Early Fault Diagnosis Research Articles

Fault Detection from Horizontal Shaft Centrifugal Pump Fan Sound Analysis Using Artificial Intelligence

Axial misalignment, over-forced and wear of the components that constitute the machine is changed in the sound. It is of critical importance to implement early fault diagnosis and predictive maintenance planning in order to prevent errors caused by machines that break down or fail during operation. In this study, data comprising 15 one-dimensional sequences and 15 two-dimensional images from MFCCs (Mel-Frequency Cepstral Coefficients) for each sound were utilized in CNN (Convolutional Neural Networks). Furthermore, the data used in ML (Machine Learning) models were created by extracting 28 features from various audio characteristics such as amplitude-time, mel-spectrogram, MFCCs, ZCRs (Zero Crossing Rates), and RMS (Root Mean Square) energy. SVM (Support Vector Machine), KNN (K-Nearest Neighbours) and EL (Ensemble Learning), which combines SVM, KNN and RF (Random Forest) models, were utilized. The results indicated that the accuracy rates varied between 76.21% and 99.59%. The EL model exhibited the highest accuracy, correctly predicting all 99 sounds for faulty, 248 sounds out of 249 sounds for slightly faulty and 143 sounds out of 144 sounds for intact. The results indicate that it is possible to diagnose faults in centrifugal pumps and preventing errors. Consequently, economic savings will be achieved by reducing the losses caused by faulty parts and energy loss caused by the decrease in the efficiency of the system when it operates incorrectly will be prevented.

Stator inter-turn shortcircuit fault diagnosis of induction motor based on characteristic current

Purpose This paper aims to facilitate reliable online diagnosis of early faults in the stator winding inter-turn short circuits of induction motors (IMs) under various operating conditions. Design/methodology/approach A novel fault characteristic component, the characteristic current amplitude, is proposed for the fault. Defined as the product of short-circuit coefficient and short-circuit current, the characteristic current is derived from the positive and negative-sequence components of the stator-side current and voltage. Findings Simulation models of the IMs pre- and postfault, along with an experimental platform for the motor’s inter-turn short circuit, were established. The characteristic current amplitude proves more robust against voltage unbalance and load variations, which offers enhanced reliability and sensitivity for early fault diagnosis of inter-turn short circuit in IMs stator windings. Originality/value A novel feature is proposed. Compared with negative-sequence current, which is considered as a traditional fault feature, the characteristic current amplitude exhibits a greater robustness against the imbalanced conditions, which simultaneously possesses the attributes of both reliability and expeditiousness in fault detection.

Stability and Fault Detection Algorithm of Grid-Connected Inverter in Complex Power Grid Environment

In order to improve the stability, this paper designs a control strategy based on adaptive grid impedance. By monitoring the grid impedance in real time and dynamically adjusting the inverter control parameters, the influence of grid impedance change on inverter stability is effectively reduced. At the same time, LCL filter is introduced, which significantly filters out the higher harmonics in the inverter output current and improves the output waveform quality. In addition, a voltage compensation device is applied to quickly generate a compensation voltage signal when the grid voltage fluctuates to ensure the stability of the inverter output voltage. In the aspect of fault detection, a data-driven fault detection algorithm is proposed, which combines machine learning and real-time monitoring technology to realize early detection and accurate diagnosis of inverter faults by collecting and analyzing inverter operation data. The experimental results show that the algorithm performs well in the detection of power switch device faults, sensor faults and other types, and has high classification accuracy. The research shows that the control strategy based on adaptive grid impedance, the addition of LCL filter and the application of voltage compensation device have significantly improved the stability of grid-connected inverter in complex grid environment. The proposed data-driven fault detection algorithm provides strong support for rapid fault location and accurate treatment of inverter.

Early Fault Diagnosis and Prediction of Marine Large-Capacity Batteries Based on Real Data

The inconsistency of battery voltages in all-electric ships is a significant issue for electric vehicle battery systems, leading to numerous safety concerns during vessel operation. Therefore, timely fault diagnosis and accurate fault prediction are crucial for the safe operation of ships. This study examines the fault alarm system of marine battery management systems in conjunction with the unique operating conditions of ships, focusing on the system’s latency. To facilitate prompt fault detection, a fault diagnosis method based on the Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm is proposed, utilizing the voltage data of battery clusters. Results indicate that the DBSCAN clustering algorithm demonstrates superior effectiveness and accuracy in identifying irregular battery clusters. Furthermore, the fault prediction method based on the iTransformer model is introduced to forecast variations in battery cluster voltages. Experimental findings suggest that this model can effectively predict consistency faults and over-/under-voltage conditions based on battery cluster voltage values and corresponding fault thresholds.

