This research presents a hybrid method for restoring missing sensor data using adaptive control, aimed at enhancing data recovery accuracy in complex situations. The proposed algorithm involves creating a training dataset, a control element, and training hybrid models. Key steps include identifying data subsets, randomly removing elements to simulate gaps, estimating their values, clustering for accuracy, and developing neuro-fuzzy models tailored to specific data groups. Implemented as a Takagi-Sugeno neurofuzzy network, the method effectively combines fuzzy rules with neural computations, allowing it to handle variability and noise in real measurements with high adaptability. Computational experiments focused on restoring gas temperature data from the TV3-117 turboshaft engine demonstrate high accuracy, with deviations ranging between 0.002 and 0.007, indicating robust performance even under sensor failures. The model achieves over 99% accuracy, a precision of 0.983, and an F1-score of 0.991, significantly outperforming traditional methods such as two-layer feedforward networks and ANFIS networks. This research offers a reliable solution for sensor data recovery and advances adaptive control systems, improving the reliability and performance of aviation technologies and other dynamic applications.
Restoring missing sensor data is one of the key tasks in technical monitoring and control systems for complex objects such as aviation engines [1], robotic systems [2], and production lines [3]. The completeness and reliability of information received from sensors are crucial for these systems maintaining safe and efficient operation. However, in practice, sensors may fail or transmit distorted data due to technical malfunctions, external influences, or communication failures [4]. These factors pose the risk of inaccurate assessments regarding the objects condition, potentially leading to undesirable outcomes such as accidents or inefficient management.
The research relevance methods for restoring sensor data arises from the need to enhance the information systems reliability and precision. Modern approaches, including neural networks and statistical models, enable not only the missing values restoring but also the systematic and random measurement errors correction. This is particularly important in environments with stringent safety and cost-efficiency requirements, where timely detection and compensation for data anomalies can extend equipment lifespan and reduce maintenance costs.
Existing research on restoring missing sensor data covers a wide range of approaches, from traditional interpolation methods to advanced machine learning algorithms and neural networks. Classical methods like linear interpolation [5] or polynomial approximation [6] are effective for small gaps in data with predictable patterns but fall short when dealing with nonlinear dependencies, noise, or dynamic systems, making them less suitable for complex applications.
With the artificial intelligence and machine learning advancement, the neural networks use has gained significant attention in data restoring. Recurrent neural networks (RNN) [7], particularly long short-term memory (LSTM) models [8,9], are frequently used to account for temporal dependencies and can recover information despite extended gaps. Other approaches [10,11] involve autoencoders, which train data representations and restore missing values. These methods show strong performance with nonlinear time series and hold promise for real-time applications.
Neuro-fuzzy systems offer another effective approach, combining neural networks with fuzzy logic to handle uncertainty and noise [12]. Models like the Sugeno approach apply flexible rules to process fuzzy data and adapt to changing data characteristics, making them especially relevant for systems with high uncertainty or significant random errors [13].
However, key challenges remain unresolved. One issue is the need for adaptive control in data restore when system characteristics change [14]. Many models are fine-tuned to specific system parameters, but their performance degrades with changing conditions. Addressing this requires models capable of adjusting their parameters dynamically. Neuro-fuzzy systems with adaptive control elements [15] offer a promising solution for real-time adaptation.
Another challenge is managing multidimensional dependencies between sensors, especially when parameters are highly interdependent. Current studies [16] often focus on single-sensor data restore, neglecting correlations across channels. Developing multichannel models that consider sensor interactions and adapt to their evolving characteristics is critical for improving restore performance.
Thus, adaptive control and neuro-fuzzy systems represent a promising direction for addressing these challenges, enhancing data restore quality while adapting to changing operational conditions.
This research foundation is a general approach to developing a hybrid model, proposed in [29]. The
original dataset portion, containing only complete data, is used for model construction, and certain
elements are randomly removed from it. For each artificially excluded element, values are estimated
using various methods. As a result, a restored set values are generated for each element, which is
then used as the input vector to build the adaptation model. The known value of the removed element
serves as the output:
= { 1, 2, 3, 4, },
(
The missing element value estimate in the original dataset, each of the four methods is first applied. The results are input into the model, producing a final estimate for the missing element value. A critical aspect in model development is the architecture choice. A linear model in the form v = w1 ∙ u1 + w2 ∙ u2 + w3 ∙ u3 + w4 ∙ u4 + w0 [17] was examined, along with various nonlinear models based on artificial neural networks [18], which implement a function in the form v = f(u1, u2, u3, u4). None of the models analyzed demonstrated an improvement in accuracy compared to the individual methods included in the model.
