Method for correcting a faulty sensor signal

Abstract

The invention provides a method for correcting a sensor signal of a faulty sensor.

Description

METHOD FOR CORRECTING A FAULTY SENSOR SIGNALTechnical field

[0001] The invention lies in the field of system monitoring and, more specifically, it relates to a method for correcting a fault in a faulty sensor signal.

[0002] Sensors are used in a variety of applications where accurate and reliable data is essential for system performance, including but not limited to environmental monitoring, industrial systems, robotic systems, and automated control systems.Background of the invention

[0003] Sensors are fundamental components of modern data-driven technologies, serving as a crucial component in different applications, such as industrial manufacturing, automotive systems, aerospace, and environmental monitoring. These devices are essential for ensuring accurate data acquisition, system efficiency, and operational safety. However, sensors are susceptible to faults caused by a range of factors, including environmental conditions (such as extreme temperatures, humidity, or dust), physical wear and tear, hardware degradation over time, electrical issues (such as voltage fluctuations or electromagnetic interference), and even software or firmware malfunctions. Such faults can lead to serious consequences, including compromised system performance, extended machine downtime, safety risks, and diminished reliability [1, 2],

[0004] Sensor-related failures contribute significantly to operational inefficiencies in large industrial facilities. On average, these facilities could lose more than a day of production each month due to machine failures, including issues with sensors. This downtime leads to significant financial losses, with Fortune Global 500 manufacturing and industrial firms facing an estimated $864 billion annually equivalent to 8% of their total revenue [4],

[0005] To address these challenges, extensive research has been conducted on Fault Detection and Diagnosis, FDD, methods and fault tolerance techniques. FDD methods aim to identify faults, isolate faulty components, and classify the fault type and characteristics. Fault tolerance techniques complement these efforts by ensuring system performance and reliability are maintained despite anomalies.

[0006] FDD has evolved significantly, offering a variety of techniques to enhance the reliability of sensor systems. Known approaches may be efficient and adaptable for different applications, but they face challenges such as high computational complexity and limited generalizability across diverse applications in addition to the need of the data reconstruction.

[0007] Fault tolerance plays a critical role in maintaining system reliability in the presence of sensor faults. Hardware redundancy, a common approach, involves using multiple sensors to monitor the same parameter, ensuring reliability. For example, a study in [5] proposed a redundancy metric to design robust multi-sensor systems, although it faces challenges related to computational complexity. Despite its effectiveness, hardware redundancy increases cost, weight, and system complexity, making it less practical for resource-constrained environments like robotics and the Internet of Things, loT.

[0008] Alternative approaches such as analytical redundancy and observer-based methods use mathematical models to detect and mitigate sensor faults, thereby decreasing the dependence on physical redundancy. Observer-based fault reconstruction and estimation methods [7, 8] are particularly effective but often require precise system modelling and significant computational resources. Known hybrid approaches, which combine hardware and analytical redundancy, achieve high detection accuracy but remain costly and complex to implement [6], Advanced methods utilizing intelligent algorithms and large datasets are also emerging but demand substantial computational power, making them less practical for real-time applications.

[0009] There is limited focus on fault compensation. Most existing methods can identify anomalies but fail to provide analytical rectification or compensation for sensor faults without relying on hardware redundancy. See Fig. 1 which represents a signal correction method according to prior art, wherein 101 represents a faulty signal from a physical sensor, 102 represents a corrected signal, and 103 represents a correction module based on hardware redundancy. This gap is particularly evident in applications requiring lightweight, cost-effective solutions, such as UAVs, loT devices, and autonomous systems.

[0010] Furthermore, many current methods are quite specialized and tailored for specific applications or systems. For example, aerospace applications prioritize fault modelling and detection to ensure mission-critical safety, lithium-ion batteries employ targeted methods to maintain energy efficiency, and automotive perception systems rely on advanced fault recoverytechniques to enhance safety and reliability. Although these approaches are effective in their respective areas, their specialization restricts adaptability to other fields, highlighting the necessity for versatile solutions that can tackle a wide array of fault scenarios at limited complexity.

[0011] Despite significant advancements in sensor fault correction, several limitations persist in the current state of the art. These drawbacks affect the practical implementation, reliability, and efficiency of existing solutions and are herein summarized.

[0012] Limited applicability: Many existing methods are tailored to specific systems or applications, making them less versatile or adaptable across diverse systems and sensor types.

[0013] Insufficient fault estimation and identification: Current solutions do not sufficiently address fault estimation and identification. The state of the art often lacks robust methodologies to estimate fault magnitudes or determine whether the fault originates from the sensor itself or the system being monitored.

[0014] Underdeveloped fault rectification and / or compensation: Fault rectification and compensation methods are insufficiently developed in the current state of the art. Most approaches emphasize fault detection and diagnosis, neglecting methods for analytically compensating for faults without relying on physical redundancy. This limitation leaves systems vulnerable, particularly in applications where additional hardware is impractical or costly.

