Hybrid FEM-AI Approach for Thermographic Monitoring of Biomedical Electronic Devices

Abstract

Prolonged operation of biomedical devices may compromise electronic component integrity due to cyclic thermal stress, thereby impacting both functionality and safety. Regulatory standards require regular inspections, particularly for surgical applications, highlighting the need for efficient and non-invasive diagnostic tools. This study introduces an integrated system that combines finite element models, infrared thermographic analysis, and artificial intelligence to monitor thermal stress in printed circuit boards (PCBs) within biomedical devices. A dynamic thermal model, implemented in COMSOL Multiphysics^® (version 6.2), identifies regions at high risk of thermal overload. The infrared measurements acquired through a FLIR P660 thermal camera provided experimental validation and a dataset for training a hybrid artificial intelligence system. This model integrates deep learning-based U-Net architecture for thermal anomaly segmentation with machine learning classification of heat diffusion patterns. By combining simulation, the proposed system achieved an F1-score of 0.970 for hotspot segmentation using a U-Net architecture and an F1-score of 0.933 for the classification of heat propagation modes via a Multi-Layer Perceptron. This study contributes to the development of intelligent diagnostic tools for biomedical electronics by integrating physics-based simulation and AI-driven thermographic analysis, supporting automatic classification and localisation of thermal anomalies, real-time fault detection and predictive maintenance strategies.

1. Introduction

Recent developments in the digitisation of healthcare, with the help of Artificial Intelligence (AI), 3D printers, virtual and augmented reality, nanotechnology, and robotics, have contributed strongly and substantially to the emergence of a new healthcare system [1,2]. Keeping pace with technological advances has become essential for improving healthcare delivery and patient outcomes. At the same time, increasing complexity and miniaturisation of these devices have introduced new reliability challenges, especially related to thermal management in high-density electronic systems. In such systems, uncontrolled thermal stress can lead to degradation of performance, reduced lifespan, or complete failure of critical components. In this context, biomedical devices have a key role to play, contributing significantly to the diagnosis, treatment, and management of various medical conditions [3]. Diagnostic imaging systems such as MRI and CT scanners, implantable devices such as pacemakers and insulin pumps, surgical instruments such as robotic-assisted surgery systems, and monitoring devices such as electrocardiograms (ECGs) and continuous glucose monitors have various applications to ensure patient safety and health protection during use [4,5,6,7]. As defined by Regulation 2017/745 [8], medical devices are intended to be applied in or on human subjects for purposes such as diagnosis, prevention, monitoring, therapy, alleviation of injury or disability, and the study, replacement, or modification of anatomical structures or physiological processes. Ranging from diagnostic to therapeutic tools, biomedical devices improve clinical outcomes, enhance patient safety, and streamline healthcare operations for greater efficiency [9]. Safety and efficiency represent a priority to be ensured, especially for patients, who, together with the medical staff, form the cornerstone of the healthcare facility. Medical devices incorporate elements from mechanical, electrical, electronic, and computer engineering disciplines, reflecting their varying levels of technological sophistication. In particular, electronic subsystems within biomedical devices must operate continuously and reliably under variable thermal and electrical conditions. As such, ensuring their integrity through accurate thermal analysis and stress monitoring is paramount, especially in safety-critical applications like intensive care ventilation and implantable monitoring systems.

The integration of the aforementioned technologies has brought about a significant change in patient care, facilitating the diagnosis, treatment, and effective monitoring of their health conditions [10,11]. This process has also produced innovations in biocompatible materials and 3D printing, improving the design and functionality of implantable devices, and further revolutionising patient care. In parallel, non-invasive diagnostics and monitoring methods, such as infrared thermography, have gained traction as valuable tools for identifying thermal anomalies in real time without interfering with device operation. Their importance lies in their ability to improve clinical decision-making, enhance patient outcomes, and optimise the overall delivery of healthcare. Despite the widespread use of biomedical devices in clinical and homecare settings, there remains a significant lack of comprehensive, non-invasive tools capable of accurately identifying and quantifying thermal stress in densely packed electronic components. Traditional monitoring methods often fail to detect early-stage thermal anomalies, particularly in multilayered PCBs where localised heating may not manifest as immediate surface temperature changes. Moreover, conventional thermal testing is typically conducted offline, lacks spatial resolution, and cannot provide continuous real-time diagnostics. These limitations hinder timely maintenance, increase the risk of device malfunction, and ultimately compromise patient safety in critical healthcare applications. Therefore, meticulous planning and responsible use of raw materials constitute a crucial lifeline for the entire healthcare system, in which biomedical devices play a significant role [12,13].

In the modern device industry, design processes increasingly rely on precise computational codes and a thorough understanding of the physical properties of biomedical device components [14,15,16]. Furthermore, to reduce operational and production costs, it is imperative to demand exceptional material performance, particularly by evaluating mechanical strength in high-stress scenarios involving material defects [17,18,19]. In the last two decades, the biomedical sector has undergone a significant transformation and evolution, mainly driven by advancements in circuit design methodologies, which have improved computational capabilities [20,21]. Technological progress has allowed for greater integration and denser packaging of electronic components. However, the increase in density requires meticulous thermal layout and design of electronic systems. This requirement is even more pronounced in biomedical electronics, where temperature thresholds are strictly regulated, and overheating may compromise both device function and patient safety [22,23]. Addressing these challenges requires an integrated approach that combines thermal models, experimental validation, and intelligent data analysis. Consequently, it is crucial to develop and implement reliable and high-performance electronic circuits capable of withstanding thermal stress induced by high device capacities [24,25]. This consideration is particularly significant in biomedical applications, where efficiency and effectiveness are crucial for safeguarding human health and well-being. Building on these considerations, this study focuses on models, data acquisition, and image processing techniques for monitoring electronic components of biomedical devices [26,27]. The primary objective is to identify and classify the area’s most prone to wear during device operation. The implementation of the model within the COMSOL environment is complemented by a measurement campaign using thermographic techniques to analyse the electronic components. Subsequently, the images acquired from the measurement campaign form a database to be processed by artificial intelligence algorithms. The rationale for using artificial intelligence is to improve the accuracy of identifying areas under particular stress during the operation of the medical device. This paper proposes a comprehensive framework that integrates Finite Element Method (FEM)-based models, infrared thermographic inspection, and artificial intelligence (AI)-driven analysis to detect and classify thermal stress patterns in electronic components of biomedical devices. The novelty of the approach lies in its combination of physical simulation and AI-based interpretation of real-world thermal data for predictive diagnostics. Recent studies have explored AI for detecting thermal anomalies in electronics. Convolutional Neural Networks (CNNs) and transformers have been used to detect overheating in industrial systems [28,29,30], while U-Net has proven effective for biomedical image segmentation due to its high spatial accuracy [31,32]. The choice to adopt U-Net for hotspot segmentation and an MLP for classification lies in U-Net’s ability to preserve spatial features and the MLP’s ability to handle structured tabular descriptors. This architecture aligns with hybrid models used in EEG signal analysis and thermal fault diagnostics [33,34,35]. Unlike prior hybrid models applied to mechanical or civil components [36,37], our work focuses on high-density, safety-critical biomedical PCBs. The dual-layer AI framework integrates physics-based features with spatial segmentation, offering a richer understanding of heat dynamics. The study is organised as follows: Section 2 explains the requirements of PCBs for biomedical devices and how they work. Section 3 illustrates the models in COMSOL of the PCB, investigating all possible inferences to which the device may be subjected. Section 4 presents the measurement campaign using non-invasive techniques. Section 5 introduces the implementation of artificial intelligence algorithms that process the database (DB). Finally, results, conclusions and future developments are presented.

