Marine cable insulation aging state evaluation method based on sea condition influence

Abstract

The invention relates to the technical field of cable testing, in particular to a marine cable insulation aging state evaluation method based on sea condition influence, and the method comprises the steps: obtaining a dielectric loss factor frequency spectrum through a broadband dielectric spectrum test, and extracting a body aging characteristic quantity to distinguish environment reversible interference and irreversible insulation aging; the mechanical damage degree and the damage development rate are obtained by applying mechanical pulse excitation and analyzing stress wave propagation characteristics; establishing a leakage current-temperature relation through a non-destructive voltage withstand test, calculating an insulation safety margin and identifying a dominant aging mode; and further fusing multi-source degradation data to construct a probability evolution model, predicting the future change process of each degradation index, and obtaining the probability distribution and confidence interval of the residual life of the cable, thereby realizing the comprehensive evaluation and life prediction of the insulation aging state of the marine cable.

Description

Technical Field

[0001] This invention relates to the field of cable testing technology, specifically to a method for assessing the insulation aging status of marine cables based on the influence of sea conditions. Background Technology

[0002] Existing methods for assessing the insulation condition of marine cables are primarily based on insulation resistance testing or dielectric loss factor measurement. Insulation resistance testing measures leakage current by applying a high DC voltage, reflecting the overall electrical performance of the insulation layer. Dielectric loss factor testing measures the dielectric loss of the insulation material at power frequency or a specific frequency using an AC bridge or spectrum analyzer, characterizing the polarization loss properties of the insulation layer. These methods are well-established in land-based cable assessment, but face significant limitations in marine environments.

[0003] The unique nature of marine environments lies in the coupling effect of environmental disturbances and intrinsic aging factors. Salt spray deposits on cable surfaces to form a conductive film, and high humidity causes the insulation layer to absorb moisture, both of which increase surface leakage current and low-frequency dielectric loss, resulting in a decrease in insulation resistance. This performance degradation caused by environmental factors can be partially recovered after cleaning or drying, and is considered a reversible change. However, traditional testing methods cannot distinguish this reversible change from irreversible aging processes such as molecular chain breakage and decreased cross-linking of insulation materials, leading to the misjudgment of temporary environmental pollution as permanent aging and a high false alarm rate.

[0004] On the other hand, when the cable surface is relatively clean, environmental factors contribute less to the test results. If microcracks or localized aging areas already exist inside the insulation layer, but have not yet significantly affected the overall insulation resistance or power frequency loss, routine tests may show normal results, leading to missed detections. In particular, internal damage to the insulation layer caused by mechanical vibration is not easily detected in electrical tests until the damage accumulates to a certain extent, at which point it suddenly manifests as a sharp deterioration in electrical performance.

[0005] Therefore, existing technologies lack effective means to separate reversible environmental disturbances from irreversible aging of the cable itself, making it difficult to accurately assess the insulation status of marine cables and reliably predict their remaining lifespan under marine conditions. There is an urgent need to develop assessment methods that can distinguish degradation mechanisms and integrate multi-source information.

[0006] Therefore, a method for assessing the insulation aging status of marine cables based on the influence of sea conditions is proposed. Summary of the Invention

[0007] The purpose of this invention is to provide a method for assessing the aging status of marine cable insulation based on the influence of sea conditions. The method obtains the aging characteristics of the cable body through dielectric spectrum analysis, obtains the degree and rate of mechanical damage by combining stress wave detection, calculates the insulation safety margin based on leakage current temperature characteristics, and integrates multi-source degradation data for probabilistic evolution analysis to achieve a probabilistic assessment of the remaining life.

[0008] To achieve the above objectives, the present invention provides the following technical solution: The method for assessing the aging status of marine cable insulation based on the influence of sea state includes: conducting broadband dielectric spectrum testing on the cable insulation layer to obtain the dielectric loss factor spectrum, extracting the low-frequency conductivity loss contribution and mid-frequency dielectric loss increment, identifying the dominant types of reversible environmental interference and irreversible aging of the cable itself, and outputting the characteristic quantities of aging of the cable itself. Mechanical pulse excitation is applied to both ends of the cable and stress wave signals are received. The propagation speed of the stress wave is calculated. The current wave speed is compared with the initial reference wave speed to obtain the wave speed attenuation rate. Trend analysis is performed to obtain the damage development rate and output the mechanical damage degree index. Non-destructive withstand voltage tests were performed on the cable insulation layer to measure the relationship between leakage current and temperature. The slope of the leakage current-temperature curve was extracted as a temperature sensitivity coefficient. Combined with the aging characteristics of the cable and the mechanical damage level indicators, the dominant aging mode was identified and the insulation safety margin was calculated. A multi-source degradation data fusion model was established to analyze the aging characteristics, mechanical damage degree indicators, damage development rate and insulation safety margin of the substrate, obtain the probability distribution of each degradation indicator, simulate the future evolution process of each indicator, and obtain the probability distribution and confidence interval of the remaining lifetime.

[0009] Preferably, the process of obtaining the dielectric loss factor spectrum includes: applying a swept AC test voltage to the cable insulation layer, scanning the frequency range from the low-frequency end to the high-frequency end, measuring the real and imaginary parts of the complex impedance at each frequency point, calculating the dielectric loss factor at the corresponding frequency point based on the complex impedance, and arranging the dielectric loss factors in frequency order to form a dielectric loss factor spectrum, wherein the low-frequency band covers the low-frequency conductivity-dominated region, the mid-frequency band covers the dielectric polarization-dominated region, and the high-frequency band covers the fast polarization response region.

[0010] Preferably, the process of obtaining the physical aging characteristic quantity includes: performing piecewise integration on the dielectric loss factor spectrum of the low-frequency band to obtain the low-frequency total loss characteristic value; performing piecewise integration on the dielectric loss factor spectrum of the mid-frequency band to obtain the mid-frequency total loss energy; calculating the difference between the mid-frequency total loss energy and the mid-frequency reference loss energy in the initial state of the cable to obtain the mid-frequency total loss characteristic value; calculating the difference between the low-frequency total loss energy and the low-frequency reference loss energy in the initial state of the cable to obtain the low-frequency loss increment; calculating the ratio of the mid-frequency loss increment to the low-frequency loss increment; when the ratio is not less than a preset discrimination threshold, determining that physical aging is dominant and outputting the mid-frequency loss increment as the physical aging characteristic quantity; when the ratio is less than the preset discrimination threshold, determining that environmental interference is dominant and outputting an environmental interference indicator.

[0011] Preferably, the process of obtaining the mechanical damage degree index includes: applying pulse excitation to one end of the cable in its brand-new state and receiving stress wave signals at the other end, recording the forward propagation time, switching the excitation end and the receiving end to record the reverse propagation time, calculating the initial reference wave velocity based on the cable length, forward propagation time, and reverse propagation time, measuring the current forward propagation time and current reverse propagation time in the same manner during the cable's service life, and calculating the current wave velocity; obtaining the wave velocity attenuation rate based on the current wave velocity and the initial reference wave velocity; analyzing the wave velocity attenuation rate sequence obtained from multiple consecutive test cycles to obtain the slope of the wave velocity attenuation rate change over time, which is used as the damage development rate, and outputting the wave velocity attenuation rate as a mechanical damage degree index.

[0012] Preferably, the process of obtaining the insulation safety margin includes: applying a non-destructive withstand voltage test to the cable insulation layer at multiple preset temperature points; measuring the steady-state leakage current at each temperature point; constructing a leakage current-temperature data point set by combining the leakage current at each temperature point with the corresponding temperature; performing linear fitting to obtain a leakage current-temperature curve; and using the slope of the leakage current-temperature curve as a temperature sensitivity coefficient. When the absolute value of the temperature sensitivity coefficient is less than a first threshold and the intrinsic aging characteristic is less than a second threshold, it is identified as an electrical aging-dominant mode. When the absolute value of the temperature sensitivity coefficient is greater than a third threshold, it is identified as a thermal aging-dominant mode. When the mechanical damage degree index is greater than a fourth threshold and the absolute value of the temperature sensitivity coefficient is in the middle range, it is identified as a mechanical damage-dominant mode. When the intrinsic aging characteristic, mechanical damage degree index, and temperature sensitivity coefficient are all in the middle range, it is identified as a composite aging mode. The equivalent value of the insulation resistance is calculated based on the test voltage and the leakage current at the lowest temperature point. The insulation safety margin is calculated by comparing the equivalent value of the insulation resistance with the minimum allowable insulation resistance under the rated operating voltage of the cable.