To create a more sophisticated model, a cluster analysis is performed on the training datasets (
Conducting cluster analysis on the training datasets allows the several main groups identification within the original data arrays, where a similar pattern is observed regarding the original methods accuracy. Analysis [19,20] demonstrated that constructing a separate hybrid model for each of these groups based on a feedforward neural network significantly improved the hybrid method accuracy compared to the original approaches. The feedforward neural network key limitation lies in its inability to effectively handle uncertainty and variability in data, particularly under conditions characterized by complex nonlinear dependencies. This necessity highlights the neuro-fuzzy networks application, which, unlike standard neural networks, can account for the information fuzziness and adapt to changing conditions, ensuring higher accuracy in tasks such as clustering and complex data analysis.
This research proposes a method for restoring missing sensor data, featuring control based on neuro-fuzzy networks, with the developed scheme illustrated in Figure 1.
Based on this scheme, the following algorithm has been developed: Step 1. The training dataset formation. 1.1. The subset S ⊆ D identification from the array containing complete data to create a reliable foundation for training, where ∣S∣ = n represent instances number. 1.2. The elements’ specified number m is randomly removed from the selected subset S, creating gaps in the data, resulting in a new dataset S′ such that:
S′ = S − {x1, x2, …, xm},
(
= 1, 2 , … , , with j1, j2, …, jk being indices of available elements in S′. 1.4. The training dataset T is formed based on the obtained estimates and missing elements known values, creating input-output pairs for model training, i.e.:
= ( , ) ∈ ′, is estimated or known 1.5. Steps 1.2–1.4 are repeated until the training dataset T amount reaches a sufficient size, defined as the instances number exceeding a predetermined threshold Tmin (e.g., 500 instances, i.e., ∣T∣ > 500).
Step 2. The control element creation. 2.1. A clustering method C (for instance, fuzzy C-means) is applied to determine elements groups
Gk ⊆ S in the array exhibiting similar accuracy in method performance. 2.2. A control element is developed and trained is a classifier Cclassifier for missing elements based on known portions xi and assigned groups Gk. The classifier primary idea is to the elements group identify (from step 2.1) to which a particular missing value belongs, based on the instance with gaps known part. Instances from the array with randomly removed elements (from step 1.2) are used for training. Thus,
Cclassifier: xi ↦ Gk .
Step 3. Training hybrid models.
For each identified group Gk, a hybrid model Hk is constructed based on a neuro-fuzzy network utilizing a feedforward structure. Training is conducted on the dataset formed in step 1 portion T, corresponding to the elements specific group Gk, ensuring that the model accounts for each group characteristics. In this context, it is advisable to employ a Takagi-Sugeno neuro-fuzzy network architecture [21–23] since it effectively combines fuzzy rules with neural computations, providing a high degree of adaptability to changing data conditions. This architecture includes fuzzy rules for managing uncertainty in data, which is crucial in the variability presence and real measurements noise typical [21, 22]. Moreover, the networks’ neural component enables modeling complex nonlinear relations between input and output data, leading to the missing values more accurate restoring [23]. This architecture use also facilitates adaptive learning mechanisms [22, 24] that can account for each group characteristics, forming flexible and highly effective models tailored to the data specifics, significantly enhancing prediction accuracy in missing value restore tasks. The Takagi-Sugeno-type architecture employs fuzzy rules Rj defined as:
Rj: IF “x” IS “Aj” THEN “y = fj(x)”,
(
Step 4. The missing values restoring.
An instance xmissing containing missing values is input into the control element, realized based on the classifier. The control element decides dk which hybrid model should be applied for the given instance, i.e.:
dk = Cclassifier(xmissing).
