In aerospace, energy development, and industrial manufacturing sectors, planetary gearboxes have emerged as critical drive components in wind turbines, aircraft control systems, machine tools, and industrial robots due to their unique structural advantages and performance characteristics. They are indispensable in applications such as wind turbines [1] and helicopter main rotors [2]. While Industry 4.0 has significantly improved productivity, it has also heightened equipment failure risks [3]. As core components of mechanical transmission systems, planetary gearboxes often operate under heavy loads and high-speed conditions, rendering their key parts susceptible to gear wear, tooth surface fatigue pitting, tooth breakage, and bearing wear [4]. Such failures not only compromise transmission performance but may also lead to severe economic and safety consequences. Thus, designing scientifically sound and efficient maintenance strategies is imperative to reduce operational costs while enhancing system reliability and safety. The current maintenance of planetary gearboxes primarily relies on manufacturer-prescribed fixed intervals. This conventional maintenance approach exhibits significant drawbacks: on one hand, it may lead to “over-maintenance”, while on the other hand, it could result in “under-maintenance”, representing one of the key industry pain points. Traditional maintenance strategies based on age or fixed thresholds have been progressively supplanted by CBM decision-making. The widespread adoption of monitoring devices further highlights its broad application prospects in the operation and maintenance of offshore wind turbines [5,6] and gearboxes [7,8]. The CBM employs sensor data acquired through comprehensive condition monitoring systems to establish data-driven reliability models. This proactive strategy enables maintenance personnel to perform continuous health assessments and implement timely, evidence-based maintenance decisions when operational conditions dictate intervention.

With the rapid advancement of information technology and big data analytics, condition monitoring data in modern systems demonstrates increasingly prominent characteristics including high diversity, rapid generation velocity, and massive volume [9]. Traditional machine learning approaches face significant limitations when processing such large-scale datasets, as they excessively rely on signal processing techniques and domain expertise for manual feature extraction. In contrast, deep learning methodologies eliminate the need for manual feature engineering by supporting automated natural feature processing, enabling direct learning of complex feature representations from raw data [10,11]. Following an end-to-end training paradigm from data input to health indicator output, the deep learning effectively circumvents human-induced biases [12]. Current CBM methods typically use statistical models or fault pattern recognition to assess equipment health and predict failures. Unlike traditional approaches relying on manual feature extraction, our TCNAE method automatically learns deep temporal degradation features directly from vibration signals.

The advent of deep learning technology has provided robust technical support for advancing CBM decision-making. Current studies leverage deep neural networks to analyze operational data [13–16], extracting features from large-scale sensor measurements to build predictive models. This enables precise equipment degradation forecasting and optimized maintenance strategies [17]. To achieve the practical implementation of deep learning-based CBM technology for planetary gearboxes, this study innovatively establishes the complete lifecycle degradation dataset for planetary gearboxes and develops an end-to-end intelligent maintenance framework that integrates temporal convolutional network autoencoders (TCNAE) with nonlinear Wiener processes, achieving closed-loop optimization from condition monitoring to maintenance decision-making.

Benefiting from rapid advancements in sensing and condition monitoring technologies, the CBM has gradually attracted significant research attention. The CBM refers to an approach that evaluates current equipment health status by detecting and analyzing condition indicators (such as temperature, pressure, metal content in lubricants, etc.) closely related to equipment health, thereby enabling optimal maintenance decision-making. This approach fundamentally overcomes the limitations of relying solely on expert experience to determine maintenance timing. By effectively monitoring relevant parameters during the degradation process, it becomes possible to infer system reliability information without actual failure occurrence [18–21]. Given the stochastic nature of failures, Markov Chains (MC) are frequently employed for effective fault modeling. Naga Srinivasa Rao and Achutha Naikan [22] proposed a Semi-Markov Decision Process (SMDP) to optimize dynamic threshold strategies. Cheng [23] leveraged reinforcement learning to develop a framework for CBM strategy optimization based on ship fatigue damage mechanisms, which has been successfully applied in practice. Kang et al. [24] addressed maintenance uncertainties and weather impacts by introducing a condition-based maintenance policy for offshore wind turbines, optimizing schedules through maintenance bundling and timing to reduce operational expenditures. Zhao et al. [25] demonstrated a conditional opportunistic maintenance strategy for multi-component systems in wind turbines, utilizing Weibull proportional hazard models to characterize individual degradation processes. However, most current CBM research still relies on strong assumptions (e.g., fixed Weibull distribution, linear degradation, etc.). This assumption-driven approach often demonstrates poor adaptability to nonlinear/abrupt degradation patterns (such as stepwise wear in gearboxes), posing significant challenges for practical engineering implementation. Beyond this, research on CBM for gearboxes remains in its nascent stages, with limited studies available in this area.