An Early Micro Internal Short Circuit Fault Diagnosis Method Based on Accumulated Correlation Coefficient for Lithium-Ion Battery Pack

Early micro internal short circuit (ISC) fault diagnosis is crucial for the safe and reliable operation of lithium-ion batteries. In order to solve the problem that the early micro ISC fault is difficult to identify due to its weak fault characteristics, this paper proposes a fault diagnosis method based on the accumulated correlation coefficient. Specifically, the method uses the accumulated voltage value within the time window as the input feature, constructs an adjustment factor based on the distance difference of the accumulated voltage value to amplify the difference between the fault voltage correlation coefficient and the normal voltage correlation coefficient, and finally achieves the purpose of highlighting the faulty cell. The effectiveness and diagnostic capability of the proposed method are verified in experiments of short circuit faults of different severity. The results show that the proposed method can effectively identify and locate early micro ISC faults within 200 s, and improve the diagnostic capability up to 0.02 C short-circuit severity. In addition, a multi-level diagnostic warning mechanism can be established according to the decrease of the fault voltage correlation coefficient, so as to measure the severity of the fault and track the fault evolution process.

Resilient fast convolutional sparse filtering with convergence directivity for the bearing fault diagnosis

The fast nonlinear convolutional sparse filtering (FNCSF), which detects fault features 42 h earlier than traditional methods in the intelligent maintenance system dataset and takes only 0.12 s, is widely considered a powerful tool for early fault diagnosis. However, random shocks caused by the structure or external interference pose challenges to the extraction accuracy of FNCSF. In addition, the extraction reliability of FNCSF is affected by computational instability and complex parameter settings. To address the above defects, resilient fast convolutional sparse filtering (RFCSF) is proposed in this study. First, the collected vibration signal is normalized by Z-score to eliminate the scale variability of the nonlinear transformation. Then, the frequency components of the signal are evenly divided by the initialized filters to indicate the convergence direction of fault and improve random shock resistance and extraction stability. Next, the nonlinear [Formula: see text] norm, which can effectively distinguish fault features from irrelevant disturbances, is regarded as the target of blind deconvolution. In the process of deconvolution, the filter converging to random shocks and noise is adaptively eliminated to improve the extraction efficiency and intelligence. Finally, the filtered signal is envelope demodulated to obtain fault information. In the simulation analysis, features under noise with −16 dB and random shocks with 50 m/s2 are accurately extracted by RFCSF with parameters robustness. Several experimental cases demonstrate that RFCSF with these advantages is a promising feature extraction tool.

Intelligent Fault Diagnosis of Inter-Turn Short Circuit Faults in PMSMs for Agricultural Machinery Based on Data Fusion and Bayesian Optimization

The permanent magnet synchronous motor (PMSM) plays an important role in the power system of agricultural machinery. Inter-turn short circuit (ITSC) faults are among the most common failures in PMSMs, and early diagnosis of these faults is crucial for enhancing the safety and reliability of motor operation. In this article, a multi-source data-fusion algorithm based on convolutional neural networks (CNNs) has been proposed for the early fault diagnosis of ITSCs. The contributions of this paper can be summarized in three main aspects. Firstly, synchronizing data from different signals extracted by different devices presents a significant challenge. To address this, a signal synchronization method based on maximum cross-correlation is proposed to construct a synchronized dataset of current and vibration signals. Secondly, applying a traditional CNN to the data fusion of different signals is challenging. To solve this problem, a multi-stream high-level feature fusion algorithm based on a channel attention mechanism is proposed. Thirdly, to tackle the issue of hyperparameter tuning in deep learning models, a hyperparameter optimization method based on Bayesian optimization is proposed. Experiments are conducted based on the derived early-stage ITSC fault-severity indicator, validating the effectiveness of the proposed fault-diagnosis algorithm.

