Vibration current feature fusion monitoring device for wear state of rotor of screw pump

Abstract

The invention discloses a vibration current feature fusion monitoring device for the wear state of a screw pump rotor, and belongs to the technical field of screw pump monitoring, which comprises the following steps: acquiring real-time vibration and current signals of the screw pump rotor, constructing a variational mode decomposition objective function with energy constraint, initially dividing the vibration signals into intrinsic mode functions, and screening correlation coefficients to obtain the wear state of the screw pump rotor. A rotor and hull structure vibration subset is obtained, and rotor vibration signals are separated by means of an independent component analysis algorithm. And a hierarchical feature fusion strategy is applied, the preprocessed signals are synchronized, a multivariable time sequence matrix is constructed, a wear feature set is extracted, phase-space reconstruction is carried out, and sudden wear points are accurately identified. Once identified, the probability of sudden wear is calculated, the wear rate is corrected in combination with the normal wear degree, the remaining life is predicted, and the maintenance level is divided. The method aims at solving the problems that an existing screw pump monitoring technology is prone to interference, lagged in response, difficult to adapt to complex working conditions, insufficient in model generalization and the like, and stable operation of a ship power system is guaranteed.

Description

Technical Field

[0001] The present invention relates to the technical field of screw pump monitoring, and more specifically to a vibration current feature fusion monitoring device for the wear state of a screw pump rotor. Background Art

[0002] At present, with the continuous acceleration of the intelligentization process of ship power systems, screw pumps, as core fluid transportation equipment on ships, the reliability of their operation plays a decisive role in navigation safety and operation economy. In actual operation, screw pumps face complex and changing working conditions, such as variable rotational speeds and variable loads during ship navigation, as well as special scenarios such as transporting low-temperature or high-viscosity media. Currently, there are many limitations in the monitoring technology for screw pumps. Most existing technologies only rely on single vibration or current signals for analysis. For example, the method based on vibration intensity threshold judgment often has a high false alarm rate due to the interference of the base vibration during ship operation, and it is difficult to accurately reflect the true wear state of the screw pump rotor. The monitoring of the effective value of the motor current not only has a relatively lagged response to initial wear, but also cannot effectively capture the high-frequency characteristics caused by clearance changes, resulting in the neglect of early potential wear risks. In addition, the diagnostic mechanism with fixed thresholds cannot flexibly adapt to the dynamic changes of ship working conditions, and the preventive maintenance mode based on fixed cycles also exposes obvious drawbacks, easily leading to problems of over-maintenance or under-maintenance, which not only causes waste of resources, but also may endanger navigation safety due to the failure to detect potential faults in time. In the scenario of transporting low-temperature or high-viscosity media, the performance of these traditional monitoring technologies is even more severely degraded. In the application of machine learning to screw pump monitoring, traditional models require a large amount of labeled data for training, but the wear data of ship screw pumps has significant strong personalized characteristics, which makes the generalization ability of traditional models seriously insufficient when facing new ship types or sudden working conditions, and it is difficult to accurately monitor and predict the wear state of screw pump rotors.

[0003] In summary, the existing screw pump monitoring technology can no longer meet the development needs of the intelligentization and high-efficiency of ship power systems. Therefore, in order to overcome these limitations, the present invention proposes a vibration current feature fusion monitoring device for the wear state of a screw pump rotor, aiming to achieve accurate and real-time monitoring of the wear state of the screw pump rotor and provide strong guarantee for the stable operation of the ship power system. Summary of the Invention

[0004] Aiming at the deficiencies of the existing technology, the purpose of the present invention is to provide a vibration current feature fusion monitoring device for the wear state of a screw pump rotor. By constructing a variational mode decomposition objective function with energy constraints, a hierarchical feature fusion strategy, and a sudden wear probability prediction based on Bayesian network and Markov chain Monte Carlo algorithm and a series of unique methods, different from the simple vibration monitoring or single feature analysis in the existing technology, it realizes the accurate separation of the rotor vibration signal from the vibration and current signals, accurately identifies the sudden wear point and the starting point, accurately predicts the sudden wear probability and the remaining life, and scientifically divides the maintenance level based on this, effectively solving the technical problems of real-time and accurate monitoring of the wear state of the screw pump rotor and the formulation of maintenance decisions.

[0005] To achieve the above purpose, the present invention provides the following technical solutions: A vibration current feature fusion monitoring device for the wear state of a screw pump rotor, comprising: Obtain the real-time data of the screw pump rotor, including vibration signals and current signals. By constructing a variational mode decomposition objective function with energy constraints, the vibration signal is initially separated into intrinsic mode functions. Based on the correlation coefficient, the intrinsic mode functions are screened. After obtaining the rotor vibration subset and the hull structure vibration subset, the rotor vibration signal is further separated by the independent component analysis algorithm; Configure a hierarchical feature fusion strategy. Through the hierarchical feature fusion strategy, the preprocessed rotor vibration signal and current signal are synchronized to construct a multivariate time series matrix; the wear characteristics are extracted from the multivariate time series matrix to construct a wear characteristic set. By performing phase space reconstruction on the wear characteristic set, the sudden wear point is identified; When a sudden wear point is identified, calculate the sudden wear probability of the screw pump rotor at the sudden wear point through a Bayesian network and a Markov chain; according to the sudden wear probability, combined with the normal wear degree of the screw pump rotor, correct the wear rate of the screw pump rotor to predict the remaining life of the screw pump rotor and divide the maintenance level.

[0006] Specifically, the hierarchical feature fusion strategy includes a bottom layer unit, a middle layer unit, and a top layer unit: The bottom layer unit synchronizes the rotor vibration signal and the current signal based on the motor speed pulse, eliminates the time deviation through an interpolation algorithm, and constructs a multivariate time series matrix containing the rotor vibration signal and the current signal; The middle layer unit is used to extract wear characteristics from the multivariate time series matrix to construct a wear characteristic set, and perform phase space reconstruction on the time series of each wear characteristic in the wear characteristic set to capture the non-linear changes of the wear characteristics, obtain the fusion correlation dimension to identify the sudden wear point, and locate the starting point of the sudden wear; The top-level unit is used to construct a Bayesian network and a state transition probability matrix through the historical wear characteristics set of the screw pump rotor when a sudden wear point is identified, and use the state obtained by discretely dividing the wear characteristics set from the starting point of sudden wear to the sudden wear point as the initial state of the Markov chain. Set the proposal distribution, generate the next candidate state of the Markov chain through the proposal distribution, and calculate the acceptance probability to obtain the sudden wear probability of the screw pump rotor at the sudden wear point.