[0015] High cost and physical complexity: Solutions relying on hardware redundancy, while effective, significantly increase the overall cost, weight, and physical complexity of the system. This is particularly disadvantageous for applications with strict constraints on these factors, such as robotics, aerospace, or portable systems.

[0016] High computational demands: Known advanced techniques, especially those based on computationally intensive signal processing or data-intensive intelligent algorithms, often demand substantial computational resources, making real-time implementation impractical in many cases.

[0017] These limitations highlight the need for more versatile, efficient, and comprehensive fault-healing solutions that can be applied across various systems. An ideal approach should notonly detect faults but also provide its estimation, in addition to its rectification or compensation to ensure a durable system reliability and performance.Technical problem to be solved

[0018] It is an objective to present a method, which overcomes at least some of the disadvantages of the prior art. In particular, it is an objective to provide a solution which ensures the integrity of continuous sensor readings by estimating, rectifying, and / or compensating for faults that may arise during operation.Summary of the invention

[0019] In accordance with a first aspect of the invention, a method for correcting a sensor signal of a faulty sensor is provided, comprising the steps: providing a faulty sensor signal from a previously identified faulty sensor; providing a reference signal; using data processing means, identifying a fault type by comparing the faulty sensor signal with the reference signal, e.g., via a pre-trained or a statistical model; estimating at least one fault parameter of said fault type; correcting the faulty sensor signal based on said fault parameter; outputting the corrected sensor signal. Herein, the reference signal is generated using a machine learning model, e.g., a generative adversarial network, a recurrent neural network or a transformer model, pre-trained on historical signal data of the sensor, previously to the identification of the fault.

[0020] The estimation of at least one fault parameter is performed via a recursive estimation, e.g., using a recursive least squares. This, at least one fault parameter, may be a magnitude of bias, rate of drift, detection time, recovery time, root mean square error compared with the reference signal, or a combination of any of these. The recursive estimation allows for fault parameters to be updated sequentially at each time step. Each new measurement updates the previous parameter estimate without re-solving a global regression problem. Thus, the recursive estimator continuously adapts parameters online; tracks time-varying fault behavior a(t), b(t); enables real-time correction; and it is computationally efficient for embedded implementation.

[0021] According to an exemplary embodiment for chaotic / unpredictable systems, the reference signal may be a sensor signal from at least one redundant sensor, i.e., measuring the same physical variable of the faulty sensor.

[0022] According to an exemplary embodiment for systems with predictable / stable measurements, the reference signal may be previously generated by a physical model, related with the physical variable measured by the first sensor, preferably being a mechanical model, a thermodynamic model or an electromagnetic model.

[0023] The fault type may be a bias fault, i.e., a constant offset, drift fault, i.e., gradual changes over time, performance degradation, i.e., reduced accuracy or responsiveness compared to the reference signal, calibration error, i.e., incorrect readings due to improper calibration, freezing, i.e., sensor output remains constant despite changes in the measured parameter, or a combination of any of the previous fault types.

[0024] The identification and estimation of a fault time may be performed using a fault model defined as: y (t) = a(t) * yh(t) + b(t), where j (t) is the faulty sensor signal, yh(t) is the reference signal, and a(t) and b(t) represent fault parameters.

[0025] For adapting the fault parameters to time-varying conditions, a recursive least squares method may be used to iteratively estimate the parameters a(t) and b(t).

[0026] When the corrected sensor signal corresponds to a correction of at least a predefined amount, preferably 60% of the faulty signal, corresponds to a compensated signal. Furthermore, when the corrected sensor signal is totally, or over 90%, compensated, corresponds to a rectified signal.

[0027] In a second aspect of the invention, a system with self-healing capabilities is provided, comprising: a sensor configured to detect a physical parameter and generate a corresponding sensor signal; a fault identification module configured for monitoring the sensor signal, e.g., for anomalies indicative of a fault; and a correction module, comprising data processing means, configured to perform any of the steps of the method for correcting a sensor signal herein described.

[0028] In a third aspect of the invention, a computer program is provided, comprising instructions which, when the program is executed cause a computer to carry out the steps of the method for correcting a sensor signal herein described.

[0029] In a fourth aspect of the invention, a computer-readable storage medium is provided, comprising instructions which, when executed by a computer, cause the computer to carry out the steps of the method for correcting a sensor signal herein described.

[0030] By using the proposed invention, it becomes possible to provide a method for real-time fault rectification or compensation and keep the system running smoothly without any external intervention. Because it works with software instead of extra hardware, this invention cuts down on costs, weight, and physical complexity. This is especially important for resource-constrained environments like robotics, aerospace, and loT devices.