[0013] Preferably, the process of obtaining the probability distribution of each degradation index includes: based on the conditional dependency table of the multi-source degradation data fusion model and the current observation evidence, calculating the posterior probability distribution of dielectric aging nodes under the current evidence conditions through probabilistic inference, calculating the posterior probability distribution of mechanical damage nodes under the current evidence conditions, and calculating the posterior probability distribution of safety margin nodes under the current evidence conditions; randomly sampling degradation state samples from the posterior probability distribution of each node, performing time-step evolution on each sample according to the degradation rate probability distribution recorded in the conditional dependency table, updating the state value of dielectric aging nodes by incrementing their degradation rate, updating the state value of mechanical damage nodes by incrementing their damage development rate, and updating the state value of safety margin nodes by decrementing their decay rate within each time step, and repeating the sampling and evolution process to obtain multiple evolution trajectories.

[0014] Preferably, the process of obtaining the probability distribution and confidence interval of the remaining lifetime includes: setting failure criteria based on the dominant aging mode; when electrical aging is identified as dominant, the aging characteristic quantity exceeding the electrical aging failure threshold is used as the failure criterion; when mechanical damage is identified as dominant, the mechanical damage degree index exceeding the mechanical failure threshold is used as the failure criterion; when a combined aging mode is identified, the insulation safety margin being lower than the safety margin failure threshold is used as the failure criterion; monitoring the degradation index state value at each time step for each evolution trajectory, and recording the time step at which the evolution trajectory first meets the failure criterion as the failure time of the trajectory; statistically analyzing the failure times of all evolution trajectories to form a failure time distribution histogram; normalizing the failure time distribution histogram to obtain the probability density distribution of the remaining lifetime; performing cumulative integration on the probability density distribution to obtain the cumulative distribution function of the remaining lifetime, and obtaining the median and confidence interval of the remaining lifetime.

[0015] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention utilizes broadband dielectric spectrum testing to perform segmented quantitative analysis of the energy distribution characteristics of the dielectric loss factor in the low-frequency and mid-frequency bands. It introduces the ratio of mid-frequency loss increment to low-frequency loss increment as a discrimination criterion, effectively distinguishing between reversible environmental disturbances such as temperature and humidity fluctuations and conductivity variations caused by sea state changes, and irreversible aging caused by the degradation of the internal structure of the insulation material. This invention avoids misjudging transient environmental influences as material aging, thereby significantly improving the accuracy and reliability of assessing the aging status of marine cable insulation, and reducing false alarms and excessive maintenance.

[0016] 2. This invention establishes a mechanical damage characterization method based on wave velocity attenuation rate by applying mechanical pulse excitation to both ends of the cable and obtaining the propagation time of the forward and reverse stress waves. Furthermore, it obtains the slope of the wave velocity attenuation rate over time through multi-cycle testing, quantifying the rate of mechanical damage development. This method does not rely on visual inspection or disassembly, enabling non-destructive monitoring of internal structural damage caused by sea conditions such as ship vibration, swaying, and tension while the cable is in service. Compared to existing technologies that only focus on electrical performance degradation, this invention achieves continuous quantitative assessment of mechanical damage and its evolution process.

[0017] 3. This invention incorporates multi-source degradation information, including aging characteristics, mechanical damage levels, damage progression rates, and insulation safety margins, into a unified degradation data fusion model. Through probabilistic reasoning and random sampling, it constructs the future evolution trajectory of degradation indicators and adaptively sets failure criteria based on different dominant aging modes, ultimately obtaining the probability distribution and confidence interval of the remaining lifespan of marine cables. This invention fully reflects the uncertainty and randomness of the aging process, providing a more practically valuable basis for condition-based maintenance, life management, and risk decision-making of marine cables. Attached Figure Description

[0018] Figure 1 A schematic diagram of the process for assessing the insulation aging status of marine cables based on the influence of sea conditions, provided by this invention. Figure 2 A schematic diagram of the method for assessing the insulation aging status of marine cables based on the influence of sea conditions provided by the present invention. Figure 3 This is a schematic diagram of the process for obtaining environmental interference and body aging data provided by the present invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the invention.

[0020] Example 1: Please see Figure 1 and Figure 2 This invention provides a method for assessing the aging status of marine cable insulation based on sea state influence. The technical solution is as follows: A broadband dielectric spectrum test is performed on the cable insulation layer to obtain the dielectric loss factor spectrum. The contribution of low-frequency conductivity loss and the increase of mid-frequency dielectric loss are extracted to determine the dominant types of reversible environmental interference and irreversible intrinsic aging, and the intrinsic aging characteristic quantities are output. Mechanical pulse excitation is applied to both ends of the cable and stress wave signals are received. The stress wave propagation speed is calculated, and the current wave speed is compared with the initial reference wave speed to obtain the wave speed attenuation rate. Trend analysis is performed to obtain the damage development rate, and the mechanical damage degree index is output. A non-destructive withstand voltage test is performed on the cable insulation layer to measure the relationship between leakage current and temperature. The slope of the leakage current-temperature curve is extracted as a temperature sensitivity coefficient. Combined with the intrinsic aging characteristic quantities and the mechanical damage degree index, the dominant aging mode is identified, and the insulation safety margin is calculated. A multi-source degradation data fusion model is established to analyze the intrinsic aging characteristic quantities, mechanical damage degree index, damage development rate, and insulation safety margin, obtain the probability distribution of each degradation index, simulate the future evolution process of each index, and obtain the probability distribution and confidence interval of the remaining lifetime.

[0021] Furthermore, the process of obtaining the dielectric loss factor spectrum includes: applying a swept AC test voltage to the cable insulation layer, scanning the frequency range from the low-frequency end to the high-frequency end, measuring the real and imaginary parts of the complex impedance at each frequency point, calculating the dielectric loss factor at the corresponding frequency point based on the complex impedance, and arranging the dielectric loss factors in frequency order to form a dielectric loss factor spectrum, wherein the low-frequency band covers the low-frequency conductivity-dominated region, the mid-frequency band covers the dielectric polarization-dominated region, and the high-frequency band covers the fast polarization response region.

[0022] Furthermore, the process of obtaining the physical aging characteristic quantity includes: performing piecewise integration on the dielectric loss factor spectrum of the low-frequency band to obtain the low-frequency total loss characteristic value; performing piecewise integration on the dielectric loss factor spectrum of the mid-frequency band to obtain the mid-frequency total loss energy; calculating the difference between the mid-frequency total loss energy and the mid-frequency reference loss energy in the initial state of the cable to obtain the mid-frequency total loss characteristic value; calculating the difference between the low-frequency total loss energy and the low-frequency reference loss energy in the initial state of the cable to obtain the low-frequency loss increment; calculating the ratio of the mid-frequency loss increment to the low-frequency loss increment; when the ratio is not less than a preset discrimination threshold, it is determined that physical aging is dominant and the mid-frequency loss increment is output as the physical aging characteristic quantity; when the ratio is less than the preset discrimination threshold, it is determined that environmental interference is dominant and an environmental interference indicator is output.

[0023] Specifically, select a test section of an in-service marine cable, ensuring that the test section includes at least one complete insulation cross-section. Use a dielectric loss testing device to apply a swept-frequency AC test voltage to the cable insulation. This voltage level needs to ensure sufficient measurement signal strength without causing additional stress damage to the insulation.

[0024] The frequency sweep process starts from the low-frequency end and proceeds towards the high-frequency end, with the specific frequency range set as follows: the starting frequency at the low-frequency end is 0.1 Hz, and the ending frequency at the high-frequency end is 10000 Hz. The frequency sweep process uses a logarithmic interval method, that is, test points are selected at equal intervals within each tenth octave, with fifteen test frequency points set within each tenth octave. The reason for using logarithmic interval is that the dielectric polarization response exhibits a logarithmic distribution characteristic in the frequency domain, and this distribution can uniformly capture changes in dielectric properties across the entire frequency band. The division between the low-frequency and mid-frequency bands is determined based on the dielectric relaxation characteristics of the insulating material. Specifically, the second derivative of the dielectric loss factor spectrum is calculated to identify the inflection point frequencies of the curve. The first inflection point frequency serves as the boundary frequency between the low-frequency and mid-frequency bands, and the second inflection point frequency serves as the boundary frequency between the mid-frequency and high-frequency bands.

[0025] At each test frequency, the testing device applies a sinusoidal AC voltage of that frequency to the cable insulation layer. The settling time is set to at least five times the frequency period to ensure a steady-state response. Simultaneously, the testing device measures the AC current flowing through the insulation layer, which includes an active component in phase with the voltage and a reactive component leading by 90 degrees. The measured current signal is decomposed into real and imaginary currents using a Fast Fourier Transform. The real current corresponds to the conductivity loss of the insulation layer, while the imaginary current corresponds to the energy storage of dielectric polarization.