[0007] Specifically, the specific steps for separating the rotor vibration signal from the vibration signal include: Set the filter passband according to the frequency ranges of the rotor and hull structure vibrations, and use a band-pass filter to filter and denoise the vibration signal. Set the number of decomposition modes K. Based on the variational mode decomposition objective function, introduce an energy entropy constraint term to construct a variational mode decomposition objective function with energy constraint. Introduce the Lagrange multiplier to convert the variational mode decomposition objective function with energy constraint into an unconstrained variational problem, and use the alternating direction multiplier method to solve it to obtain K intrinsic mode functions, and each intrinsic mode function represents a vibration signal with different frequency components.

[0008] Specifically, the specific steps for separating the rotor vibration signal from the vibration signal also include: Obtain the rotor vibration reference signal and the hull structure vibration reference signal from the signal database, and calculate the correlation coefficients between the intrinsic mode functions and the rotor vibration reference signal and the hull structure vibration reference signal respectively. According to the magnitudes of the correlation coefficients, perform mode screening to screen out the rotor vibration subset and the hull structure vibration subset from the K intrinsic mode functions. Combine the screened rotor vibration subset and the hull structure vibration subset into a mode matrix, and each column of the mode matrix represents an intrinsic mode function signal. After performing mean centering processing and whitening processing on the mode matrix, use the independent component analysis algorithm to further separate the mode matrix into the rotor vibration signal and the hull structure vibration signal.

[0009] Specifically, the specific steps for identifying the sudden wear point and locating the starting point of sudden wear include: Set the delay range. Within the delay range, use the mutual information method to calculate the mutual information values of each wear characteristic in the wear characteristics set at different delays, select the target delay, and set the embedding dimension. For the time series of each wear characteristic in the wear characteristics set, perform phase space reconstruction. For the phase space of each wear feature, set its neighborhood radius according to the statistical value of the phase space vector distance. For each pair of phase space vectors in the phase space, calculate the distance between the phase space vectors to calculate the correlation integral of the wear feature; Perform a logarithmic transformation on the correlation integral and conduct a linear fit to obtain the slope of the fitted line as the correlation dimension, and normalize the weights of the wear feature importance scores of the wear feature set to assign weights to each wear feature to obtain the fused correlation dimension.

[0010] Specifically, the specific steps for identifying sudden wear points and locating the specific starting point of sudden wear also include: Configure a correlation dimension threshold based on the historical data of the screw pump rotor. If the fused correlation dimension is greater than the correlation dimension threshold, it is determined that there is a sudden wear point and the sudden wear point is marked; Set a backtracking period to form a backtracking window. Within the backtracking window, start backtracking search from the sudden wear point, calculate the relative change rate of the fused correlation dimension at each time point to calculate the path cost at each time point within the backtracking window, and obtain the path cost curve within the backtracking window; Calculate the slope of the path cost curve at each time point within the backtracking window, screen the slope mutation points within the backtracking window, sort them in chronological order, and use the time point where the slope mutation point far from the sudden wear point is located as the starting point of sudden wear.

[0011] Specifically, the specific steps for predicting the sudden wear probability of the screw pump rotor include: Obtain the historical wear feature set of the screw pump rotor and mark the actual wear state corresponding to each data sample; and perform discretization processing on the historical wear feature set. For each wear feature, divide the state interval separately; Construct a Bayesian network, determine the causal relationship between each node in the Bayesian network, and use the historical wear feature set of the screw pump rotor to obtain the conditional probability distribution of each node under different state combinations of its parent nodes; Based on the discretization processing result of the historical wear feature set, determine the number of state transitions, and based on the Bayesian network, calculate the probability of transitioning from one state to another state, thereby constructing a state transition probability matrix; Obtain the wear feature set from the starting point of sudden wear to the sudden wear point and perform discretization. According to the state divided by the discretization of the wear feature set from the starting point of sudden wear to the sudden wear point, it is used as the initial state of the Markov chain.

[0012] Specifically, the specific steps for predicting the sudden wear probability of the screw pump rotor also include: According to the state divided by the discretization of the wear feature set at each time point from the starting point of sudden wear to the sudden wear point, set a proposal distribution for generating the next candidate state of the Markov chain; After generating the next candidate state, according to the Bayesian network and the conditional probability distributions of each node, calculate the joint probability of the current state and the candidate state in the state space, and based on the proposal distribution, calculate the probability of transitioning from the candidate state to the current state and the probability of transitioning from the current state to the candidate state respectively to calculate the acceptance probability; Generate a random number that follows a uniform distribution. If the random number is less than or equal to the acceptance probability, accept the candidate state and use it as the next state of the Markov chain; otherwise, reject the candidate state and maintain the current state; Perform iterative sampling until the Markov chain converges. Count the number of samples in the sudden wear state and the total number of sampling times, and calculate the ratio of the number of samples in the sudden wear state to the total number of sampling times as the sudden wear probability of the screw pump rotor at the sudden wear point.

[0013] Specifically, the specific steps for constructing the multivariate time series matrix include: Obtain the rotational speed pulse signal of the motor shaft as the physical synchronization reference for the rotor vibration signal and the current signal, generate a timestamp mark, and establish a synchronous clock reference coordinate system; Perform timestamp marking on the rotor vibration signal and the current signal, and map the timestamps of the rotor vibration signal and the current signal into the synchronous clock reference coordinate system; Judge whether to trigger interpolation correction according to the cumulative timestamp deviation between the rotor vibration signal and the current signal; If interpolation correction is triggered, then: calculate the curvature values of each sampling point of the rotor vibration signal and the current signal, screen the local curvature extreme points as interpolation candidate nodes, and select an interpolation node sequence from the interpolation candidate nodes; Based on the interpolation node sequence, obtain the corresponding timestamps of the rotor vibration signal and the current signal respectively, and calculate the time offset between the interpolation nodes at the same position of the rotor vibration signal and the current signal; Construct a time deviation matrix with the calculated time offset to obtain the non - linear mapping relationship between the rotor vibration signal and the current signal; Taking the current signal time series as the reference, obtain the interpolation time points of the rotor vibration signal through the non - linear mapping relationship, and use the interpolation algorithm to generate the aligned rotor vibration signal; Taking the rotor vibration signal time series as the reference, obtain the interpolation time points of the current signal through the non - linear mapping relationship, and use the interpolation algorithm to generate the aligned current signal; Arrange the aligned rotor vibration signal and the current signal in chronological order to generate a spatio - temporally aligned multivariate time series matrix.