[0031] Its versatility allows it to adapt to a wide range of sensor types and applications, including environmental monitoring and physically supervised systems, making it broadly applicable. One of its most significant features is a high healing rate of 90% to 100%, effectively restoring faulty data to near-reference quality. Furthermore, its low computational requirements make it an efficient option for resource-constrained systems. These combined advantages establish the disclosed method as a practical, and highly effective solution for addressing sensor faults in modern applications.Brief description of the drawings

[0032] Several embodiments of the present invention are illustrated by way of figures, which do not limit the scope of the invention, wherein:figure 1 shows a signal correction method according to prior art.figure 2 shows a flowchart of an embodiment of a method for correcting a faulty sensor signal.figure 3 shows an embodiment of the fault estimation module.figure 4 shows a graphical representation of different sensor faults.figures 5A and 5B show an embodiment of the fault correction module for a predictable environment sensor and for an unpredictable environment sensor, respectively. figures 6A and 6B show a comparison of faulty, reference, and corrected data for a temperature sensor under fault scenario F1.figure 7 shows an estimation of fault parameters (multiplicative and additive) for a temperature sensor under fault scenario F1.figures 8A and 8B show a comparison of faulty, reference, and corrected data for a humidity sensor under fault scenario F2.figure 9 shows an estimation of fault parameters (multiplicative and additive) for a humidity sensor under fault scenario F2.figures 10A and 10B show a comparison of faulty, reference, and corrected data for a joint position sensor under fault scenario F3.figure 11 shows an estimation of fault parameters (multiplicative and additive) for a joint position sensor under fault scenario F3figures 12A and 12B show a comparison of faulty, reference, and corrected data for a joint position sensor under fault scenario F4.figure 13 shows an estimation of fault parameters (multiplicative and additive) for a joint position sensor under fault scenario F4.

[0033] For figures 6A / 6B, 8A / 8B, 10A / 10B, and 12A / 12B the following signals are represented: Healthy Sensor Data, i.e., the reference signal representing normal, fault-free conditions; Faulty Sensor Data, i.e., the signal affected by the introduced sensor faults; and Corrected Sensor Data, i.e., the output after applying the self-healing module, showcasing a successful fault correction.Detailed description of the invention

[0034] This section describes aspects of the invention in further detail based on preferred embodiments and on the figures. The figures do not limit the scope of the invention. Throughout the description, like numerals will be used to describe like concepts in different embodiments. Details that are described in the context of a particular embodiment are applicable to other embodiments, unless otherwise stated.

[0035] The description puts focus on those aspects that are relevant for understanding the invention. It will be clear to the skilled person that a module for correcting a sensor signal also comprises other commonly known aspects, such as connectors / ports, signal conditioning circuits, an appropriately dimensioned power supply, analog-to-digital converter, controller / processor, or a feedback control unit configured to validate a corrected signal, a communication interface configured to transmit a corrected sensor data to an external system, even if those aspects are not explicitly mentioned.

[0036] Figure 2 represents a flowchart of an embodiment of a method for correcting a faulty sensor signal, wherein 201 represents a fault estimation module, 202 represents a fault correction module, and 203 represents a corrected / healed sensor signal.

[0037] In an embodiment, the fault estimation (201) module calculates key fault parameters, such as the magnitude and main characteristics of the fault over time, providing a detailed understanding of the fault's behaviour. This estimation serves as the foundation for the subsequent correcting / healing process.

[0038] The fault correction (202) module may use analytical methods for compensating and rectifying a previously identified and estimated faulty sensor signal. The result is the corrected sensor signal, which closely matches a healthy sensor signal. For example, the corrected signal corresponds to at least 90% of the expected healthy sensor output, in particular for highly sensitive domains, such as medical or surgical applications. The matching between the two signals depends on several factors, including the type of sensor, the specific application, and a predetermined acceptable margin of error for the system in question. If the fault is fully corrected, the output is a rectified signal. If the fault's effect is reduced to an acceptable level, e.g., at least 60%, it is termed compensation, ensuring the system operates at nominal performance levels.

[0039] The output from the self-healing module is the Healed Sensor Data (203), which may be further used later on. This healed data may be used later by subsequent processing systems, such as control systems, decision-making processes, and data collection mechanisms, ensuring that the entire system operates smoothly and efficiently without interruptions caused by a faulty sensor.

[0040] In an embodiment, the present method starts once a fault is detected and identified as originating from a sensor, followed by an estimation of the characteristics of the fault in a fault estimation module (201). This module (201) comprises comparing the faulty sensor data with a reference signal, i.e., healthy sensor data, to understand the nature and extent of the fault.

[0041] As discussed below, the reference signal is generated by a machine learning model pretrained on historical signal data of the sensor previous to the identification of the fault (see embodiment 2). Herein, the machine learning model used to generate a reference signal represents the expected healthy behaviour of a target sensor. It serves as the baseline fordetecting and identifying sensor faults, estimating fault parameters, and correcting the measured faulty sensor output.

[0042] As shown in Figure 3, the fault estimation module (201) consists of two main stages: an offline stage and a online stage.

[0043] In the offline stage, a fault model is created to simulate various types of faults and their impact on sensor data. This involves developing a mathematical model that can represent different fault behaviours, such as bias, i.e., a constant offset (402), drift, i.e., gradual changes overtime (403), performance degradation, i.e., reduced accuracy or responsiveness (404), calibration errors, i.e., incorrect readings due to improper calibration (405) and freezing, i.e., sensor output remains constant despite changes in the measured parameter. This fault model provides the foundation for estimating and correcting faulty signals in real time during an online stage.