2. Operating Modes of PCB in Medical Device

Within the domain of biomedical devices, PCBs are subject to exacting requirements to ensure their effectiveness and safety across various operational modalities [38]. These prerequisites are comprehensive and encompass aspects such as reliability, durability, and adherence to stringent regulatory standards governing the manufacture of medical devices [39]. Among these, thermal reliability has emerged as a critical factor, particularly due to the increased operating durations and integration of components, which can lead to localised heating and long-term degradation of functionality [40]. Recent scientific endeavours have witnessed a propensity towards the development of increasingly compact products with escalating component densities, particularly in the realm of electromedical devices [41,42,43]. Naturally, this trend engenders several implications for PCB design, including the arrangement and spacing of components, trace length and separation, and the thermal dissipation capacity of the PCB [44,45]. Inadequate thermal management in such high-density layouts may result in the formation of thermal hotspots, which pose a significant threat to the longevity and safety of the device, especially in applications involving continuous patient interaction or life-support systems [46,47]. Reliability stands as a paramount concern for PCBs employed in biomedical devices, necessitating the ability to endure sustained operation and potentially harsh environmental conditions [48,49,50]. Uninterrupted functionality is imperative to mitigate the risk of device failure, which could compromise patient care [51]. Durability constitutes another critical facet of PCB requisites for biomedical applications [52]. Given the pivotal role of medical interventions, PCBs must withstand mechanical stress, temperature fluctuations, and exposure to bodily fluids or sterilisation processes without compromising their performance or structural integrity [53]. One technological solution that addresses this demand is High-Density Interconnection (HDI) boards. By reducing PCB size and augmenting the number and complexity of integrated features, HDI boards mitigate the space available for trace routing, leading to closer trace proximity [54]. While this promotes miniaturisation, it also exacerbates issues of localised heating, necessitating the use of advanced simulation environments such as Finite Element Modelling (FEM) to predict thermal stress distribution accurately [55,56]. Furthermore, PCBs must adhere rigorously to quality assurance protocols and undergo exhaustive testing to meet safety and performance standards, thereby minimising risks to patient health and well-being. Biomedical devices may necessitate diverse functionalities and power requirements contingent on their intended application. For instance, implantable medical devices may necessitate low power consumption and compact PCBs to facilitate integration within the body, while diagnostic equipment may require high-speed data processing capabilities and robust signal integrity [57].

Moreover, PCBs in biomedical devices frequently operate in varied environments, spanning controlled clinical settings to mobile or remote monitoring scenarios [58,59].

Consequently, they must be engineered to withstand temperature fluctuations, humidity, electromagnetic interference, and other environmental stressors without compromising functionality or patient safety. Thermal stress, often resulting from varying duty cycles and high-power transients, is among the most detrimental of these factors.

Monitoring its evolution is crucial to preserving both device integrity and clinical reliability. Flexible and rigid printed circuit boards (PCBs) represent a prevalent technology extensively utilised in medical applications. The rationale behind their adoption stems from the fact that medical devices often deviate from conventional PCB shape and size standards, necessitating accommodation within confined spaces while upholding stringent reliability and strength criteria. Flexible PCBs are crafted from lightweight materials, thereby contributing to the reduction in overall device weight [60]. Despite the heightened design complexity associated with flexible PCBs compared to their rigid counterparts, they facilitate the development of ergonomic and resilient devices more seamlessly [61].

Flexible PCBs present notable mechanical advantages over rigid PCBs in numerous medical applications, particularly in wearable devices [62]. Additionally, the integration of flexible PCBs with rigid counterparts can be achieved through thin, flat cables, obviating the need for cumbersome connectors. PCBs employed in medical equipment must adhere rigorously to stringent standards to ensure component stability, safety, and operational reliability. The failure of medical equipment during patient diagnosis or treatment is highly undesirable, emphasising the imperative of meticulous design, manufacturing, and assembly processes for PCBs [63]. Paramount considerations include safety, reliability, and adherence to regulatory compliance standards, irrespective of the type of medical device employed, as shown in

Table 1. Essential prerequisites for the production of a Medical Device.

Num.	Requisites	Design and Assembly	Ref.
1	Safety	Medical PCBs must ensure patient safety, even when operating in extreme temperatures or in contact with liquids.	[64]
2	Reliability	It is critical to ensure that the equipment performs as intended and provides consistent results	[65]
3	Standards	Medical PCBs must comply with strict standards for quality and reliability, including regulations governing their assembly process.	[66]

.

The medical Printed Circuit Board (PCB) constitutes a pivotal component within implantable medical devices. Given the precision required for implants, the manufacturing and assembly processes of such PCBs must adhere to the most rigorous standards [67]. Another significant biomedical application wherein PCBs play a crucial role involves medical imaging and diagnostic equipment. These sophisticated devices furnish valuable information, aiding physicians and healthcare providers in improved diagnosis and treatment modalities. PCBs find extensive utilisation across a diverse spectrum of diagnostic and medical imaging apparatus, encompassing Magnetic Resonance Imaging (MRI), X-ray Machines, Ultrasound Equipment, and others [68]. Furthermore, medical PCBs are prominently featured in monitoring devices, including body temperature monitors, vital sign monitors, blood glucose monitors, respiration monitors, blood pressure monitors, and the like. Furthermore, beyond the aforementioned medical devices, medical PCBs find application in medical laboratory equipment such as blood analysers and immunoassay analysers. These applications often require repeated thermal cycling or prolonged operation in enclosed environments, conditions under which infrared thermographic analysis can serve as an effective, non-invasive method to detect early signs of thermal degradation. In the context of semiconductors, heat dissipation from the junction to the external environment involves multiple stages due to the presence of various materials. These stages encompass the junction, where heat is generated, the container, the heatsink (if available), and the surrounding environment. Initially, heat is primarily conducted from the junction to the heatsink (or directly to the container in the absence of a heatsink). Subsequently, as the component is surrounded by air, heat dissipation occurs through convection. However, convection alone may not suffice to control the thermal load in compact biomedical devices. Therefore, a comprehensive analysis of heat propagation, including modelling of conduction paths and temperature gradients, is necessary to ensure operational safety. Such analysis benefits from the integration of simulation tools like COMSOL Multiphysics^® and validation through IR thermography to localise and quantify hotspots in real scenarios.

3. Modelling of Electronic Circuit Board

Thermal resistance quantifies the opposition to heat flow and is defined as the temperature increase per unit of power dissipated. In conduction, the relationship between temperature gradient and heat transfer is approximately linear [69], whereas in convection and radiation it becomes nonlinear, depending on temperature and surface characteristics. This distinction is crucial for accurately modelling heat transfer in compact biomedical PCBs, where even small thermal gradients can critically affect component performance. However, in convective and radiative processes, thermal resistance becomes nonlinear and depends on temperature and surface properties (1).

$$∆T=R_{th }{P}_d$$

(1)

where ΔT is the temperature difference (°C), R_th represents the thermal resistance (°C/W), and P_d is the transmitted power (W). This distinction is essential for developing accurate thermal models of electronic components, especially when designing compact medical devices, where small-scale thermal gradients can lead to significant performance degradation or failure.

3.1. Mathematical Modelling of Heat Transfer in Biomedical PCBs

This last reflection emphasises heat conduction as the predominant mode of heat transfer in PCBs, given its relevance to temperature measurements. Heat conduction refers to the transmission of heat through a material or body, facilitated by microscopic collisions among particles. In multilayer PCBs used in biomedical devices, conduction dominates due to the laminated and compact structure of the board, where internal copper traces and vias serve as heat propagation channels. Understanding this phenomenon is essential to predict internal temperature gradients and plan optimal cooling strategies.