[0014] Specifically, the specific steps for dividing the maintenance level include: When a sudden wear point is identified, obtain the sudden wear probability of the screw pump rotor at the sudden wear point, and based on the historical wear data of the screw pump rotor during normal operation, obtain the wear degree per unit time; Set a correction factor, and correct the wear degree per unit time according to the sudden wear probability to obtain the corrected wear rate; Determine the wear limit value when the screw pump rotor reaches scrapping or requires major maintenance, obtain the cumulative usage duration of the screw pump rotor, the number of sudden wear points, and the sudden wear probability of the screw pump rotor at the sudden wear point, so as to obtain the current wear amount of the screw pump rotor, and predict the remaining life using the corrected wear rate; Set maintenance thresholds, including an upper maintenance threshold and a lower maintenance threshold, and divide the screw pump rotor into different maintenance levels according to the predicted remaining life.

[0015] Advantages of the present invention: By fusing the vibration and current dual signals, constructing a variational mode decomposition objective function with energy constraints, and combining the correlation coefficient screening and independent component analysis algorithms, the rotor vibration signal is accurately separated from the complex vibration signal. This process effectively shields the interference of the hull structure vibration, greatly improves the accuracy of signal analysis, and significantly reduces the false alarm rate. In the hierarchical feature fusion strategy, the bottom layer units are based on the motor speed pulse, and the interpolation algorithm is used to construct a multivariate time series matrix to ensure signal synchronization; the middle layer units extract features and identify sudden wear points through phase space reconstruction; the top layer units calculate the sudden wear probability by constructing a Bayesian network and a Markov chain. The units cooperate closely to achieve a comprehensive and in-depth analysis of the wear state, timely and accurately capture the sudden wear points and starting points, and make up for the defect of the traditional technology's lagging response.

[0016] In the entire monitoring process, from signal processing, feature extraction to probability prediction, a complete and efficient technical chain is formed. Finally, it realizes the accurate prediction of the sudden wear probability and the remaining life, reasonably divides the maintenance levels, avoids waste of resources caused by excessive maintenance, and potential safety hazards caused by insufficient maintenance, and effectively guarantees the stable and efficient operation of the ship power system under complex working conditions. Description of the Drawings

[0017] Figure 1 It is a schematic diagram of the logical structure of the vibration-current feature fusion monitoring device for the wear state of the screw pump rotor of the present invention; Figure 2 It is a flowchart of the specific steps for separating the rotor vibration signal and the hull structure vibration signal of the present invention; Figure 3 It is a schematic diagram of the hierarchical feature fusion strategy of the present invention; Figure 4Flow chart of the specific steps for constructing the multi-variable time series matrix of the present invention; Figure 5 Flow chart of the specific steps for identifying sudden wear points and locating the starting points of sudden wear in the present invention;

[0018] Figure 6 Flow chart of the specific steps for generating maintenance decisions in the present invention. Detailed implementation manners

[0019] Please refer to Figure 1 , in this embodiment, a vibration-current feature fusion monitoring device for the wear state of a screw pump rotor is introduced, including a signal acquisition module, a feature processing module, a maintenance decision module, and a user interaction module; The signal acquisition module is used to perform real-time data acquisition through a sensor array, including vibration signals and current signals. Specifically, three-axis accelerometers are arranged axially along the stator housing of the screw pump to collect vibration signals, and the variational mode decomposition and independent component analysis algorithms are used to separate the rotor vibration signals and the hull structure vibration signals, and at the same time, the current signal of the screw pump motor is collected; In this embodiment, three-axis accelerometers are evenly arranged axially along the stator housing of the screw pump. To ensure that the sensors are firmly installed and do not affect the normal operation of the pump, a magnetic adsorption installation method is adopted to fix the sensors on the surface of the stator housing. At the same time, the installation positions of each sensor are numbered and marked for convenient subsequent data processing and analysis. The three-axis accelerometers collect the vibration signals of the stator housing of the screw pump in real time and capture high-frequency vibration signals according to the set acquisition frequency. The collected vibration signals are a mixed signal of the screw pump rotor vibration signals and the hull structure vibration signals. A Rogowski coil is wound around the input phase line of the screw pump motor and fixed with a special fixing clip to ensure that the coil is closely attached to the phase line to collect the current signal.

[0020] Please refer to Figure 2 , preferably, the specific steps for separating the rotor vibration signals and the hull structure vibration signals include: A band-pass filter is used to set the filter passband according to the frequency ranges of the rotor and hull structure vibrations, and the vibration signals are filtered and denoised to remove the high-frequency noise and low-frequency interference of the vibration signals; by analyzing the vibration characteristics of the rotor and hull structure under normal operating conditions, the intervals of their respective vibration frequencies are determined. Based on this interval, the passband range of the band-pass filter is set so that the vibration signals within this range can pass smoothly, while the high-frequency noise and low-frequency interference are effectively filtered out.

[0021] According to the experimental data, the number of decomposition modes K is set. On the basis of the traditional variational mode decomposition objective function, an energy entropy constraint term is introduced to construct a variational mode decomposition objective function with energy constraint, that is: ;

[0022] wherein, represents minimizing the sum of the estimated bandwidths of each intrinsic mode function, wherein, is the unit impulse function, is the imaginary unit, is the time variable, is the partial derivative with respect to the time variable , is the convolution operator, is the complex demodulation factor, is the central frequency of the k-th mode, used to characterize the characteristic frequency of the mode, is the k-th intrinsic mode function, representing the vibration signal of a certain frequency component, is the penalty term, which is used to balance the signal fidelity and the mode bandwidth, is the penalty factor, and its value range is [2000, 5000], which is adjusted according to the signal complexity, is the original vibration signal, is the energy entropy of the k-th mode, used to measure the uniformity of the energy distribution of the mode, is the constraint weight, used to adjust the influence degree of the energy entropy constraint term, and its value range is [0.1, 0.5].

[0023] Introduce the Lagrange multiplier to transform the variational mode decomposition objective function with energy constraint into an unconstrained variational problem, and use the alternating direction multiplier method to solve it to obtain K intrinsic mode functions. Each intrinsic mode function represents the vibration signal of different frequency components; this decomposition method introducing energy entropy constraint can better consider the energy distribution characteristics of the signal and improve the accuracy and rationality of the decomposition.