[0044] Figure 4 shows a graphical representation of different sensor faults, wherein 401 represents an expected signal, 402 represents a bias signal output, 403 represents a drift signal output, 404 represents a performance degradation signal output, and 405 represents a calibration error signal output.

[0045] Here a bias signal output is defined as jy (t) =(t) + b for all t > tF. A drift signal output is defined as yf(t) = yh(t) + di(t),|dj(t)l = 0 < << 1 for all t > tF. A performance degradation signal output is defined as yf(t) = yh(t) + di(t), |dj(t)l dt, di(t) 0. The accuracy coefficient dte [-emin,emax], where emin, emax> 0 for all t > tF. A calibration error signal output is defined as jy(t) = cL(t). yh(t), 0 < cL< cL(t) < 1. The effectiveness coefficient cte [c, 1], where ct> 0 for all t > tF.

[0046] Building upon the various types of sensor faults herein discussed, a fault model to capture the behaviour of these faults using a time-varying linear model, is expressed as follows: y / (0 = a(t) * yh(t) + b(t) (1).

[0047] Where j (t) is the faulty signal, yh(t) is the healthy signal in fault-free conditions, and a(t) and b(t) represent fault parameters.

[0048] In the absence of faults (fault-free case), the parameters may be initialized as a(t) = 1 and b(t) = 0, ensuring that the faulty signal j (t) is equivalent to the healthy signal yh(t). This scenario represents the ideal condition in which the sensor operates without any faults.

[0049] During fault occurrences (t > t_F), a(t) and b(t) may become time-varying parameters, capturing the dynamics of the fault over time. This flexibility allows the proposed model to accurately represent a wide range of fault scenarios, facilitating effective analysis and mitigation strategies.

[0050] In the online stage, the present disclosure uses the pre-defined fault model (1) to estimate fault parameters in real time.

[0051] This step computes the estimated fault parameters (t) and b(t), which characterize the time-varying behavior of the fault.

[0052] For this case, where the model is linear in the parameters a(t) and b(t), the recursive Least Squares, RLS, algorithm is particularly suitable due to its efficiency in tracking time-varying parameters in a linear setting.

[0053] The RLS algorithm is used to estimate the parameters a(t) and b(t) by processing the healthy reference signal yh(t) and the faulty measured signal yf(t) as inputs. The RLS algorithm operates by minimizing the weighted sum of squared errors over time, which allows it to adapt to time-varying faults.

[0054] The recursive parameter update is given by: 0(t) = 0(t - 1) + F(t)(y(t) - y(t))where 0(t) represents the parameter vector [ (t), b(t)]T, and F(t) is the gain matrix that determines how much the current prediction error influences the parameter update.

[0055] The predicted output y(t) is computed as: y(t) =- 1)where ^(t) is the regressor vector: ^(t) =[L0056]JThe gaain matrix K(vt)7is defined as: K(vt)7= - Z —+ipT(t)P(t-l) —ip(t)with P(t) being the covariance matrix, updated as:P(t- l)ip(t)ipT(t)P(t- l)P(t) =I1 JA + ipT(t)P(t - l)ip(t)

[0057] Here, A is the forgetting factor, typically in the range 0.98 < A < 0.995, which ensures that recent data points are weighted more heavily than older ones. This property allows the algorithm to estimate time-varying parameters, which is critical in the presence of dynamic faults. The RLS algorithm provides real-time estimates of the fault parameters, which are subsequently used for fault correction.

[0058] In an embodiment, the fault estimation module comprises the following steps:Inputs to the Fault Estimation module (201): the measured sensor data, which is the faulty signal from the sensor, and a healthy sensor data, which represents a reference signal that reflects the expected behaviour of the faulty sensor.Identification / Estimation of Fault Parameters: The module uses the fault model (1), as described previously, to estimate parameters that describe the fault. These parameters may include the magnitude of bias, rate of drift, and more. The estimation may be performed using an online algorithm such as Recursive Estimation, which continuously updates the fault parameters as new sensor data arrives.Outputs of the Fault Estimation module (201): The outputs of the Fault Estimation Block are the estimated fault parameters, such as the magnitude of bias or drift, which provide detailed information about the fault’s nature and extent. These estimated fault parameters are later forwarded to the Fault Correction module (202) to correct the faulty sensor signal provided.

[0059] In an embodiment, the fault correction module (202) comprises the following steps:Inputs: The measured sensor data, which is the raw, faulty data collected from the faulty sensor, and the estimated fault parameters, which include the characteristics of the fault, such as bias magnitude or drift rate, determined in the fault estimation process.Analytical Compensation: The pre-developed fault model is used to understand how thespecific fault affects the sensor data. The estimated fault parameters are applied to adjust the faulty sensor data.Output: The result is the corrected sensor data, which should closely match the healthy signal. If the fault is fully compensated, the output is a rectified signal. If the fault's effect is reduced to an acceptable level, it is termed compensation, ensuring the measured system operates at a nominal performance level. Additionally, the estimated fault parameters can also be analysed for further analysis and research to understand the root causes and types of faults, helping to prevent similar issues in the future.