Accurate health state evaluation constitutes the fundamental premise for implementing effective CBM strategies. Health Indicator (HI) curves, typically exhibiting monotonic trends, enable equipment health assessment through threshold-based evaluation methods [26]. Shen et al. [27] proposed an approach utilizing Adaptive Order Bispectral Slices (AOBS) and Fault Characteristic Energy Ratio (FCER) to investigate vibration signal characteristics. Huang and Chang [28] developed a wireless measurement system to identify vibration signal models featuring Amplitude Modulation (AM) and Frequency Modulation (FM) induced by gear damage. Al-Bedhany et al. [29] and Huang et al. [30] respectively investigated premature failure of wind turbine gearbox bearings, along with the impact of lubricant selection on gearbox efficiency and energy production. Within the context of CBM for gearboxes, current research exhibits a notable gap in literature integrating fault diagnosis with maintenance decision-making, failing to establish a closed-loop system from data-driven analysis to maintenance strategies.

Accurate degradation modeling represents a pivotal element in CBM systems. The Wiener process has demonstrated superior capability in characterizing degradation patterns of various mechanical components (e.g., rolling bearings, lasers, and gyroscopes) during practical maintenance operations, establishing itself as a predominant model for degradation trend analysis [31]. Li et al. [32] developed a two-phase degradation model accounting for bearing performance deterioration characteristics, employing an autoregressive model coupled with nonlinear Wiener processes to delineate performance degradation in each phase, while utilizing extended Kalman filtering to disregard state increment dynamics during state updates. Sun et al. [33] proposed a comprehensive framework for multi-performance, multi-phase Wiener process modeling and reliability analysis, incorporating a biphasic nonlinear Wiener degradation model with Schwarz Information Criterion (SIC) for change-point identification. The Wiener process is defined by its memoryless property, Markovian nature, and Brownian motion, where stochasticity is key. These traits enable broad applications in modeling stochastic degradation. Due to its intuitive physical interpretation and computational efficiency, the Wiener process effectively describes degradation in critical mechanical components (e.g., rolling bearings, lasers, and gyroscopes).

In recent years, deep learning techniques have achieved remarkable progress in the field of the CBM, emerging as a core methodology for prognostic and health management [34]. The inherent uncertainty and stochastic nature of equipment failures have led to widespread adoption of deep learning models for condition assessment and decision-making. These models demonstrate superior capability in processing high-dimensional, nonlinear, and non-stationary sensor data, thereby delivering precise predictive outcomes. Huang et al. [35] proposed a fault diagnosis method based on cloud computing, wavelet transform, and CADRN deep residual networks. By utilizing the channel attention mechanism (CAM), this approach addresses the issues of information redundancy in training samples and the difficulty of conventional networks in extracting subtle fault features. Comparative experiments demonstrated that incorporating the channel attention module into deep residual networks can effectively improve fault diagnosis accuracy. Under different load or rotational speed conditions, the Collaborative Adversarial Domain Adaptation network (CADA) can reduce domain shift through adversarial training, thereby enhancing the generalization ability of degradation feature extraction. To address the limitation that unsupervised domain adaptation (UDA) models struggle to dynamically adjust according to changes in target tasks, Wang et al. [36] proposed a Dynamic Collaborative Adversarial Domain Adaptation Network (DCADAN) for unsupervised fault diagnosis of rotating machinery. The advantage of the Multiscale Lifting Wavelet Contrastive Network (MLWCN) in multi-resolution analysis of vibration signals lies in its ability to capture both high-frequency fault components and low-frequency degradation trends simultaneously. Addressing the issues of insufficient interpretability of deep models and inadequate capability in mining features from small samples, Dong et al. [37] proposed an interpretable multi-scale lifting wavelet contrastive network for fault diagnosis of planetary gearboxes. The Meta-Learning Network with Sensitivity Penalty (MLSP) discusses its robustness with a small amount of labeled data, especially the improved sensitivity to early weak faults in planetary gearboxes. Mu et al. [38] developed an Enhanced Meta-Learning Network with Sensitivity Penalty (EMLN-SP) for the diagnosis of rare faults under severe domain bias. Nevertheless, the opaque “black-box” nature of deep learning models frequently impedes interpretability in maintenance decision-making, revealing significant gaps in integrating these models with condition information for maintenance strategy formulation.