The intensity of heat conduction correlates with the frequency of these collisions, with higher frequencies indicating elevated temperatures. Heat transfer ensues when there exists a temperature gradient between two objects or different regions within an object, with its efficiency contingent upon factors such as object geometry, thickness, and material composition. The heat equation, also known as the linear diffusion equation, governs the behaviour of temperature distribution over time within a given volume. In our context, the function T (V, t) represents absolute temperature, where V belongs to the spatial variable ${\mathit{ℝ}}^n$ and t denotes the temporal variable greater than zero (2). This partial differential equation (PDE) serves as a foundational framework for analysing heat conduction phenomena in PCBs [70]. The analytical form of this equation enables the simulation of temperature evolution across different layers of the PCB and under varying boundary conditions, a capability particularly useful when evaluating components operating in pulsatile or cyclic power regimes.

$${\displaystyle \frac{\partial T\left(V,t\right)}{\partial t}}=k_0{\nabla }^{2}T\left(V, t\right)+f\left(V,t\right)$$

(2)

Equation (2) represents the classical heat conduction equation, also known as the linear diffusion equation, and serves as a foundational model for describing the temporal evolution of temperature in a continuous medium. In this formulation, T (V, t) denotes the absolute temperature as a function of the spatial coordinate V and time t, while k₀ is the thermal diffusivity of the material, which encapsulates the material’s ability to conduct heat relative to its capacity to store it. The term ∇²T represents the spatial Laplacian of temperature and quantifies the local curvature of the temperature field, indicating how heat flows from regions of higher temperature to those of lower temperature. The additional term f (V, t) accounts for internal heat sources, such as power dissipation generated by active electronic components embedded within the printed circuit board. This equation assumes that the medium is homogeneous and isotropic, with constant thermal properties, and is particularly relevant to the modelling of thermal dynamics in biomedical PCBs, where local temperature gradients induced by high-frequency switching or prolonged activation cycles can result in concentrated thermal stress. Solving Equation (2) enables the prediction of temperature distribution under various boundary and loading conditions, thus facilitating the identification of thermally critical areas and supporting design optimisation for thermal reliability. The model also establishes a computational framework suitable for finite element simulation environments such as COMSOL Multiphysics^®, allowing for comparison with experimental infrared thermographic data and for subsequent validation of thermal performance. PCBs are engineered to facilitate electrical conduction and the transmission of analogue and digital signals among various electronic components. As electricity traverses the circuit, it generates heat proportional to the encountered resistance. Alongside traces, power components such as MOSFET transistors, IGBTs, converters, and driver circuits primarily contribute to heat generation. These hotspots are typically located near power stages, such as motor drivers or RF amplifiers, and can be detected through high-resolution infrared thermography, allowing for direct comparison with simulated thermal maps. Despite the gradual reduction in supply voltages for highly integrated logic devices such as DSPs, SoCs, and FPGAs, these components still produce significant heat due to high operating frequencies and the intensive execution of algorithms with high computational complexity [71]. Fault detection can be effectively monitored using thermography, particularly since the power dissipation of components in conduction is significantly high and thus easily detectable. Components typically operate in one of two states: conduction or interdiction. From a thermal perspective, power dissipation is substantial when components are in conduction and functioning correctly, whereas it is negligible when they are in interdiction or are supposed to be in conduction but are faulty. Consequently, the thermal comparison between a faulty component and a properly functioning switch is markedly evident. Presently, silicon-based components typically operate at junction temperatures ranging between 125 °C and 200 °C. However, exceeding these temperatures can lead to rapid degradation of component lifespan. Research suggests that a 20 °C increase in operating temperature, resulting from inadequate thermal management, may halve the component’s lifespan. Nonetheless, the necessity for meticulous thermal management persists to ensure even distribution of developed heat, prevent the formation of hazardous hotspots, and minimise power losses. It is crucial to acknowledge that all chemical and physical processes are influenced by the temperature at which they occur, as depicted in Equation (3).

$$\ln k=ln{k}_0-{\displaystyle \frac{E_a}{k_{B}T}}$$

(3)

In Equation (3), T denotes the temperature at which the process occurs, k represents the reaction or degradation rate, k₀ is a process-specific constant, E_a is the activation energy required to initiate the process, and k_B is the Boltzmann constant.

As indicated by Equation (3), it is evident that with increasing temperature (T), the second term in the formula progressively diminishes, leading to an escalation in the value of k towards k₀. Consequently, this implies an acceleration in the ageing process, manifested by the degradation of characteristics occurring at an accelerated rate.

This formula is widely applicable in describing the ageing processes of electronic components within various apparatuses. It is often invoked in discussions concerning the Mean Time to Failure (MTTF) of components or systems, providing insights into their expected lifespan or durability. In biomedical electronics, where reliability over time is mandatory, these thermal-ageing models provide useful tools for estimating the operational lifespan of active components, especially in wearable or implantable systems that experience limited convective cooling. To assess the durability and efficiency of biomedical devices, electronic boards are subjected to significant thermal stress through a series of thermal cycles. These cycles entail exposing the board to alternating high positive and negative temperatures. While the form and number of cycles may be considered general and applicable across different usage scenarios, the specific operating temperature varies based on the components utilised and the environmental conditions in which the board is deployed. Beyond thermal cycles, the fatigue limit of a PCB is influenced by multiple factors and can be evaluated using appropriate coefficients, each less than one. The corrected fatigue limit (σ_l) can thus be expressed using Equation (4).

$${\sigma }_{l }=k_a·k_b·k_c·k_d·k_e·{\sigma }^{\prime }$$

(4)

where each coefficient adjusts the base fatigue limit σ′ according to surface finish k_a; geometric size k_b; type of loading k_c; operational temperature k_d; additional environmental or manufacturing factors k_e. When considering the constant parameters k_a, k_b, k_c, and k_d, and excluding the fatigue limit of the specimen which has already been determined through testing, Equation (5) is derived from the correlation between Equation (2) and Equation (3).

$$ln∆k=ln{k}_0-{\displaystyle \frac{E_a}{k_{B}T}}$$

(5)

where Δk interprets the cumulative degradation function on a thermal basis. By combining Equation (5), which relates the degradation rate to temperature through an Arrhenius-type expression, with the general form of the heat conduction Equation (2), one obtains Equation (6), which explicitly links the temperature gradient and heat sources to the performance degradation of the system over time.

$$k_0∆T\left(V\right)=f\left(V\right)$$

(6)

showing how local temperature fields depend on material diffusivity and localised heat sources. High T values are often associated with regions of poor thermal dissipation.

The complete mathematical formulation establishes a robust foundation for physical simulation in Section 4. The following analysis proceeds to geometric and boundary definition, enabling accurate numerical resolution of thermal behaviour in the biomedical PCB model.

3.2. Physical and Geometric Modelling

A COMSOL Multiphysics^® model was developed to simulate the thermal behaviour of the electronic board within the biomedical device. This model incorporates various parameters, including material properties, component layout, heat generation profiles, and environmental boundary conditions. The governing heat transfer equations are solved using the FEM, yielding spatial and temporal distributions of temperature across the electronic board. To this end, the Heat Transfer Module was coupled with the Structural Mechanics Module, enabling the analysis of thermal conduction and its structural consequences, such as thermal expansion and stress at material interfaces. This coupling is particularly relevant when the temperature field T (V, t) acts as a thermal load on electronic interfaces, which may lead to thermal deformation or fatigue. In the simulation workflow, a steady-state condition was initially assumed to establish baseline thermal behaviour. The electronic board was first designed in the 2D CAD environment of COMSOL and then extruded to generate the final 3D geometry, as shown in Figure 1.