[0024] Obtain the rotor vibration reference signal and the hull structure vibration reference signal from the signal database. The reference signals are obtained by separately collecting the rotor's individual vibration and the hull's individual vibration in an ideal experimental environment; calculate the correlation coefficients between the intrinsic mode functions and the rotor vibration reference signal and the hull structure vibration reference signal respectively; According to the magnitudes of the correlation coefficients, perform mode screening, and select the rotor vibration subset and the hull structure vibration subset from the K intrinsic mode functions; that is, according to the magnitudes of the correlation coefficients, group the intrinsic mode functions with higher correlations into the corresponding vibration types. For example, if the correlation coefficient of a certain intrinsic mode function with the rotor vibration reference signal is greater than that with the hull structure vibration reference signal, and the correlation coefficient is greater than the set correlation threshold, then group this intrinsic mode function into the intrinsic mode function related to rotor vibration; otherwise, group it into the intrinsic mode function related to hull structure vibration. Finally, select the rotor vibration subset and the hull structure vibration subset related to rotor vibration and hull structure vibration.

[0025] The filtered rotor vibration subset and the hull structure vibration subset are combined into a modal matrix. Each column of the modal matrix represents an eigenmode function signal. The filtered signals are integrated to form an input data structure suitable for processing by the independent component analysis algorithm. This matrix representation can effectively organize signal information and facilitate further separation operations on the signals by the independent component analysis algorithm.

[0026] After performing mean centering and whitening processing on the modal matrix, the independent component analysis algorithm is used to further separate the modal matrix. Based on the assumption of signal independence, the separation matrix is continuously adjusted through iterative calculations. After multiple iterations, the modal matrix is finally separated into independent rotor vibration signals and hull structure vibration signals. This separation method utilizes the statistical independence between signals and can effectively separate different source signals mixed together.

[0027] The feature processing module is used to perform data preprocessing on the rotor vibration signal and the current signal. Specifically, for the rotor vibration signal separated by the signal acquisition module, the adaptive noise cancellation technology is used to effectively remove interference noise. For the acquired current signal, discrete wavelet transform is used for noise reduction processing, and then the Park transform is used to extract the DC component of the current signal to more clearly analyze the characteristics of the current signal. A hierarchical feature fusion strategy is configured to perform reference alignment and wear feature extraction on the preprocessed rotor vibration signal and current signal, and then identify potential wear points and predict the potential wear probability. Please refer to Figure 3 , preferably, the hierarchical feature fusion strategy includes a bottom layer unit, a middle layer unit, and a top layer unit: The bottom layer unit is used to construct a spatio-temporal aligned multivariate time series matrix. The rotor vibration signal and the current signal are synchronized based on the motor speed pulse. The time deviation is eliminated through an interpolation algorithm to construct a multivariate time series matrix containing the rotor vibration signal and the current signal, ensuring data spatio-temporal consistency. Please refer to Figure 4 , specifically, the specific steps for constructing the multivariate time series matrix include: The rotational speed pulse signal of the motor shaft is obtained through an optoelectronic sensor configured on the screw pump rotor motor shaft. One synchronization pulse is generated per revolution, which serves as the physical synchronization reference for the rotor vibration signal and the current signal, and a timestamp mark is generated to establish a synchronous clock reference coordinate system. The timestamp marks of the sampling points of the rotor vibration signal and the current signal are respectively obtained, and the timestamp deviation between the rotor vibration signal and the current signal is calculated in real time. Configure a time deviation threshold, and continuously accumulate the timestamp deviation between the rotor vibration signal and the current signal in real time. If the timestamp deviation is greater than the time deviation threshold, trigger interpolation correction; If interpolation correction is not triggered, arrange the rotor vibration signal and the current signal in chronological order to generate a spatio-temporal aligned multivariate time series matrix: If interpolation correction is triggered, then: Calculate the curvature value of each sampling point of the rotor vibration signal and the current signal, and mark the local curvature extreme points, which usually correspond to the positions where the signal mutates or changes violently, as interpolation candidate nodes; Through the dynamic programming algorithm, select a set of interpolation node sequences from the interpolation candidate nodes so that the curvature change rate between adjacent nodes in the interpolation node sequence is less than the preset curvature threshold, and the number of nodes in the interpolation node sequence is the least; For the interpolation node sequences of the rotor vibration signal and the current signal, obtain the corresponding timestamps respectively, and calculate the time offset between the interpolation nodes at the same position of the rotor vibration signal and the current signal; Construct a time deviation matrix with the calculated time offset. The number of rows of the matrix is the number of nodes of the rotor vibration signal, and the number of columns is the number of nodes of the current signal; Use methods such as polynomial fitting or neural network to construct a non-linear mapping relationship between the vibration signal time and the current signal time according to the time deviation matrix; Based on the current signal time series, obtain the interpolation time points of the rotor vibration signal through the non-linear mapping relationship, and use the interpolation algorithm to generate an aligned rotor vibration signal; Based on the rotor vibration signal time series, obtain the interpolation time points of the current signal through the non-linear mapping relationship, and use the interpolation algorithm to generate an aligned current signal; Arrange the aligned rotor vibration signal and the current signal in chronological order to generate a spatio-temporal aligned multivariate time series matrix.

[0028] The middle layer unit is used to extract wear characteristics from the multivariate time series matrix to construct a wear characteristic set, and perform phase space reconstruction on the time series of each wear characteristic in the wear characteristic set to capture the non-linear changes of the wear characteristics, obtain the fusion correlation dimension to identify sudden wear points, and locate the starting point of sudden wear; In this embodiment, after data cleaning, data outlier processing, and data standardization of the multivariate time series matrix generated by the bottom layer unit, wear characteristics are extracted, and through methods such as correlation analysis and variance analysis, wear characteristics with high correlation with the wear state are selected, and the principal component analysis or linear discriminant method is used to reduce the dimension of the wear characteristics to obtain the final wear characteristic set; Specifically, the wear characteristic extraction includes: Extract the time-domain features of the multivariate time series, including signal kurtosis, which reflects the sharpness of the signal; signal kurtosis, which measures the prominence of the signal peak; root mean square value, which reflects the energy level of the signal; waveform index, which reflects the variation of the signal relative to the average situation. Extract the frequency-domain features of the multivariate time series. Perform frequency-domain transformation on the multivariate time series to obtain the frequency-domain signal. Extract the amplitudes of different frequency components in the frequency-domain signal to reflect the energy distribution of the frequency-domain signal at each frequency, and extract the phase information of the frequency components to analyze the relative position and synchronization of the frequency-domain signal. Calculate the frequency centroid of the frequency-domain signal to reflect the main frequency distribution of the frequency-domain signal.