Apply the selected hybrid model Hk to restore missing values yrestored:
yrestored = Hk(xmissing). (
Additionally, a confidence assessment mechanism Cconfidence is implemented, which analyzes the
uncertainty level when selecting a model, considering factors such as the initial data quality and the
(
Cconfidence(dk) = quality(xmissing) + performance(Hk). (
The proposed algorithm scientific novelty lies in its comprehensive approach to restoring missing values, which includes stages for forming a training dataset, clustering elements, and adaptively selecting hybrid models. Unlike similar methods [17, 19, 20], the algorithm does not simply apply a single universal model to all data; it first elements groups identifies with similar performance accuracy, allowing for the specialized hybrid models optimized construction for each group. Furthermore, the control element implementation in the classifier form, which makes decisions regarding model selection based on the instance specific characteristics, ensures higher accuracy and reliability in restoring missing values under data uncertainty and variability conditions.
The Takagi-Sugeno neuro-fuzzy network architecture (Figure 2) for missing value restore is
designed to combine the fuzzy logic strengths for handling uncertainty and neural networks for
modeling complex, nonlinear relations between inputs and outputs.
y(х)
(
... μА1(х1) μ12(х1) μ22(х1)
... μА2(х1)
... μ1i (х1) μ2i (х1)
... μАi (х1) * * * w1 w2 wi + + x = [x1, x2, …, xk, _, _, …, _]. ( ) = exp − − 2 ∙ 2 2
The input layer receives the available data from an instance x ∈ R, which contains some missing elements. The input layer goal is to feed the known values of the instance into the subsequent layers, where x1, x2, …, xk are known elements and y1, y2, …, ym are the missing elements. For each instance, the input is:
In fuzzification layer, each input is mapped to fuzzy sets. The fuzzification process uses membership functions (typically Gaussian or triangular) to represent uncertainty in the input values. Each input xi is associated with a fuzzy set Aj, where the membership degree is computed: takes the form: input space. where fj(x) is the inputs linear function:
Rj: IF (x1 is Aj1) AND (x2 is Aj2) AND … THEN yj = fj(x),
fj(x) = w1 ∙ x1 + w2 ∙ x2 + … + wk ∙ xk + bj.
The rule layer consists of fuzzy IF-THEN rules in the Takagi-Sugeno form [21, 23]. Each rule Rj
(
Step name Initialization
Error Calculation
rule fuzzy conditions. output by applying a modified center of gravity equation [25]:
This layer output is the firing strength μj of each rule, indicating how well the input matches the In the defuzzification layer, the network merges the results from all rules to generate the final Here, fj(x) represents the linear function output corresponding to the j-th rule, and μj is the firing strength of the j-th rule.
The output layer produces the restored missing values yrestored. The result is the estimated values set for the missing elements based on the weighted contribution from the fuzzy rules. Table 1 presents the Takagi-Sugeno neuro-fuzzy network training algorithm.
The Takagi-Sugeno neuro-fuzzy network's architecture and training process allows for flexible, adaptive modeling of complex relations in data, making it highly effective for restoring missing values in datasets with uncertainty and variability. By clustering elements and assigning specialized models, this approach enhances accuracy and robustness in challenging restoring tasks. The Takagi-Sugeno neuro-fuzzy network training algorithm (author’s research). The error gradient with respect to the parameters wj, bj of the linear functions in the rule layer is computed. For each weight wj, the gradient is calculated as: The gradients for the membership function parameters wj, bj are also computed using the chain rule, adjusting the centers and widths of the fuzzy sets: updated as:
. ∙
.
∙ ( ), where ( ) = ( ), ( ) = ∙ ( −1) + (1 − ) ∙ ( ) 2 is the decay rate (usually set to 0.9), and gradients running average, η is the training rate, ϵ is a small value (e.g., 10−8) added for numerical stability, θj represent each parameter (which can be wj, bj, cj, or σj).
( ) is the squared
Repeat
4).
The research presents the results from a computational experiment focused on restoring missing gas temperature before the compressor turbine ∗ data in the TV3-117 TE [26], which is part of the Mi8MTV helicopter’s power plant. The parameter values are recorded by a dual sensor comprising 14 T-101 thermocouples [27] at 1-second intervals (Figure 3). Data recording was carried out over a 256second time interval. The application of temporal discretization and adaptive quantization with a dynamic range to the reconstructed ∗ signal diagram (Figure 3) resulted in its discrete form (Figure onboard the helicopter during the 256-second study interval. (author’s research).