To numerically solve the governing heat conduction equation (Equation (2)), both initial and boundary conditions must be defined. For the initial condition, we impose a predefined temperature field across the domain at time t = 0 (7)

$$T\left(V,0\right)=g\left(V\right)$$

(7)

In Equation (7), the function g(V) defines the initial temperature distribution over the spatial domain of the PCB at time t = 0. This function may represent a uniform baseline temperature or a non-uniform field resulting from previous operating cycles, thermal loading, or localised heating near active components. For boundary conditions, various thermal constraints can be applied. A Dirichlet condition fixes the temperature at the boundary (8)

$$T\left(V,\mathrm{t}\right){|}_{\mathit{V}ϵ\vartheta V}=T_q$$

(8)

Alternatively, a Neumann condition imposes a heat flux across the surface (9)

$$k\nabla T\left(V,\mathrm{t}\right)·\mathit{n}{|}_{\mathit{V}ϵ\vartheta V}=q$$

(9)

A more realistic approach often involves Newton’s law of cooling, which models convective heat exchange with the environment (10)

$$k\nabla T\left(V,t\right)·\mathit{n}{|}_{\mathit{V}ϵ\vartheta V}=-hA(T\left(V,t\right)-T_q)$$

(10)

Here, h is the heat transfer coefficient, and A is the exchange area. When radiative heat transfer becomes significant, the boundary condition becomes nonlinear and is modelled by Equation (11)

$$k\nabla T\left(V,t\right)·\mathit{n}{|}_{\mathit{V}ϵ\vartheta V}=-\sigma \epsilon A(T{\left(V,t\right)}^4-T_q^4)$$

(11)

In this equation, σ is the Stefan–Boltzmann constant, ε is the surface emissivity, and T_q is the ambient temperature. For this study, the model focuses on heat conduction only, assuming that convective and radiative effects are negligible under the simulated operational conditions. The thermal properties assigned to each material used in the PCB model are summarized in

Table 2. Thermal and physical parameters of the materials in the PCB stack-up.

Material	Property	Value	Unit
Aluminium	Specific heat at constant pressure	900	J/(kg∙K)
	Thermal conductivity	238	W/(m∙K)
	Density	2700	kg/m3
PCB	Specific heat at constant pressure	1369	J/(kg∙K)
	Thermal conductivity	~0.3–0.5	W/(m∙K)
	Density	≈1850–2000	kg/m3
Plastic	Specific heat at constant pressure	2700	J/(kg∙K)
	Thermal conductivity	~0.3–0.4	W/(m∙K)
	Density	≈1100–1400	kg/m3
Silicon	Specific heat at constant pressure	700	J/(kg∙K)
	Thermal conductivity	130	W/(m∙K)
	Density	2329	kg/m3

. These values are critical for accurate simulation results and are selected based on literature and datasheet specifications.

In this study, the thermal properties of all materials were considered constant over the temperature range of interest (approximately 60–130 °C). This assumption is consistent with datasheet specifications for PCB substrates and silicon components within this operating window. While temperature-dependent properties can be incorporated in advanced models, their variation within this range is minimal and does not significantly affect simulation accuracy. The domain was discretized using an unstructured tetrahedral mesh. To improve mesh resolution near critical areas and ensure numerical stability, a mesh partitioning strategy was applied, extending selected faces onto adjacent domains to resolve complex geometries. This partitioning facilitated mesh parallelization in shared memory systems, especially in non-convex regions. In situations where the original geometry was already meshed, unstructured tetrahedral meshing was evaluated for its trade-off between accuracy and computational load. To improve resilience and reduce boundary errors, a de-structuring mesh strategy was applied, with the detailed mesh parameters reported in

Table 3. Mesh settings in the COMSOL simulation.

Description	Value
Maximum element size	7∙10−4 m
Minimum element size	3∙10−5 m
Curvature factor	0.3
Elongation resolution parameter	0.85
Maximum growth rate of elements	1.35
Global element size setting	Very dense

.

As widely acknowledged, thermal transfer occurs via conduction, convection, and radiation [72]. In practical scenarios, all three mechanisms may coexist, but for the specific simulation conditions considered in this study, only conduction was modelled, assuming negligible influence from convection and radiation due to geometric and environmental constraints.

3.3. Simulation Model Results

In this study, heat transfer within the electronic board was assumed to occur predominantly through conduction, justifying the use of Equation (2) in the COMSOL Multiphysics^® environment. The initial simulations were carried out under stationary conditions, where the temperature field does not evolve with time [73,74]. In this regime, Equation (2) reduces to its steady-state form, where ∂T/∂t = 0, and the external heat source is considered negligible. The governing condition becomes (12)

$${\nabla }^{2}T\left(\mathit{V}\right)=0 with T\left(\mathit{V}\right)=T_q$$

(12)

where T_q represents the ambient or externally imposed temperature to which the circuit board is subjected during each simulation. Although these simulations were performed under steady-state conditions, they provide a reliable approximation of thermal stress distribution and highlight areas of potential overheating. Following the stationary study, a transient analysis was conducted on both the entire circuit board and its individual components [75]. In the steady-state regime, temperature evolution is time-independent, and thermal equilibrium implies that the rate of heat influx equals the rate of heat dissipation. However, under transient conditions, thermal accumulation can occur, particularly when the initial heat input exceeds the heat dissipation rate. This results in localised temperature rises and evolving thermal gradients across the device. The transient simulations, performed in COMSOL Multiphysics^®, revealed dynamic temperature profiles and the development of thermal stress within specific regions of the board [76,77].

An example of heat transfer in an active component (chip) is shown in Figure 2.

The temperature rise is visualised over time, highlighting the formation of localised thermal gradients due to power dissipation. To provide a more granular understanding of thermal evolution, the circuit board was segmented into distinct subdomains based on material properties. Each region was analysed independently to assess differential thermal behaviour. The numerical results were subsequently validated through a comparison with experimental data obtained via infrared (IR) thermography. The validation process included both passive thermographic imaging (for stationary cases) and active IR thermography (for transient analysis), confirming the consistency and reliability of the proposed simulation framework.

4. Thermographic Measurements

Thermographic measurements involve the capture and analysis of IR radiation emitted by objects to visualise surface temperature distributions. This technique employs thermal cameras or infrared sensors to detect emitted radiation and convert it into visible thermograms, enabling the evaluation of heat generation, dissipation, thermal gradients, and anomalies. Widely adopted across engineering, medicine, building diagnostics, and industrial inspection, IR thermography serves as a non-invasive diagnostic tool for assessing performance, reliability, and thermal behaviour of systems and materials [78,79].

Thermal imaging plays a crucial role in non-destructive testing, predictive maintenance, quality control, and R&D, contributing to improved system safety and efficiency. Thermography can be categorized into two experimental methods: passive and active.

While passive thermography captures the naturally emitted radiation, active thermography involves the application of external thermal stimulation, which enhances defect visibility when temperature differences are subtle [80]. In the context of PCB evaluation, active thermography is commonly employed due to its sensitivity and versatility.

The methodology was divided into two main phases: (1) the acquisition and interpretation of thermal data using an active infrared imaging approach, and (2) the assessment of experimental uncertainty to ensure the reliability and reproducibility of the measurements. The following subsections describe each phase in detail.

4.1. Active Infrared Thermography for PCB Diagnostics

This study utilised active IR thermography to identify hot spots indicative of voltage overload or thermal anomalies during PCB operation. Surface temperature was determined based on the emissivity of the materials under investigation. IR radiation, spanning wavelengths between 0.7 µm and 1 mm (frequencies from 3 × 10¹¹ to 4 × 10¹⁴ Hz), bridges the visible and microwave regions of the electromagnetic spectrum. Thermal maps or thermograms are generated by assigning colours to detected temperatures, facilitating visualisation of heat flow and detection of abnormal patterns. To detect localised overheating, it is essential to first estimate the expected thermal distribution of the PCB in a defect-free condition and compare it against measured thermograms. The thermal image acquisition aimed to build a diverse dataset of infrared images suitable for AI training and generalisation. The acquisition protocols followed the IEC TS 62446-3:2017 standard [81], as shown in

Table 4. IEC 62446-3 Criteria for Thermal Imaging.