[0026] Based on the measured real and imaginary parts of the current, combined with the test voltage and the geometric parameters of the insulating layer, the complex impedance at that frequency point is calculated. The real part of the complex impedance equals the test voltage amplitude divided by the real part of the current, and the imaginary part of the complex impedance equals the test voltage amplitude divided by the imaginary part of the current. Furthermore, the real and imaginary parts of the dielectric constant are calculated based on the complex impedance. The real part of the dielectric constant equals the imaginary part of the complex impedance multiplied by the angular frequency and then multiplied by the geometric constant of the insulating layer capacitance, and the imaginary part of the dielectric constant equals the real part of the complex impedance multiplied by the angular frequency and then multiplied by the geometric constant of the insulating layer capacitance.

[0027] The dielectric loss factor is equal to the imaginary part of the dielectric constant divided by the real part of the dielectric constant. This parameter characterizes the ability of an insulating material to convert electrical energy into heat energy at a given frequency. The dielectric loss factors at each test frequency point across the entire frequency band are arranged in frequency order to form a dielectric loss factor spectrum. This spectrum data is stored in a two-dimensional array, with the first column representing the frequency value and the second column representing the corresponding dielectric loss factor value.

[0028] Based on dielectric polarization theory, the obtained spectrum is divided into three characteristic segments: the low-frequency band (0.1 Hz to 1 Hz) is characterized by dielectric loss primarily originating from ionic conductivity within and on the surface of the insulating material. Increased free ion concentration due to salt spray contamination or moisture absorption significantly raises the loss factor in this band. The mid-frequency band (1 Hz to 100 Hz) is characterized by dielectric loss primarily originating from dipole reversal polarization of the insulating material's molecular chains. Aging of the insulating material leads to chain breakage, generating polar groups such as carbonyl and hydroxyl groups, further increasing the loss factor. The high-frequency band (100 Hz to 10000 Hz) is characterized by dielectric loss primarily originating from electronic displacement polarization and rapid dipole polarization. This band is highly sensitive to changes in the material's bulk structure. The formula for calculating the contribution of conductivity loss is: multiply the dielectric loss factor value at each test frequency point within the low-frequency band by the logarithm of the frequency interval and then sum the results. The baseline total energy loss of the cable under initial conditions is obtained during factory inspection or initial commissioning. The test conditions should be consistent with those for in-service testing, including the same temperature (standard temperature is 25 degrees Celsius), humidity (relative humidity less than 65%), and test voltage level. The baseline data is stored in the cable file, including the low-frequency baseline total energy loss, the medium-frequency baseline total energy loss, and the corresponding test date and environmental condition records.

[0029] After obtaining the dielectric loss factor spectrum, loss energy is calculated for both the low-frequency and mid-frequency bands. The low-frequency band loss energy is calculated by multiplying the dielectric loss factor values ​​at all test frequency points within the low-frequency band by the frequency intervals between adjacent frequency points and then summing the results. Specifically, the contribution of the i-th frequency point is equal to its dielectric loss factor value multiplied by half the frequency difference between the (i+1)-th and (i-1)-th frequency points. The mid-frequency band loss energy is calculated using the same method, performing trapezoidal integration on all test frequency points within the mid-frequency band to obtain the mid-frequency total loss characteristic value.

[0030] When a cable is put into operation for the first time, a benchmark test must be performed on the same type of cable to obtain the low-frequency reference loss characteristic value and the medium-frequency reference loss characteristic value of the cable under the initial healthy state.

[0031] When testing in-service cables, the difference between the currently measured low-frequency total loss characteristic value and the low-frequency reference loss characteristic value is used to obtain the low-frequency loss increment. Similarly, the difference between the currently measured mid-frequency total loss characteristic value and the mid-frequency reference loss characteristic value is used to obtain the mid-frequency loss increment.

[0032] The ratio of the increase in mid-frequency loss to the increase in low-frequency loss is calculated. This ratio reflects the dominance of intrinsic aging loss relative to environmental interference loss. The method for determining the threshold of this ratio is as follows: Through tracking tests on multiple in-service cables under different sea conditions, statistical analysis shows that when the ratio is greater than 1.5, it indicates that the loss growth rate in the mid-frequency band is significantly faster than that in the low-frequency band, at which point intrinsic aging mechanisms such as molecular chain breakage of the insulation material dominate. When the ratio is less than 1.5, it indicates that the loss growth in the low-frequency band is relatively faster, at which point environmental factors such as surface salt spray pollution and moisture absorption dominate. This threshold is determined based on statistical analysis of a large amount of measured data, and the specific value will vary depending on the type of insulation material.

[0033] When the ratio exceeds a preset threshold, it is determined to be dominated by the aging of the host. Figure 3 The increase in intermediate frequency loss is output as a characteristic quantity of the cable's aging. This characteristic quantity has the same unit as the dielectric loss factor and is a dimensionless value. When the ratio is less than a preset threshold, it is determined that environmental interference is dominant, and an environmental interference indicator is output, suggesting that the cable surface should be cleaned before testing.

[0034] Furthermore, the process of obtaining the mechanical damage degree index includes: applying pulse excitation to one end of the cable in its brand-new state and receiving stress wave signals at the other end, recording the forward propagation time, switching the excitation end and the receiving end to record the reverse propagation time, calculating the initial reference wave velocity based on the cable length, forward propagation time, and reverse propagation time, measuring the current forward propagation time and the current reverse propagation time in the same manner during the cable's service life, and calculating the current wave velocity; obtaining the wave velocity attenuation rate based on the current wave velocity and the initial reference wave velocity; analyzing the wave velocity attenuation rate sequence obtained from multiple consecutive test cycles to obtain the slope of the wave velocity attenuation rate change over time, which is used as the damage development rate, and outputting the wave velocity attenuation rate as a mechanical damage degree index.

[0035] Specifically, an initial reference wave velocity calibration is performed before the cable is put into operation or when it is in good condition during the initial operation period. The exciter is driven by a pulse generator, the pulse signal is a square wave pulse, the pulse width is set to fifty microseconds, and the pulse amplitude is set to make the vibration acceleration generated by the exciter reach ten to twenty times the acceleration due to gravity.

[0036] When a pulse is applied by the exciter at end A, the data acquisition system is synchronously triggered to start recording. The stress wave signal received by the accelerometer at end B is amplified and filtered before being recorded by the acquisition system. During signal processing, a threshold triggering method is used to determine the waveform arrival time. Specifically, the trigger threshold is set to five times the background noise amplitude; the moment the received signal first exceeds this threshold is the waveform arrival time. The time interval from pulse transmission to waveform arrival is recorded; this time is the forward propagation time.

[0037] Subsequently, the excitation and receiving ends are swapped. The same pulse excitation is applied at end B, and the stress wave signal is received at end A. The same data processing method is used to record the backward propagation time. The purpose of using bidirectional measurement is to eliminate the systematic errors of excitation delay and reception delay, and to improve the accuracy of wave velocity measurement.

[0038] The length of the cable test section is known. The initial reference wave velocity is calculated by dividing twice the cable length by the sum of the forward propagation time and the reverse propagation time.

[0039] During cable service, stress wave measurements are performed according to a predetermined testing cycle. The testing cycle is determined based on the cable's operating environment and importance level. For critical power supply cables, a monthly testing cycle is recommended, while for general cables, a quarterly cycle is acceptable. Each test uses the exact same testing methods and parameter settings as the benchmark calibration to ensure consistency of testing conditions.

[0040] The current forward propagation time and current reverse propagation time are measured, and the current wave velocity is calculated using the same two-way time difference method. The difference between the current wave velocity and the initial reference wave velocity is used to obtain the absolute wave velocity attenuation. The absolute wave velocity attenuation is divided by the initial reference wave velocity to obtain the wave velocity attenuation rate, which is a dimensionless percentage value.

[0041] The physical meaning of wave velocity attenuation rate is: the propagation speed of stress waves in insulating materials is equal to the square root of the ratio of elastic modulus to density. When defects such as microvoids, microcracks or interface debonding occur inside the insulating layer, the equivalent elastic modulus of the defect area decreases, which leads to a decrease in the propagation speed of stress waves in that area.

[0042] Time series analysis was performed on the wave velocity attenuation rate data obtained from multiple consecutive test cycles. The test time was used as the horizontal axis and the wave velocity attenuation rate was used as the vertical axis to plot the wave velocity attenuation rate as a function of time. The curve was then fitted with linear regression using the least squares method.

