A cable branch box cable joint temperature field real-time inversion method and system

Abstract

The application relates to the technical field of power equipment state monitoring, and discloses a cable branch box cable joint temperature field real-time inversion method and system. The method comprises the following steps: collecting joint temperature data and distributed power output data, obtaining temperature sequences and output sequences; analyzing the dynamic correlation between temperature changes and output fluctuations, and constructing a joint temperature field inversion model; inverting the global temperature field distribution of the cable joint from discrete temperature measurement point data, and identifying a temperature abnormal area; extracting a load sudden increase feature from the output sequence, and calculating the spatial distribution of heat generation rate; inverting joint contact resistance parameters and calculating a thermal resistance network model parameter correction value to generate temperature field correction data; calibrating the joint temperature field inversion model to obtain a high-precision temperature field inversion result; and updating the parameters of dynamic correlation analysis according to time sequence data to determine the evolution trend of the joint temperature field. The application improves the precision of real-time inversion of the cable joint temperature field.

Description

Technical Field

[0001] This application relates to the field of power equipment condition monitoring technology, and in particular to a method and system for real-time inversion of the temperature field of cable joints in cable branch boxes. Background Technology

[0002] Cable distribution boxes are key node devices in power distribution networks, enabling cable line branching, splicing, and transfer. They are widely used in urban power distribution networks, distributed renewable energy access, and power supply to industrial and commercial users. Internal cable joints, due to long-term exposure to electrothermal cycles, mechanical vibration, and environmental corrosion, are prone to defects such as contact surface oxidation, loosening of fastening force, or insulation deterioration. This leads to increased contact resistance and localized overheating. If overheating defects are not detected and addressed in a timely manner, they may further cause joint burning, insulation breakdown, or even short circuits and fires, resulting in power outages and equipment damage, seriously threatening the safe operation of the power grid and public safety.

[0003] Existing temperature monitoring methods mainly include discrete temperature sensors placed on the joint surface, infrared thermometry, and fiber optic thermometry. However, these methods can only obtain the surface temperature at a limited number of measurement points, failing to reveal the spatial distribution characteristics of the three-dimensional temperature field inside the joint, and making it even more difficult to locate hidden internal defects. Some technical solutions use finite element or finite difference numerical simulation methods to establish a joint temperature field calculation model. However, in actual operation, there are significant uncertainties in material thermophysical parameters, convective heat transfer boundary conditions, and load current, leading to large deviations between simulation results and measured temperatures. Furthermore, there is a lack of ability to use real-time measurement data to correct the model online. On the other hand, while temperature prediction methods based on pure data-driven approaches can fit historical temperature change patterns, they lack the support of heat conduction physical mechanisms. Under extreme conditions such as sudden load increases and heat dissipation failures, their extrapolation reliability is insufficient, making it difficult to meet the needs of real-time assessment and early warning of cable branch box joint status. Therefore, there is an urgent need for a method that can deeply integrate measured data with heat conduction physical mechanisms to achieve real-time inversion and evolution trend prediction of the entire joint temperature field. Summary of the Invention

[0004] To address the aforementioned technical issues, this application provides a method and system for real-time inversion of the temperature field of cable joints in cable branch boxes, which improves the accuracy of real-time inversion of the temperature field of cable joints.

[0005] In a first aspect, this application provides a method for real-time inversion of the temperature field of cable joints in cable branch boxes, the method comprising: Temperature data of the joint and output data of the distributed power source are collected by a sensor network deployed in the cable branch box to obtain temperature sequence and output sequence; based on the temperature sequence and output sequence, the dynamic correlation between temperature change and output fluctuation is analyzed to construct a joint temperature field inversion model. Using the joint temperature field inversion model, the global temperature field distribution of the cable joint is inverted from discrete temperature measurement point data to identify temperature anomaly areas; based on the temperature anomaly areas, load surge characteristics are extracted from the output sequence to calculate the spatial distribution of heat generation rate; Based on the spatial distribution of the heat generation rate, the joint contact resistance parameters are inverted and the correction values ​​of the thermal resistance network model parameters are calculated to generate temperature field correction data; based on the temperature field correction data, the joint temperature field inversion model is calibrated to obtain high-precision temperature field inversion results. Time-series data is generated based on the high-precision temperature field inversion results from multiple consecutive time windows. The parameters of the dynamic correlation analysis are updated according to the time-series data to determine the evolution trend of the joint temperature field.

[0006] Secondly, this application provides a real-time temperature field inversion system for cable joints in cable branch boxes, the system comprising: The data acquisition unit is used to acquire joint temperature data and distributed power output data through a sensor network deployed in the cable branch box, and obtain temperature sequence and power output sequence; based on the temperature sequence and the power output sequence, it analyzes the dynamic correlation between temperature change and power output fluctuation, and constructs a joint temperature field inversion model. The model inversion unit uses the joint temperature field inversion model to invert the global temperature field distribution of the cable joint from discrete temperature measurement point data and identify temperature anomaly areas; based on the temperature anomaly areas, it extracts load surge characteristics from the output sequence and calculates the spatial distribution of heat generation rate. The inversion correction unit is used to invert the joint contact resistance parameters and calculate the correction values ​​of the thermal resistance network model parameters based on the spatial distribution of the heat generation rate, and generate temperature field correction data; based on the temperature field correction data, the joint temperature field inversion model is calibrated to obtain high-precision temperature field inversion results. The control unit is used to generate time-series data based on the high-precision temperature field inversion results of multiple consecutive time windows, update the parameters of dynamic correlation analysis based on the time-series data, and determine the evolution trend of the joint temperature field.

[0007] Compared with the prior art, the beneficial effects of the present invention are at least as follows: First, a sensor network deployed within the cable branch box synchronously collects joint temperature sequences and distributed power output sequences. A recursive least squares method with a forgetting factor or a subspace identification method is used to extract the dynamic response kernel function, establishing a time-delay dynamic correlation between power output fluctuations and temperature response. The equivalent heat source intensity estimated by the kernel function is used as the internal heat source input, embedded into a heat conduction partial differential equation model constructed based on the finite element method or finite difference method, achieving a physical inversion from discrete measurement point data to the global temperature field distribution of the joint. A variational assimilation algorithm is used to correct the prior simulation results with the measured temperature as the observed true value, obtaining a posterior temperature field that fits the measured data. Through a dual mechanism of spatial gradient verification and temporal causality verification using the difference field temperature rise threshold, temperature gradient threshold, and cross-correlation analysis with the power output sequence, abnormal temperature regions are accurately identified. Then, based on the energy conservation equation and the truncated singular value decomposition regularization method, the distribution of abnormal heat sources is inverted, and the equivalent contact resistance is inverted. The thermal resistance parameter set of the lumped parameter thermal network model is calibrated using the least squares fitting method. By spatially superimposing the calibration temperature at key nodes with the residual temperature distribution map, the computational efficiency of the lumped parameter thermal network model and the spatial accuracy of the distribution model are balanced, resulting in a high-precision temperature field inversion. Finally, the inversion is iteratively executed according to a preset time window to form time-series data. The recursive least squares method with a forgetting factor is used to calibrate the dynamic correlation parameters. A long short-term memory network is used, with the output of the calibrated inversion model as an exogenous input variable, to predict the temperature field evolution path under normal operation, load surge, and heat dissipation failure scenarios. Combined with the temperature safety index and the remaining time expected to reach the dangerous temperature, a temperature over-limit warning is achieved. Therefore, this invention overcomes the technical shortcomings of traditional point temperature measurement, which cannot reflect the internal temperature distribution of the joint; pure physical simulation, which is greatly affected by the uncertainty of boundary conditions; and pure data-driven models, which lack physical interpretability. It achieves real-time, high-precision, full-domain inversion of the temperature field of cable joints and trend prediction in multiple scenarios. Attached Figure Description

[0008] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0009] Figure 1 This is a flowchart illustrating a real-time temperature field inversion method for cable joints in a cable branch box, as described in this application. Figure 2 This is a schematic diagram of the spatial distribution of heat generation rate according to an embodiment of this application; Figure 3 This is an embodiment of the present application; Figure 4This is a schematic diagram of a real-time temperature field inversion system for cable joints in a cable branch box, according to an embodiment of this application. Detailed Implementation

[0010] This application provides a method and system for real-time inversion of the temperature field of cable joints in cable branch boxes. The terms "first," "second," "third," "fourth," etc. (if present) in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments described herein can be implemented in a sequence other than that illustrated or described herein. Furthermore, the terms "comprising" or "having" and any variations thereof are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or device that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or devices.