Current research still exhibits several limitations, which can be categorized into three key issues: First, existing studies generally lack systematic full-lifecycle experimental data support, predominantly relying on fragmented operational data or simplified accelerated aging tests under idealized conditions, which fail to accurately reflect the true degradation patterns in actual complex operating scenarios. Second, there exists a severe disconnection in the workflow from data acquisition to maintenance decision-making, where independent development of each stage leads to substantial information loss, resulting in a significant performance gap between laboratory models and real-world engineering applications. Third, purely data-driven methods suffer from insufficient interpretability, while traditional reliability theories oversimplify actual degradation processes, making current models unable to simultaneously meet the dual requirements of prediction accuracy and engineering applicability.

To address these challenges, this study proposes a novel deep learning-based CBM framework for planetary gearboxes. A comprehensive lifecycle degradation experiment was conducted to collect raw vibration signals, which were processed using the TCNAE to extract deep temporal degradation features. Kernel principal component analysis (KPCA) was employed to fuse and normalize these features, enhancing the degradation process characterization. A nonlinear Wiener process model was implemented to characterize the degradation trajectory, with parameters optimized through maximum likelihood estimation. The maintenance strategy was optimized to minimize costs per unit time, determining both the optimal maintenance timing and preventive maintenance thresholds. The principal innovations of this research can be summarized as follows: (1)

Lifecycle experimentation and high-quality dataset construction. This study pioneers systematic full lifecycle degradation experiments for planetary gearboxes, acquiring comprehensive time-series vibration data that fills a critical gap in high-quality degradation datasets for this field. The dataset is conducive to discovering the degradation law of the gearbox, providing an essential foundation for data-driven degradation modeling research.

The remainder of this paper is organized as follows: Section 2 introduces the TCNAE-based method for extracting degradation features from planetary gearboxes. Section 2.1 details the parameter estimation procedures. Section 3 develops the nonlinear Wiener process-based CBM decision model and details the parameter estimation procedures. Section 4 describes the full life-cycle degradation experiment and data processing workflow. Section 5 presents the application results integrating the methodologies from Sections 3, 4. Section 6 concludes the study.

Current research on equipment degradation trend extraction reveals that mechanical systems typically exhibit a biphasic life cycle, as illustrated in Fig. 1. The initial phase represents normal operation, followed by a degradation phase. The transition point, termed First Predicting Time (FPT), is identified when the signal trend crosses a predetermined threshold, marking the onset of accelerated degradation. This critical juncture serves as the optimal timing for initiating CBM decision-making. Fig. 2 presents the systematic implementation workflow for equipment degradation trend extraction methodology.

The proposed methodology enables precise monitoring of equipment health status, facilitating the detection of subtle operational variations by maintenance personnel. This enhanced monitoring capability supports more accurate maintenance intervention decisions. Furthermore, the extracted degradation trends allow for predictive assessment of equipment health progression, thereby providing critical data support for CBM decision-making processes.

This study employs the computationally efficient Fast Fourier Transform (FFT) algorithm to perform spectral transformation of raw vibration signals. The transformed data is input into TCNAE network. The vibration signals of mechanical systems are typical time-series data, containing rich temporal features and local temporal dependencies. The TCNAE structure can automatically capture these local temporal features through convolutional layers. while its autoencoder structure enables effective feature dimensionality reduction and reconstruction, extracting more representative and robust degradation features. Compared with traditional feature extraction methods or some recurrent neural networks (such as LSTM and GRU), TCNAE does not suffer from gradient vanishing or explosion problems when dealing with long sequence data, and achieves higher computational efficiency. It can better meet the needs of degradation feature extraction for complex mechanical systems like planetary gearboxes, providing a high-quality feature basis for subsequent degradation modeling and maintenance decision making.