[0043] A positive damage development rate indicates that the wave velocity is continuously decreasing and mechanical damage is continuously accumulating; a damage development rate close to zero indicates that the wave velocity is relatively stable and mechanical damage is progressing slowly; a negative damage development rate should not theoretically occur, but if it does, it may be due to measurement error or the cable has undergone maintenance.

[0044] The current wave velocity attenuation rate is output as an indicator of the degree of mechanical damage, and the slope of change obtained from linear regression is output as the damage development rate.

[0045] Further, the process of obtaining the insulation safety margin includes: applying non-destructive withstand voltage test voltages to the cable insulation layer at multiple preset temperature points, measuring the steady-state leakage current at each temperature point, constructing a leakage current-temperature data point set by combining the leakage current at each temperature point with the corresponding temperature, performing linear fitting to obtain a leakage current-temperature curve, and using the slope of the leakage current-temperature curve as a temperature sensitivity coefficient; identifying an electrical aging-dominant mode when the absolute value of the temperature sensitivity coefficient is less than a first threshold and the intrinsic aging characteristic quantity is less than a second threshold; identifying a thermal aging-dominant mode when the absolute value of the temperature sensitivity coefficient is greater than a third threshold; identifying a mechanical damage-dominant mode when the mechanical damage degree index is greater than a fourth threshold and the absolute value of the temperature sensitivity coefficient is in the middle range; and identifying a composite aging mode when the intrinsic aging characteristic quantity, mechanical damage degree index, and temperature sensitivity coefficient are all in the middle range; calculating the equivalent value of the insulation resistance based on the test voltage and the leakage current at the lowest temperature point, and calculating the insulation safety margin by comparing the equivalent value of the insulation resistance with the minimum allowable insulation resistance under the rated operating voltage of the cable.

[0046] Specifically, a non-destructive withstand voltage test is performed on the cable insulation layer, with the test voltage set to 1.5 to 2 times the cable's rated operating voltage. This voltage level is far below the insulation breakdown voltage and will not cause permanent damage to the insulation layer, thus falling within the scope of non-destructive testing.

[0047] The cable test section is placed in a temperature-controlled environment chamber, which can precisely control the temperature at preset points with an accuracy of ±1 degree Celsius. The preset temperature points cover the actual operating temperature range of the cable, specifically set at five temperature points: 20 degrees Celsius, 40 degrees Celsius, 60 degrees Celsius, 80 degrees Celsius, and 90 degrees Celsius.

[0048] At each temperature point, the ambient temperature is first stabilized to the target temperature for at least two hours to ensure that the cable insulation temperature reaches thermal equilibrium with the ambient temperature. The cable temperature is then monitored in real time using temperature sensors installed on the cable surface. Thermal equilibrium is determined to have been reached when the temperature fluctuation is less than 0.5 degrees Celsius and persists for at least 30 minutes.

[0049] A non-destructive withstand voltage test voltage is applied to the cable insulation layer, and the test voltage is kept constant. The voltage is applied using a slow ramp-up method, with the ramp-up rate controlled within 100 volts per second to avoid the transient charging current generated by rapid voltage ramp-up affecting the measurement. Once the voltage reaches the target value, it is kept stable for at least ten minutes to allow the polarization process inside the insulation layer to reach a steady state.

[0050] Measure the steady-state leakage current, which is the DC or AC current flowing through the insulation layer, including the conductivity current and polarization current of the insulation layer. Use a high-precision microammeter to measure the leakage current, with an accuracy at the microampere level. Record the steady-state leakage current value at this temperature point, in microamperes or milliamperes.

[0051] The above test process was repeated sequentially at all preset temperature points to obtain five leakage current values ​​corresponding to the five temperature points. The leakage current at each temperature point and the corresponding temperature were used to form a data point set, which contained five coordinate points, with the horizontal axis representing temperature and the vertical axis representing leakage current.

[0052] A linear fit was performed on the leakage current-temperature data set using the least squares method. The slope obtained from the fit is the temperature sensitivity coefficient, which characterizes the rate of increase of leakage current with increasing temperature. The magnitude of the temperature sensitivity coefficient reflects the dependence of the conductivity of the insulating material on temperature, and this coefficient exhibits different characteristics under different aging modes.

[0053] Based on three parameters—temperature sensitivity coefficient, intrinsic aging characteristics, and mechanical damage level—a multi-threshold discrimination logic is employed to identify the dominant aging mode. The specific discrimination rules and threshold settings are as follows: The first threshold is a temperature sensitivity coefficient with an absolute value less than 0.1 microamps per degree Celsius. This threshold is determined based on the following: for insulating materials dominated by electrical aging, the growth of electrical trees is primarily controlled by the electric field strength rather than temperature, and their conductivity has a weak dependence on temperature, resulting in a small temperature sensitivity coefficient. When the absolute value of the temperature sensitivity coefficient is less than the first threshold, and the bulk aging characteristic value is less than 0.002 (this value is the threshold for the increase in intermediate frequency losses, determined based on statistical analysis), it is judged to be an electrical aging-dominated mode.

[0054] The second threshold is a bulk aging characteristic value greater than 0.005. This threshold is determined based on statistical analysis of a large amount of electrical aging test data. When the increase in intermediate frequency loss exceeds this value, it indicates a significant increase in polar groups inside the insulating material and a severe degree of molecular chain breakage.

[0055] The third threshold: the absolute value of the temperature sensitivity coefficient is greater than 0.3 microamps per degree Celsius. This threshold is determined based on the following: for insulating materials dominated by thermal aging, high temperatures accelerate the oxidative degradation of the material, and the conductivity is highly sensitive to temperature; for every ten degrees Celsius increase in temperature, the conductivity can increase several times, resulting in a large temperature sensitivity coefficient. When the absolute value of the temperature sensitivity coefficient exceeds the third threshold, it is determined to be a thermal aging-dominated mode.

[0056] The fourth threshold is a mechanical damage index, specifically a wave velocity attenuation rate greater than 10%. This threshold is determined based on the following: when wave velocity attenuation exceeds 10%, it indicates the presence of numerous microcracks or voids within the insulation layer, resulting in a significant decrease in mechanical strength. When the mechanical damage index exceeds the fourth threshold, and the absolute value of the temperature sensitivity coefficient is within the intermediate range of 0.1 μA / °C to 0.3 μA / °C, it is determined to be a mechanical damage-dominated mode.

[0057] When the aging characteristics, mechanical damage level, and temperature sensitivity coefficient are all within the middle range of their respective thresholds, i.e., the aging characteristics are between 0.002 and 0.005, the mechanical damage level is between 5% and 10%, and the absolute value of the temperature sensitivity coefficient is between 0.1 μA per degree Celsius and 0.3 μA per degree Celsius, it is determined to be a composite aging mode, indicating that the three mechanisms of electrical aging, thermal aging, and mechanical damage exist simultaneously and are coupled with each other.

[0058] Failure criteria are set according to the dominant aging mode: when electrical aging is identified as dominant, the failure criterion is that the aging characteristic quantity of the body exceeds the electrical aging failure threshold; when thermal aging is identified as dominant, the failure criterion is that the absolute value of the temperature sensitivity coefficient exceeds the thermal aging failure threshold or the insulation safety margin is lower than the safety margin failure threshold; when mechanical damage is identified as dominant, the failure criterion is that the mechanical damage degree index exceeds the mechanical failure threshold; when a combined aging mode is identified, the failure criterion is that the insulation safety margin is lower than the safety margin failure threshold.

[0059] The minimum permissible insulation resistance under the cable's rated operating voltage is determined according to the national standard based on the cable's voltage rating. The insulation safety margin is calculated by comparing the current equivalent insulation resistance with the minimum permissible insulation resistance. This insulation safety margin data, along with the dominant aging mode identifier, is output and passed to the subsequent fusion model input step.

[0060] Furthermore, the process of obtaining the probability distributions of each degradation index includes: based on the conditional dependency table of the multi-source degradation data fusion model and the current observation evidence, calculating the posterior probability distribution of dielectric aging nodes under the current evidence conditions through probabilistic inference, calculating the posterior probability distribution of mechanical damage nodes under the current evidence conditions, and calculating the posterior probability distribution of safety margin nodes under the current evidence conditions; randomly sampling degradation state samples from the posterior probability distributions of each node, performing time-step evolution on each sample according to the degradation rate probability distribution recorded in the conditional dependency table, updating the state value of dielectric aging nodes by incrementing their degradation rate, updating the state value of mechanical damage nodes by incrementing their damage development rate, and updating the state value of safety margin nodes by decrementing their decay rate within each time step, and repeating the sampling and evolution process to obtain multiple evolution trajectories.