[0029] Please refer to Figure 5 , preferably, the specific steps for identifying sudden wear points and locating the starting point of sudden wear include: According to the rotation frequency range of the screw pump, set the delay range. Within the delay range, use the mutual information method to calculate the mutual information values of each wear feature in the wear feature set at different delays. Mutual information is used to measure the dependence between two random variables. In the monitoring of the screw pump, for each wear feature in the wear feature set and its delayed wear feature, mutual information reflects the correlation of the wear feature at different delays. When the mutual information value is large, it indicates that the correlation of the wear feature at this delay is strong; when the mutual information value is small, it indicates that the dependence relationship between the wear features is weak, and at this time the signal may contain more new information. According to the size of the mutual information value, select the target delay. ; The selection of the target delay is usually based on the minimum value of the mutual information value. When the mutual information value reaches the minimum, it means that the correlation between the wear feature at this delay and the original wear feature is the weakest, contains more independent information, and is more suitable for phase space reconstruction.

[0030] Set the embedding dimension , the embedding dimension can be determined by the Cao method. By calculating the Cao index under different embedding dimensions, when the index tends to be stable, obtain the minimum embedding dimension as the embedding dimension. . Avoid information loss or redundancy caused by improper dimension selection, and provide a suitable space structure for accurately analyzing the changes of wear features in the follow-up.

[0031] For the time series of each wear feature in the wear feature set, perform phase space reconstruction. For the wear feature , the phase space reconstruction includes: ; where is the th dimensional phase space vector after reconstruction, is the wear feature The th original data point of the time series, is the target delay, is the embedding dimension, The value range of is , and

[0032] is the length of the time series; enabling the changes in wear characteristics to be presented in a more intuitive and easier-to-analyze manner in the phase space, providing an effective data representation form for further analyzing the dynamic behavior of wear characteristics. For each phase space of wear characteristics, according to the statistical values of the phase space vector distances, including the mean and median, set its neighborhood radius ; where is the correlation integral of the wear characteristics when the neighborhood radius is , is the th and th distance between phase space vectors, is the step function. When , , and when , ; Quantifying the correlation degree between vectors in the phase space, thereby reflecting the distribution and mutual relationship of wear characteristics in the phase space.

[0033] Perform a logarithmic transformation on the correlation integral and perform a linear fit to obtain the slope of the fitted line as the correlation dimension, and perform weight normalization on the wear characteristic importance scores of the wear characteristic set to assign weights to each wear characteristic to obtain the fused correlation dimension; The wear characteristic importance scores can be obtained from the eigenvalues of the characteristic covariance matrix of principal component analysis or the ratio of the between-class scatter matrix to the within-class scatter matrix of linear discriminant methods; According to the historical data of the screw pump rotor, configure the correlation dimension threshold. If the fused correlation dimension is greater than the correlation dimension threshold, it is determined that there is a sudden wear point, and the sudden wear point is marked; It can timely detect abnormal wear conditions during the operation of the screw pump, providing important early warning information for subsequent corresponding measures, and helping to avoid equipment failures and downtime losses caused by wear problems. If the fused correlation dimension is not greater than the correlation dimension threshold, no processing is performed.

[0034] Set the backtracking cycle to form a backtracking window. In the backtracking window, perform backtracking search starting from the sudden wear point, calculate the relative change rate of the fusion correlation dimension at each time point, calculate the path cost at each time point in the backtracking window, and obtain the path cost curve in the backtracking window. The calculation formula of the path cost is as follows: ; in, is the time point of the sudden wear point, is the time point within the lookback window The path cost, is a positive integer used to determine the time point in the backtracking window relative to the time point of the sudden wear point position offset. Indicates the time point within the backtracking window from the sudden wear point have By changing the time point of the time interval The value of can be used to calculate the path cost at different time points in the backtracking window. It's time point By calculating the relative change rate of the fused correlation dimension at each time point and calculating the path cost, the cumulative degree of wear feature changes at each time point before the sudden wear point can be quantified. Obtaining the path cost curve within the backtracking window intuitively shows the cumulative trend of the degree of wear feature changes over time, which provides an important basis for further analysis of the starting point of sudden wear.

[0035] Calculating the slope of the path cost curve at each time point in the backtracking window can reflect the rate of change of the path cost over time, screening the slope mutation points in the backtracking window, and sorting them in chronological order, taking the time point where the slope mutation point far away from the sudden wear point is located as the starting point of the sudden wear. Finding the time point when the wear characteristic changes begin to intensify from the changes in the path cost curve provides accurate time positioning for in-depth understanding of the occurrence and development process of sudden wear, helps to more accurately analyze the causes and mechanisms of wear, and provides more targeted suggestions for equipment maintenance and management.

[0036] The top-level unit is used to construct a state transition probability matrix through the Bayesian network when a sudden wear point is identified, and combine the Markov chain Monte Carlo algorithm to predict the sudden wear probability of the screw pump rotor at the sudden wear point; Preferably, the specific steps of predicting the probability of sudden wear of the screw pump rotor include: Obtain the historical wear feature set of the screw pump rotor, including the wear feature set of the screw pump under normal operation and abnormal operation, and mark the actual wear state corresponding to each data sample, that is, whether sudden wear occurs; Discretize the historical wear feature set. For each wear feature, divide the state intervals respectively. For example, divide the kurtosis value of the vibration signal into states such as low kurtosis, medium kurtosis, and high kurtosis; divide the rotational speed into states such as low speed, medium speed, and high speed. This step is to prepare for constructing the conditional probability distribution of the Bayesian network in the follow-up.

[0037] According to the working principle of the screw pump, construct a Bayesian network, determine the causal relationship between each node in the Bayesian network, and construct a directed acyclic graph. For example, the rotational speed of the screw pump will affect the vibration signal characteristics and current signal characteristics, and then affect the wear state. Therefore, there are directed edges from the rotational speed node to the vibration signal characteristic node and the current signal characteristic node, and from the vibration signal characteristic node and the current signal characteristic node to the wear state node.