[0060] As a generally applicable embodiment, the corrected signal yc(t) may be computed using the measured faulty signal jy(t) and the estimated fault parameters a(t) and b(t) as follows:lyr(t) - h(t)lyc(0 =L / ', for a(t) #= 0a(t)

[0061] By substituting yy(t) with its formulated model, it is obtained the following equation:„ [a(0y / i(0 +yc(t) =1- T777 - < for Cl(t) * 0a(t)yc(t) = b(t), for (t) = 0

[0062] The effectiveness of the compensation yc(t) is directly related to the accuracy of the estimated fault parameters { (t),The closer the estimates are to the actual fault, the better yc(t) approximates the healthy signal yh(t). This accurate compensation rectifies the fault, thereby restoring the reliability of the sensor system.

[0063] In an embodiment, the fault estimation provides key fault parameters, such as magnitude and main behaviour features overtime, allowing a detailed understanding of the fault's characteristics. This step serves as the foundation for subsequent healing process, i.e., correcting a faulty sensor signal.

[0064] Embodiments 1 and 2

[0065] This embodiment has a superior performance for sensors that monitor and measureparameters in controlled and / or supervised systems such as robotics, industrial machinery, automotive systems, and other similar physical systems. In these cases, the healthy signal generation (404) can leverage a physical model (embodiment 1) or data-driven approaches, e.g., a machine learning model pre-trained on historical signal data of the sensor previous to the identification of the fault (embodiment 2). These methods work effectively because the behaviour of supervised systems is well-defined and predictable and / or modellable.

[0066] In an embodiment, the machine learning model comprises a pre-trained nominal behaviour machine learning model per sensor, generating a real-time nominal reference signal, and applies a recursive time-varying fault parameter estimation between the measured faulty signal and its own nominal reference. The machine learning model is trained offline using verified healthy historical data and learns the mapping:yh(t) = / (z(t))where: yh(t)= predicted nominal (healthy) sensor output, z(t)= selected measurable variables. The trained model is then deployed online to generate the nominal reference signal in real time.

[0067] Several embodiments are envisioned: embodiment 2.1 - System-Level (Input-Output) Modelling, embodiment 2.2 - Sensor Correlation Modelling, and embodiment 2.3 - hybrid approach.

[0068] For the embodiment 2.1, the machine learning model represents the system behaviour and predicts the expected sensor output from system inputs and states:yh(0 = / (u(t),s(t))where: u(t)= control inputs, s(t)= measurable system states, yh(t)= predicted healthy sensor signal

[0069] Example applications span various industries and devices, showcasing their versatility and adaptability. In the realm of unmanned aerial vehicles (UAVs), an accelerometer can benefit from inputs such as motor commands, angular rates, velocity, and altitude. By utilizing a machine learning model like a Multilayer Perceptron (MLP) or a Long Short-Term Memory (LSTM) neural network, it is possible to predict healthy accelerometer readings, enhancing the UAV's performance and reliability.

[0070] For industrial pumps, predictive maintenance and operational efficiency can be significantly improved with inputs including motor torque command, flow rate, and valve position. Employing Support Vector Regression (SVR) as the machine learning model, the output would be a predicted pressure signal, crucial for maintaining optimal pump operation and preventing failures.

[0071] In the automotive sector, particularly concerning engine performance, inputs such as throttle position, engine speed, and intake air mass are critical. By leveraging Random Forest regression, one can accurately predict the manifold pressure, thereby ensuring the engine runs smoothly and efficiently.

[0072] Battery thermal monitoring is another application where machine learning can play a vital role. Inputs such as current, voltage, and ambient temperature contribute to the model's understanding of the battery's thermal dynamics. With Gaussian Process regression, the predicted output is the battery temperature, which is essential for managing thermal conditions and extending battery life.

[0073] Several machine learning techniques are applicable across different domains. Linear regression, with or without regularization, can provide simple yet effective predictive models. Support Vector Regression is suitable for applications requiring robust prediction capabilities. Random Forest and Gradient Boosting offer ensemble methods that improve accuracy and consistency. For complex patterns and sequences, Multilayer Perceptron (MLP) and Recurrent Neural Networks (RNN, LSTM) are beneficial due to their ability to capture intricate relationships within data. Finally, Gaussian Processes offer a probabilistic approach for regression tasks, ensuring reliable predictions and uncertainty quantification.

[0074] For the embodiment 2.2, the machine learning model learns correlations between sensors and predicts one sensor from others:yh(0 = f Mt), y t),-..,yn t))where: y2,y3,...,yn=correlated sensor signals, yh(t)= predicted healthy value of the target sensor. The model is trained on historical healthy multi-sensor datasets.