[0061] The multi-source degradation data fusion model adopts a Bayesian network architecture, and the conditional dependency table, i.e. the conditional probability table, is stored in the form of a multidimensional array. Taking the dielectric aging node as an example, its parent node is the environmental stress node, and the conditional probability table (dielectric aging state|environmental stress state) records the conditional probability value of each dielectric aging state under a given environmental stress state.

[0062] The degradation rate probability distribution was modeled using a normal distribution N, and the degradation rate distribution parameters were determined through statistical analysis of accelerated aging test data.

[0063] Probabilistic reasoning is implemented using the joint tree algorithm. The specific steps are as follows: (1) Transform the Bayesian network into a joint tree structure; (2) Input the observed evidence into the corresponding node of the joint tree; (3) Propagate the probability information bidirectionally in the joint tree through message passing; (4) Extract the marginal probability distribution of the target node as the posterior probability.

[0064] The time step is set to one month, which matches the actual testing cycle of marine cables and balances calculation accuracy and efficiency.

[0065] Specifically, the multi-source degradation data fusion model establishes a probabilistic graphical model with five nodes, which are connected by directed edges to form a directed acyclic graph structure. These nodes are: environmental stress node, dielectric aging node, mechanical damage node, safety margin node, and remaining lifetime node.

[0066] The environmental stress node is set as the root node, and it has no parent node. The environmental stress node characterizes the severity of the external environment in which the cable operates, including factors such as salt spray concentration, temperature and humidity fluctuations, and mechanical vibration intensity. The state space of this node is divided into three levels: low stress, medium stress, and high stress, corresponding to good, average, and severe environmental conditions, respectively. The determination of the environmental stress level is based on meteorological data and vibration monitoring data of the ship's navigation area. The specific determination rules are as follows: if the salt spray deposition rate is less than 0.1 grams per square meter per day, the daily temperature fluctuation is less than ten degrees Celsius, and the vibration intensity is less than five times the gravitational acceleration, it is determined to be low stress; if any parameter exceeds the above thresholds but does not exceed twice the above thresholds, it is determined to be medium stress; if any parameter exceeds twice the above thresholds, it is determined to be high stress.

[0067] Dielectric aging nodes and mechanical damage nodes are set as intermediate nodes, with their parent nodes being environmental stress nodes. Environmental stress directly affects the dielectric aging rate and mechanical damage rate; high salt spray environments accelerate dielectric aging, while strong vibration environments accelerate mechanical damage. The state space of the dielectric aging node is divided into three levels based on the bulk aging characteristics: mild aging, moderate aging, and severe aging. The state space of the mechanical damage node is divided into three levels based on the wave velocity attenuation rate: mild damage, moderate damage, and severe damage, with thresholds of 5% and 10%, respectively.

[0068] The parent node of the safety margin node is set as both the dielectric aging node and the mechanical damage node. The insulation safety margin is affected by both dielectric aging and mechanical damage. Dielectric aging reduces insulation resistance, while mechanical damage generates microcracks that reduce insulation strength. The combined effect of these two factors determines the safety margin level. The state space of the safety margin node is divided into three levels: high margin, medium margin, and low margin.

[0069] The remaining lifetime node is set as a leaf node, and its parent node is the safety margin node. The remaining lifetime of the cable ultimately depends on when the insulation safety margin drops to the failure threshold. The state space of the remaining lifetime node is a continuous-time variable.

[0070] For dielectric aging nodes, the conditional probability table records the probability distribution of dielectric aging degree and aging rate distribution under different environmental stress levels.

[0071] For mechanically damaged nodes, the conditional probability table records the probability distribution of the degree of mechanical damage and the distribution of damage development rate under different vibration intensities. Through accelerated aging tests, long-term vibration tests were conducted on cable samples under different vibration intensities to measure the change in wave velocity attenuation rate over time.

[0072] For safety margin nodes, the conditional probability table records the decay rate distribution of the safety margin under different combinations of dielectric aging and mechanical damage. This table is established by jointly analyzing the impact of dielectric aging and mechanical damage on insulation performance.

[0073] The condition dependency table is stored in the form of a multidimensional array. The array dimension corresponds to the node state space dimension. The array elements record the probability value and degradation rate parameter under the corresponding state combination.

[0074] The measured data obtained from the preceding steps are used as observational evidence and input into the probabilistic graphical model. Specifically, the current value of the bulk aging characteristic is mapped to the dielectric aging node. The mapping method is as follows: the current state level of the node is determined based on the range in which the bulk aging characteristic value is located.

[0075] The mechanical damage severity indicators, namely wave velocity attenuation rate and damage development rate, are mapped to mechanically damaged nodes. The wave velocity attenuation rate is used to determine the current state level of the node, and the damage development rate is used as the rate parameter for the subsequent evolution process.

[0076] The insulation safety margin is mapped to the safety margin node, and the state level is determined based on the range of the values.

[0077] The observed values ​​of each node are fixed in the probabilistic graphical model as evidence; this operation is called evidence setting or observation setting in probabilistic inference algorithms. After setting the evidence, the degrees of freedom of the model decrease, and the probability distribution of unobserved nodes will be updated according to the conditional dependency table. The data structure of the probabilistic graphical model with evidence includes: a set of nodes, a set of edges, a conditional dependency table, and a set of observed evidence. Based on the conditional dependency table of the probabilistic graphical model and the current observed evidence, the posterior probability distribution of each node under the current evidence condition is calculated. The calculation of the posterior probability distribution adopts the probabilistic inference method. The core idea of ​​this method is to use Bayes' theorem to combine the prior probability distribution with the observed evidence to obtain the updated posterior probability distribution.

[0078] For dielectric aging nodes, although observational evidence has been established, their probability distribution still needs to be calculated to reflect measurement uncertainty. Assuming that the measurement error follows a normal distribution and the uncertainty of the measurement value is 10% of the true value, the posterior probability distribution of the dielectric aging node is: with the state level corresponding to the observation value as the center, adjacent state levels also have a certain probability.

[0079] For mechanically damaged nodes, the same method is used to handle measurement uncertainties, and the posterior probability distribution of the mechanically damaged nodes is obtained.

[0080] For a safety margin node, since the state of its parent node is known, the conditional probability of each state of the safety margin node under the current state combination of the parent node can be directly queried according to the conditional dependency table. This conditional probability is the posterior probability distribution.

[0081] For environmental stress nodes, although they are root nodes, inferences can be made based on observational data. The current environmental stress level is determined based on meteorological and vibration monitoring data for the current navigation area, and a corresponding probability distribution is established.

[0082] Degenerate state samples are randomly drawn from the posterior probability distribution of each node. The sampling method is Monte Carlo sampling, which involves generating uniformly distributed random numbers between zero and one, and determining the state corresponding to the random numbers based on the cumulative probability distribution function.

[0083] Taking dielectric aging nodes as an example, their posterior probability distribution is: 10% mild aging, 80% moderate aging, and 10% severe aging. Random numbers are generated. If the random number is less than 0.1, the mild aging state is selected; if the random number is between 0.1 and 0.9, the moderate aging state is selected; and if the random number is greater than 0.9, the severe aging state is selected.

[0084] The same method is used to randomly sample mechanical damage nodes and safety margin nodes. A single sampling yields a complete set of system state samples, including the specific state values ​​of each node.

[0085] For each extracted sample, time-step evolution is performed to simulate its future degradation trajectory.

[0086] Within each time step, the state values ​​of each node are updated according to the degradation rate probability distribution recorded in the conditional dependency table. The state value of the dielectric aging node, i.e., the bulk aging characteristic, is updated according to its degradation rate increment. The update formula is: the bulk aging characteristic at the next time step equals the bulk aging characteristic at the current time step plus the degradation rate multiplied by the time step. The degradation rate is obtained from the conditional dependency table. This rate itself is a random variable that follows a normal distribution; therefore, a rate value needs to be randomly selected from this distribution for each update.

[0087] The state value of a mechanically damaged node, i.e., the wave velocity attenuation rate, is updated according to the increment of its damage development rate. The update formula is: the wave velocity attenuation rate at the next moment equals the wave velocity attenuation rate at the current moment plus the damage development rate multiplied by the time step. The damage development rate is also randomly selected from the conditional dependency table.

[0088] The state value of the safety margin node is updated by decreasing its decay rate. The update formula is: the safety margin at the next time step equals the safety margin at the current time step minus the decay rate multiplied by the time step. The decay rate depends on the current state of dielectric aging and mechanical damage, and is randomly selected from the corresponding position in the condition dependency table.

[0089] At each time step, the state value of each node is updated, forming a new state combination. This process continues iterating until the termination condition is met. The evolution process records the state values ​​at all time steps, forming a complete evolutionary trajectory.