[0038] Using the historical wear feature set of the screw pump rotor, obtain the conditional probability distribution of each node under different state combinations of its parent nodes through maximum likelihood estimation or Bayesian estimation. For example, for the wear state node, determine the probabilities of being in states such as sudden wear and normal under different state combinations of the known vibration signal characteristics and current signal characteristics.

[0039] According to the discretization result of the historical wear feature set, determine the number of state transitions. Based on the Bayesian network, calculate the probability of transitioning from one state to another state, that is, for each pair of states (p, q), calculate the probability of transitioning to state q at the next moment when currently in state p, so as to construct a state transition probability matrix; Obtain the wear feature set from the starting point of sudden wear to the sudden wear point, and perform discretization. According to the states divided by the discretization of the wear feature set from the starting point of sudden wear to the sudden wear point, use it as the initial state of the Markov chain; According to the states divided by the discretization of the wear feature set at each time point from the starting point of sudden wear to the sudden wear point, set a proposal distribution for generating the next candidate state of the Markov chain. The proposal distribution can be designed as a certain random perturbation mode based on the current state. For example, for the state of each wear feature, with a certain probability, make a transition between its adjacent states, or make a small random adjustment to the state combination of multiple wear features.

[0040] After generating the next candidate state, calculate the acceptance probability , that is: ; where and are the probabilities of the current state and the next candidate state under the state transition probability matrix determined by the Bayesian network, respectively, and are accurately calculated through the joint probability distribution of the Bayesian network; and is the probability of the proposed distribution, representing the transition from the candidate state to the current state , and the probability of transitioning from the current state to the candidate state .

[0041] Generate a random number that follows a uniform distribution. If the random number is less than or equal to the acceptance probability, accept the candidate state , and use it as the next state of the Markov chain; otherwise, keep the current state; Repeat the above steps of generating candidate states, calculating acceptance probabilities, and accepting or rejecting candidate states for iterative sampling until the Markov chain converges to a stationary distribution; After the Markov chain converges, count the number of samples in the sudden wear state and the total number of sampling times, calculate the ratio of the number of samples in the sudden wear state to the total number of sampling times, and calculate the sudden wear probability of the screw pump rotor at the sudden wear point.

[0042] The maintenance decision-making module is used to correct the wear rate of the screw pump rotor according to the predicted sudden wear probability, combined with the normal wear degree of the screw pump rotor during normal use, and predict the remaining life of the screw pump rotor to divide the maintenance level; Please refer to Figure 6 , preferably, the specific steps for generating a maintenance decision include: When a sudden wear point is identified, obtain the sudden wear probability of the screw pump rotor at the sudden wear point; Obtain the historical wear data of the screw pump rotor during normal operation, and obtain the wear degree per unit time under normal use , which can be obtained by measuring the wear amount at different time points and then calculating the ratio of the difference to the time interval; Set a correction factor , correct the wear degree per unit time according to the sudden wear probability. The correction factor can be determined by establishing a function related to the sudden wear probability to adjust the influence degree of the sudden wear probability on the wear rate, and can also be determined by analyzing the correlation between sudden wear events and wear rate changes in historical data.

[0043] Obtain the corrected wear rate according to the correction factor , when the sudden wear probability is high, the wear rate will increase accordingly to more accurately reflect the actual wear situation faced by the equipment.

[0044] According to the design specifications and safe operation standards of the screw pump rotor, determine the wear limit value when the rotor reaches scrapping or requires major repairs; Obtain the cumulative usage duration of the screw pump rotor, the number of sudden wear points, and the sudden wear probability of the screw pump rotor at the sudden wear points to obtain the current wear amount of the screw pump rotor, and use the corrected wear rate to predict the remaining life, that is: ; Wherein, is the predicted remaining life, is the wear limit value, is the current wear amount of the screw pump rotor, is the corrected wear rate; Set maintenance thresholds, including an upper maintenance threshold and a lower maintenance threshold. According to the predicted remaining life, divide the screw pump rotor into different maintenance levels; for example, when the predicted remaining life is greater than the upper maintenance threshold, it is determined as a low maintenance level, and routine inspection and maintenance measures can be taken, such as regularly checking the equipment operation parameters and cleaning the equipment. When the predicted remaining life is less than or equal to the upper maintenance threshold and greater than the lower maintenance threshold, it is determined as a medium maintenance level. In addition to routine inspection, the detection frequency of key components needs to be increased, spare parts that may need to be replaced are prepared, and training for maintenance personnel is considered to be arranged in advance. When the maintenance level is less than or equal to the lower maintenance threshold, it is determined as a high maintenance level, and a full shutdown inspection is immediately arranged, and a detailed maintenance plan is formulated, including replacing severely worn components and comprehensively overhauling and debugging the equipment.

[0045] During the operation of the screw pump, regularly measure the actual wear amount, track the wear situation in real time, regularly recalculate the sudden wear probability, corrected wear rate, and predicted remaining life, and update the maintenance decision accordingly. If abnormal conditions are found during the monitoring process, the maintenance decision should be immediately re-evaluated and adjusted to ensure that the equipment is always in a safe and reliable operating state.

[0046] The user interaction module is used to display the remaining life trend curve and maintenance level of the screw pump rotor in an intuitive chart form. Use color coding to visually reflect the state of the screw pump rotor. When the state of the screw pump rotor is in the red area, it means that the equipment has a serious wear risk and immediate maintenance is required; when it is in the yellow area, it means that the equipment has a certain wear risk and needs to be closely monitored; when it is in the green area, it means that the equipment is operating normally.

[0047] Working principle and its effects: Use sensors to collect the real-time vibration and current signals of the screw pump rotor. For the vibration signal, first, according to the vibration frequency ranges of the rotor and the hull structure, a band-pass filter is used for filtering and denoising. Then, set the number of decomposition modes, introduce an energy entropy constraint term into the traditional variational mode decomposition objective function to construct a new objective function, transform it into an unconstrained variational problem by the Lagrange multiplier method, and solve it with the alternating direction multiplier method to obtain K intrinsic mode functions. Next, calculate the correlation coefficients between these functions and the vibration reference signals of the rotor and the hull structure obtained from the signal database, screen out the rotor vibration subset and the hull structure vibration subset, combine them into a modal matrix, and after mean centering and whitening processing, further separate the pure rotor vibration signal by the independent component analysis algorithm.