[0011] For ease of understanding, the specific process of the embodiments of this application is described below. Please refer to [link / reference]. Figure 1 One embodiment of the real-time inversion method for the temperature field of cable joints in a cable branch box, as described in this application, includes: Step S1: Collect joint temperature data and distributed power output data through a sensor network deployed in the cable branch box to obtain temperature and power output sequences; based on the temperature and power output sequences, analyze the dynamic correlation between temperature changes and power output fluctuations, and construct a joint temperature field inversion model.

[0012] Further, the temperature sequence and output sequence are obtained, including: The temperature changes of each joint in the cable branch box are monitored in real time by a sensor network, which includes multiple temperature sensors arranged on the surface of the joint and the connecting wires between the joints. The temperature value is recorded every unit time to form a temperature sequence. At the same time, the output data of the distributed power source is collected in the same time period, and the output fluctuation is recorded to form an output sequence. The temperature sequence and the output sequence are time-stamped and preprocessed.

[0013] Furthermore, a joint temperature field inversion model is constructed, including: By employing a recursive least squares method with a forgetting factor or a subspace identification method, the temperature sequence of each temperature measuring point is used as the system output, and the current square sequence obtained by converting the output sequence is used as the system input. The dynamic response kernel function characterizing the temperature of each measuring point to the current thermal effect is identified. The dynamic response kernel function adopts a structure of first-order inertial element plus pure delay, which quantifies the gain, delay and time constant of the response of each temperature measuring point under unit power pulse input.

[0014] Based on the geometric structure and material thermal properties of the cable joint, a partial differential equation model of heat conduction is established using the finite element method or finite difference method to describe the heat conduction and convection process inside and on the surface of the joint. The equivalent heat source intensity in the neighborhood of each temperature measuring point is estimated in real time using the dynamic response kernel function and output data.

[0015] The equivalent heat source intensity is used as the heat source input or internal constraint condition and substituted into the heat conduction partial differential equation model. By solving the heat conduction partial differential equation, a joint temperature field inversion model can be constructed that can invert the global temperature field from the discrete measurement point temperature and real-time output.

[0016] Specifically, by deeply integrating data-driven system identification with physical-driven heat conduction models, and utilizing the data from a limited number of temperature sensor points and distributed power output data within the cable branch box, real-time reconstruction of the entire temperature field inside the joint is achieved.

[0017] A sensor network is a wired or wireless measurement system composed of multiple temperature sensors and data acquisition units. These temperature sensors are arranged on the surfaces of each joint inside the cable branch box and on the connecting wires between the joints to sense temperature changes at the joints in real time. Distributed power output data refers to the active power output data of distributed power sources such as photovoltaic and wind power at the grid connection point, reflecting the real-time fluctuations of the load carried by the cable branch box. A temperature sequence is a collection of collected values ​​from various temperature measurement points arranged in chronological order, while a power output sequence is a collection of distributed power output values ​​synchronized with the temperature sequence.

[0018] The system employs a sensor network to monitor temperature changes at each joint within the cable branch box in real time, recording the temperature value per unit time to form a temperature sequence. Simultaneously, it collects output data from distributed power sources within the same time period, recording output fluctuations to form an output sequence. Synchronization timestamps assign a unified time reference to both sets of data, ensuring strict alignment between temperature and output data in the time dimension. This is a prerequisite for subsequent analysis of the dynamic correlation between temperature changes and output fluctuations. Data preprocessing includes outlier removal, missing value imputation, and data smoothing filtering, aiming to eliminate the impact of sensor noise and communication interference on data quality and improve the accuracy of subsequent model identification.

[0019] The essence of constructing a joint temperature field inversion model lies in establishing a mathematical relationship between the temperature measurement point response and the power output, and embedding this data-driven relationship into a physical-driven heat conduction model to form a temperature field reconstruction framework that integrates measured data and physical constraints. Dynamic correlation refers to the time-delay and nonlinear coupling relationship between temperature changes and power output fluctuations. Due to the thermal inertia of cable joints, changes in power output do not immediately cause a temperature response, but are only reflected at the temperature measurement point after a certain delay. This correlation characteristic needs to be quantified and extracted through system identification methods. Specifically, this includes: First, the recursive least squares method with a forgetting factor is an online parameter estimation algorithm. Its basic principle is to update the model parameters using newly acquired data in each iteration, while applying exponentially decaying weights to historical data through a forgetting factor, enabling the model to track the dynamic characteristics of the time-varying system. The subspace identification method is a multivariable system identification technique based on a state-space model. It directly estimates the system's state matrix and output matrix by projecting input and output data into a specific subspace, and is suitable for complex thermal systems with multiple inputs and multiple outputs. The current square sequence is obtained by converting the output sequence of a distributed power source into a current sequence based on its rated voltage and then squared. Its physical basis is Joule's law, which states that the heating power of a conductor is proportional to the square of the current. Therefore, the current square sequence can directly characterize the input intensity of the thermal effect. The dynamic response kernel function is a mathematical function describing the dynamic mapping relationship between the system's input and output. In this invention, a first-order inertial element with a pure delay structure is used. The gain coefficient in its mathematical expression represents the steady-state amplitude of the temperature response under a unit power pulse input. The time constant characterizes the time required for the temperature response to reach a certain proportion of the steady-state value and reflects the magnitude of the system's thermal inertia. The pure delay time represents the delay between the input change and the start of the output response, mainly determined by the time required for heat conduction within the junction. These three parameters together quantify the dynamic characteristics of the temperature response at each temperature measurement point under a unit power pulse input. Based on the dynamic response kernel function, the convolution relationship between the temperature response at the temperature measurement point and the current square sequence can be expressed as: In the formula, Let be the temperature value of the i-th temperature measuring point at time t; It is a sequence of squared currents; The discrete sequence of the dynamic response kernel function corresponding to the i-th measurement point; The expression can be discretized to represent the sampling time interval. The physical meaning of this convolution relationship is that the temperature response at any given time is equal to the cumulative sum of the current-thermal effects at all historical times, weighted by the dynamic response kernel function. The exponential decay characteristic reflects the physical nature of the thermal system's memory of historical inputs decaying exponentially over time. The time-domain expression of the dynamic response kernel function is: In the formula, t is the time variable; For a unit step function, when Its value is 0 when When its value is 1, this function guarantees that during pure delay time... The internal temperature response remains at 0, which is consistent with the fact that heat has not yet been conducted to the measuring point in the actual physical process; K is the gain coefficient and T is the time constant.

[0020] Using the above identification methods, the recursive least squares method with forgetting factor or the subspace identification method is based on this convolutional structure as a model framework. It can extract the gain, time constant and pure delay parameter corresponding to each temperature measurement point from the historical temperature sequence and the current square sequence, thereby establishing a complete dynamic mapping from power fluctuation to temperature response.

[0021] The finite element method (FEM) is a numerical solution method that discretizes the continuous solution domain into a finite number of elements, establishes approximate functions on each element using variational principles or the weighted residual method, and assembles them into a global system of equations. It is suitable for joint structures with complex geometries and non-uniform materials. The finite difference method (FDM) is a numerical method that divides the solution domain into a regular mesh, replaces partial differentials with difference quotients to transform differential equations into a system of algebraic equations. It is simple to implement and computationally efficient. The governing equations of the heat conduction partial differential equation model describe that the rate of temperature change of any infinitesimal element inside the joint is equal to the sum of the net heat flow into that element and the heat generated by the internal heat source. In essence, the heat conduction partial differential equation model is a mathematical description of the physical laws of heat transfer inside the joint. It is a continuous heat conduction partial differential equation, and its governing equations under three-dimensional unsteady conditions with an internal heat source have the following general form: In the formula, Let be the temperature field distribution function, which is a continuous function of spatial coordinates x, y, z and time t; The density of the material; Specific heat capacity; Thermal conductivity; The equivalent heat source intensity is given by equation . The physical meaning of this equation is that the rate of temperature change of any infinitesimal element within the joint over time is equal to the sum of the net heat flow from the surrounding environment and the heat generated by the internal heat source. It exists independently of any solution method and is a mathematical model describing objective physical laws. Material density, specific heat capacity, and thermal conductivity are collectively referred to as material thermal property parameters, which are the fundamental physical property data required to establish this equation. Boundary conditions include convective heat transfer boundaries and radiative heat transfer boundaries between the joint surface and the surrounding air. The convective heat transfer boundary uses Newton's law of cooling to describe the heat exchange between the surface and the environment, while the radiative heat transfer boundary uses the Stefan-Boltzmann law to describe the heat radiation loss. Since partial differential equations of heat conduction are often difficult to solve analytically under complex geometries and boundary conditions, numerical methods (finite element method or finite difference method) are needed to transform them into a system of discrete algebraic equations solvable on a computer.