[0090] Each time, new initial samples are drawn from the posterior probability distribution, and an independent evolutionary process is performed to generate new evolutionary trajectories. The number of repeated sampling and evolution is set to 10,000, generating 10,000 independent evolutionary trajectories.

[0091] All evolutionary trajectory data are stored in a three-dimensional array, with the array dimensions being trajectory number, time step, and node number. Array elements represent the state value of the corresponding node at the corresponding time step for each trajectory. This dataset represents the state distribution of each degradation index at different times and is passed to the subsequent lifetime prediction step.

[0092] Furthermore, the process of obtaining the probability distribution and confidence interval of the remaining lifetime includes: setting failure criteria based on the dominant aging mode; when electrical aging is identified as dominant, the aging characteristic quantity exceeding the electrical aging failure threshold is used as the failure criterion; when mechanical damage is identified as dominant, the mechanical damage degree index exceeding the mechanical failure threshold is used as the failure criterion; when a combined aging mode is identified, the insulation safety margin being lower than the safety margin failure threshold is used as the failure criterion; monitoring the degradation index status value at each time step for each evolution trajectory, and recording the time step at which the evolution trajectory first meets the failure criterion as the failure time of the trajectory; statistically analyzing the failure times of all evolution trajectories to form a failure time distribution histogram; normalizing the failure time distribution histogram to obtain the probability density distribution of the remaining lifetime; performing cumulative integration on the probability density distribution to obtain the cumulative distribution function of the remaining lifetime, and obtaining the median and confidence interval of the remaining lifetime.

[0093] Specifically, corresponding failure criteria are set according to the dominant aging mode. The failure criteria are the critical conditions for determining cable insulation failure. When the degradation index reaches the condition, the cable is considered to be unable to operate safely.

[0094] The specific values ​​for each failure threshold are determined based on industry test data: Electrical aging failure threshold: The bulk aging characteristic value is ≥0.015, which corresponds to a decrease in dielectric breakdown strength to 50% of the rated value; Thermal aging failure threshold: The absolute value of the temperature sensitivity coefficient is ≥0.8 μA / ℃, which corresponds to the thermal aging index of the insulating material being lower than the safety limit; Mechanical failure threshold: Wave velocity attenuation rate ≥30%, which corresponds to the insulation layer's mechanical strength decreasing to 60% of its rated value; Safety margin failure threshold: Insulation safety margin <1.0, that is, the equivalent value of insulation resistance is lower than the minimum allowable insulation resistance; When a composite aging mode is identified, due to the synergistic effect of multiple aging mechanisms, the most stringent failure criterion is adopted, namely the insulation safety margin as the failure judgment index. When it is lower than one time the minimum allowable insulation resistance, it is judged as a failure.

[0095] Specifically, corresponding failure criteria are set according to the dominant aging mode. The failure criteria are the critical conditions for determining cable insulation failure. When the degradation index reaches the condition, the cable is considered to be unable to operate safely.

[0096] When the dominant aging mode is identified as electrical aging-dominated, the failure criterion is set as the intrinsic aging characteristic exceeding the electrical aging failure threshold. The electrical aging failure threshold is determined based on the breakdown strength test of the insulation material.

[0097] When the dominant aging mode is identified as mechanical damage-driven, the failure criterion is set as the mechanical damage severity index, i.e., the wave velocity attenuation rate exceeding the mechanical failure threshold. The mechanical failure threshold is determined based on the mechanical strength test of the insulation layer.

[0098] When the dominant aging mode is identified as thermal aging, the failure criterion is set as the insulation safety margin falling below the safety margin failure threshold. The safety margin failure threshold is set to one time the minimum allowable insulation resistance; that is, failure is determined when the safety margin drops to one.

[0099] When the dominant aging mode is identified as composite aging, the failure criterion adopts a combination of multiple conditions. The failure threshold for composite aging is more stringent than that for a single aging mode because the synergistic effect of multiple aging mechanisms accelerates the failure process.

[0100] For each evolution trajectory, the degradation index state value at each time step is checked. For the i-th trajectory, starting from the initial moment, the state values ​​at each time step (first month, second month, third month, etc.) are checked sequentially to determine whether the failure criterion is met.

[0101] When a trajectory first meets the failure criterion, the time step is recorded as the failure time of that trajectory. If the trajectory fails to meet the failure criterion during its evolution, the maximum evolution time is recorded as the failure time of that trajectory. In practical terms, this means that the cable corresponding to that trajectory has not failed within ten years.

[0102] The failure times of all trajectories are statistically analyzed to form a failure time series, which contains ten thousand time values.

[0103] Perform statistical analysis on the failure time series and plot a histogram of failure time distribution. The horizontal axis of the histogram represents the failure time, and the vertical axis represents the number of failure trajectories within that time interval. The time interval width is set to one month, that is, to count the number of trajectories in each interval such as zero to one month, one to two months, two to three months, etc.

[0104] Normalizing the histogram involves dividing the number of trajectories in each interval by the total number of trajectories (ten thousand) to obtain the probability value for that interval. The normalized histogram represents the probability density distribution of the remaining lifetime, which physically represents the probability of cable failure within each time period.

[0105] The probability density distribution is represented in discrete form, and the data structure is a two-dimensional array. The first column is the midpoint value of the time interval, and the second column is the probability density value of the corresponding interval.

[0106] By performing a cumulative integral on the probability density distribution, the cumulative distribution function of the remaining lifetime is obtained. The cumulative distribution function represents the cumulative probability that the cable will fail before a certain time. It is calculated by starting from time zero and successively accumulating the probability density values ​​of each time interval.

[0107] Specifically, the cumulative probability corresponding to the nth time interval is equal to the sum of the probability densities of the previous n time intervals. The cumulative distribution function is a monotonically increasing function, with an initial value of zero (the probability of failure is zero at time zero) and a terminal value close to one (failure is almost inevitable after a sufficiently long time).

[0108] The cumulative distribution function is also stored in the form of a two-dimensional array, with the first column being the time value and the second column being the corresponding cumulative probability value.

[0109] Feature statistics are extracted from the cumulative distribution function. The median remaining lifetime is defined as the time value corresponding to when the cumulative probability reaches 50%. Its physical meaning is that half of the evolutionary trajectories fail before this time and half fail after this time. This value represents the most likely remaining lifetime.

[0110] The extraction method is as follows: find the data point in the cumulative distribution function array whose cumulative probability is closest to 0.5. If the cumulative probability is exactly equal to 0.5, directly read the corresponding time value. If there is no point that is exactly equal to 0.5, perform linear interpolation between two adjacent points.

[0111] The confidence interval is defined as the time range containing a 95% probability, specifically the time interval corresponding to a cumulative probability from 2.5% to 97.5%. The lower limit of the confidence interval is the time value corresponding to a cumulative probability of 0.025, and the upper limit is the time value corresponding to a cumulative probability of 0.975. The extraction method is the same as for the median, obtained by searching or interpolating within the cumulative distribution function.

[0112] The output includes four components: median remaining lifetime, lower confidence interval, upper confidence interval, and remaining lifetime probability distribution curve. The probability distribution curve is presented graphically or in a table format, with time on the horizontal axis and probability density or cumulative probability on the vertical axis, allowing users to intuitively understand the failure probability at different time points.

[0113] Simultaneously, it outputs the dominant aging mode identifier and the current values ​​of various degradation indicators, providing comprehensive information for maintenance decisions. Based on the remaining life prediction results and confidence intervals, the system can automatically generate maintenance recommendations: if the lower limit of the confidence interval is less than three months, it is recommended to arrange cable replacement immediately; if the lower limit of the confidence interval is between three and six months, it is recommended to arrange maintenance and inspection at the next port of call; if the lower limit of the confidence interval is greater than six months, monitoring can continue as planned.

[0114] Example 2: This embodiment, based on the basic detection process disclosed in Embodiment 1, further introduces an aging acceleration stage identification process for dielectric spectrum characteristic peak drift, an adaptive correction process for degradation rate of multi-cycle test data, and a collaborative mechanism for aging acceleration identification and rate adaptive correction.

[0115] The steps for identifying the accelerated aging stage are as follows: Peak detection is performed on the mid-frequency band of the dielectric loss factor spectrum obtained from multiple consecutive test cycles. The maximum value of the dielectric loss factor in the mid-frequency band of each test cycle and its corresponding frequency are identified. The peak frequencies of each test cycle are arranged in chronological order to form a peak frequency time series. Linear regression fitting is performed on the peak frequency time series to obtain the drift rate of the peak frequency over time. When the absolute value of the drift rate is greater than the preset acceleration threshold and the peak frequency shifts significantly, the aging is determined to have entered the accelerated stage and an acceleration warning sign is output. The acceleration warning sign and the body aging feature quantity are input into the multi-source degradation data fusion model.