[0048] Configure a hierarchical feature fusion strategy. The bottom layer units use the motor speed pulse as a reference to timestamp the rotor vibration signal and the current signal, map them to the synchronous clock reference coordinate system, determine whether to trigger interpolation correction according to the cumulative timestamp deviation, screen the interpolation candidate nodes by calculating the curvature value, construct a time deviation matrix to obtain the non-linear mapping relationship, and generate a spatio-temporally aligned multi-variable time series matrix. The middle layer units extract the wear features from this matrix, construct a wear feature set, perform phase space reconstruction on each wear feature time series, calculate the correlation integral by setting the neighborhood radius, obtain the correlation dimension through logarithmic transformation and linear fitting, and combine the wear feature importance score weight normalization to obtain the fused correlation dimension, and accordingly identify the sudden wear points and locate the starting points.

[0049] After the top layer units identify the sudden wear points, obtain the historical wear feature set of the screw pump rotor, construct a Bayesian network, determine the causal relationships of each node to obtain the conditional probability distribution, and construct a state transition probability matrix. Take the discretized state of the sudden wear starting point as the initial state of the Markov chain, set the proposal distribution to generate candidate states, calculate the joint probability and acceptance probability according to the Bayesian network, and after iterative sampling until the Markov chain converges, calculate the sudden wear probability. Combine the normal use wear degree to correct the wear rate, calculate the current wear amount according to the wear limit value, cumulative use duration, etc., predict the remaining life, and set the maintenance threshold to divide the maintenance levels.

[0050] The present invention effectively eliminates the interference of the hull structure vibration, accurately obtains the rotor vibration signal, lays a reliable data foundation for subsequent in-depth analysis, and greatly reduces the monitoring false alarm rate. The adopted hierarchical feature fusion strategy can comprehensively capture the wear features, accurately identify the sudden wear points and their starting points, thoroughly solve the problem of lagging response in traditional technologies, and give early warnings for potential faults. By accurately predicting the sudden wear probability and the remaining life, reasonably dividing the maintenance levels, avoiding over-maintenance or under-maintenance situations, effectively ensuring the stable operation of the screw pump, effectively reducing the ship operation cost, and significantly improving the navigation safety.

[0051] The above are only the preferred embodiments of the present invention, and the protection scope of the present invention is not limited to the above embodiments. All technical solutions falling within the concept of the present invention belong to the protection scope of the present invention. It should be noted that for those of ordinary skill in the art, several improvements and refinements made without departing from the principle of the present invention should also be regarded as within the protection scope of the present invention.

Claims

1. Vibration current feature fusion monitoring device for the wear state of a screw pump rotor, characterized in that Including: Obtain the real-time data of the screw pump rotor, including vibration signals and current signals. By constructing a variational mode decomposition objective function with energy constraints, preliminarily separate the vibration signals into intrinsic mode functions. Based on the correlation coefficient, screen the intrinsic mode functions to obtain the rotor vibration subset and the hull structure vibration subset, and then separate the rotor vibration signals through the independent component analysis algorithm; Configure a hierarchical feature fusion strategy, and through the hierarchical feature fusion strategy, perform data synchronization processing on the preprocessed rotor vibration signals and current signals to construct a multivariate time series matrix; extract wear features from the multivariate time series matrix to construct a wear feature set, and through phase space reconstruction of the wear feature set, identify sudden wear points; When it is identified that there are sudden wear points, calculate the sudden wear probability of the screw pump rotor at the sudden wear points through a Bayesian network and a Markov chain; according to the sudden wear probability, combined with the normal wear degree of the screw pump rotor, correct the wear rate of the screw pump rotor to predict the remaining life of the screw pump rotor and divide the maintenance level.

2. The vibration current feature fusion monitoring device for the wear state of a screw pump rotor according to claim 1, characterized in that The hierarchical feature fusion strategy includes a bottom layer unit, a middle layer unit, and a top layer unit: The bottom layer unit synchronizes the rotor vibration signals and current signals based on the motor speed pulse, eliminates the time deviation through an interpolation algorithm, and constructs a multivariate time series matrix containing the rotor vibration signals and current signals; The middle layer unit is used to extract wear features from the multivariate time series matrix to construct a wear feature set, and perform phase space reconstruction on the time series of each wear feature in the wear feature set to capture the non-linear changes of the wear features, obtain the fused correlation dimension to identify sudden wear points, and locate the starting point of sudden wear; The top layer unit is used to, when it is identified that there are sudden wear points, construct a Bayesian network and a state transition probability matrix through the historical wear feature set of the screw pump rotor, and use the state discretely divided from the wear feature set from the starting point of sudden wear to the sudden wear point as the initial state of the Markov chain, set a proposal distribution, generate the next candidate state of the Markov chain through the proposal distribution, and calculate the acceptance probability to obtain the sudden wear probability of the screw pump rotor at the sudden wear points.

3. The vibration current feature fusion monitoring device for the wear state of a screw pump rotor according to claim 1, characterized in that The specific steps for separating the rotor vibration signals from the vibration signals include: Set the filter passband, and use a band-pass filter to filter and denoise the vibration signals; Set the number of decomposition modes K, and on the basis of the variational mode decomposition objective function, introduce an energy entropy constraint term to construct a variational mode decomposition objective function with energy constraints; Introduce a Lagrange multiplier to convert the variational mode decomposition objective function with energy constraints into an unconstrained variational problem, and use the alternating direction multiplier method for solution to obtain K intrinsic mode functions, and each intrinsic mode function represents a vibration signal with different frequency components.

4. The vibration current feature fusion monitoring device for the wear state of a screw pump rotor according to claim 3, characterized in that The specific steps for separating the rotor vibration signals from the vibration signals also include: Obtain the rotor vibration reference signal and the hull structure vibration reference signal from the signal database, and calculate the correlation coefficients between the intrinsic mode functions and the rotor vibration reference signal and the hull structure vibration reference signal respectively; Perform modal screening according to the correlation coefficients, and select the rotor vibration subset and the hull structure vibration subset from the K intrinsic mode functions; Combine the selected rotor vibration subset and hull structure vibration subset into a modal matrix, where each column of the modal matrix represents an intrinsic mode function signal; After performing mean centering processing and whitening processing on the modal matrix, use the independent component analysis algorithm to separate the modal matrix into the rotor vibration signal and the hull structure vibration signal.