[0022] Next, using the identified dynamic response kernel function and real-time output data, combined with measured temperature data, the equivalent heat source intensity in the neighborhood of each temperature measurement point is estimated. The logic here is that the dynamic response kernel function establishes a positive dynamic mapping from output fluctuations to temperature response. This mapping takes the current square sequence as input and the temperature sequence as output, and its gain coefficient implicitly contains the comprehensive transfer characteristics from the current heating effect to the temperature response. When output fluctuates, the theoretical expected value of the temperature response can be calculated based on the dynamic response kernel function, while the deviation between the measured temperature data and the expected response reflects the degree to which the actual heat source intensity deviates from the theoretical assumption. The specific estimation process is as follows: The current output data is converted to current and input into the dynamic response kernel function to obtain the theoretical temperature response value for each measuring point; the difference between the measured temperature and the theoretical temperature response value is calculated, representing the additional heat effect not included in the model; based on this difference and the sensitivity relationship between temperature and heat source intensity in the partial differential equation model of heat conduction, the equivalent heat source intensity correction amount in the neighborhood of each temperature measuring point is derived through linearization approximation; this correction amount is superimposed with the theoretical Joule heat source to obtain the estimated value of the equivalent heat source intensity. The equivalent heat source intensity is the intensity value after comprehensively equating various heat-generating factors such as conductor resistance loss, contact resistance loss, and dielectric loss inside the joint into a distributed heat source, with units of watts per cubic meter. The neighborhood range is determined based on the spatial resolution of the temperature sensor and the geometry of the cable connector. It is typically a spherical or cylindrical region centered on the temperature sensor location with a radius equal to half the distance between adjacent sensors. Within this neighborhood, a uniform heat source intensity distribution is assumed, simplifying the continuously distributed heat source field into a set of points away from the heat dissipation source, thus reducing the inversion complexity of solving the subsequent partial differential equations of heat conduction. The input data for this estimation process includes dynamic response kernel function parameters, real-time output data, and measured temperature data. The output data is the estimated equivalent heat source intensity within the neighborhood of each measuring point. Its working principle can be summarized as using a data-driven model to capture the temperature residual caused by heat source disturbances, and then converting the temperature residual into a heat source intensity correction value through the sensitivity relationship of the physical model, achieving a complementary fusion of data-driven and physical-driven approaches.

[0023] Finally, the estimated equivalent heat source intensity is used as the heat source input or internal constraint condition and substituted into the aforementioned partial differential equation model of heat conduction. By solving this partial differential equation, a joint temperature field inversion model is constructed that can invert the global temperature field from discrete measuring point temperatures and real-time output. The logical chain here is that the equivalent heat source intensity is substituted as a known term into the source term of the heat conduction control equation, and the equation is solved in combination with boundary conditions and initial conditions to obtain the temperature field distribution inside and on the surface of the joint. Since the temperature sensors are only arranged on a limited number of discrete measuring points, while the temperature field is continuously distributed, this model realizes the inversion from discrete measuring point data to the global temperature field distribution. The input data of this model are discrete temperature measuring point data and real-time output data, and the output data is the global temperature field distribution of the joint. Its working principle can be summarized as estimating the equivalent heat source in a data-driven manner, and transferring heat in a physical-driven manner, and the two are integrated to reconstruct the global temperature field.

[0024] Step S2: Using the joint temperature field inversion model, the global temperature field distribution of the cable joint is inverted from discrete temperature measurement point data to identify temperature anomaly areas; based on the temperature anomaly areas, the load surge characteristics are extracted from the output sequence to calculate the spatial distribution of heat generation rate.

[0025] Furthermore, areas of abnormal temperature are identified, including: Using the joint temperature field inversion model, the output sequence of the current time window is used as input to perform forward physical simulation and obtain the prior temperature field distribution driven only by the load. The discrete temperature measurement point data collected by the sensor network is used as the observed true value. The prior temperature field distribution is corrected by the variational assimilation algorithm to obtain the posterior temperature field distribution that fits the measured data, which is used as the global temperature field distribution of the cable joint.

[0026] The difference field between the posterior temperature field distribution and the prior temperature field distribution is calculated. In the difference field, regions where the temperature rise exceeds a preset difference threshold are identified as preliminary abnormal regions. In the posterior temperature field distribution, the temperature gradient of the preliminary abnormal region is calculated to confirm that the corresponding gradient value exceeds a preset gradient threshold. The temperature time series of the preliminary abnormal region is extracted and cross-correlation analysis is performed with the output series to confirm the correlation between the two and that the time delay is within a preset physical delay range.

[0027] The initial anomaly region that simultaneously meets both spatial gradient verification and temporal causality verification is set as the temperature anomaly region; and the location coordinates, temperature peak, overtemperature amplitude, and temperature gradient of the temperature anomaly region are output.

[0028] Furthermore, the spatial distribution of heat generation rates is calculated, including: For load surge events identified in the output sequence, the instantaneous actual temperature rise rate is compared with the theoretical heat generation benchmark value in the temperature anomaly region to calculate the thermal anomaly index characterizing the degree of thermal response anomaly. Regions where the thermal anomaly index exceeds the preset screening threshold are set as candidate anomaly subdomains.

[0029] By analyzing the measured temperature changes and temperature gradients within the candidate anomaly subdomains, the heat storage rate and heat conduction loss rate are calculated based on the energy conservation equation. The total heat generation rate at each location within the candidate anomaly subdomain is then solved using the truncated singular value decomposition regularization method.

[0030] The total heat generation rate is filled into the corresponding positions of the candidate abnormal subdomains, while the theoretical heat generation baseline value is filled into the positions of all other regions, generating a complete thermal map that quantitatively highlights the abnormal heat source against a normal background, serving as the spatial distribution of the heat generation rate.

[0031] From the spatial distribution of heat generation rate, the abnormal heat generation rate distribution is separated, and based on the abnormal heat generation rate distribution, the peak heat source intensity and total heat generation power of the defect are calculated. When the calculation result exceeds the preset risk threshold, an alarm is triggered.

[0032] Specifically, the core logic of step S2 is to obtain a more reliable global temperature field estimate than a single method by fusing theoretical predictions driven by physical models with observational constraints driven by measured data, and then identify the abnormal heat source caused by joint defects from the spatial distribution characteristics and temporal evolution of the temperature field.

[0033] Forward physics simulation refers to the calculation process of deriving results from causes based on the physical laws described by the partial differential equation of heat conduction, under known boundary conditions, initial conditions, and heat source input. Its input data includes the output sequence within the current time window, converted to a current square sequence, as well as external parameters such as ambient temperature and heat dissipation boundary conditions. The output data is the theoretical temperature distribution at various spatial locations inside and on the surface of the joint, i.e., the a priori temperature field distribution. The a priori temperature field distribution represents a preliminary estimate of the joint temperature state based on physical laws and known load conditions. However, due to uncertainties in model parameters and the difficulty in precisely defining boundary conditions, this distribution often deviates from the actual temperature field.