Early Failure Diagnosis of Scraper Conveyor Gearboxes Based on DS Evidence Theory and Multimodal Data Fusion

ABSTRACTA scraper conveyor is one of the important equipment to ensure reliable, efficient and stable mining and transportation of coal. As the most important transmission system of the scraper conveyor, the gearbox takes the role of transmitting power and torque. Due to the influence of working conditions in underground coal mines, the gear transmission system is often subject to the impact of nonuniform large loads, which is very prone to failures, and affected by environmental interference, it is difficult to detect the early abnormal signals of the scraper conveyor gearbox in the conventional industrial scenarios of fault monitoring methods. To ensure the stability and reliability of its work, this paper carries out the research on the multi‐parameter fusion of gearbox early fault diagnosis method under strong background noise interference. Aiming at the problem that the change of fluid physical and chemical characteristic parameters can reflect the early health condition of the gear transmission system and the single vibration signal is difficult to be extracted under the strong background noise, a model based on the fluid physical and chemical characteristic parameters and vibration signals is constructed by utilizing the RBF neural network and the Random Forest algorithm, and the body of evidence of the two models is fused at the decision‐making level through the DS evidence theory, which forms the fluid‐vibration multi‐parameter fusion judgment of the early fault diagnosis method of scraper conveyor gearbox. Through comparison, it is found that compared with the fusion methods, such as high‐dimensional variational self‐encoder, and single diagnosis methods, such as the Random Forest Algorithm, the method researched in this paper is more suitable for the early fault warning of the scraper conveyor gearbox of the well coal mine, and the experimental validation finds that the average accuracy rate of the early fault recognition can be up to 96.6%.

Signature investigation of misaligned jet in Pelton turbines due to flow obstruction in nozzle

Abstract This paper presents a part of the research works related to early stage fault detection and diagnosis of hydraulic turbines. The research works are currently focused on creating a database of the distinctive signals of the faults in the turbine through CFD investigations. The faults in the turbine are induced based on experience and literature review of the common sediment erosion patterns. In the case of Pelton turbines, erosion in the needle with ripple and groove shapes and wavy scales on the buckets are found to be the most common erosion patterns. This paper focuses on asymmetrical erosion patterns of buckets and the needle caused due to flow obstruction in nozzle and consequent misalignment of the jet. The partial blockage for CFD is modelled as a sector of an annulus distributed around the needle. Velocity, pressure, output torque and erosion rates on the needle and buckets are studied. By integrating the trend analysis with machine learning techniques, a real-time condition monitoring tool and procedure can be developed. Since a predictive maintenance of the turbines can be implemented, the outcomes of these research works can have a commercial value for sediment affected power plants globally.

Intelligent fault diagnosis for tribo-mechanical systems by machine learning: Multi-feature extraction and ensemble voting methods

Timely fault detection is crucial for preventing issues like worn clutch plates and excessive friction material degradation, enhancing fuel efficiency, and prolonging clutch lifespan. This study focuses on early fault diagnosis in dry friction clutch systems using machine learning (ML) techniques. Vibration data is analyzed under different load and fault conditions, extracting statistical, histogram, and auto-regressive moving average (ARMA) features. Feature selection employs the J48 decision tree algorithm, evaluated with eight ML classifiers: support vector machines (SVM), k-nearest neighbor (kNN), linear model tree (LMT), random forest (RF), multilayer perceptron (MLP), logistic regression (LR), J48, and Naive Bayes. The evaluation revealed that individual classifiers achieved the highest testing accuracies with statistical feature selection as 83% for both MLP and LR at no load, 90% for MLP at 5 kg, and 93% for KNN at 10 kg. For histogram feature selection, KNN and MLP both reached 85% at no load, MLP achieved 91% at 5 kg, and RF attained 97% at 10 kg. With ARMA feature selection, KNN reached 93% at no load, LR achieved 94% at 5 kg, and RF reached 86% at 10 kg. The voting strategy notably improved these results, with the RF-KNN-J48 ensemble reaching 98% for histogram features at 10 kg, the KNN-LMT-RF ensemble achieving 94% for ARMA features at no load, and the SVM-MLP-LMT ensemble attaining 95% for ARMA features at 5 kg. Hence, a combination of three classifiers using the majority voting rule consistently outperforms standalone classifiers, striking a balance between diversity and complexity, facilitating robust decision-making. In practical applications, selecting the optimal combination of feature selection method and classifier is vital for accurate fault classification. This study provides valuable guidance for engineers and practitioners implementing robust load classification systems in industrial settings.