5. The vibration current feature fusion monitoring device for the wear state of a screw pump rotor according to claim 2, characterized in that The specific steps for identifying the sudden wear point and locating the starting point of sudden wear include: Set the delay range. Within the delay range, use the mutual information method to calculate the mutual information values of each wear feature in the wear feature set at different delays, select the target delay, and set the embedding dimension; Perform phase space reconstruction on the time series of each wear feature in the wear feature set; For the phase space of each wear feature, set its neighborhood radius according to the statistical value of the phase space vector distance. For each pair of phase space vectors in the phase space, calculate the distance between the phase space vectors to calculate the correlation integral of the wear feature; Perform logarithmic transformation on the correlation integral and perform linear fitting to obtain the slope of the fitting line as the correlation dimension, and perform weight normalization on the importance scores of the wear features in the wear feature set to assign weights to each wear feature to obtain the fused correlation dimension.

6. The vibration current feature fusion monitoring device for the wear state of a screw pump rotor according to claim 5, characterized in that The specific steps for identifying the sudden wear point and locating the starting point of sudden wear also include: Configure the correlation dimension threshold according to the historical data of the screw pump rotor. If the fused correlation dimension is greater than the correlation dimension threshold, it is determined that there is a sudden wear point and the sudden wear point is marked; Set the backtracking period to form a backtracking window. Within the backtracking window, perform backtracking search starting from the sudden wear point, calculate the relative change rate of the fused correlation dimension at each time point, calculate the path cost at each time point within the backtracking window, and obtain the path cost curve within the backtracking window; Calculate the slope of the path cost curve at each time point within the backtracking window, screen the slope mutation points within the backtracking window, sort them in chronological order, and take the time point where the slope mutation point far from the sudden wear point is located as the starting point of sudden wear.

7. The vibration current feature fusion monitoring device for the wear state of a screw pump rotor according to claim 2, characterized in that The specific steps for predicting the sudden wear probability of the screw pump rotor include: Obtain the historical wear feature set of the screw pump rotor, mark the actual wear state corresponding to each data sample; and perform discretization processing on the historical wear feature set. For each wear feature, divide the state interval respectively; Construct a Bayesian network, determine the causal relationship between the nodes in the Bayesian network, and use the historical wear feature set of the screw pump rotor to obtain the conditional probability distribution of each node under different state combinations of its parent nodes; According to the discretization processing result of the historical wear feature set, determine the number of state transitions, and based on the Bayesian network, calculate the probability of transitioning from one state to another state, thereby constructing a state transition probability matrix; Obtain the wear feature set from the sudden wear starting point to the sudden wear point, and discretize it. The state divided according to the discretization of the wear feature set from the sudden wear starting point to the sudden wear point is used as the initial state of the Markov chain.

8. The vibration current feature fusion monitoring device for the wear state of the screw pump rotor according to claim 7, characterized in that, The specific steps for predicting the sudden wear probability of the screw pump rotor further include: According to the state divided by the discretization of the wear feature set at each time point from the sudden wear starting point to the sudden wear point, set a proposal distribution for generating the next candidate state of the Markov chain; After generating the next candidate state, according to the Bayesian network and the conditional probability distribution of each node, calculate the joint probability of the current state and the candidate state in the state space, and based on the proposal distribution, calculate the probability of transferring from the candidate state to the current state and the probability of transferring from the current state to the candidate state respectively to calculate the acceptance probability; Generate a random number that follows a uniform distribution. If the random number is less than or equal to the acceptance probability, accept the candidate state and use it as the next state of the Markov chain; otherwise, reject the candidate state and keep the current state; Perform iterative sampling until the Markov chain converges. Count the number of samples in the sudden wear state and the total number of sampling times, and calculate the ratio of the number of samples in the sudden wear state to the total number of sampling times as the sudden wear probability of the screw pump rotor at the sudden wear point.

9. The vibration current feature fusion monitoring device for the wear state of the screw pump rotor according to claim 2, characterized in that, The specific steps for constructing a multivariate time series matrix include: Obtain the rotational speed pulse signal of the motor shaft as the physical synchronization reference for the rotor vibration signal and the current signal, generate a timestamp mark, and establish a synchronous clock reference coordinate system; Perform timestamp marking on the rotor vibration signal and the current signal, and map the timestamps of the rotor vibration signal and the current signal into the synchronous clock reference coordinate system; Judge whether to trigger interpolation correction according to the cumulative timestamp deviation between the rotor vibration signal and the current signal; If interpolation correction is triggered, then: calculate the curvature value of each sampling point of the rotor vibration signal and the current signal, screen the local curvature extreme points as interpolation candidate nodes, and select an interpolation node sequence from the interpolation candidate nodes; Based on the interpolation node sequence, obtain the corresponding timestamps of the rotor vibration signal and the current signal respectively, and calculate the time offset between the interpolation nodes at the same position of the rotor vibration signal and the current signal; Construct a time deviation matrix with the calculated time offset to obtain the non-linear mapping relationship between the rotor vibration signal and the current signal; Taking the current signal time series as the reference, obtain the interpolation time points of the rotor vibration signal through the non-linear mapping relationship, and use the interpolation algorithm to generate the aligned rotor vibration signal; Taking the rotor vibration signal time series as the reference, obtain the interpolation time points of the current signal through the non-linear mapping relationship, and use the interpolation algorithm to generate the aligned current signal; Arrange the aligned rotor vibration signal and current signal in chronological order to generate a spatio-temporally aligned multivariate time series matrix.

10. The vibration current feature fusion monitoring device for the wear state of the screw pump rotor according to claim 1, characterized in that, The specific steps for dividing the maintenance level include: When the sudden wear point is identified, obtain the sudden wear probability of the screw pump rotor at the sudden wear point, and obtain the wear degree per unit time according to the historical wear data of the screw pump rotor during normal operation; Set a correction factor to correct the wear degree per unit time according to the sudden wear probability, so as to obtain the corrected wear rate; Determine the wear limit value when the screw pump rotor reaches the end - of - life or requires major maintenance, obtain the cumulative service duration of the screw pump rotor, the number of sudden wear points, and the sudden wear probability of the screw pump rotor at the sudden wear points, so as to obtain the current wear amount of the screw pump rotor, and predict the remaining life using the corrected wear rate; Set maintenance thresholds, including an upper maintenance threshold and a lower maintenance threshold, and divide the screw pump rotors into different maintenance levels according to the predicted remaining life.

Images