[0034] To eliminate the aforementioned bias, discrete temperature measurement point data collected by the sensor network are used as the observed true values. A variational assimilation algorithm is then used to correct the prior temperature field distribution, resulting in a posterior temperature field distribution that fits the measured data, which serves as the global temperature field distribution for the cable joint. The variational assimilation algorithm is a data assimilation method that constructs and minimizes a cost function to achieve optimal fusion of observed data and model predictions. Its cost function typically consists of two terms: a background term, which measures the deviation between the analyzed field and the prior temperature field; and an observation term, which measures the fitting error between the analyzed field value at the measurement point and the actual observed temperature. These two terms are weighted by the background error covariance and the observation error covariance. The algorithm's input data includes the prior temperature field distribution, discrete temperature measurement point data, the background error covariance matrix, and the observation error covariance matrix. The output data is the optimal temperature field analysis value that minimizes the cost function, i.e., the posterior temperature field distribution. The physical significance of the posterior temperature field distribution lies in the fact that it not only obeys the physical laws of heat conduction, but also closely approximates the measured data at the measurement point location. Therefore, it can better reflect the real temperature state than simple physical simulation or simple data interpolation. Thus, it is used as the global temperature field distribution of the cable joint.

[0035] The difference field is the spatial distribution of temperature deviation obtained by subtracting the prior temperature field distribution from the posterior temperature field distribution point by point. Its physical meaning lies in revealing the degree of deviation between the temperature information contained in the measured data and the prediction of the pure physical model. This deviation often indicates the presence of abnormal heat sources or changes in heat transfer paths inside the joint that the model fails to describe. The preset difference threshold is determined comprehensively based on the normal operating temperature range of the cable joint and the measurement uncertainty. First, the normal operating temperature range is statistically determined based on the steady-state operating data of the cable joint under rated load. The measurement uncertainty characterizes the combined influence of random and systematic errors introduced by the temperature sensor and data acquisition system, and is usually determined through sensor calibration experiments and repeatability tests. To distinguish between normal fluctuations and abnormal deviations, the preset difference threshold should be greater than the sum of the maximum dynamic fluctuation amplitude and the measurement uncertainty within the normal operating temperature range. The specific calculation formula is: the preset difference threshold is equal to half the difference between the upper and lower limits of the normal operating temperature range, plus the absolute value of the expanded uncertainty, and then multiplied by the safety factor. The safety factor is usually taken as 1.5 to 2.0 to accommodate model simplification errors and uncertainties of unaccounted boundary conditions. When the difference value of a certain region exceeds the threshold, it indicates that the thermal state of the region deviates significantly from normal physical expectations, and is thus marked as a preliminary abnormal region.

[0036] Subsequently, the temperature gradient of the initial anomaly region is calculated in the posterior temperature field distribution, confirming that the corresponding gradient value exceeds the preset gradient threshold. The temperature gradient is the rate of change of the temperature field in space, mathematically represented as the partial derivative vector of temperature with respect to spatial coordinates. Its physical meaning lies in indicating the direction and intensity of heat transfer. According to Fourier's law of heat conduction, a larger temperature gradient means a higher local heat flux density, often corresponding to local overheating or impeded heat dissipation. The preset gradient threshold is set based on the thermal conductivity of the joint material and the temperature distribution characteristics under normal operating conditions. When the temperature gradient of the initial anomaly region exceeds this threshold, it indicates that the abnormal heat source has spatial concentration rather than a globally uniform temperature rise, thus eliminating false alarms caused by factors such as overall changes in ambient temperature.

[0037] Based on this, the temperature time series of the initial anomaly area is extracted and cross-correlation analysis is performed with the output series to confirm the correlation between the two and that the time delay is within the preset physical delay range. Cross-correlation analysis is a statistical method to measure the similarity between two time series at different time offsets. Its basic principle is to calculate the correlation coefficient between the temperature time series and the output series at different time delays and find the optimal time delay that maximizes the correlation coefficient. The input data for this method are the temperature time series of the initial anomaly area and the synchronous output series, and the output data are the cross-correlation function curve and the optimal time delay estimate. The preset physical delay range is determined based on the pure delay time parameter of the dynamic response kernel function identified in step S1. If the optimal time delay obtained from the cross-correlation analysis falls within this range, it indicates that there is a physical causal relationship between the temperature anomaly and the load fluctuation, and that the temperature anomaly is caused by the current heating effect rather than external random interference, thus verifying time causality.

[0038] The spatial gradient verification ensures that the anomaly has local concentration and heat flow accumulation characteristics, while the temporal causality verification ensures that the anomaly is physically related to the load fluctuation. Both conditions must be met simultaneously to confirm it as a true temperature anomaly region, thereby improving the accuracy and reliability of anomaly identification.

[0039] Specifically, a load surge event refers to a phenomenon where the power value in a power sequence increases significantly within a short period of time, usually identified by setting a power change rate threshold. The instantaneous actual temperature rise rate refers to the temperature rise amplitude at each point within the temperature anomaly area per unit time, obtained by numerical differentiation of the temperature time series. The theoretical heat generation benchmark value refers to the theoretical heating power calculated according to Joule's law, where the contact resistance uses the factory nominal value or historical statistical average, representing the expected heating level under normal contact conditions. The thermal anomaly index is defined as the ratio of the instantaneous actual temperature rise rate to the theoretical temperature rise rate. The theoretical temperature rise rate is calculated by dividing the theoretical heat generation benchmark value by the equivalent heat capacity of the joint. This index has a dimension of 1, and its physical meaning is to quantify the deviation of the actual thermal response from the normal theoretical expectation by a factor of 1. An index equal to 1 indicates normal operation, while an index greater than 1 indicates the presence of an abnormal heat source; the larger the index, the more severe the anomaly. The preset screening threshold is determined based on the statistical characteristics under normal operating conditions. When the thermal anomaly index exceeds this threshold, it indicates that the thermal response of the area significantly deviates from the normal benchmark, thus being designated as a candidate anomaly subdomain.

[0040] The specific form of the energy conservation equation within the candidate anomaly subdomain is that the total heat generation rate equals the sum of the heat storage rate and the heat conduction dissipation rate. The heat storage rate represents the heat absorbed by the joint material due to temperature increase, determined by the material density, specific heat capacity, volume, and rate of temperature change. The heat conduction dissipation rate represents the heat transferred to the surrounding area through heat conduction, determined by the thermal conductivity, heat transfer cross-sectional area, and temperature gradient. The truncated singular value decomposition regularization method is a numerical stabilization technique for solving ill-conditioned linear inverse problems. Its basic principle is to perform singular value decomposition on the sensitivity matrix of the inversion problem, retaining larger singular values ​​while discarding smaller ones, thereby suppressing the amplification effect of measurement noise on the solution. The input data for this method are the temperature measurements and temperature gradient values ​​within the candidate anomaly subdomain, as well as the kernel matrix formed by discretizing the energy conservation equation. The output data is the stable spatial distribution of the total heat generation rate. Since inverting the heat source distribution in a continuous space from temperature data at finite measurement points is a typical ill-conditioned inverse problem, direct solution will make the solution extremely sensitive to noise. Therefore, the truncated singular value decomposition regularization method must be used to obtain a physically reasonable stable solution.

[0041] The total heat generation rate within the candidate anomalous subdomain includes both normal Joule heat and anomalous additional heat sources, while other regions only contain normal Joule heat. By comparing the high heat source intensity in the anomalous region with the baseline heat source intensity in the normal region, the location, range, and intensity of the anomalous heat source can be clearly marked in space, forming an intuitive thermal map, which can serve as the spatial distribution of the heat generation rate.

[0042] The abnormal heat generation rate distribution refers to the pure abnormal heat source component obtained by subtracting the theoretical heat generation baseline value from the total heat generation rate. Its physical sources are mainly defects such as increased contact resistance, partial discharge, or insulation degradation. The peak heat source intensity is the maximum value in the abnormal heat generation rate distribution, reflecting the location of the most severe defect. The total heat generation power is the integral of the abnormal heat generation rate over the abnormal area volume, reflecting the overall severity of the defect. The preset risk threshold is determined based on the heat resistance grade of the cable joint material and the safe operation procedures. When the peak heat source intensity or the total heat generation power exceeds the corresponding threshold, it indicates that the defect has developed to the point where immediate action is required, and the system automatically generates an alarm message.