[0075] Example applications for this embodiment spans from UAV inertial systems, e.g., accelerometer along the X-axis. The inputs feeding into this system include signals from gyroscopes, accelerometers on other axes, as well as readings from a magnetometer. To predict the nominal accelerometer value on the X-axis, an LSTM machine learning model may be utilized. This model effectively processes the various signals to provide accurate output values.

[0076] In the realm of smart grid monitoring, a target is a voltage sensor. Key inputs for this system consist of readings from current sensors, measures of frequency, and the power factor. A Random Forest model may be employed to predict the nominal voltage, leveraging the diverse input data to ensure the efficient management and stability of the grid.

[0077] For industrial robotics applications, the focus is on ensuring the health of joint torque sensors. Inputs for this system include data about joint positions, their velocities, and the torques in neighbouring joints. A neural network model may process these inputs to predict the healthy torque value for each joint, ensuring optimal performance of the robotic systems.

[0078] Importantly, fault detection and isolation are conducted before using these systems. This initial step involves identifying any faulty sensors and ensuring that only those sensors not flagged as faulty are used as inputs for the machine learning models. This careful process prevents fault propagation and maintains the stability of reference generation across various applications.

[0079] For the embodiment 2.3, both system inputs and correlated sensors are used jointly to improve robustness, thus providing an hybrid approach.

[0080] Figure 5A shows an embodiment of the fault correction module (202) for a predictable environment sensor.

[0081] Embodiment 3

[0082] The fault compensation process for unpredictable environment sensor faults, such as in environmental monitoring sensors, can be managed in two ways, as shown in Figure 5B.

[0083] The first approach involves using the estimated fault parameters to adjust the faulty sensor data through analytical compensation, similar to the method used in embodiments 1 and2. This ensures the corrected data closely aligns with the expected healthy signal.

[0084] The second approach involves switching to data from a healthy redundant sensor, bypassing the faulty sensor entirely. Both strategies ensure the system continues to operate with accurate and reliable data. Additionally, the estimated fault parameters remain valuable for fault quantification, understanding the fault's nature, and addressing potential root causes to mitigate future occurrences.

[0085] To validate the effectiveness of the present method comprehensive laboratory tests were performed on three different types of sensors, with data collected and analysed using MATLAB / Simulink R2024b, chosen for its advanced capabilities in modelling, simulation, and analysis.

[0086] In these examples, for each sensor type, a particular corresponding embodiment of the invention was applied. To thoroughly evaluate the self-healing strategy, a comprehensive and challenging fault scenarios were designed for each sensor. These scenarios aimed to test the invention’s robustness and effectiveness in executing the self-healing process under realistic conditions.

[0087] The primary outcomes evaluated of the tests were: the fault estimation, i.e., how accurately is the estimation of the fault parameters, such as bias or drift magnitude; and the fault correction, i.e., the rectification or compensation of the faulty sensor data to closely match the healthy reference signal.

[0088] Additionally, key evaluation metrics were used to quantify the performance of the present disclosure:Recovery Time: The time taken to compensate for the fault and restore accurate data. Root Mean Square Error (RMSE): A measure of the corrected output's accuracy compared to the healthy reference signal.

[0089] These metrics demonstrate the module's capability to maintain accurate and reliable sensor outputs even in the presence of faults.

[0090] Example F1 - Unpredictable environment sensors

[0091] For this example, the unpredictable environment sensor chosen was the temperaturesensor Model STTS751.

[0092] A challenging fault scenario (F1) was designed to simulate real-world sensor issues, incorporating a series of faults occurring successively at different times and with varying durations. The faults also differ in type:Drift: A gradual change in sensor readings over time, which could be caused by wear and tear of the sensor. For instance, in temperature sensors, this can occur when the sensor's internal components degrade over time, leading to a slow, continuous shift in its measurements.Intermittent Bias: A sudden offset in sensor readings, often due to power issues or voltage fluctuations. For example, a temperature sensor might experience a bias when the sensor's power supply fluctuates, causing the sensor to report a constant deviation from the true value.Random Fault: This fault can arise from external noise or environmental factors like dust, electromagnetic interference. Such noise can cause irregular, unpredictable variations in the sensor’s data.

[0093] As illustrated in Figures 6A and 6B, the sensor data under faulty conditions scenario F1 and after the application of fault correction (202) module is presented. This figure compares three distinct data sets: Faulty Sensor Data (Solid line), i.e., a sensor output under fault conditions; Reference Data (Dotted line), i.e., a healthy sensor data used as a reference; and Corrected Data (Dashed line), i.e., data after applying the present disclosure to correct the sensor's faulty output.

[0094] Upon the detection of a fault, the faulty data was adjusted using estimated fault parameters. The Root Mean Squared Error (RMSE) between corrected and reference data was calculated to measure accuracy.RMSE = 0.0658, indicating that the corrected data closely aligns with the healthy reference. As shown in Figure 6A, the corrected data (dashed line) closely matches the reference (dotted line), effectively mitigating the fault effects.Recovery Time: After the fault is detected, the present disclosure immediately compensates for the fault, restoring the sensor data to a stable state.