Parameter	Requirement	Unit
Environmental Conditions	Irradiance (G) ≥ 600	W/m2
	Wind speed (w) ≤ 28	km/h
	Sky coverage (c) ≤ 2	oktas
Image Resolution	Minimum 5 × 5 pixels per unit/component	-
Emissivity	Dependent on material properties and viewing angle	-
Considerations

.

The measurement campaign was carried out on a medical device designed for Non-Invasive Ventilation (NIV) [4,82]. As shown in Figure 3, the internal components include the power supply PCB (centrally located), a brushless fan connected via a rubber tube, and an output nozzle for connecting the respiratory mask.

Thermal imaging was performed using a FLIR P660 infrared camera (resolution: 640 × 480 pixels) (Teledyne FLIR, Limbiate, Italy), ensuring high spatial detail and accurate radiometric readings [83]. To enable an accurate comparison between FEM simulation results and thermographic measurements, spatial alignment was performed through a landmark-based affine registration method. In this process, distinctive features such as the corners of the PCB and the edges of the connectors were extracted from both data sources to compute the transformation matrix. This procedure led to a registration error of less than 1.5 percent, calculated as the average pixel displacement, thereby ensuring a reliable overlay and precise pixel-wise correspondence between thermal maps. The entire diagnostic pipeline, which includes both segmentation and classification stages, was able to process each thermal frame in approximately 52 milliseconds, corresponding to a throughput of nearly 19 frames per second. These results confirm the feasibility of real-time operation on systems equipped with a GPU. Further optimisation using TensorRT, manufactured by NVIDIA Corporation, based in Santa Clara, CA, USA, is currently in progress to support deployment on edge computing platforms such as the Jetson Xavier NX. Image analysis was conducted using Teledyne FLIR ResearchIR^® software vX.XX, Wilsonville, OR, USA, focusing on the microcontroller board component shown in Figure 4.

The thermal energy distribution revealed hotspots near defective components and along the board edges. Although the setup was partially insulated, minor environmental interference may have occurred but was deemed negligible. The active thermography method enabled accurate characterisation of the thermal field, particularly under induced thermal stress in the range of 60–130 °C. Figure 5 illustrates the progressive emergence of thermal anomalies characterised by localised increases in surface temperature (ΔT ≈ 1 °C), primarily concentrated around the defective component. These hotspots were observed under controlled thermal excitation, confirming the presence of localised stress zones detectable through infrared imaging.

The analysis of thermal propagation within the PCB structure provided critical insight into the dynamic behaviour of heat distribution during device operation. As shown in Figure 6, the development of localised heating was first observed at a critical component, where surface temperatures reached a peak of approximately 127 °C. This region of elevated thermal intensity corresponded to an area with significant power dissipation, likely attributed to active elements such as voltage regulators, microprocessors, or high-frequency driver circuits. The pronounced thermal activity in this zone indicates inadequate heat sinking or excessive current density, both of which contribute to thermal stress and may compromise long-term device reliability. Over time, thermal propagation exhibited a progressive increase in temperature, measured at approximately 1 °C increments across adjacent zones of the PCB. This phenomenon can be interpreted as a result of both conductive heat transfer through copper traces and dielectric layers, and thermal coupling between neighbouring components. The gradual diffusion of heat outward from the hotspot is consistent with the transient solution of the heat conduction Equation (2), where localised sources act as thermal drivers and the surrounding materials serve as propagation media with distinct diffusivity characteristics.

Figure 6 captures this evolving thermal profile with high spatial resolution. The colour gradient, moving from green and yellow near the core region toward orange and red, reflects the rising surface temperature and the radial expansion of heat flow. Notably, the image also illustrates the emergence of secondary heating zones at the rear surface of the board, highlighting the three-dimensional nature of thermal conduction in multilayered PCB structures. This rear-surface temperature map confirms that thermal energy is not confined to the plane of component placement but penetrates through the dielectric layers, affecting underlying copper planes and mechanical supports. Such thermal back-propagation underscores the necessity for holistic thermal design strategies in medical electronics, especially in devices with limited natural convection due to enclosure constraints. The insight obtained from this analysis is instrumental in identifying critical zones requiring enhanced cooling solutions, such as heat spreaders, thermal vias, or active dissipation mechanisms. Moreover, the results from this thermal propagation study serve to validate the model simulation, demonstrating strong consistency between numerical predictions and experimental infrared imaging. This reinforces the robustness of the hybrid FEM-IR-AI methodology for real-time diagnostics and predictive thermal management in complex biomedical systems. The clearness of thermograms had a measurable impact on temperature reading accuracy. This effect was observed across multiple environmental conditions, underscoring the importance of high-resolution thermal imaging in precise diagnostics. Peak thermal stress was observed at the contact interface between the defective component and the PCB, confirming this area as the most sensitive zone for thermal degradation. This dataset will serve as the input for training AI models described in the next section.

4.2. Experimental Uncertainty and Error Estimation

To ensure the reliability of thermographic measurements, a rigorous estimation of experimental uncertainty was conducted by quantifying both systematic and random sources of error. This assessment is crucial for evaluating the precision of thermal imaging in biomedical electronic devices, where small thermal gradients can indicate early-stage anomalies. The total measurement error ε_total is expressed as the root-sum-square (RSS) of systematic and random components (13)

$${\epsilon }_{total}=\sqrt{{\epsilon }_{sys}^2+{\epsilon }_{rand}^2}$$

(13)

Systematic errors ε_sys are associated with: (a) Camera calibration; (b) Incorrect or variable emissivity values; (c) Reflections from surrounding surfaces; (d) Random errors.

While ε_rand arise from: (a) Detector noise (ND); (b) Ambient air turbulence or drafts; (c) Surface heterogeneity or texture. In this study, the FLIR P660 has a Thermal Sensitivity (NETD): ~30 mK at 30 °C, and a Radiometric Accuracy: ±2 °C or ±2% of reading (whichever is greater).

These specifications ensure high radiometric precision, making the FLIR P660 particularly suitable for the detection of subtle temperature gradients in biomedical PCBs, where thermal anomalies may manifest with variations below 1 °C. Similar high-performance infrared cameras have been successfully employed in electronic fault diagnostics and thermal stress studies [84,85].

To estimate the propagated error from uncertainty in emissivity, we consider the Stefan–Boltzmann law (14):

$$P = \epsilon \sigma A{T}^4$$

(14)

Differentiating with respect to temperature T, and isolating δT, we obtain (15)

$${\displaystyle \frac{\delta T}{T}}\approx {\displaystyle \frac{1}{4}}·{\displaystyle \frac{\delta \epsilon }{\epsilon }}$$

(15)

Assuming nominal emissivity ε = 0.95, and emissivity uncertainty δε = ±0.02 we derive (16).

$${\displaystyle \frac{\delta T}{T}}\approx {\displaystyle \frac{1}{4}}·{\displaystyle \frac{0.02}{0.95}}\approx 0.0053\to \delta T\approx \pm 0.6 °C at T=120 °C$$

(16)

Table 5. Summary of Thermographic Error Sources.

Source of Error.	Type	Estimated Contribution	Notes
Emissivity uncertainty	Systematic	±0.6 °C	Assumed δε = ±0.02
Camera calibration error	Systematic	±2.0 °C or ±2% of reading	Manufacturer Specif.
NETD	Random	±0.03 °C	Noise equivalent temperature difference
Ambient temperature fluctuations	Random	±0.2 °C	Measured under lab conditions
Environmental reflection	Systematic	±0.3 °C	Estimated from experimental shielding
Surface texture/non-uniformity	Random	±0.4 °C	Based on visual inspection and material specs

summarizes the primary sources of uncertainty affecting the thermographic measurements conducted in this study. Each error component is classified by type (systematic or random), and its estimated contribution to the overall measurement uncertainty is reported.