[0116] Specifically, peak analysis was performed on the dielectric loss factor spectrum obtained from multiple consecutive test cycles. Taking the mid-frequency band as the analysis object, the peak value of the dielectric loss factor in this band corresponds to the dipole relaxation process of the molecular chain segments of the insulating material.

[0117] For the mid-frequency spectrum data of each test cycle, a peak detection algorithm is used to identify the maximum value point. If multiple candidate peak points exist, the point with the largest value is selected as the peak point of that test cycle. The maximum dielectric loss factor of this peak point and its corresponding frequency value are recorded.

[0118] The parabolic interpolation method is used to improve the detection accuracy of peak frequency. A quadratic parabolic fitting is performed using three data points: the peak point and the two points to its left and right. The x-coordinate of the vertex of the parabola is the interpolated peak frequency.

[0119] The peak frequencies of each test period are arranged in chronological order of test time to form a peak frequency time series. The data structure of this series is a two-dimensional array, with the first column representing the test time and the second column representing the peak frequency at the corresponding test time.

[0120] The time series needs to include data from at least five test periods because linear fitting requires at least three data points, and considering the impact of measurement random errors, increasing the number of data points can improve the reliability of the fit.

[0121] A linear regression was performed on the peak frequency time series, and the fitting equation was that the peak frequency equals the initial frequency plus the drift rate multiplied by time. The linear regression used the least squares method to calculate the deviation between the time coordinates and the time average for each test point, and the deviation between the frequency coordinates and the frequency average for each test point. The drift rate is equal to the sum of the products of the time deviation and the frequency deviation divided by the sum of the squares of the time deviations.

[0122] The preset acceleration threshold was determined based on statistical analysis of numerous cable aging tests. Dielectric spectroscopy tests were conducted on cable samples with different aging levels to statistically analyze the relationship between peak frequency drift rate and the degree of aging acceleration. The test results show that when the absolute value of the peak frequency drift rate is less than 0.5 Hz per month, the cable is in a slow aging stage, and the monthly growth rate of its intrinsic aging characteristics remains at a low level. When the absolute value of the drift rate exceeds 0.5 Hz per month, the cable enters an accelerated aging stage, and the monthly growth rate of its intrinsic aging characteristics increases significantly.

[0123] Therefore, the preset acceleration threshold is set to 0.5 Hz per month. This threshold applies to cross-linked polyethylene insulated cables. For other insulation material types, the threshold value may differ and needs to be determined based on the actual test data of the material.

[0124] When the absolute value of the drift rate obtained from linear regression is greater than the preset acceleration threshold of 0.5 Hz per month, and the peak frequency shifts significantly, the aging process is considered to have entered the accelerated phase. The criterion for a significant shift is that the absolute value of the change in peak frequency relative to the initial reference frequency exceeds 10% of the initial reference frequency.

[0125] An acceleration warning flag is output, stored as a Boolean variable. A true value indicates that the acceleration phase has begun, while a false value indicates that the slow aging phase is still in progress. This acceleration warning flag, along with the ontological aging features, is passed to the multi-source degradation data fusion model. An acceleration state node is added to the fusion model, with its parent node being the dielectric aging node. When the acceleration warning flag is true, this node is set to the acceleration state, triggering subsequent adaptive rate parameter correction and profile prediction mechanisms.

[0126] Before simulating the future evolution of each indicator, an adaptive correction step for degradation rate is included: extracting the measured values ​​of the bulk aging characteristic quantity and the mechanical damage degree index for at least three consecutive test cycles; calculating the difference between the bulk aging characteristic quantity and the time interval between adjacent test cycles to obtain the measured dielectric aging rate; calculating the difference between the mechanical damage degree index and the time interval between adjacent test cycles to obtain the measured mechanical damage rate; comparing the measured dielectric aging rate with the preset average dielectric aging rate corresponding to the current environmental stress level in the condition dependency table; when the absolute value of the deviation between the measured rate and the preset rate is greater than twice the standard deviation of the preset rate, updating the average dielectric aging rate under that environmental stress level in the condition dependency table to the moving average of the measured rate; applying the same adaptive correction method to the mechanical damage rate; and using the corrected condition dependency table to simulate the subsequent future evolution process.

[0127] Specifically, extract the measured value sequence of the body aging characteristic quantity and the measured value sequence of the mechanical damage degree index for at least three consecutive test cycles.

[0128] Calculate the difference in bulk aging characteristics between adjacent test cycles. Taking the i-th test cycle and the (i-1)-th test cycle as an example, the difference in bulk aging characteristics is equal to the bulk aging characteristics of the i-th cycle minus the bulk aging characteristics of the (i-1)-th cycle. Divide this difference by the time interval between the two tests to obtain the measured dielectric aging rate within that time interval. Repeat this calculation for all adjacent cycle pairs to obtain the measured dielectric aging rate sequence.

[0129] The measured mechanical damage rate was calculated using the same method, which is the difference in wave velocity attenuation rate between adjacent cycles divided by the time interval. The unit of the measured rate is consistent with the unit of the original index divided by the time unit; the dielectric aging rate is a dimensionless value per month, and the mechanical damage rate is a percentage per month.

[0130] The mean and standard deviation of the preset dielectric aging rate corresponding to the current environmental stress level are retrieved from the condition dependency table. The environmental stress level is determined based on the sea state data of the current navigation area and is divided into three levels: low stress, medium stress, and high stress.

[0131] The average value of the measured dielectric aging rate sequence is compared with the average value of the preset rate, and the absolute value of the deviation between the two is calculated. The deviation judgment threshold is set to twice the standard deviation of the preset rate, which corresponds to the boundary of the 95% confidence interval in statistics. When the absolute value of the deviation is greater than this threshold, it indicates that the actual degradation rate deviates significantly from the model preset value, and the model parameters need to be updated.

[0132] The same deviation determination method is used for mechanical damage rate. The preset mechanical damage rate parameters corresponding to the environmental stress level are queried in the condition dependency table. The deviation between the measured value and the preset value is calculated and compared with twice the standard deviation threshold.

[0133] When the deviation exceeds the threshold, the rate parameter is updated. The moving average of the measured dielectric aging rate sequence is calculated, with the sliding window length set to the three most recent test cycles. The moving average is equal to the sum of the three most recent measured rates divided by three. This average smooths out the random fluctuations of a single measurement and more accurately reflects the average degradation rate at the current stage.

[0134] The mean dielectric aging rate parameter under the corresponding environmental stress level in the condition dependency table is updated to the moving average. The rate standard deviation parameter is updated synchronously. The new standard deviation is equal to the square root of the sum of the squares of the deviations of the three most recent measured rates from the moving average, divided by the square root of three minus one.

[0135] The same moving average calculation and parameter update method is used for the mechanical damage rate to ensure that the degradation rate parameters of the dielectric aging node and the mechanical damage node in the fusion model match the current actual situation.

[0136] The modified conditional dependency table is used to simulate the subsequent future evolution process. During the time-step evolution, rate values ​​are randomly selected from the modified degradation rate probability distribution. These rate values ​​are closer to the degradation patterns under the current actual sea conditions, avoiding the accumulation of prediction biases caused by fixed-parameter models when the environment changes.

[0137] The adaptive correction mechanism is automatically executed after each new test cycle, forming a closed-loop feedback control that enables the model to always track the actual degradation state of the cable, improving the dynamic adaptability and long-term accuracy of the remaining life prediction.

[0138] When the accelerated aging stage identification step outputs an accelerated warning flag, the deviation judgment threshold is reduced from twice the preset rate standard deviation to one time the preset rate standard deviation in the degradation rate adaptive correction step. This improves the trigger sensitivity of rate correction, and the corrected accelerated stage degradation rate is added as a separate rate level to the condition dependency table. In subsequent evolution process simulations, when the accelerated warning flag is detected, the accelerated stage degradation rate is used first for state updates.

[0139] Specifically, when the accelerated aging stage identification step outputs an accelerated warning flag as true, the system enters accelerated response mode. In this mode, the deviation judgment threshold in the degradation rate adaptive correction step is automatically adjusted.

[0140] The original deviation threshold was twice the preset rate standard deviation; after adjustment, it was reduced to once the preset rate standard deviation. This reduction in threshold means that the trigger sensitivity for rate correction is increased, and smaller measured deviations can trigger parameter updates. The basis for the threshold adjustment is that the degradation rate changes rapidly during the acceleration phase, requiring more frequent updates to model parameters to track the rapidly changing degradation process.