The TCN was first proposed by Lea et al. in 2016 [39] and has since gained widespread application in time series analysis. The causal convolution, a unidirectional architecture, determines the current output based solely on present and past inputs. Given an input time series X=(x1,x2,…,xT), X∈Rn and filter F=(f1,f2,…,fK), the causal convolution operation at position x_T can be expressed as: (1)Y(T)=(X∗f)(T)=∑i=0k−1F(i)⋅xT−i

In Eq. (1), k denotes the filter size, representing the number of time steps involved in each convolution operation. The term T − i encodes historical information by considering past temporal directions.

Fig. 3 illustrates the sampling patterns of dilated convolution vs. standard convolution. As shown in Fig. 4, the architecture of dilated convolution employs a base dilation rate d = 1 at the bottom layer, indicating direct sampling of each input element. When d > 1, the hierarchical structure ensures that even shallow networks can cover extensive input ranges. From Fig. 4, given an input time series X=(x1,x2,…,xT), X∈Rn and filter F=(f1,f2,…,fK), the dilated convolution operation at position x_T is formulated as: (2)Y(T)=(X∗df)(T)=∑i=0k−1F(i)⋅xT−dgiwhere d represents the dilation rate, k is the filter size, and T − dgi maintains temporal causality by exclusively encoding past-oriented information.

TCN incorporates universal residual modules, whose architecture is depicted in Fig. 5. The residual module replaces simple inter layer connections in conventional networks, enhancing model stability during deep layer propagation while improving generalization capability. The residual module’s operation can be formalized as: (3)Output=Activation(x+f(x))where Activation denotes the activation function and f represents the transformation performed within the residual module. The residual module allows the network to learn identity mappings more effectively, mitigating issues such as gradient vanishing and degradation in deep networks.

The AE architecture comprises two symmetric components: an encoder that compresses high-dimensional inputs into low-dimensional latent features, and a decoder that reconstructs the original input from these features. In this study, our designed AE processes vibration signals transformed via FFT and progressively compresses the features through multiple layers of dilated causal convolution. This yields compressed bottleneck-layer features containing essential degradation-related information. The decoder then expands these features via a fully connected layer, restores temporal structure using a RepeatVector layer, and fine-tunes temporal correlations with a lightweight single-layer TCN. Finally, a multilayer perceptron (MLP) efficiently reconstructs the input signal, balancing computational cost and processing efficiency.

The TCNAE network’s final residual block employs multiple neurons to preserve feature diversity and discriminative power, enabling multidimensional temporal feature extraction. Experimental validation confirms that a single-neuron configuration performs poorly, as unidimensional features cannot effectively capture complex degradation patterns. Since predictive maintenance models require a single degradation trajectory, this study utilizes KPCA [40,41] to fuse multidimensional outputs into a one-dimensional representation, and the polynomial kernel function is adopted to address nonlinearity: (4)Φ(x,y)=(ε⋅x⋅y+η)υwhere ε = 1 and η = 1. The parameter ν is determined through distance matrix computation: (1) replacing zero values with infinity, (2) identifying the global minimum distance, (3) computing the average minimum distance, and (4) scaling the average by a factor of 5. The distance matrix itself is obtained by calculating pairwise Euclidean distances between sample points.

The unique temporal features after KPCA processing undergo normalization per Eq. (5): (5)xi=x−xminxmax−xminwhere xmax and xmin represent the maximum and minimum values of the temporal feature, respectively.

This study employs monotonicity, correlation, and robustness as evaluation criteria to quantitatively assess the performance of the extracted degradation trend [42]. First, the degradation trend is decomposed into a smooth trend and random error using polynomial fitting: (6)H(tn)=HT(tn)+HR(tn)where H(tn) represents the degradation trend value at time t_n, HT(tn) denotes the smoothed trend, and HR(tn) is the random error.

Monotonicity evaluates whether the degradation trend exhibits a consistent increasing or decreasing pattern. It is calculated as: (7)Mon(HI)=|dHT(tn)>0m−1−dHT(tn)<0m−1|where Mon(HI) is the monotonicity index and m is the length of the degradation trend vector. A higher Mon value indicates a stronger monotonic trend.