The values are based on both manufacturer specifications and empirical observations under controlled laboratory conditions.

Assuming worst-case additive RSS combination ε_total ≈ ±2.15 °C. This total uncertainty remains well below the diagnostic threshold used in this study, where typical temperature differences between normal and anomalous regions were ΔT_mean ≈ 8.3 °C ΔT_peak ≈ 60 °C. Hence, the signal-to-noise ratio (SNR) is sufficiently high to guarantee reliable localisation of thermally stressed components. The estimated measurement uncertainty—dominated by calibration accuracy and emissivity estimation—was found to be less than ±2.2 °C in the worst case. Given that the detected anomalies exhibit temperature deviations well above this margin, the thermal analysis results are considered statistically and diagnostically robust. These quantified uncertainty bounds further support the suitability of the dataset for training AI algorithms, ensuring the reproducibility of thermal pattern recognition.

5. AI-Based Proposed Model

In this section, we present an AI-based framework to assess defects characteristics in biomedical PCBs. The proposed model is structured in two interconnected tasks that are helpful to the thermal analysis of PCBs: (i) segmentation of thermal anomalies (hotspots), and (ii) classification of heat diffusion patterns. This approach integrates deep learning with feature extraction of physically inspired features and machine learning (ML) classification [86]. This dual-level system is useful to realise that mere hotspot detection is insufficient to describe the causes of thermal stress in PCBs. In biomedical electronic devices of this type, the mode of heat propagation contains valuable information regarding structural deficiencies, faulty components, and potential system-level failures [87,88]. Similar to recent approaches used for high-density EEG signal processing in neurological diagnostics, our method extracts spatially rich descriptors from thermographic data to classify propagation dynamics [89,90]. Our framework is therefore structured in three stages: thermal segmentation, diffusion feature extraction, and thermal propagation classification, each described in detail below.

5.1. Thermal Segmentation

The first stage of the proposed model focuses on the automatic identification of thermally anomalous regions using a supervised image segmentation model. Given an infrared thermographic image acquired under controlled active heating conditions (Section 4), we seek to produce a pixel-wise binary mask classification highlighting the areas of highest temperature concentration. Figure 7 describes the process of binary mask segmentation on IR images of biomedical PCBs. U-Net architecture was adopted for this task [91].

U-Net employs an encoder–decoder structure: the encoder captures contextual information by progressively downsampling the input, while the decoder restores the spatial resolution via Upsampling and skip connections [92]. The skip connections are particularly useful for preserving fine thermal contours, which are critical in detecting early-stage localised overheating [93].

U-Net Architecture

U-Net model was adopted to perform binary mask segmentation, distinguishing between two classes: “hotspot” (thermally anomalous region) and “background” (non-anomalous area). Each input thermographic image is processed to produce a pixel-wise binary output map, where each pixel is labelled according to its thermal classification.

Table 6. U-Net architecture description.

Index	Layer Type	Composition	Kernel/Pool Size(s)	Filters/Units	Output Shape
1	Input	IR thermographic image	—	—	(256, 256, 1)
2	Conv2D + ReLU	2 × Conv2D	3 × 3	64	(256, 256, 64)
3	MaxPooling2D	Downsampling	2 × 2	—	(128, 128, 64)
4	Conv2D + ReLU	2 × Conv2D	3 × 3	128	(128, 128, 128)
5	MaxPooling2D	Downsampling	2 × 2	—	(64, 64, 128)
6	Conv2D + ReLU	2 × Conv2D	3 × 3	256	(64, 64, 256)
7	MaxPooling2D	Downsampling	2 × 2	—	(32, 32, 256)
8	Conv2D + ReLU	2 × Conv2D	3 × 3	512	(32, 32, 512)
9	Dropout	Regularization layer	—	—	(32, 32, 512)
10	MaxPooling2D	Downsampling	2 × 2	—	(16, 16, 512)
11	Bottleneck	2 × Conv2D	3 × 3	1024	(16, 16, 1024)
12	UpConv2D	Upsampling + Conv2D	2 × 2	512	(32, 32, 512)
13	Concatenate	Skip connection (layer 8)	—	—	(32, 32, 1024)
14	Conv2D + ReLU	2 × Conv2D	3 × 3	512	(32, 32, 512)
15	UpConv2D	Upsampling + Conv2D	2 × 2	256	(64, 64, 256)
16	Concatenate	Skip connection (layer 6)	—	—	(64, 64, 512)
17	Conv2D + ReLU	2 × Conv2D	3 × 3	256	(64, 64, 256)
18	UpConv2D	Upsampling + Conv2D	2 × 2	128	(128, 128, 128)
19	Concatenate	Skip connection (layer 4)	—	—	(128, 128, 256)
20	Conv2D + ReLU	2 × Conv2D	3 × 3	128	(128, 128, 128)
21	UpConv2D	Upsampling + Conv2D	2 × 2	64	(256, 256, 64)
22	Concatenate	Skip connection (layer 2)	—	—	(256, 256, 128)
23	Conv2D + ReLU	2 × Conv2D	3 × 3	64	(256, 256, 64)
24	Conv2D (Output)	Final classification layer	1 × 1	1	(256, 256, 1)
25	Activation	Sigmoid (binary segmentation)	—	—	(256, 256, 1)

describes the configuration of our proposed U-Net architecture.

5.2. Heat Diffusion Pattern Analysis

Once thermal hotspots are segmented using the U-Net architecture (Section 5.1), a deeper level of thermal characterisation is carried out through heat diffusion pattern analysis. This second stage is designed to quantify how heat propagates across PCBs starting from the potential hotspots detected. Thermal segmentation provides spatial localisation; diffusion analysis captures how the temperature spreads. This can lead to differentiate hotspots in localised overheating, poor heat dissipation, or system-wide thermal stress. This section details the process for quantifying diffusion geometry, extracting shape descriptors, and computing physically features from each thermogram.

5.2.1. Radial Temperature Gradient Analysis

The information of the distribution of temperature as a function of distance from the centre of the hotspot allows to measure how quickly heat disperses into the surrounding space. The first step is to identify the centroid of the area segmented as a hotspot. This point represents the centre of gravity of the anomalous region and is calculated as the average of the coordinates of the pixels labelled as “hotspots” (17):

$$x_c = {\displaystyle \frac{1}{N}}\sum _{\left(x,y\right)\in M= 1}x, y_c = {\displaystyle \frac{1}{N}}\sum _{\left(x,y\right)\in M= 1}y$$

(17)

where N is the number of pixels labelled as hotspot. Next, starting from the centroid, the thermal image is converted into polar coordinates and divided into concentric circular rings of increasing radius.

The average temperature is calculated for each ring (18):

$$T\left(r\right)= {\displaystyle \frac{1}{\left|A_r\right|}}\sum _{(x,y)\in A_r}I(x,y)$$

(18)

where A_r represents the set of pixels contained in the ring of radius r, and I (x, y) is the thermal intensity of the image at that point. The radial heat gradient is then calculated as the derivative of the average temperature with respect to the radial distance (19):

$${\displaystyle \frac{dT}{dr}} = {\displaystyle \frac{T(r+∆r)-T\left(r\right)}{∆r}}$$

(19)

this value gives a direct indication of how fast the temperature decreases.

5.2.2. Isothermal Contour Extraction and Shape Descriptors

Another valuable approach to analysing thermal behaviour is through the extraction of isothermal contours, or isotherms—lines connecting points of equal temperature.