[0095] As the disclosed method was implemented in MATLAB / Simulink, the recovery time was 0.01 seconds, which corresponds to the sampling time used during execution. This means thatif the sampling time is changed to 0.05 seconds, the recovery time will also be 0.05 seconds. Thus, the recovery occurs immediately in the step following fault detection.

[0096] A relevant part of the correction process is the estimation of the fault parameters. As depicted in Figure 7, it is estimated multiplicative and additive fault parameters that affect the sensor’s output. These parameters are crucial for two purposes:Fault Compensation: Used to adjust faulty data to align with the reference.Further Analysis and Research: Offers valuable data for diagnosing root causes and refining future sensor design.

[0097] The performance of the self-healing strategy for the Temperature Sensor in an F1 scenario is evaluated based on key performance metrics. The detection time measures how quickly a fault is identified once it exceeds a predefined threshold for ensuring rapid response. Similarly, the recovery time represents the duration required for the system to correct faulty data, achieving immediate recovery, as previously explained the response is solely be limited by the sampling rate. Additionally, the accuracy of fault compensation was quantified using the Root Mean Squared Error (RMSE), which was recorded at 0.0658, indicating a high level of precision in error correction.

[0098] These results demonstrate that the disclosed method is highly efficient in estimating, and compensating for faults in an unpredictable environment such as a temperature sensor. The immediate fault detection and correction ensure that the system can continue to operate reliably, even in the presence of complex faults.

[0099] Example F2 - Unpredictable environment sensor

[0100] For this example, the unpredictable environment sensor chosen was the humidity sensor Model HTS221.

[0101] To evaluate the effectiveness of the present correction method on humidity sensors, a challenging fault scenario F2 that combines three common fault types, occurring successively at different times and with varying durations was applied.Drift: A gradual deviation in sensor readings over time.Loss of Accuracy: This represents a reduction in the sensor’s ability to provide precise measurements, often due to sensor degradation or calibration issues after prolonged use.Freezing: The sensor output remains constant despite changes in the actual humidity level, which may be due to power supply interruptions or firmware / software malfunctions.

[0102] As shown in Figures 8A and 8B, the system's outputs demonstrate the following: a faulty sensor data, illustrating the effects of the drift, loss of accuracy, and freezing faults; a healthy signal, serving as the reference; and a corrected sensor output after applying the present disclosure to correct the sensor's faulty output.

[0103] Here it can be seen that the corrected signal aligns closely with the reference signal, demonstrating the disclosed method’s ability to effectively compensate for multiple fault types.

[0104] The compensation process relies on accurate fault estimation. As depicted in Figure 9, The fault estimation process identified multiplicative and additive fault parameters. These parameters enabled precise real-time correction of the faulty data, ensuring the sensor output closely matched the expected behaviour.

[0105] As for the previous example of the temperature sensor, it was found that for both the detection time and for the recovery time was in the order of hundreds of seconds, i.e., corresponding to an immediate fault detection upon exceeding the predefined threshold and an immediate correction of the faulty signal after detection. Additionally, the accuracy of fault compensation was quantified using the Root Mean Squared Error (RMSE), which was recorded at 0.012, indicating an exceptionally high level of compensation accuracy.

[0106] These results validate the robustness and accuracy of the disclosed method in addressing complex faults for the particular case of humidity sensors.

[0107] For the examples F3 and F4, the predictable environment sensor chosen was a joint position sensor integrated into the UR5e manipulator robot.

[0108] The present correction method was tested by using data collected from a real robot, with fault scenarios implemented in MATLAB / Simulink. The self-healing module was developed and executed similarly to the previous cases.

[0109] Example F3 - Predictable environment sensors

[0110] In this fault scenario, two faults were considered: a drift, which represents gradual inaccuracies over time, which could result from sensor wear and tear or aging electronic; and a random fault, which simulates loss of accuracy due to external disturbances or electromagnetic interference.

[0111] As illustrated in Figures 10Aand 10B, the sensor data under faulty conditions scenario F3 and after the application of fault correction (202) module is presented. This figure compares three distinct data sets: Faulty Sensor Data (Solid line), i.e., a sensor impacted by drift and random faults; Reference Data (Dotted line), i.e., a healthy sensor data used as a reference; and Corrected Data (Dashed line), i.e., data after applying the present disclosure to correct the sensor's faulty output.

[0112] Example F4 - Predictable environment sensors

[0113] In this fault scenario an intermittent bias was considered. Here, a sequence of sudden constant offsets were applied, simulating voltage fluctuations or connector issues in the sensor.

[0114] As illustrated in Figures 12A and 12B, the sensor data under faulty conditions scenario F4 and after the application of fault correction (202) module is presented. This figure compares three distinct data sets: Faulty Sensor Data (Solid line), i.e., a sensor impacted by intermittent bias faults; Reference Data (Dotted line), i.e., a healthy sensor data used as a reference; and Corrected Data (Dashed line), i.e., data after applying the present disclosure to correct the sensor's faulty output.