The linear correlation between the degradation trend and time is measured using: (8)Cor(HI,T)=|∑n=1N(H(tn)−H¯)(tn−T¯)|∑n=1N(H(tn)−H¯)2∑n=1N(tn−T¯)2

In Eq. (8), Cor(HI) represents the correlation between the degradation trend and time, where H¯=1N∑n=1NH(tn), T¯=1N∑n=1Ntn. A higher Cor value indicates a stronger linear relationship.

Robustness evaluates the tolerance of the Health Indicator (HI) to outliers, computed as: (9)Rob(HI)=1N∑n=1Nexp⁡(−|HR(tn)H(tn)|)where Rob(HI) is the robustness index. A higher Rob value indicates better resistance to noise and outliers.

To holistically evaluate degradation trend performance, a Comprehensive Indicator (CI) integrating all three metrics is defined: (10)CI=0.4∗Mon+0.3∗Cor+0.3∗Rob

By combining these three metrics, the degradation trend can be comprehensively assessed. A well-performing trend accurately reflects the equipment’s health state, facilitating precise degradation analysis and CBM decision-making.

A 900-h full-life degradation experiment was conducted, and the main components of the experimental platform are as follows: the main motor is a three-speed electromagnetic speed-regulating motor (model YCT180-4A) with a rated power of 4 kW; the speed-torque sensor (model JN338) is used to collect the speed and torque signals of the input shaft of the planetary gearbox; the magnetic powder brake (model FZJ-5) provides load to the planetary gearbox, and the SC-1D (3A) load controller adjusts the load value of the magnetic powder brake by controlling the current [47], as shown in Fig. 6.

The test employed an NGW11 single-stage planetary gearbox, with its internal structure schematic shown in Fig. 7 and detailed component parameters provided in Table 1. During operation, the gearbox achieved a transmission ratio of 12.5. Four vibration acceleration sensors were strategically mounted on the gearbox housing at locations depicted in Fig. 8, enabling comprehensive vibration signal acquisition from multiple orientations to effectively monitor degradation progression.

The main operating parameters of the experiment are as follows: (1) Input shaft speed: 1000 revolutions per minute (rpm). (2) Load current applied to the magnetic powder brake: 1 ampere (A), equivalent to a load of approximately 340 Newton-meters (N·m) on the planetary gearbox. (3) Vibration signal sampling frequency: 20 kHz, with a single sampling duration of 1 s and a sampling interval of 5 min. (4) The ambient temperature in the laboratory is controlled at 20 ± 1°C, and the relative humidity is maintained at 55 ± 5%.

This study selects the sample data collected by Sensor 2 for feature analysis. The planetary gearbox dataset obtained from the PHM laboratory consists of 900 CSV files with a total storage capacity of approximately 2.09 GB. Each file is sequentially named from data-T155412Z to data-T161513Z in chronological order, precisely recording continuous monitoring data throughout the experimental process to ensure the integrity of signal details. Every CSV file contains vibration acceleration data organized in a single column with 240,000 rows, capturing the vertical vibration signals of the planetary gearbox with a precision of five decimal places.

An electromagnetic brake provided a stable load during the experiment, with a load controller precisely adjusting the current to regulate braking torque. The magnetic powder brake operates via electromagnetic effects: when the controller supplies a 1A DC current, the magnetic powder forms chains, coupling the inner and outer rotors to produce a braking torque proportional to the current. To minimize instability effects, vibration signals were collected only during steady-state operation, excluding transient data from motor start-up and shutdown phases.

Following the complete life-cycle testing, the planetary gearbox exhibited multiple failure modes across its primary components, including inner and outer race wear, cracking damage, and varying degrees of tooth surface wear on major gears, as shown in Fig. 9. From Fig. 9, it can be observed that there are obvious signs of fatigue pitting and wear on the tooth surface of the sun gear. A small number of tooth surfaces on the planet gears exhibit wear and local fractures. The tooth surface wear of the ring gear is relatively uniform, but fracture traces were found in some areas. These damage patterns match typical planetary gearbox degradation under prolonged high-load operation, confirming the experimental data’s reliability.

According to the experimental protocol outlined in Section 4, the acceleration values of the vibration signals in the vertical direction of the power input shaft are presented in Fig. 14. As shown in Fig. 14, the planetary gearbox exhibited stable operation with minor fluctuations, followed by progressive degradation. A sharp signal change at 750 h indicated component failure, culminating in severe vibration and audible noise at 900 h that marked complete gearbox failure.