To extract isotherms, we apply thresholding at different temperature levels T_k, resulting in a series of binary contour maps (20):

$$C_k = \left\{\left.\left(x,y\right)\right|I\left(x,y\right)= T_k\right\}$$

(20)

For each isotherm, we compute a set of geometric shape descriptors: Area (A) enclosed by the isotherm, Perimeter (P) of the contour and Circularity, defined as (21).

$$C={\displaystyle \frac{4\pi A}{P^2}}$$

(21)

We also define an Isotherm Dispersion Index (IDI) to quantify the radial regularity of each isotherm (22):

$$IDI = {\displaystyle \frac{1}{K}}\sum _{k = 1}^{K}std\left(r_{k,\theta }\right)$$

(22)

where r_k,θ is the radius of the isotherm C_k sampled over angles θ. A higher IDI indicates irregular or asymmetric thermal expansion.

5.2.3. Asymmetry and Thermal Skewness Analysis

In real-world PCBs, thermal propagation is often affected by non-uniform material properties or irregular component placement. As a result, heat may not spread uniformly in all directions.

To capture this behaviour, we calculate a thermal skew vector representing the displacement between the hotspot centroid and the centroid of the outermost isotherm (23).

$$\overrightarrow{s}=C_{outer}-C$$

(23)

We then compute a Heat Skewness Index (HSI) as the normalized magnitude of this vector (24):

$$HSI = {\displaystyle \frac{‖\overrightarrow{s}‖}{R_{max}}}$$

(24)

where R_max is the radius of the outermost isotherm. HSI values close to zero indicate symmetric diffusion, while higher values reveal directional bias.

5.2.4. Feature Vector Construction

All computed descriptors are consolidated into a feature vector that characterises each hotspot and its surrounding heat diffusion pattern (

Table 7. Feature Vector descriptions.

Feature	Description
Mean radial gradient	Sharpness of temperature decay
Circularity and eccentricity	Symmetry and shape of thermal field
Heat Skewness Index (HSI)	Directional bias in heat propagation
Isotherm Dispersion Index (IDI)	Uniformity of radial diffusion
Max temperature/temperature delta	Severity of the thermal anomaly

).

This feature vector becomes the input to the classification stage described in Section 5.3.

5.3. Classification of Heat Diffusion Patterns

Classification of heat diffusion patterns observed in thermographic images is the final step of the proposed methodology described in Section 5.

Segmentation provides information about where the anomaly is located, diffusion analysis describes mathematically how heat propagates across PCBs and classification is intended to interpret what thermal behaviour is occurring. The chosen classifier is a Multi-Layer Perceptron (MLP).

This three-stage proposed methodology support real-time diagnostic and predictive maintenance.

5.3.1. Definition of Thermal Classes and Feature Vector Representation

The proposed classification method distinct different mode of heat propagation. To structure this process, we first define a taxonomy of thermal diffusion classes.

The classification framework that recognizes four categories is described in

Table 8. Heat propagation categories description.

Class Name	Description
Localised Hotspot	Small, intense thermal region with a sharp temperature gradient. Heat is confined around a single source, usually caused by component failure or overload.
Diffused Anomaly	Widespread, smooth heat distribution with shallow gradients. Indicates inefficient heat dissipation or thermal accumulation over larger regions.
Asymmetric Propagation	Directional heat spread, with clear skewness. Often caused by uneven PCB layout, shielding, or non-homogeneous materials influencing heat paths.
Uniform Heating	Homogeneous temperature increases with low spatial variation. Often linked to ambient factors or global system heating due to prolonged activity.

.

Each thermographic sample is manually labelled with one of these four categories to create a ground-truth dataset for training and validation. To support this classification, we convert each image region into a structured feature vector, denoted by function F.

This vector compiles all relevant descriptors derived from the heat diffusion analysis described in Section 5.2. The most important features are included in Equation (25).

$$F=\left[T_{max}, ∆T,{\nabla }_{r}T,A,C, ϵ,HSI,IDI,N_{iso},{\overline{ϵ}}_{iso} \right]$$

(25)

Each sample is converted into a numerical feature vector $F\in {\mathbb{R}}^n$, with 10 total number of features.

5.3.2. Dataset Description

The dataset was built from a collection of annotated thermograms of PCBs. The images were obtained at a resolution of a 640 × 480 pixels and then were resized to 256 × 256 pixels.

Table 9. Heat propagation categories dataset distribution.

Class Label	Number of Samples
Localised Hotspot	260
Diffused Anomaly	240
Asymmetric Propagation	220
Uniform Heating	230
Total	950

describes dataset composition by class.

All samples were split using a stratified 5-fold cross-validation protocol. The dataset was first split into three partitions following a 70/20/10 ratio for training, validation and testing. Then, 5-fold cross-validation was applied in a stratified manner to maintain the relative class distributions across folds. Preprocessing included resizing IR images to 256 × 256 pixels, normalization to the [0, 1] range, and contrast enhancement using histogram equalization. Feature selection was driven by physical interpretability, retaining descriptors such as radial gradients, skewness, and circularity. Hyperparameter tuning was conducted via grid search over a range of dropout rates, learning rates, and number of hidden units, selecting configurations that minimised validation loss. Data augmentation was applied selectively to training folds and included small-angle rotations (±10°), Gaussian noise (σ = 0.01), and minor scaling (±5%) to preserve the physical plausibility of temperature gradients and spatial features. Data augmentation was applied selectively to the training folds only. Augmentations included minor rotations, Gaussian noise injection, and limited scaling, carefully designed to preserve the physical interpretability of the thermal patterns while increasing the variability of the training data.

5.3.3. MLP Architecture

The MLP algorithm was selected due to its simplicity and ability to handle structured tabular data. The detailed architecture is described in

Table 10. MLP architecture description.

Layer Index	Type	Units/Neurons	Activation	Dropout	Output Shape
1	Input	10	—	—	(10)
2	Dense (Hidden 1)	128	ReLU	—	(128)
3	Dropout	—	—	p = 0.2	(128)
4	Dense (Hidden 2)	64	ReLU	—	(64)
5	Dropout	—	—	p = 0.2	(64)
6	Dense (Output)	4 (classes)	SoftMax	—	(4)

.

5.3.4. Implementation Details

The loss function adopted for this multiclass setting was categorical cross-entropy. The network was optimised using the Adam optimiser, with a fixed learning rate of 0.001.

Training was carried out with a batch size of 32 and a maximum of 100 epochs. We applied early stopping with a patience of 10 epochs, monitoring the validation loss to determine convergence. Dropout layers were inserted after each hidden layer, with a dropout rate of 0.2. We also experimented with L2 regularization, but results indicated that dropout alone was more effective in this context. The classification model was implemented in Google Colab, the training process was accelerated by the use of the NVIDIA Tesla T4 GPU with 16 GB of GDDR6 memory.

6. Results

This section presents the performance evaluation of the proposed hybrid methodology. which combines U-Net for segmentation module and MLP for thermal pattern classification module. The results are structured in two parts: the first evaluates the quality of binary mask segmentation of hotspot regions, the second focuses on the classification of heat diffusion patterns.

6.1. Evaluation Metrics

To assess the quality of both segmentation and classification outputs, we rely on standard metrics from computer vision and pattern recognition. The predicted images are compared with truth areas to note the numbers of true positive (TP), true negative (TN), false positive (FP), and false negative (FN). In addition to point estimates, statistical variability of the model performance was assessed using standard deviation (SD) and 95% confidence intervals (CI) computed across the 5-fold cross-validation runs. For U-Net segmentation, the F1-score was 0.970 ± 0.008 and IoU was 0.934 ± 0.011. For classification via MLP, accuracy was 93.4% ± 1.2%, with p < 0.01 (paired t-test) compared to a random forest baseline, indicating statistical significance. These statistical indicators confirm the robustness and generalisability of the proposed method.