The generated diagrams (Figures 3 and 4) play a key role in creating the training dataset. According to the Nyquist theorem, the sampling rate must be at least twice the maximum frequency for accurate signal reconstruction [28]. With 256 readings over 256 seconds, the sampling rate is 256 / 256 = 1.0 readings per second, which corresponds to a time interval between readings of approximately 7 seconds. This frequency is well-suited for tracking slowly varying parameters and provides the necessary detail without excessive data amount [27, 28]. Thus, selecting 256 readings represents an optimal compromise between sampling rate, data volume, and computational costs, ensuring a balance between accuracy and data processing efficiency. As shown in Figure 4, the training dataset for the ∗ parameter has been created and is presented in Table 2. After normalization, it appears as shown in Table 3.
Thus, the normalized values for the ∗ parameter range from 0.95 to 0.99. Let’s assume there are missing values for the ∗ parameter between 56 and 65 seconds, 137 and 144 seconds, and 215 and 223 seconds.
According to the developed algorithm, at the initial stage, we select a subset S ⊆ D from the complete dataset, containing all ∗ parameter values over the entire period without missing data. Let’s assume, for example, that ∣S∣ = 256 records.
Next, we remove data from S corresponding to the periods from 56 to 65 seconds, 137 to 144 seconds, and 215 to 223 seconds. Thus, S′ is the subset S with the removed values, and its size becomes ∣S′∣ = 256 … … … … – 28 = 228 values. The missing values will be restored using various methods (regression, interpolation, machine learning). It is assumed that the implementation of fuzzy rules by a neuro-fuzzy network (Figure 2) for restoring the missing values is carried out according to expressions such as: 56 = 55 +2 66 , 57 = 56 +2 67 , … , 65 = 64 +2 66. (17)
Similarly, interpolation is performed for the other intervals with missing data. At the next stage, a training set T is created, including pairs of inputs xi and their corresponding restored values yi, using the missing and known data. The dataset size is ∣T∣ > 500. After that, a fuzzy clustering method (such as fuzzy C-means) is applied to divide the data into groups Gk with similar restoring characteristics. For example, let the data be divided into 3 groups: 1: [0.95 … 0.96], 2: [0.96 … 0.97], 3: [0.97 … 0.99]. (18)
The classifier is trained on the data to determine which group Gk the missing values belong to, based on the data known portion. For example, if the missing ∗ parameter value is 0.955, the classifier will assign it to group G1. For each group Gk, a hybrid model Hk is constructed based on the Takagi-Sugeno neuro-fuzzy network (Figure 2). A separate model H1 will be built for group G1, model H2 for group G2, and so on. These models are trained on the corresponding data from the training set T according to the proposed training algorithm (see Table 1).
For the missing value at the 56th second, using the known data, for example, T55 = 0.956, the classifier Cclassifier determines that this value belongs to group G1. To restore the temperature value at the 56th second, model H1 (corresponding to group G1) is applied, which reconstructs the missing value y56 = H1(T55, T57, …). The confidence score Cconfidence is calculated based on the quality of the input data and the performance of model H1, helping to improve the restoration accuracy. Let the neighboring parameter values for the adjacent seconds appear as follows (in normalized form): T54 = 0.960, T55 = 0.955, T66 = 0.957, T67 = 0.958. For the 56th second, using the neuro-fuzzy network (Figure 2), the missing value is restored as:
56 = 55 +2 66 = 0.955 +2 0.957 = 0.956. (19)
Similarly, other missing values are restored by applying hybrid models and regression methods for more accurate restoring. Table 4 presents the results evaluating the quality of solving the missing ∗ parameter values restoring task. The experimental results show that for most values, the deviations are only 0.002…0.005, confirming the high accuracy achieved by the restoration models. The maximum deviation of 0.007 also falls within acceptable error limits, proving the stability and reliability of the proposed approach. Thus, hybrid models and regression methods demonstrate excellent performance in restoring critical parameters, ensuring accurate system operation even in the event of sensor failures. 0.961 0.961 missing sensor values on helicopters, Accuracy reflects the proportion of correctly restored values compared to the actual sensor data. Loss measures the prediction error, indicating how far the restored values deviate from the true ones [30]. Precision and Recall evaluate the model's effectiveness in correctly identifying and recovering missing values, while F1-score provides a balance between Precision and Recall, ensuring both completeness and accuracy in the restoration process [29, 30]. These metrics are determined using the formulas provided in [29]: , =
+ , − = ∙ −1( ) . 1 ∙ =1 =
( = ) , 1 − = 2 ∙
∙ +
In the context of restoring missing sensor-registered parameters on board the helicopter, TP (True Positives) refers to correctly restored values that match the actual sensor data when the sensor is functioning. TN (True Negatives) represents cases where missing data were correctly identified as non-recoverable or not requiring restoration. FP (False Positives) indicates instances where data were incorrectly restored, leading to discrepancies between the restored and actual values. FN (False Negatives) refers to cases where the system failed to restore missing data correctly, leaving a gap in the sensor readings. effectiveness. Specifically, the Accuracy exceeds 99 %, while the Loss metric decreases from 2.5% to 0.5% over 180 training epochs, indicating significant improvement in model quality and training efficiency. This confirms the network's capability for high-precision classification tasks with minimal error.