[0115] The performance of the present disclosure for the joint position sensor under fault conditions F3 and F4 was assessed using the Root Mean Squared Error (RMSE), with values of 0.0187 for F3 and 0.0278 for F4, reflecting high precision in error correction.

[0116] These results highlight the effectiveness of the present disclosure in maintaining the reliability and accuracy of joint position sensors in robotic systems. Given the critical importance of precision in such applications, the method's ability to correct dynamically faults in real time ensures stable sensor performance, even under challenging conditions. This enhances theoverall robustness and efficiency of the robotic system, minimizing disruptions caused by sensor faults.

[0117] Unlike existing FDD and fault-tolerant methods, which are often tailored to specific systems, the present disclosure is highly versatile and adaptable, thus it can be used across a wide range of applications, also in particular for real-time self-healing sensor data. It is suitable for sensors in predictable environments, such as robots, automated guided vehicles (AGVs), and industrial systems, as well as for sensors in unpredictable environments, like those used for environmental monitoring (e.g., temperature and humidity).

[0118] The present disclosure aims to estimate a fault and extract its main characteristics such as size, amplitude, analytical integration to the supervised system (additive / multiplicative fault). The fault identification specifies the location of the fault, which could be sensor-related or related to another system’s component. This is a major improvement over current technologies, which often don’t estimate faults well.

[0119] Throughout this document, "anomaly" and "fault" as well as "healing" and "correcting" are used interchangeably and should be interpreted as synonyms.

[0120] It should be noted that features described for a specific embodiment described herein may be combined with the features of other embodiments unless the contrary is explicitly mentioned. Based on the description and on the figures that have been provided, a person with ordinary skills in the art will be enabled to implement a computer program for executing the described methods without undue burden and without requiring additional inventive skill.

[0121] It should be understood that the detailed description of specific preferred embodiments is given by way of illustration only, since various changes and modifications within the scope of the invention will be apparent to the person skilled in the art. The scope of protection is defined by the following set of claims.

[0122] References[1] Fault Detection and Diagnosis Methods for Sensor Systems: A Scientific Literature Review (2023)[2] Sensor Fault Detection and Diagnosis: Methods and Challenges (2024)[3] Recent Advances in Intelligent Algorithms for Fault Detection and Diagnosis (2024) [4] World’s Largest Manufacturers Lose Almost $1 Trillion a Year to Machine Failures," Automation.com, Jun. 2021. [Online]. Available: https: / / www.automation.com / enus / articles / june-2021 / world-largest-manufacturers-lose- almost-1-trillion. Accessed: Nov. 11, 2024.[5] Sensor Fault Detection, Isolation, and Estimation in Lithium-Ion Batteries (2016)[6] A Redundancy Metric Set within Possibility Theory for Multi-Sensor Systems (2021) [7] A review of fault types and analytical and hardware redundancy for the sensor functional safety (2024)[8] Sensor Fault Reconstruction Using Robustly Adaptive Unknown-Input Observers (2024)

Claims

Claims1. Method for correcting a sensor signal of a faulty sensor comprising the steps:providing a faulty sensor signal from a previously identified faulty sensor;providing a reference signal;using data processing means:identifying a fault type by comparing the faulty sensor signal with the reference signal:estimating at least one fault parameter of said fault type (201);correcting the faulty sensor signal based on said fault parameter (202);outputting the corrected sensor signal;wherein the reference signal is generated using a machine learning model pre-trained on historical signal data of the sensor, previous to the identification of the fault; wherein the estimation of at least one fault parameter is performed via a recursive estimation.

2. Method according to any of the previous claims wherein the at least one fault parameter is a magnitude of bias, rate of drift, detection time, recovery time, root mean square error compared with the reference signal, or a combination of any of these.

3. Method according to any of the previous claims wherein the fault type is a bias fault, drift fault, performance degradation, calibration error, freezing, or a combination of any of the previous fault types.

4. Method according to any of the previous claims wherein the identification and estimation of a fault type is performed using a fault model defined as: jy (t)= a(t) * (t) + b(t), where y (t) is the faulty sensor signal, yh(t) is the reference signal, and a(t) and b(t) represent fault parameters.

5. Method according to the previous claim wherein a recursive least squares method is used to iteratively estimate the parameters a(t) and b(t).

6. Method according to any of the previous claims wherein the corrected sensor signal corresponds to a correction of at least 60% of the faulty signal.

7. System, comprising:a sensor configured to detect a physical parameter and generate a corresponding sensor signal;a fault identification module configured for monitoring the sensor signal; anda fault correction module, comprising data processing means, configured to perform any of the steps of the method for correcting a sensor signal of any of the claims 1-6.

8. Computer program comprising instructions which, when the program is executed cause a computer to carry out the steps of the method for correcting a sensor signal of any of the claims 1-6.

9. Computer-readable storage medium comprising instructions which, when executed by a computer, cause the computer to carry out the steps of the method for correcting a sensor signal of any of the claims 1-6.

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