A comprehensive bearing prognosis framework based on piecewise function stacking convolution auto-encoder and XGBoost algorithm

Abstract Accurately forecasting the remaining useful life (RUL) stands as a pivotal and formidable task within the realm of prognostics and health management. However, there is limited research that considers integrating early fault diagnosis during the bearing’s lifecycle with the prediction of its RUL. In this article, a comprehensive bearing prognosis framework based on piecewise function stacking convolution auto-encoder (AE) and XGBoost algorithm is proposed. To achieve this, an unsupervised piecewise function-based deep stacked convolutional AE was designed to construct the health indicator (HI) of the bearing for reducing the dependency on prior knowledge and furnishing a dynamic foundation for predicting RUL. The 4σ criterion based on HI’s increment was proposed for determining the fault occurrence time (FOT) of the bearing’s operational process. Subsequently, an XGBoost algorithm model was utilized to predict the RUL of faulty bearings. The efficacy of the bearing prognosis framework was validated by two real bearing test datasets. Results indicate the employed criterion of construct HI can flexibly adjust to various operational conditions and accurately pinpoint the bearing’s FOT. Furthermore, the findings demonstrate the proposed bearing prognosis framework achieves superior performance compared with several conventional anomaly detection methods.

Efficient Network-based Fault Detection in Elevator Vibration Signals: A Weighted Fusion Approach of Displacement and Acceleration Data

This research addresses human vibration analysis, rule-based lift fault detection algorithm noise interference, and early fault diagnosis. A new network-based defect diagnosis system uses lift sensor acceleration and displacement data. Convolutional Neural Networks CNNs automatically extract features like motor current (average, maximum, lowest values during a recording session) from this fused data stream and sensor data. CNNs learn key features from pooled data to reduce noise and detect faults early. To build a baseline for normal operation, 132 vibration signal characteristics (RMS, peak-to-peak, mean, standard deviation), lift ID, timestamp, operating mode (Up/Down/Idle), and load condition (Empty/Low/Medium/High) data points are used. Regular operational data and 201 gearbox fault data points are collected. The problem affects motor behaviour via vibration signals, timestamps, lift data, and motor current values. Learning to distinguish this defect type from normal operational data allows the network-based technique identify it. Research shows that network-based strategies outperform traditional methods. It finds weaknesses better than before researches. This method automatically extracts features from the fused data stream to detect defects in real time. Displacement and acceleration data, motor current readings, and CNNs improve noise resistance and failure signal detection. Network-based lift failure detection is advanced in real time problem identification. Precision, early detection, noise resistance, and real-time defect categorization are its strengths. Study affects lift maintenance and find defects early to keep lifts functioning. Real-time defect classification eliminates laborious analysis, simplifying maintenance in which enhancements improve lift performance and reliability.

An early fault warning and diagnosis model based on a two-step analysis strategy for wind turbine bearings

Early bearing fault diagnosis plays a crucial role in ensuring the reliability and safety of wind turbines. This process encounters two primary challenges, that is, weak fault characteristics and strong background noise. Consequently, they restrict the effectiveness of conventional diagnosis methods. To address these difficulties, a two-step early fault diagnosis model is proposed based on an anomaly monitoring index [Formula: see text] and improved successive variational mode decomposition-fast spectral correlation (ISVMD-FSC). Initially, [Formula: see text] enables early anomaly detection. Subsequently, the fault type is further identified using ISVMD-FSC. The ISVMD adaptive decomposition of early warning signals can effectively reduce the noise and isolate the fault impact characteristics. Then, the fault characteristic frequency is extracted using spectral coherence analysis to achieve the purpose of fault diagnosis. This model is tested and validated on simulated data, laboratory accelerated bearing life span data, and real high-speed bearing fault data of wind turbines. Notably, the comparative study shows that [Formula: see text] is capable of detecting the fault earlier than the spectral L2/L1 norm, the sum of the weighted normalized square envelope, index 8, and index 9. Additionally, the fault feature extraction effect of ISVMD-FSC is better than many more advanced time-frequency analysis methods. These results emphasize the model’s excellent performance in early bearing fault diagnosis and its good generalization ability.