Specifically, the Accuracy (see Figure 5) exceeds 99 %, while the Loss (see Figure 6) metric decreases from 2.5 to 0.5 % over 180 training epochs, indicating significant improvement in model quality and training efficiency. This confirms the network's capability for high-precision classification tasks with minimal error.
These results highlight the robustness and reliability of the neuro-fuzzy network in achieving high classification accuracy with minimal loss. The steady reduction in the Loss metric demonstrates the model's ability to generalize well to new data, further supporting its applicability in real-world scenarios requiring precise decision-making and control.
In the context of restoring missing sensor-registered parameters on board the helicopter, obtained Precision is 0.983 means that 98.3 % of the values identified as successfully restored are indeed correct, indicating a very low false positive rate. Recall is 1.0 means that the method was able to correctly restore all the missing values (no false negatives), achieving 100 % completeness in the restoration process. The F1-score is 0.991 combines Precision and Recall, indicating a balance between accuracy and completeness, with a near-perfect performance in restoring the missing sensor data.
A comparison (Table 5) of the proposed approaches for restoring missing sensor-registered parameters on board the helicopter was conducted by replacing the developed neuro-fuzzy network with a two-layer feedforward network (alternative approach 1) and the ANFIS neuro-fuzzy network (alternative approach 2), using a traditional training algorithm. This comparison aimed to evaluate the performance of different neural network structures in the context of the restoration task.
The comparative analysis of the proposed neuro-fuzzy network against alternative approaches revealed superior performance in restoring missing sensor-registered parameters on board the helicopter. The proposed approach achieved an accuracy of 0.991, significantly higher than the 0.932 obtained by the two-layer feedforward network and the 0.976 from the ANFIS network. Furthermore, the proposed method demonstrated exceptional precision (0.983) and an F1-score (0.991), indicating its effectiveness in accurately identifying and restoring missing values compared to the alternative methods, which showed lower precision and recall rates.
This research lies foundation in the development of a hybrid method for restoring missing sensor data with adaptive control (see Figure 1). The proposed method is based on an algorithm that involves forming a training dataset, creating a control element, and training hybrid models. The restoration of missing values includes identifying a data subset, randomly removing elements to create gaps, estimating their values using various methods, clustering to identify groups with similar accuracy, developing and training a classifier, constructing neuro-fuzzy models for each group, and utilizing a control element to select the model and assess the classifier's confidence. This collective approach enhances the accuracy of restoring missing values in complex situations. Unlike similar methods, this algorithm does not use a single universal model for all data; instead, it first identifies groups of elements with similar accuracy, allowing for the development of specialized hybrid models optimized for each specific group.