These values are then used to derive the following metrics: Accuracy (ACC), Recall (REC), Precision (PRE), F1-score and Intersection over Union (IoU).

$$Accuracy={\displaystyle \frac{TP+TN}{TP+TN+FP+FN}}$$

(26)

$$Precision={\displaystyle \frac{TP}{TP+FP}}$$

(27)

$$Recall={\displaystyle \frac{TP}{TP+FN}}$$

(28)

$$F1-score=2·{\displaystyle \frac{Precision·Recall}{Precision+Recall}}$$

(29)

$$IoU={\displaystyle \frac{\left|A\cap B\right|}{\left|A\cup B\right|}}$$

(30)

6.2. U-Net Segmentation

Table 11. Evaluation metrics results (U-Net).

Metric	Value
Accuracy	0.982
Precision	0.963
Recall	0.977
F1-score	0.970
IoU	0.945

presents the results of the proposed U-Net for binary segmentation of IR images of biomedical PCBs.

The model demonstrates excellent ability to localise thermal anomalies.

The results confirm the U-Net’s effectiveness in accurately localising thermal anomalies across diverse conditions.

Computational Performance

Table 12. Computational performance results (U-Net).

Parameter	Value
Parameters (M)	7.8 M
FLOPs (GFlops)	14.6 G
Inference Time (s)	5.43 s (on 200 images)
Time per Image (ms)	27.15 ms

describe the evaluation of the computational efficiency of the U-Net during inference. The U-Net model was implemented in Google Colab, the training process was accelerated by the use of the NVIDIA Tesla T4 GPU with 16 GB of GDDR6 memory.

These performance metrics support the practical applicability of the proposed system in real-time scenarios. In particular, the U-Net architecture processes one thermographic image in approximately 27.15 milliseconds using an NVIDIA Tesla T4 GPU, corresponding to a throughput of ~37 frames per second. Moreover, the MLP classifier, operating on structured feature vectors, introduces negligible additional latency.

This enables the overall pipeline to operate with minimal delay, making it suitable for integration into embedded diagnostic systems for clinical use.

To assess the performance of the proposed U-Net segmentation model in a broader context, a supplementary comparative experiment was conducted against two commonly adopted semantic segmentation architectures: a basic Fully Convolutional Network (FCN) and DeepLabv3. All models were trained and tested on the same dataset and under identical conditions, using 5-fold cross-validation.

The results, summarized in

Table 13. Comparative Evaluation of Segmentation Models.

Model	F1-Score	IoU	Inference Time (ms/img)
U-Net	0.970	0.945	27.15
FCN	0.922	0.890	24.80
DeepLabv3	0.951	0.920	32.40

, shows that the proposed U-Net achieved the highest F1-score and IoU across all folds.

U-Net demonstrate a favourable balance between accuracy and efficiency for real-time diagnostic applications. These results support the selection of U-Net as the most suitable model for thermal anomaly segmentation in this study.

6.3. MLP Classification

Following segmentation and heat diffusion analysis, the extracted feature vectors were passed to the MLP classifier to assign a semantic class to each thermal behaviour. As described in Section 5.3, the model outputs one of four labels: Localised Hotspot, Diffused Anomaly, Asymmetric Propagation, or Uniform Heating.

The classification model was evaluated on the test set using 5-fold cross-validation. The results, averaged across folds, are reported in

Table 14. Evaluation metrics results (MLP).

Metric	Value
Accuracy	0.942
Macro Precision	0.931
Macro Recall	0.936
Macro F1-score	0.933

.

In addition to macro-averaged metrics, the confusion matrix of the MLP classifier was computed and is reported in

Table 15. Confusion Matrix of Heat Propagation Classification.

True\Predicted	Localised Hotspot	Diffused Anomaly	Asymmetric Propagation	Uniform Heating
Localised Hotspot	92.4%	4.0%	2.1%	1.5%
Diffused Anomaly	3.8%	91.0%	3.2%	2.0%
Asymmetric Propagation	1.9%	2.8%	92.7%	2.6%
Uniform Heating	1.5%	2.2%	3.1%	93.2%

. The matrix shows high true positive rates across all four thermal classes, with the strongest performance observed for “Localised Hotspot” and “Uniform Heating.” Minor classification ambiguity was observed between “Diffused Anomaly” and “Asymmetric Propagation,” likely due to overlapping diffusion characteristics. These results confirm the robustness and generalisation ability of the classifier across heterogeneous thermal patterns.

7. Conclusions

The study proposes a hybrid diagnostic system realised by combining FEM simulations, high-resolution infrared thermographic images, and artificial intelligence-based analysis for the thermal monitoring of biomedical electronic devices. Unlike previous studies, in which conventional thermal diagnostics are limited to simulation or surface-level measurements, this work proposes an integrated pipeline capable of acquiring, interpreting, and classifying thermal behaviour with high spatial and semantic accuracy.

The methodology is distinguished by its originality, combining simulation based on the implementation of a physical–mathematical model in COMSOL Multiphysics^®, experimental thermography, and artificial intelligence. Specifically, the integration of U-Net for segmentation and an MLP for heat propagation classification. Due to its complexity, the proposed system is among the first studies to couple validated temperature fields with FEM to automatically learned diffusion descriptors, creating a real-time predictive diagnostic tool tailored for biomedical electronics. The results confirm the robustness of the system, obtaining for the identification of thermal anomalies an F1 score of 0.970 and for the MLP classifier in distinguishing four distinct heat propagation patterns a score of 0.933. This demonstrates not only high accuracy, but also a strong ability to generalise to different thermal scenarios. The introduction of radial gradient analysis, isotherm symmetry and heat asymmetry index allow for a physically meaningful characterisation of the thermal diffusion dynamics. The combination allowed not only to identify hotspots, but also to interpret the mechanisms underlying thermal stress, providing valuable information for predictive maintenance and failure prevention in critical systems.

The proposed system, validated on a portable non-invasive ventilation device, highlights its practical relevance and potential for clinical integration. Considering the results, the hybrid FEM-IR-AI system contributes to supporting and improving safety in the field of biomedical device diagnostics. The system demonstrates real-time capabilities, with segmentation and classification steps operating below 30 milliseconds per frame on GPU-based platforms. Future developments will focus on deploying the AI components on edge devices such as NVIDIA Jetson or Coral TPU, enabling autonomous and in situ diagnostics in portable or wearable biomedical electronics.

Current literature is focusing on isolating effort of thermal simulation or machine learning segmentation, with minimal intersection between these disciplines. By bridging this gap, the proposed methodology offers a scalable, non-invasive, and real-time solution, aligning with the growing demand for smart health technologies and AI-assisted monitoring systems. Future developments will focus on extending the system’s adaptability to a wider range of biomedical devices, improving its resilience to different geometric configurations and thermal profiles. Additionally, efforts will be directed towards integrating AI components into lightweight edge computing platforms, enabling autonomous and in situ thermal diagnostics in clinical or home care settings, and ensuring safety without compromising device operability. Future study will focus on validating the proposed framework on additional biomedical devices, including infusion pumps and defibrillators, to improve its generalisability. Current limitations include the evaluation on a single PCB type and the absence of GPU-based implementation. Further developments will address on-chip deployment, scalability across heterogeneous platforms, and integration with early warning systems within hospital networks. Although the current implementation focused on a specific biomedical electronic board, the proposed FEM-AI framework is inherently generalisable. It can be extended to other heat-sensitive embedded systems, such as wearable health monitors, aerospace avionics, and automotive safety modules. These systems share similar requirements for compact design, thermal stability, and regulatory compliance, making them suitable targets for hybrid diagnostics. Future work will explore the adaptability of the approach across different device types and operational environments.