Early Hotspot Detection in Photovoltaic Modules using Deep Learning Methods

Photovoltaic (PV) energy systems have been widely used in energy production especially in recent years due to their clean, reliable, environmentally friendly and resource continuity. The electrical energy to be obtained must be uninterrupted and of high quality. For this reason, faults that may cause production losses in PV power plants should be detected quickly and accurately. In this study, an approach that can automatically detect hotspot fault in solar PV modules is presented. In the proposed approach, firstly, Jet colormap based colored image transformation process is applied to gray scale infrared image data. Then, using three different deep learning models such as MobilNetV2, ResNet-18, InceptionV3, both original grey scale data and Jet colormap data are detected and evaluation metric values are obtained. The importance of this research lies in the potential of deep learning-based effective detection, especially in the early and rapid diagnosis of PV hotspot faults.

Period enhanced feature mode decomposition and its application for bearing weak fault feature extraction

Abstract Decomposition methods which can separate the fault components into different modes have been widely applied in bearing fault diagnosis. However, early fault diagnosis is always a challenge for the signal processing methods as well as the traditional decomposition methods due to the heavy noise. Therefore, how to extract the weak fault information from the complicated signal with low SNR is of significance. To overcome this issue, a period-enhanced feature mode decomposition (PEFMD) method is proposed in this paper. Firstly, the initialized filters used for the mode decomposition are adaptively designed according to the spectrum of the original vibration signal. Secondly, time synchronized averaging is used in the iterative process to excavate and identify accurately the weak period components and determine the period of the iterative signal. Finally, the period information can promote the proposed method to decompose the fault component into the hopeful modes by setting correlation kurtosis as the optimation objective and the mode selection. Relative to FMD, the proposed PEFMD achieves further improvement in extracting weak fault information. The practicability and superiority of the proposed PEFMD are verified by the simulated and experimented data. Compared with the feature mode decomposition method and variational mode decomposition, the proposed decomposition method shows an obvious performance advantage under low SNR situations.

Fault detection and diagnosis of grid-connected photovoltaic systems using energy valley optimizer based lightweight CNN and wavelet transform

Early fault detection and diagnosis of grid-connected photovoltaic systems (GCPS) is imperative to improve their performance and reliability. Low-cost edge devices have emerged as innovative solutions for real-time monitoring, reducing latency, and improving response times. In this work, a lightweight Convolutional Neural Network (CNN) is designed and fine-tuned using Energy Valley Optimizer (EVO) for fault diagnosis. The CNN input consists of two-dimensional scalograms generated using Continuous Wavelet Transform (CWT). The proposed diagnosis technique demonstrated superior performance compared to benchmark architectures, namely MobileNet, NASNetMobile, and InceptionV3, achieving higher test accuracies and lower losses on binary and multi-fault classification tasks on balanced, unbalanced, and noisy datasets. Further, a quantitative comparison is conducted with similar recent studies. The obtained results indicate good performance and high reliability of the proposed fault diagnosis method.

Early micro-short circuit fault diagnosis of lithium battery pack based on Pearson correlation coefficient and KPCA

Though lithium batteries have been extensively applied in electric vehicles as the power sources due to the excellent advantages in recent years, the safety risk of them is always existed inarguably. For the effect of early micro-short circuit faults on the electrical characteristics of the batteries is minor, it is hard to be detected and diagnosed timely, as a result it may evolve into direct short circuit and cause severe safety accidents, such as thermal runaway, explosion and so on. This paper proposes a method for diagnosing micro-short circuit fault in battery pack based on Pearson correlation coefficients (PCCs) and kernel principal component analysis (KPCA). Firstly, the voltage values of each battery in various operation states are measured and denoised using a moving filter method, then PCCs between each battery's voltage of the same series branch are calculated to form a dataset. Secondly, the dataset of PCCs is taken to train KPCA algorithm to obtain the control threshold by calculating the squared prediction error (SPE) statistic. After the training process finished, the PCCs of real-time voltage values of the batteries are calculated, then the related SPE statistic is calculated to determine whether the threshold is exceeded or not, meanwhile the contribution graph will be drawn if the threshold is exceeded. Finally, the faulty cell can be cross localized according to the feature of contribution rate in the contribution graph. Experiments are carried out under the condition of Dynamic Stress Test (DST), and comparisons are performed with principal component analysis (PCA) algorithm by using the different input features, such as raw voltage data, Kendall and Spearman correlation coefficient, respectively. The experimental results show that, the proposed method can diagnose the fault as soon as it occurred, and the feature of contribution rate is more obvious than other methods, which is beneficial to the fault localization. Moreover, for the fault judgment only depends on the correlation of the battery's voltages rather than the absolute values of them, which always vary obviously in different operation states, the proposed method can be applied in various engineering scenarios expediently.