[0043] For example, Figure 2 This is a spatial distribution diagram of the heat generation rate. The light gray background area represents the theoretical baseline value of heat generation, indicating the expected heat generation level of the cable joint under normal contact conditions. The dark gray to black highlighted areas are candidate abnormal sub-domains, and their gray levels indicate the overall heat generation rate (see the grayscale bar on the right). Figure 2 As shown, two distinct abnormal heat source regions are located slightly to the left of the center of the joint contact surface and at the right conductor connection point, respectively. The right heat source has a darker gray scale, indicating a higher rate of total heat generation at that location, corresponding to increased contact resistance or more severe local defects. This figure allows for a direct and quantitative determination of the spatial location, range, and relative intensity of the abnormal heat sources, verifying the effectiveness of inverting the distribution of abnormal heat sources based on the energy conservation equation and the truncated singular value decomposition regularization method.

[0044] Step S3: Based on the spatial distribution of heat generation rate, invert the joint contact resistance parameters and calculate the correction values ​​of thermal resistance network model parameters to generate temperature field correction data; based on the temperature field correction data, calibrate the joint temperature field inversion model to obtain high-precision temperature field inversion results.

[0045] Furthermore, temperature field correction data is generated, including: Based on the spatial distribution of heat generation rate and the inverted global temperature field distribution of the cable joint, the equivalent contact resistance of the joint is calculated under the assumption of uniform contact resistance distribution along the contact surface or under constraints based on the principle of minimum entropy generation. Simultaneously, the node temperatures and inter-node heat flows in the global temperature field distribution of the cable joint are extracted, and the thermal resistance parameter set of the lumped parameter thermal network model is calibrated using the least squares fitting method. For key nodes of the lumped parameter thermal network model, the internal temperature distribution of the corresponding physical components is extracted. By subtracting the calibration temperature of the key nodes from the internal temperature distribution, a residual temperature distribution map is generated. The equivalent contact resistance, thermal resistance parameter set, and residual temperature distribution map are encapsulated into structured temperature field correction data.

[0046] Furthermore, high-precision temperature field inversion results are obtained, including: Using the equivalent contact resistance and thermal resistance parameter set of the temperature field correction data, the physical parameters of the lumped parameter thermal network model used in the joint temperature field inversion model are calibrated. Based on the real-time acquired current load and ambient temperature, the calibration temperature of at least one key node is calculated using the calibrated lumped parameter thermal network model. The calibration temperature of at least one key node is spatially superimposed with the corresponding residual temperature distribution map in the temperature field correction data to generate the temperature field distribution of the key node, which serves as the high-precision temperature field inversion result.

[0047] Specifically, step S3, based on the spatial distribution of heat generation rate, inverts the joint contact resistance parameters and calculates the correction values ​​for the thermal resistance network model parameters, generating temperature field correction data. This correction data is then used to calibrate the joint temperature field inversion model, obtaining high-precision temperature field inversion results. The core logic of this step lies in transforming the abnormal heat source information obtained from the inversion of the partial differential equation model of heat conduction into the physical parameter correction values ​​of the thermal resistance network model, while retaining the local temperature non-uniformity information described by the distributed parameter model. This allows for the recovery of detailed temperature field features within a simplified computational framework, achieving a balance between computational efficiency and spatial accuracy.

[0048] The physical source of the abnormal heat generation rate component in the spatial distribution of heat generation rate is mainly contact resistance loss. According to Joule's law, the power of contact resistance loss is equal to the product of the square of the current and the contact resistance. Therefore, given the abnormal heat generation rate and current load, the magnitude of the contact resistance can be deduced. However, inverting contact resistance from the heat source distribution is a typical ill-conditioned inverse problem, with non-unique solutions and sensitivity to noise. Therefore, additional physical constraints are needed to ensure the rationality of the solution. Assuming that the contact resistance is uniformly distributed along the contact surface means simplifying the microscopic contact state on the contact interface into a spatially constant equivalent resistance value. This transforms the distributed heat source inversion problem into a single lumped parameter estimation problem, significantly reducing the solution complexity. The minimum entropy generation principle is a variational principle in linear non-equilibrium thermodynamics. Its physical meaning is that under steady-state conditions, the system tends to a state that minimizes the entropy generation rate. Using this principle as a constraint can mathematically narrow the feasible solution space for contact resistance inversion, forcing the inversion result to tend towards the most thermodynamically stable and uniform distribution state, thereby improving the physical rationality of the solution. The input data for this inversion process are the spatial distribution of heat generation rate, the global temperature field distribution of the cable joint, and the real-time current load. The output data is the equivalent contact resistance of the joint. Its working principle can be summarized as separating the component caused by contact resistance from the abnormal heat source intensity and inversely calculating its resistance value under the combined effect of energy conservation and additional physical constraints.

[0049] The lumped-parameter thermal network model (thermal resistance network model) simplifies a continuously distributed temperature field into an equivalent circuit model composed of several nodes with thermal resistance and thermal capacity. Each node represents a physical component with a uniform temperature, thermal resistance represents the resistance to heat transfer between nodes, and thermal capacity represents the heat storage capacity of each node. This model reduces the complex three-dimensional heat conduction problem to a problem of calculating the thermal paths between nodes, significantly reducing the computational burden of real-time inversion. Node temperature refers to the average temperature of the physical component corresponding to each lumped node, typically taken as the volume average temperature of the component in the corresponding spatial region within the global temperature field distribution. Inter-node heat flow refers to the amount of heat flowing from one node to an adjacent node per unit time, calculated according to Fourier's law of heat conduction, and is determined by the temperature difference between the two nodes and the thermal resistance along the heat transfer path.

[0050] Specifically, cable joints are physically composed of several relatively homogeneous components, including a conductor core, insulation layer, shielding layer, and outer sheath. While the temperature distribution within each component is not perfectly uniform, it can be approximated as a single node temperature within the limits of engineering precision. Heat transfer between components is simplified to thermal resistance connections between nodes, thus reducing the continuous three-dimensional heat conduction problem to a discrete node thermal path calculation problem. This simplification in heat transfer is known as the lumped parameter method. The nodes are divided based on the natural boundaries of material interfaces and the main links in the heat transfer path. For example, the conductor core can be considered as a node, the insulation layer as a node, and the outer surface as a node. The thermal resistance between nodes is formed by the series or parallel connection of the thermal conductivity and contact resistance of the corresponding material layers. Therefore, the node topology of the lumped parameter thermal network model is directly derived from the layered physical structure of the joint. Its initial thermal resistance parameters can be theoretically calculated from the geometric dimensions and thermophysical properties of each layer. Subsequently, the least squares fitting method is used to calibrate and correct the node temperature and inter-node heat flow data in the global temperature field distribution, bringing it closer to the equivalent thermal resistance value under actual operating conditions from the theoretical initial value.

[0051] Least squares fitting is an optimization method that estimates model parameters by minimizing the sum of squared errors between the model output and the observed data. Its input data consists of the temperature observations of each node extracted from the global temperature field distribution and the heat flow values ​​between nodes calculated based on the temperature gradient. The output data is the optimal estimate of the thermal resistance parameter, which minimizes the deviation between the temperature response of the lumped parameter thermal network model and the calculation results of the distributed parameter model under the same boundary conditions. Its working principle is to iteratively adjust the thermal resistance parameter until the sum of squared residuals between the node temperature trajectory of the lumped parameter thermal network model and the reference temperature trajectory of the distributed parameter model reaches a minimum, thereby establishing a quantitative correspondence between the lumped parameter thermal network model and the refined physical model.

[0052] Critical nodes are nodes that have a decisive influence on the overall temperature field distribution. They are typically selected based on the highest temperature, maximum heat flux, or strongest coupling with other nodes. The accuracy of temperature calculations at these nodes directly affects the reliability of the entire temperature field inversion. Internal temperature distribution refers to the detailed spatial distribution of the physical component corresponding to the critical node within the global temperature field, rather than a simple node average temperature. A residual temperature distribution map is generated by subtracting the calibration temperature of the critical node from this internal temperature distribution. The calibration temperature here refers to the reference temperature value of the critical node calculated using a distributed parameter model, typically the average temperature of the spatial region corresponding to that node. The residual temperature distribution map shows the difference between the actual temperature at each point within the physical component and the node's calibration temperature. Its physical significance lies in revealing local temperature non-uniformities that the lumped parameter model cannot describe, such as local hot spots due to poor contact or temperature gradients due to uneven heat dissipation. This residual information is crucial for recovering the spatial details of the temperature field. The equivalent contact resistance, thermal resistance parameter set, and residual temperature distribution map are encapsulated into structured temperature field correction data. Structured means that multiple types of correction information are integrated according to a predetermined data format so that the subsequent model calibration module can directly call them. Its input data is the aforementioned three correction information items, and the output data is a temperature field correction data package in a unified format.