[0141] When rate correction is triggered, if the acceleration warning flag is true, the corrected degradation rate will be used as the dedicated rate level for the acceleration phase. Specifically, an acceleration state dimension will be added to the condition dependency table. The original condition dependency table was divided into rate levels according to environmental stress level, and now two sub-levels, normal state and acceleration state, will be added.

[0142] The corrected rate calculated by the moving average is stored in the acceleration sub-gear under the corresponding environmental stress level, while the normal state sub-gear retains the original preset rate. This forms a rate parameter system with different gears, where the normal rate is used in the normal stage and the acceleration rate is used in the acceleration stage.

[0143] In the evolutionary process simulation, at the beginning of each time step, it is checked whether there is an acceleration warning indicator. If the acceleration warning indicator is true, the degradation rate is extracted from the acceleration state sub-level of the conditional dependency table for state update; if the acceleration warning indicator is false, the degradation rate is extracted from the normal state sub-level.

[0144] This priority switching ensures that the evolution simulation uses rate parameters that match the current aging stage. Since the accelerated stage rate is based on measured data and is typically significantly higher than the normal rate, using the accelerated rate will significantly shorten the failure time of the evolution trajectory and correspondingly reduce the predicted remaining lifetime, consistent with the actual accelerated aging state.

[0145] The complete workflow of the collaborative mechanism is as follows: peak frequency drift detection identifies the aging acceleration trend and issues an early warning sign; the early warning sign triggers the rate correction mechanism to improve sensitivity and quickly capture rate mutations; the corrected acceleration rate is immediately applied to evolution prediction, achieving a seamless connection from identification to correction to prediction.

[0146] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for assessing the aging condition of marine cable insulation based on the influence of sea state, characterized in that, include: Broadband dielectric spectrum testing is performed on the cable insulation layer to obtain the dielectric loss factor spectrum, extract the low-frequency band conductivity loss contribution and mid-frequency band dielectric loss increment, identify the dominant types of reversible environmental interference and irreversible physical aging, and output physical aging characteristic quantities. Mechanical pulse excitation is applied to both ends of the cable and stress wave signals are received. The propagation speed of the stress wave is calculated. The current wave speed is compared with the initial reference wave speed to obtain the wave speed attenuation rate. Trend analysis is performed to obtain the damage development rate and output the mechanical damage degree index. Non-destructive withstand voltage tests were performed on the cable insulation layer to measure the relationship between leakage current and temperature. The slope of the leakage current-temperature curve was extracted as a temperature sensitivity coefficient. Combined with the aging characteristics of the cable and the mechanical damage level indicators, the dominant aging mode was identified and the insulation safety margin was calculated. A multi-source degradation data fusion model was established to analyze the aging characteristics, mechanical damage degree indicators, damage development rate and insulation safety margin of the substrate, obtain the probability distribution of each degradation indicator, simulate the future evolution process of each indicator, and obtain the probability distribution and confidence interval of the remaining lifetime.

2. The method for assessing the aging state of marine cable insulation based on sea state influence as described in claim 1, characterized in that, The process of obtaining the dielectric loss factor spectrum includes: applying a swept AC test voltage to the cable insulation layer, with the frequency range scanning from the low-frequency end to the high-frequency end, measuring the real and imaginary parts of the complex impedance at each frequency point, calculating the dielectric loss factor at the corresponding frequency point based on the complex impedance, and arranging the dielectric loss factors in frequency order to form the dielectric loss factor spectrum, wherein the low-frequency band covers the low-frequency conductivity-dominated region, the mid-frequency band covers the dielectric polarization-dominated region, and the high-frequency band covers the fast polarization response region.

3. The method for assessing the aging state of marine cable insulation based on sea state influence as described in claim 2, characterized in that, The process of obtaining the physical aging characteristic quantity includes: performing piecewise integration on the dielectric loss factor spectrum of the low-frequency band to obtain the low-frequency total loss characteristic value; performing piecewise integration on the dielectric loss factor spectrum of the mid-frequency band to obtain the mid-frequency total loss energy; calculating the difference between the mid-frequency total loss energy and the mid-frequency reference loss energy in the initial state of the cable to obtain the mid-frequency total loss characteristic value; calculating the difference between the low-frequency total loss energy and the low-frequency reference loss energy in the initial state of the cable to obtain the low-frequency loss increment; calculating the ratio of the mid-frequency loss increment to the low-frequency loss increment; when the ratio is not less than a preset discrimination threshold, it is determined that physical aging is dominant and the mid-frequency loss increment is output as the physical aging characteristic quantity; when the ratio is less than the preset discrimination threshold, it is determined that environmental interference is dominant and an environmental interference indicator is output.

4. The method for assessing the aging state of marine cable insulation based on sea state influence as described in claim 1, characterized in that, The process of obtaining the mechanical damage degree index includes: applying a pulse excitation to one end of the cable in its brand-new state and receiving a stress wave signal at the other end, recording the forward propagation time, switching the excitation end and the receiving end to record the reverse propagation time, calculating the initial reference wave velocity based on the cable length, forward propagation time, and reverse propagation time, measuring the current forward propagation time and the current reverse propagation time in the same way during the cable's service life, and calculating the current wave velocity; obtaining the wave velocity attenuation rate based on the current wave velocity and the initial reference wave velocity; analyzing the wave velocity attenuation rate sequence obtained from multiple consecutive test cycles to obtain the slope of the wave velocity attenuation rate change over time, which is used as the damage development rate, and outputting the wave velocity attenuation rate as the mechanical damage degree index.

5. The method for assessing the insulation aging status of marine cables based on sea state influence as described in claim 4, characterized in that, The process of obtaining the insulation safety margin includes: applying non-destructive withstand voltage test voltages to the cable insulation layer at multiple preset temperature points; measuring the steady-state leakage current at each temperature point; constructing a leakage current-temperature data point set by combining the leakage current at each temperature point with the corresponding temperature; performing linear fitting to obtain a leakage current-temperature curve; and using the slope of the leakage current-temperature curve as a temperature sensitivity coefficient. When the absolute value of the temperature sensitivity coefficient is less than a first threshold and the intrinsic aging characteristic is less than a second threshold, it is identified as an electrical aging-dominant mode. When the absolute value of the temperature sensitivity coefficient is greater than a third threshold, it is identified as a thermal aging-dominant mode. When the mechanical damage degree index is greater than a fourth threshold and the absolute value of the temperature sensitivity coefficient is in the middle range, it is identified as a mechanical damage-dominant mode. When the intrinsic aging characteristic, mechanical damage degree index, and temperature sensitivity coefficient are all in the middle range, it is identified as a composite aging mode. The equivalent value of the insulation resistance is calculated based on the test voltage and the leakage current at the lowest temperature point. The insulation safety margin is calculated by comparing the equivalent value of the insulation resistance with the minimum allowable insulation resistance under the rated operating voltage of the cable.

6. The method for assessing the insulation aging status of marine cables based on sea state influence as described in claim 5, characterized in that, The process of obtaining the probability distributions of each degradation index includes: based on the conditional dependency table of the multi-source degradation data fusion model and the current observation evidence, calculating the posterior probability distribution of dielectric aging nodes under the current evidence conditions through probabilistic inference, calculating the posterior probability distribution of mechanical damage nodes under the current evidence conditions, and calculating the posterior probability distribution of safety margin nodes under the current evidence conditions; randomly sampling degradation state samples from the posterior probability distributions of each node, performing time-step evolution on each sample according to the degradation rate probability distribution recorded in the conditional dependency table, updating the state value of dielectric aging nodes by incrementing their degradation rate, updating the state value of mechanical damage nodes by incrementing their damage development rate, and updating the state value of safety margin nodes by decreasing their decay rate within each time step, and repeating the sampling and evolution process to obtain multiple evolution trajectories.

7. The method for assessing the insulation aging status of marine cables based on sea state influence as described in claim 6, characterized in that: The process of obtaining the probability distribution and confidence interval of remaining lifetime includes: setting failure criteria based on the dominant aging mode; when electrical aging is identified as dominant, the failure criterion is that the aging characteristic quantity of the body exceeds the electrical aging failure threshold; when mechanical damage is identified as dominant, the failure criterion is that the mechanical damage degree index exceeds the mechanical failure threshold; when a combined aging mode is identified, the failure criterion is that the insulation safety margin is lower than the safety margin failure threshold; monitoring the degradation index status value at each time step for each evolution trajectory, and recording the time step at which the evolution trajectory first meets the failure criterion as the failure time of the trajectory; statistically analyzing the failure times of all evolution trajectories to form a failure time distribution histogram; normalizing the failure time distribution histogram to obtain the probability density distribution of remaining lifetime; performing cumulative integration on the probability density distribution to obtain the cumulative distribution function of remaining lifetime, and obtaining the median and confidence interval of remaining lifetime.

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