, interpretability, and generalization capability, certain limitations define its present scope and point toward natural directions for future improvement. First, the current validation relies primarily on physics-inspired synthetic acoustic emission (AE) signals generated using a damped-sinusoidal formulation. This approach successfully captures the key spectral and temporal characteristics associated with progressive damage, but it does not yet account for the full complexity of multimodal stress-wave propagation, mode conversion, and boundary reflections that arise in heterogeneous materials and complex geometries. Future work will therefore incorporate wavelet-based signal synthesis and finite element–assisted acoustic modeling to better represent dispersive and anisotropic AE behavior under realistic loading conditions. Second, the Remaining Useful Life (RUL) estimation strategy currently adopts an empirical, monotonic relationship between degradation severity and residual life. While this formulation is physically consistent with observed fatigue progression trends, it remains a simplified representation of fracture-mechanics-driven degradation kinetics. Ongoing efforts will focus on explicitly embedding physics-guided fatigue and fracture relations, such as Paris' crack growth law and Miner's cumulative damage rule, to establish a more direct and causal link between AE signal energetics and material life prediction, thereby further improving interpretability and material transferability. Third, although cross-domain validation using the NASA Prognostics Center of Excellence (PCoE) dataset demonstrated encouraging robustness and adaptability to unseen signal domains, broader validation across additional experimental and simulation-based AE datasets is still required. Future studies will therefore adopt hybrid datasets that combine synthetic, finite element, and laboratory AE recordings to systematically evaluate performance across different materials, geometries, and sensor configurations, ensuring scalability and industrial relevance. Finally, the present implementation operates primarily in an offline inference mode, which is suitable for proof-of-concept evaluation but limits direct integration into continuous monitoring environments. Future developments will focus on edge-optimized deployment, real-time inference acceleration, and adaptive retraining through continual learning, allowing the digital twin to evolve dynamically as new operational data become available. Overall, these limitations are progressive rather than fundamental in nature and define clear research pathways toward a fully hybrid, self-adaptive, and real-time physics-informed digital twin. Addressing them will support the development of a scalable and industry-ready framework for intelligent structural prognostics within Industry 4.0 environments, effectively bridging physics-based understanding with trustworthy AI-driven decision-making.

This study presented a physics-informed, AI-driven digital twin framework for acoustic emission (AE)–based health prognostics of pressure vessels. The proposed approach integrates a parameterized damped-sinusoidal AE signal model with a multi-task CNN–LSTM architecture, effectively combining physical insight with deep learning capability. By relying on physics-consistent synthetic AE data, the framework reduces dependence on costly experimental campaigns and computationally intensive finite element analyses while retaining the essential temporal and spectral characteristics associated with structural degradation. The digital twin demonstrated strong predictive performance, achieving 99% health-state classification accuracy and a Remaining Useful Life (RUL) prediction error of approximately 4.8 under controlled synthetic conditions. The hybrid CNN–LSTM architecture successfully captured both spectral–spatial and temporal degradation patterns, while interpretability tools such as t-SNE visualization and residual analysis provided transparency into the model's internal representations and decision-making process. These results indicate that physics-guided synthetic AE data can serve as an effective foundation for building accurate, interpretable, and computationally efficient digital twins for structural prognostics. While the present study focuses on synthetic data validation, the framework establishes a scalable and extensible foundation for future hybrid digital twins. Ongoing and future work will integrate real AE sensor measurements, finite element–assisted simulations, and multi-sensor data fusion to further improve robustness and generalization. Additional efforts will target adaptive retraining through continual learning and edge-optimized deployment, enabling real-time, autonomous monitoring of safety-critical assets within Industry 4.0 environments. Overall, the proposed framework represents a meaningful step toward practical, physics-aware, and trustworthy AI-enabled prognostic digital twins for intelligent condition monitoring.