[0053] Specifically, calibration refers to replacing the original initial or default parameters in the model with corrected parameters, making the physical description of the model closer to the actual operating state. Specifically, this involves substituting the equivalent contact resistance into the heat source calculation to correct the amount of Joule heat generated, and substituting the thermal resistance parameter set into the thermal circuit equation to correct the heat transfer characteristics between nodes, thereby ensuring that the steady-state and dynamic response characteristics of the lumped parameter model are consistent with the actual thermal behavior of the joint. Based on real-time acquired current load and ambient temperature, the calibration temperature of at least one critical node is calculated using the calibrated lumped parameter thermal network model. The calibration temperature here refers to the critical node temperature value calculated after model calibration. Because the calibrated model parameters have absorbed refined information from the distributed parameter model, its calculation accuracy is higher than the initial calculated value before calibration, and it can more accurately reflect the true temperature level of the critical node under the current operating conditions. The input data for this calculation process is real-time current load and ambient temperature, and the output data is the calibration temperature of the critical node. Its working principle is to substitute the real-time operating conditions into the calibrated thermal circuit equation and obtain the temperature response of each node by solving the node thermal balance equation.

[0054] Based on this, the calibration temperature of at least one key node is spatially superimposed with the corresponding residual temperature distribution map in the temperature field correction data to generate the temperature field distribution of the key node, which serves as the high-precision temperature field inversion result. The mathematical operation of spatial superposition involves adding the residual temperature distribution point by point to the calibration temperature. That is, the high-precision temperature field equals the sum of the calibration temperature and the residual temperature. Its physical meaning is that the calibration temperature provides the overall temperature level of the physical component corresponding to the key node, while the residual temperature distribution map provides details of the local temperature non-uniformity within the component, such as the temperature rise amplitude and spatial range of local hot spots. The superposition of the two ensures the accuracy of the overall temperature and restores the spatial details of the local temperature field, thereby overcoming the shortcomings of insufficient spatial resolution of the simple lumped parameter model and poor real-time performance of the simple distributed parameter model, and obtaining a high-precision temperature field inversion result that combines computational efficiency and spatial accuracy. The input data for this process are the calibration temperature of the key nodes and the corresponding residual temperature distribution map. The output data is the high-precision temperature field distribution of the key nodes. Its working principle can be summarized as follows: taking the accurate node temperature of the lumped parameter thermal network model as the benchmark and the residual information of the distribution model as the correction, the overall level of the temperature field and the local details are integrated and reconstructed through spatial superposition.

[0055] Step S4: Based on the high-precision temperature field inversion results of multiple consecutive time windows, time series data is generated. The parameters of dynamic correlation analysis are updated according to the time series data to determine the evolution trend of the joint temperature field.

[0056] Furthermore, determining the evolution trend of the joint temperature field also includes: Temperature field inversion is performed iteratively within a preset time window. The high-precision temperature field inversion results from multiple consecutive time windows are organized into time-series data. Spatiotemporal evolution characteristics of the temperature field are extracted from the time-series data, including hotspot location migration trajectories, temperature peak change curves, and changes in the temperature surface topology corresponding to the temperature field. Based on the spatiotemporal evolution characteristics, the recursive least squares method with a forgetting factor is used to analyze the actual correlation between temperature changes and power output fluctuations. The dynamic correlation parameters of the joint temperature field inversion model are calibrated and updated. The dynamic correlation parameters include the gain coefficient of the dynamic response kernel function, the time constant, and the pure delay time. Based on the updated model output, the evolution trend of the joint temperature field in the future time period is predicted to determine whether there is a risk of continuous temperature rise or hotspot diffusion. The evolution trend and the corresponding predicted temperature field distribution are stored in the database.

[0057] Furthermore, determining the evolution trend of the joint temperature field also includes: Based on the high-precision temperature field inversion results, combined with the rated operating temperature and safety margin of the cable branch box, the temperature safety index of each joint is calculated. If the temperature safety index is lower than the preset safety threshold, a temperature over-limit warning is generated, which includes the location of the abnormal joint, the current peak temperature of the temperature field, and the remaining time expected to reach the dangerous temperature. Based on time-series data, a long short-term memory network is used to construct a spatiotemporal prediction model for the temperature field. The output of the calibrated joint temperature field inversion model is used as the exogenous input variable of the spatiotemporal prediction model for the temperature field, predicting the temperature field evolution path under normal operation, load surge, and heat dissipation failure scenarios, and outputting multi-scenario temperature field prediction results. Based on the multi-scenario temperature field prediction results, the operational risk assessment and temperature runaway prevention and control decisions for the cable branch box are output.

[0058] Specifically, step S4 generates time-series data based on the high-precision temperature field inversion results across multiple consecutive time windows. The parameters of the dynamic correlation analysis are then updated according to the time-series data to determine the evolution trend of the joint temperature field. The core of this step lies in utilizing the temporal continuity of historical inversion results to dynamically track the changing patterns of the joint's thermal state and predict future trends accordingly, thereby extending the monitoring from condition monitoring to trend warning.

[0059] A preset time window refers to a fixed analysis period set to balance temporal resolution and computational efficiency, typically ranging from several minutes to tens of minutes. Adjacent windows can overlap to ensure temporal continuity. Time-series data refers to multiple frames of temperature field distribution data arranged chronologically, with each frame corresponding to the global temperature field inversion result within a time window, thus forming a four-dimensional data volume depicting the evolution of the temperature field over time. From this time-series data, the spatiotemporal evolution characteristics of the temperature field are extracted, including the migration trajectory of hotspot locations, temperature peak variation curves, and changes in the topological structure of isothermal surfaces within the temperature field. The hotspot migration trajectory refers to the curve showing the change of the spatial coordinates of the highest temperature point within each time window over time. Its physical significance lies in reflecting the spatial movement trend of the heat source center inside the joint. If the trajectory shows directional drift or diffusion, it indicates a deterioration in the contact condition or the expansion of defects. The temperature peak change curve refers to the curve showing the change of the highest temperature value in the entire region within each time window over time. Its physical significance lies in reflecting the deterioration or mitigation trend of the overall thermal state of the joint. The slope and curvature of the curve can be used to determine whether the temperature rise is accelerating. The isothermal surface topological structure change refers to the change in the shape, connectivity, and enclosing volume of the isosurface formed by a specific temperature threshold in space over time. Its physical significance lies in reflecting the overall evolution of the spatial morphology of the temperature field. For example, if the isothermal surface develops from an isolated clump to a connected sheet, it indicates that the hotspot is spreading and the temperature field is becoming non-uniform.

[0060] As the joint operates over a long period, oxidation of the contact surface, material aging, or loosening of the fastening force can cause a slow drift in heat transfer characteristics. The dynamic response kernel function parameters identified in step S1 may gradually deviate from the current actual state. Therefore, it is necessary to continuously update these parameters using the latest time-series data. The recursive least squares method with a forgetting factor takes as input recent temperature time series segments and synchronous output sequence segments extracted from the time-series data, and outputs updated dynamic correlation parameters, namely the gain coefficient, time constant, and pure delay time of the dynamic response kernel function. Its working principle is to estimate the parameters with the latest observation residuals in each update step, while reducing the weight of early historical data through the forgetting factor, so that the model parameters always track the current state of the joint's thermal characteristics, thereby ensuring the accuracy of the inversion model in describing the actual physical process.

[0061] This study predicts the evolution trend of the joint temperature field over future periods to assess the risk of sustained temperature increases or hotspot spread. The prediction process involves forward integration or extrapolation of the updated dynamic response kernel function and thermal network model parameters. Under the assumption that future loads will continue according to the current trend or change according to the predicted curve, the temperature field distribution for multiple future time windows is calculated. The risk of sustained temperature increases is assessed by checking whether the predicted slope of the temperature peak change curve remains positive and exceeds the safe growth rate. The risk of hotspot spread is assessed by checking the diffusion rate of the hotspot location migration trajectory and the predicted growth rate of the isothermal surface-enclosed volume. The evolution trend and the corresponding predicted temperature field distribution are stored in a database for subsequent querying, statistical analysis, and historical comparison.