The developed algorithm is implemented as a Takagi-Sugeno neuro-fuzzy network (see Figure 2), as it effectively combines fuzzy rules and neural computations (see Table 1), ensuring high adaptability to changing data conditions and allowing for the processing of uncertainty. This is particularly important in environments with variability and noise in real measurements, as well as modeling complex nonlinear dependencies between input and output data, facilitating more accurate restoration of missing values. A computational experiment has been conducted to restore missing gas temperature data before the compressor turbine (see Figures 3 and 4, Tables 2 and 3) for the TV3-117 TE. The results confirm the high accuracy of the restoration models, with deviations for most values ranging from 0.002 to 0.005, and the maximum deviation of 0.007 falling within acceptable error limits (see Table 4). This indicates the stability and reliability of the approach, ensuring precise system operation even in cases of sensor failures.
The quality of the proposed Takagi-Sugeno neuro-fuzzy network (see Figure 2) has been assessed based on traditional quality metrics: Accuracy, Loss, Precision, Recall, and F1-score. The model's accuracy exceeds 99 % (see Figure 5), while the Loss value decreases from 2.5 to 0.5 % (see Figure 6) over 180 training epochs, demonstrating a significant improvement in model quality and training efficiency. These results confirm the capability of the neuro-fuzzy network to perform high-precision classification tasks with minimal errors, highlighting its reliability and robustness. In the context of restoring missing values recorded by sensors on board the helicopter, the achieved Precision of 0.983 indicates that 98.3 % of the values identified as successfully restored are indeed correct. The Recall of 1.0 confirms the complete restoration of all missing values, while the F1-score of 0.991 indicates a balance between accuracy and completeness, demonstrating nearly perfect performance in restoring missing sensor data.
The comparative analysis of the proposed approaches for restoring missing sensor-registered values on board the helicopter showed superior results for the developed neuro-fuzzy network compared to alternative methods, such as a two-layer feedforward network and the ANFIS neurofuzzy network (see Table 6). The proposed approach achieved an accuracy of 0.991, significantly higher than 0.932 for the two-layer network and 0.976 for the ANFIS network. Furthermore, the method demonstrated exceptional precision (0.983) and an F1-score (0.991), indicating its high efficiency in identifying and restoring missing values compared to alternative methods, which exhibited lower accuracy and completeness metrics.
Despite the successes achieved in developing the hybrid method for restoring missing data, the research faces certain limitations. The effectiveness of the algorithm depends on the quality and completeness of the original data, as insufficient representation in the training dataset may negatively impact the accuracy of the restored values. The method may encounter challenges when working with data containing high levels of noise or anomalies, which could lead to a decrease in overall reliability. Although the proposed algorithm has demonstrated high accuracy, its performance may vary based on the specifics of different sensor types and helicopter operating conditions.
Prospects for further research include expanding the developed method to process data from other sensor types and in various operating conditions. It would also be beneficial to consider integrating the algorithm with machine learning methods, such as deep neural networks, to enhance adaptability and improve restoration quality. Additionally, developing more complex strategies for handling noise and anomalies in the data could significantly increase the algorithm's reliability, allowing for effective application in real-world scenarios that require high precision and resilience to failures.
This research successfully presents a hybrid method for restoring missing sensor data through adaptive control, emphasizing the development of specialized hybrid models tailored to specific groups of data. The algorithm incorporates multiple stages, including data subset identification, random removal of elements to simulate missing values, and various estimation methods, culminating in the construction of a Takagi-Sugeno neuro-fuzzy network. This approach not only enhances the accuracy of missing value restoration but also demonstrates adaptability to changing data conditions and the ability to handle uncertainty in real-world measurements.
The computational experiments conducted on the gas temperature data before the compressor turbine of the TV3-117 turboshaft engine confirm the efficacy of the proposed method. The results show deviations in the restored values ranging from 0.002 to 0.005, with a maximum deviation of 0.007, all within acceptable error limits. This indicates the method's stability and reliability in operational scenarios, even when sensor failures occur. The ability to maintain precision within these limits underscores the method's potential for practical applications in critical systems, such as helicopter avionics.
Furthermore, the performance metrics indicate that the model's accuracy exceeds 99%, with a Precision of 0.983 and an F1-score of 0.991, validating the robustness of the Takagi-Sugeno neurofuzzy network. These metrics demonstrate that the proposed method effectively balances accuracy and completeness, achieving near-perfect performance in the restoration of missing sensor data. The comparative analysis with alternative methods, such as a two-layer feedforward network with an accuracy of 0.932 and an ANFIS network with an accuracy of 0.976, illustrates the superiority of the developed approach.