Comparative analysis of Fig. 15 and Table 3 clearly demonstrates TCNAE’s superior performance over LSTM and GRU in three key aspects. First, it exhibits stronger feature representation capability, with normalized feature values significantly higher than LSTM/GRU across most sample intervals, indicating more effective capture of vibration signal patterns and higher compression efficiency for high-dimensional FFT signals in its hidden states. Second, it shows better temporal stability, with notably smaller curve fluctuations compared to the pronounced oscillations observed in LSTM/GRU. The fixed receptive field in TCN stabilizes long range feature extraction, making it more suitable for stable industrial monitoring. Third, it demonstrates higher fault sensitivity, displaying significant feature value increases in tail sample intervals through multi-scale convolutional kernels that amplify fault-band energy, whereas LSTM/GRU shows weak responses.

Using the comprehensive evaluation criteria for degradation trend performance proposed in Section 2.3, the CI values (also known as health factors) of the degradation trends derived from six time-domain features and the TCNAE method were calculated, as shown in Table 4.

As indicated in Table 4, most time-domain features exhibit severe fluctuations, while the degradation trend extracted by the TCNAE method yields the highest CI value, demonstrating the best characterization effect for the degradation trend of the planetary gearbox.

Based on the parameter estimation method described in Section 3, data fitting was performed on the deep time-series features extracted by TCNAE. Through operations such as nonlinear least squares, matrix computation, and vector manipulation, the estimated value of the drift coefficient λ~ was determined to be 4.5 × 10⁻³, and the estimated value of the diffusion coefficient squared σ~2 was 1.4256 × 10⁻⁴. The estimation process is illustrated in Fig. 16.

The planetary gearboxes degradation progresses through two distinct phases: an initial stable operation phase where degradation remains below the preventive maintenance threshold, followed by an accelerated degradation phase where deterioration exceeds this threshold and may reach failure levels. Based on fused degradation features, we identified four characteristic stages, with degradation paths shown in Fig. 17 and parameters listed in Table 5.

Using cost parameters C_in = 100, C_pm = 3500, C_cm = 4800, and C_puni = 50, Monte Carlo simulation yielded the following results: Under static thresholds, the minimum objective function CR value was 60.9736 with optimal decision variables of 155 and 0.907. With a threshold decay rate of 0.2, the minimum CR value reduced to 55.5556, with optimal decision variables of 151 and 0.752. The corresponding 3D surface plots and contour maps at estimated values are presented in Figs. 18 and 19, respectively.

A comparison of Figs. 18 and 19 reveals the impact of inspection intervals on cost rates. Short intervals yield high costs due to excessive expenses from frequent inspections, leading to “over-maintenance”. While extending intervals initially reduces costs, excessively long intervals risk undetected degradation, causing “under-maintenance” and increasing failure risk and repair costs. Fig. 18a exhibits a smooth surface, suitable for idealized scenario. In contrast, after introducing threshold decay, Fig. 19a displays a rugged surface, accurately reflecting real-world performance degradation from aging and environmental factors. This model simulates a closed loop interaction between dynamic maintenance decisions and cost fluctuations, showing lower final cost rates with dynamic thresholds compared to fixed ones notably. In practical operations, equipment performance and degradation thresholds are not static but naturally deteriorate over time. Fig. 19 more accurately depicts the real-world relationship among “maintenance strategy, dynamic thresholds, and cost control”.

Based on the above research findings, to ensure the effectiveness and reliability of the degradation model for planetary gearboxes of the same type, the following conditions for model applicability can be summarized: First, the model is applicable to gearboxes with the same or similar design characteristics (such as gear size, module, and number of teeth) and material properties (such as material type, hard-ness, and toughness). These characteristics and properties directly affect the degradation mechanisms and rates. Second, the model is applicable to gearboxes operating under similar working conditions, including load levels, speed ranges, operating temperatures, and lubrication conditions. Significantly different working conditions may lead to substantial differences in degradation behavior. Third, the model is applicable to gearboxes operating under similar environmental conditions, such as humidity, temperature, and vibration environments. These factors may influence gearboxes’ degradation rates and patterns.