[0062] Specifically, the rated operating temperature refers to the highest temperature that a cable joint is allowed to reach under long-term normal operating conditions, determined by the heat resistance grade of the insulation material; the safety margin refers to the difference between the rated operating temperature and the dangerous temperature, used to accommodate the effects of load fluctuations and measurement uncertainties; the temperature safety index is a comprehensive quantitative indicator of the current thermal safety level of the joint, and its calculation can be in a normalized form, for example, defined as the difference between the rated operating temperature and the current peak temperature divided by the safety margin. The closer the index is to one, the more sufficient the safety margin; the closer it is to zero, the closer it is to a dangerous state. If the temperature safety index is lower than the preset safety threshold, a temperature over-limit warning is generated. This warning includes the location of the abnormal joint, the current peak temperature field, and the remaining time expected to reach the dangerous temperature. The estimated time remaining to reach the hazardous temperature is calculated by substituting the current peak temperature, the recent rate of temperature rise, and the hazardous temperature threshold into a linear or exponential extrapolation model. Its physical meaning is to provide maintenance personnel with a time window to take emergency measures. The input data of this extrapolation model are the current peak temperature, the recent rate of temperature rise, and the hazardous temperature threshold, and the output data is the estimated time remaining. Its working principle is to assume that the current temperature rise trend remains unchanged in the short term and calculate the time required for the temperature to rise from the current value to the hazardous temperature.

[0063] Long Short-Term Memory (LSTM) networks are a special type of recurrent neural network that addresses the gradient vanishing and long-term dependency problems faced by traditional recurrent neural networks when processing long sequences by introducing three gating mechanisms: input gate, forget gate, and output gate. This allows them to effectively capture long-term trends and short-term fluctuations in time series. The network's input data includes historical time-series temperature field data, the current inversion model output, and exogenous input variables. The output data is a prediction of the temperature field distribution for multiple future time steps. Exogenous input variables refer to variables not generated internally by the temperature field spatiotemporal prediction model but input from an external system. Specifically, it refers to the high-precision temperature field distribution output by the calibrated junction temperature field inversion model. This distribution, as an exogenous input variable, provides the prediction model with accurate initial conditions and boundary constraints for the current thermal state, creating an information loop between data-driven prediction and physics-driven inversion.

[0064] Normal operation scenario refers to a scenario where the load fluctuates smoothly according to historical statistical patterns, with boundary conditions including a normal heat dissipation environment and a typical load curve. Load surge scenario refers to a scenario with a high-power impact load or a sudden increase in distributed power output, with boundary condition being a short-term, significant increase in current. Heat dissipation failure scenario refers to a scenario where cooling fan failure, vent blockage, or excessive ambient temperature leads to deterioration of heat dissipation conditions, with boundary conditions including a significant decrease in the convective heat transfer coefficient or an abnormal increase in ambient temperature. The boundary conditions for these three scenarios are set based on equipment operation and maintenance experience and environmental monitoring data. By substituting the boundary conditions of different scenarios into the temperature field spatiotemporal prediction model, the predicted temperature field evolution path under the corresponding scenario can be obtained.

[0065] Operational risk assessment involves a comprehensive analysis of temperature field prediction results under various scenarios, providing risk indicators such as joint failure probability and insulation life loss rate. Its input data consists of temperature field prediction results for multiple scenarios, and its output data is a quantitative risk level assessment. Temperature runaway prevention and control decision-making automatically generates or recommends control measures based on the risk assessment results, such as load transfer, derated operation, activation of backup cooling devices, or maintenance scheduling. Its input data consists of risk level assessment and current operating status, and its output data is specific control instructions or suggested solutions, thereby achieving closed-loop management from temperature monitoring to risk warning and then to proactive control.

[0066] For example, Figure 3 This diagram illustrates the prediction and verification of the joint temperature field evolution trend under different operating conditions. The horizontal axis represents time (minutes), and the vertical axis represents the temperature at key joint points (°C). The solid black line represents the measured temperature evolution curve, and the dark gray dashed line represents the LSTM model prediction curve. Figure 3In the figure, subfigure (a) shows the normal operation scenario: the temperature rises slowly with load fluctuations and then stabilizes, with the predicted curve and the measured curve showing a high degree of agreement, and the relative error is less than ±0.5°C; subfigure (b) shows the load surge scenario: a sudden increase in power occurs at about 40 minutes, and the measured temperature rises rapidly. The LSTM model accurately captures this surge trend, and the prediction response delay is less than one sampling period; subfigure (c) shows the heat dissipation failure scenario: the temperature rises rapidly after about 60 minutes due to deteriorating heat dissipation conditions. The LSTM model can still predict this acceleration trend in advance based on historical correlations. The validation results of the three scenarios show that the constructed LSTM spatiotemporal prediction model has good extrapolation ability and robustness, and can provide a reliable decision-making basis for the prevention and control of temperature runaway in cable branch boxes.

[0067] The above describes a method for real-time inversion of the temperature field of cable joints in cable branch boxes according to embodiments of this application. The following describes a system for real-time inversion of the temperature field of cable joints in cable branch boxes according to embodiments of this application. Please refer to [link to relevant documentation]. Figure 4 One embodiment of the real-time temperature field inversion system for cable joints in a cable branch box according to this application includes: The acquisition unit is used to collect joint temperature data and distributed power output data through a sensor network deployed in the cable branch box, and obtain temperature sequence and power output sequence; based on the temperature sequence and power output sequence, it analyzes the dynamic correlation between temperature change and power output fluctuation, and constructs a joint temperature field inversion model.

[0068] The model inversion unit uses the joint temperature field inversion model to invert the global temperature field distribution of the cable joint from discrete temperature measurement point data and identify temperature anomaly areas. Based on the temperature anomaly areas, it extracts the load surge characteristics from the output sequence and calculates the spatial distribution of heat generation rate.

[0069] The inversion correction unit is used to invert the joint contact resistance parameters and calculate the correction values ​​of the thermal resistance network model parameters based on the spatial distribution of the heat generation rate, and generate temperature field correction data; based on the temperature field correction data, the joint temperature field inversion model is calibrated to obtain high-precision temperature field inversion results.

[0070] The control unit is used to generate time-series data based on the high-precision temperature field inversion results of multiple consecutive time windows, update the parameters of dynamic correlation analysis based on the time-series data, and determine the evolution trend of the joint temperature field.

[0071] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0072] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0073] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A method for real-time inversion of the temperature field of cable joints in cable branch boxes, characterized in that, The method includes: Temperature data of the joint and output data of the distributed power source are collected by a sensor network deployed in the cable branch box to obtain temperature sequence and output sequence; based on the temperature sequence and output sequence, the dynamic correlation between temperature change and output fluctuation is analyzed to construct a joint temperature field inversion model. Using the joint temperature field inversion model, the global temperature field distribution of the cable joint is inverted from discrete temperature measurement point data to identify temperature anomaly areas; based on the temperature anomaly areas, load surge characteristics are extracted from the output sequence to calculate the spatial distribution of heat generation rate; Based on the spatial distribution of the heat generation rate, the joint contact resistance parameters are inverted and the correction values ​​of the thermal resistance network model parameters are calculated to generate temperature field correction data; based on the temperature field correction data, the joint temperature field inversion model is calibrated to obtain high-precision temperature field inversion results. Time-series data is generated based on the high-precision temperature field inversion results from multiple consecutive time windows. The parameters of the dynamic correlation analysis are updated according to the time-series data to determine the evolution trend of the joint temperature field.

2. The method according to claim 1, characterized in that, Obtain the temperature and output sequences, including: The temperature changes of each joint in the cable branch box are monitored in real time by a sensor network, which includes multiple temperature sensors arranged on the surface of the joint and the connecting wires between the joints. The temperature value is recorded every unit time to form the temperature sequence. At the same time, the output data of the distributed power source in the same time period is collected and the output fluctuation is recorded to form the output sequence. The temperature sequence and the output sequence are time-stamped and preprocessed.