This research contributes significantly to the field by addressing the challenges of missing data recovery in sensor systems. The proposed hybrid method, achieving an accuracy of 0.991, demonstrates substantial improvements over traditional approaches, paving the way for further advancements in the adaptive restoration of missing values. Future research could explore the extension of this method to different sensor types and operational conditions, potentially integrating advanced machine learning techniques to enhance adaptability and further improve restoration quality.
This paper is supported by the EU Erasmus+ programme within the Capacity Building Project “WORK4CE” (619034-EPP-1–2020-1-UA-EPPKA2-CFHE-JP).
[16] K. Sun, A. Yin, Multi-sensor temporal-spatial graph network fusion empirical mode decomposition convolution for machine fault diagnosis, Information Fusion 114 (2025) 102708. [17] F. Yang, R. Kang, Q. Liu, C. Shen, R. Du, A new active learning method for reliability analysis based on local optimization and adaptive parallelization strategy, Probabilistic Engineering Mechanics 75 (2024) 103572. doi: 10.1016/j.probengmech.2023.103572. [18] K. El Hamidi, M. Mjahed, A. El Kari, H. Ayad, Adaptive Control Using Neural Networks and Approximate Models for Nonlinear Dynamic Systems, Modelling and Simulation in Engineering 2020 (2020), 1–13. doi: 10.1155/2020/8642915. [19] B. Yu, Z. Zheng, M. Cai, W. Pedrycz, W. Ding, FRCM: A fuzzy rough c-means clustering method,
Fuzzy Sets and Systems 480 (2024), 108860. doi: 10.1016/j.fss.2024.108860. [20] Z. Yu, Z. Zhang, Q. Jiang, X. Yan, Neural network-based hybrid modeling approach incorporating Bayesian optimization with industrial soft sensor application, Knowledge-Based Systems 301 (2024), 112341. doi: 10.1016/j.knosys.2024.112341. [21] L. H. Tran, A modified Takagi-Sugeno-Kang neuro-fuzzy network in estimation of shortage faults location and resistance on transmission lines, Engineering Applications of Artificial Intelligence 133 (2024), 108358. doi: 10.1016/j.engappai.2024.108358. [22] E.-J. Pérez-Pérez, V. Puig, F.-R. López-Estrada, G. Valencia-Palomo, I. Santos-Ruiz, Neuro-fuzzy Takagi Sugeno observer for fault diagnosis in wind turbines, IFAC-PapersOnLine 56:2 (2023), 3522– 3527. doi: 10.1016/j.ifacol.2023.10.1508. [23] Y. Zhang, G. Wang, T. Zhou, X. Huang, S. Lam, K. S. Choi, J. Cai, W. Ding, Takagi-Sugeno-Kang fuzzy system fusion: A survey at hierarchical, wide and stacked levels, Information Fusion 101 (2024), 101977. doi: 10.1016/j.inffus.2023.101977. [24] U. K. Gupta, D. Sethi, P. K. Goswami, Adaptive TS-ANFIS neuro-fuzzy controller based single phase shunt active power filter to mitigate sensitive power quality issues in IoT devices, e-Prime Advances in Electrical Engineering, Electronics and Energy 8 (2024), 100542. [25] S. Vladov, L. Scislo, V. Sokurenko, O. Muzychuk, V. Vysotska, A. Sachenko, A. Yurko, Helicopter Turboshaft Engines’ Gas Generator Rotor R.P.M. Neuro-Fuzzy On-Board Controller Development, Energies, 17:16 (2024), 4033. doi: 10.3390/en17164033. [26] R. M. Catana, G. Dediu, Analytical Calculation Model of the TV3-117 Turboshaft Working Regimes
Based on Experimental Data, Applied Sciences 13:19 (2023) 10720. [27] J. Liu, Sensor fault analysis of aero-engine using ensemble SCNN and Bayesian interval estimation,
Engineering Applications of Artificial Intelligence 125 (2023) 106675.
[28] V. D. Deepak, N. K. Arun, K. V. Shihabudheen, An investigation into the stability of helicopter
control system under the influence of time delay using an improved LKF, Journal of the Franklin
Institute 361 (