Enhanced prediction of transformers vibrations under complex operating conditions

Vibrations occurring in transformer are a physical phenomenon that can be used for condition monitoring, since when the amount of vibrations changes significantly, a faulty condition is in progress (or is incipient). Consequently, vibration prediction becomes crucial for condition monitoring of transformers; however accurately predicting them is challenging, especially in complex scenarios like unbalanced loads and current harmonics. To address this challenge, two methodologies are introduced: one employs a Random Forest (RF) algorithm while the second one is a physical based model. Both methodologies use current information as inputs for vibration prediction, with temperature information serving as additional inputs in the machine learning-based model. Experimental tests, conducted on a distribution transformer during real operations and exposed to unbalanced loads and harmonic currents, demonstrate that both methods are capable of predicting the fundamental component of the vibrations, together with higher harmonics with different degrees of accuracy. The proposed methodologies seem promising as techniques for early diagnosis of faults in transformers or used as an aid to implement possible preventive maintenance techniques.

Fault root cause analysis using degree of change and mean variable threshold limit in non-linear dynamic distillation column

The chemical industrial processes are both dynamic and complex. The presence of instability and danger in the production process poses significant challenges to safety management. Early and accurate fault diagnosis is essential to ensure a sustainable and stable chemical process performance. Most studies in literature do not provide detailed information about diagnosing the root cause of faults in distillation columns using contribution plots. Using principal component analysis (PCA) in conventional contribution plots leads to a large number of contributing variables, making it difficult to identify the root cause of a specific fault. In this study, the authors suggest employing the Degree of Change of Contribution Values (DCC) and Mean Variable Threshold Limit (LMVT) techniques alongside the Wavelet Transform-Principal Component Analysis (WT-PCA) method to decrease the quantity of fault identification variables in a non-linear system (distillation column). The Aspen Plus software is utilized to perform a dynamic simulation of a distillation column, generating data for both normal and faulty operations. Two distinct types of faults are considered, which include loss of feed flow and feed temperature changes. This study aims to analyze the results obtained from the Hotelling T2 and SPE contribution plots by calculating the average difference between the normal and faulty conditions using the Degree of Change in Contribution Values. This procedure is performed to determine the extent of deviation from the standard state. Subsequently, the variables that have surpassed the threshold limit for means variables (LMVT) are designated as the variables that serve as the primary underlying cause of the fault. The technique was employed in a case study involving a nonlinear distillation column, and the results indicate that only one "dominant" variable intersects the LMVT by Hotelling T2, which represents the true underlying cause of the corresponding fault.

The Uncertainty Evaluation of Determining the Trace H2S in SF6/N2 Insulating Gas Mixture by Cavity Ring-Down Spectroscopy

Abstract H2S is one of the most important characteristic components of sulfur hexafluoride gas insulated electrical equipment. The detection of trace H2S is of great significance for early fault diagnosis of such equipment. Based on the 1578 nm wavelength distributed feedback diode laser (DFB-DL), cavity ring-down spectroscopy (CRDS) can effectively measure the concentration of trace H2S in SF6/N2 gas mixtures. Starting from the principle of methodology, this article establishes a mathematical model for evaluating the measurement uncertainty of CRDS and analyzes its sources of uncertainty: gas constant R1 , temperature T, Avogadro constant NA , gas pressure p in the optical cavity, volume V of the optical cavity, speed c of light, the absorption cross-section parameter σ(ν) of H2S molecules in the laser frequency ν, the ring-down time τ with absorption sample H2S and the ring-down time τ0 without absorption sample. After evaluating the uncertainty components, it was found that the main component was σ(ν) and the secondary components were τ and τ0. The H2S content in the 80% SF6-20% N2 mixed gas measured is (7.64 ± 0.12) × 10−6 mol/mol.