3. The method according to claim 1, characterized in that, Constructing a joint temperature field inversion model, including: Using a recursive least squares method with a forgetting factor or a subspace identification method, the temperature sequence of each temperature measuring point is used as the system output, and the current square sequence obtained by converting the output sequence is used as the system input. The dynamic response kernel function characterizing the temperature of each measuring point to the current thermal effect is identified. The dynamic response kernel function adopts a structure of first-order inertial element plus pure delay, which quantifies the gain, delay and time constant of the response of each temperature measuring point under unit power pulse input. Based on the geometric structure and material thermal properties of the cable joint, a partial differential equation model of heat conduction describing the heat conduction and convection process inside and on the surface of the joint is established using the finite element method or finite difference method. Using the dynamic response kernel function and output data, the equivalent heat source intensity in the neighborhood of each temperature measuring point can be estimated in real time. The equivalent heat source intensity is used as the heat source input or internal constraint condition and substituted into the heat conduction partial differential equation model. By solving the heat conduction partial differential equation, the joint temperature field inversion model that can invert the global temperature field from the discrete measurement point temperature and real-time output is constructed.

4. The method according to claim 1, characterized in that, Identify areas of abnormal temperature, including: Using the joint temperature field inversion model, the output sequence of the current time window is used as input to perform forward physical simulation, obtaining the prior temperature field distribution driven only by the load; the discrete temperature measurement point data collected by the sensor network is used as the observed true value, and the prior temperature field distribution is corrected through variational assimilation algorithm to obtain the posterior temperature field distribution that fits the measured data, which is used as the global temperature field distribution of the cable joint. Calculate the difference field between the posterior temperature field distribution and the prior temperature field distribution, and identify regions in the difference field where the temperature rise exceeds a preset difference threshold as preliminary abnormal regions; In the posterior temperature field distribution, the temperature gradient of the initial anomaly region is calculated, and it is confirmed that the corresponding gradient value exceeds the preset gradient threshold; the temperature time series of the initial anomaly region is extracted and cross-correlation analysis is performed with the output series to confirm the correlation between the two and that the time delay is within the preset physical delay range. The preliminary abnormal region that simultaneously meets the spatial gradient verification and temporal causality verification is set as the temperature abnormal region; and the location coordinates, temperature peak, over-temperature amplitude, and temperature gradient of the temperature abnormal region are output.

5. The method according to claim 1, characterized in that, Calculating the spatial distribution of heat generation rates includes: For load surge events identified in the output sequence, the instantaneous actual temperature rise rate is compared with the theoretical heat generation benchmark value in the temperature anomaly region to calculate the thermal anomaly index characterizing the degree of thermal response anomaly. Regions where the thermal anomaly index exceeds a preset screening threshold are set as candidate anomaly subdomains. By analyzing the measured temperature changes and temperature gradients within the candidate anomaly subdomain, the heat storage rate and heat conduction loss rate are calculated based on the energy conservation equation, and the total heat generation rate at each location within the candidate anomaly subdomain is solved using the truncated singular value decomposition regularization method. The total heat generation rate is filled into the positions corresponding to the candidate abnormal subdomains, while the theoretical heat generation benchmark value is filled into the positions of all other regions to generate a complete thermal map that quantitatively highlights the abnormal heat source against a normal background, serving as the spatial distribution of the heat generation rate. From the spatial distribution of heat generation rate, an abnormal heat generation rate distribution is separated, and based on the abnormal heat generation rate distribution, the peak heat source intensity and total heat generation power of the defect are calculated. An alarm is triggered when the calculation result exceeds a preset risk threshold.

6. The method according to claim 1, characterized in that, Generate temperature field correction data, including: Based on the spatial distribution of the heat generation rate and the inverted global temperature field distribution of the cable joint, the equivalent contact resistance of the joint is calculated by inversion under the assumption that the contact resistance is uniformly distributed along the contact surface or under the constraint of the minimum entropy generation principle. Simultaneously, the node temperature and inter-node heat flow in the global temperature field distribution of the cable joint are extracted, and the thermal resistance parameter set of the lumped parameter thermal network model is calibrated using the least squares fitting method. For key nodes in the lumped parameter thermal network model, the internal temperature distribution of the corresponding physical components is extracted; by subtracting the calibration temperature of the key nodes from the internal temperature distribution, a residual temperature distribution map is generated. The equivalent contact resistance, thermal resistance parameter set, and residual temperature distribution map are encapsulated into structured temperature field correction data.

7. The method according to claim 6, characterized in that, Obtain high-precision temperature field inversion results, including: Using the equivalent contact resistance and thermal resistance parameter set of the temperature field correction data, the physical parameters of the lumped parameter thermal network model used in the joint temperature field inversion model are calibrated. Based on real-time collected current load and ambient temperature, the calibration temperature of at least one key node is calculated using a calibrated lumped parameter thermal network model. The calibration temperature of at least one key node is spatially superimposed with the corresponding residual temperature distribution map in the temperature field correction data to generate the temperature field distribution of the key node, which serves as the high-precision temperature field inversion result.

8. The method according to claim 1, characterized in that, Determining the evolution trend of the joint temperature field also includes: Temperature field inversion is performed iteratively according to a preset time window, and the high-precision temperature field inversion results of multiple consecutive time windows are organized into time series data. The spatiotemporal evolution features of the temperature field are extracted from the time series data, including the migration trajectory of hotspot locations, the temperature peak change curve, and the changes in the temperature surface topology corresponding to the temperature field. Based on the spatiotemporal evolution characteristics, the recursive least squares method with forgetting factor is used to analyze the actual correlation between temperature change and output fluctuation, and to calibrate and update the dynamic correlation parameters of the joint temperature field inversion model. The dynamic correlation parameters include the gain coefficient, time constant and pure delay time of the dynamic response kernel function. Based on the updated model output, predict the evolution trend of the joint temperature field in the future period and determine whether there is a risk of continuous temperature rise or hot spot spread. The evolution trend and the corresponding predicted temperature field distribution are stored in the database.

9. The method according to claim 8, characterized in that, Determining the evolution trend of the joint temperature field also includes: Based on the high-precision temperature field inversion results, and combined with the rated operating temperature and safety margin of the cable branch box, the temperature safety index of each joint is calculated. If the temperature safety index is lower than the preset safety threshold, a temperature over-limit warning message is generated. The temperature over-limit warning message includes the location of the abnormal joint, the current peak temperature field, and the remaining time expected to reach the dangerous temperature. Based on the time series data, a temperature field spatiotemporal prediction model is constructed using a long short-term memory network. The output of the calibrated joint temperature field inversion model is used as the exogenous input variable of the temperature field spatiotemporal prediction model to predict the temperature field evolution path under normal operation scenario, load surge scenario and heat dissipation failure scenario, and output the temperature field prediction results for multiple scenarios. Based on the temperature field prediction results of multiple scenarios, the operation risk assessment and temperature runaway prevention and control decisions of the output cable branch box are made.

10. A real-time temperature field inversion system for cable joints in cable branch boxes, used to implement the real-time temperature field inversion method for cable joints in cable branch boxes as described in any one of claims 1-9, characterized in that, The system includes: The data acquisition unit is used to acquire joint temperature data and distributed power output data through a sensor network deployed in the cable branch box, and obtain temperature sequence and power output sequence; based on the temperature sequence and the power output sequence, it analyzes the dynamic correlation between temperature change and power output fluctuation, and constructs a joint temperature field inversion model. The model inversion unit uses the joint temperature field inversion model to invert the global temperature field distribution of the cable joint from discrete temperature measurement point data and identify temperature anomaly areas; based on the temperature anomaly areas, it extracts load surge characteristics from the output sequence and calculates the spatial distribution of heat generation rate. The inversion correction unit is used to invert the joint contact resistance parameters and calculate the correction values ​​of the thermal resistance network model parameters based on the spatial distribution of the heat generation rate, and generate temperature field correction data; based on the temperature field correction data, the joint temperature field inversion model is calibrated to obtain high-precision temperature field inversion results. The control unit is used to generate time-series data based on the high-precision temperature field inversion results of multiple consecutive time windows, update the parameters of dynamic correlation analysis based on the time-series data, and determine the evolution trend of the joint temperature field.

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