Power supply integrity simulation method based on multi-physics field coupling

Abstract

The invention relates to the technical field of multi-physics field coupling simulation, in particular to a power supply integrity simulation method based on multi-physics field coupling, which comprises the following steps of: performing accumulative correction on deviation nodes by adopting a residual network in the calculation process of the electromagnetic energy density and the temperature rise rate of a conductor layer; local power abnormal nodes are more easily highlighted in numerical value, the recognition capability of power supply network simulation on fine granularity deviation is remarkably enhanced, a plurality of energy correction sequences are constructed by adopting a Markov chain Monte Carlo method in a temperature and current residual judgment stage, and multi-field coupling solution presents more stable current distribution and temperature distribution in a steady-state stage. The prediction of the voltage fluctuation amplitude and the noise peak position is closer to the actual operation condition, and the high-risk node positioning, the power supply integrity evaluation credibility and the design parameter adjustment efficiency are synchronously improved by counting the high-deviation nodes on the basis of the steady-state response result and forming the multi-source coupling deviation feature set.

Description

Technical Field

[0001] This invention relates to the field of multiphysics coupling simulation technology, and in particular to a power integrity simulation method based on multiphysics coupling. Background Technology

[0002] The field of multiphysics coupling simulation technology mainly studies the interaction mechanism and coupling calculation method between different physical fields in the same system. Multiphysics coupling simulation realizes the synchronous calculation of the comprehensive response of the system in multiple aspects such as electricity, heat, and force by establishing a unified mathematical model across physical domains. The core lies in adopting a unified solution framework and iterative algorithm to perform numerical solution and coupling iteration on multiple field variables in order to obtain high-precision prediction results of the overall system performance.

[0003] A power integrity simulation method based on multi-physics coupling aims to evaluate the voltage fluctuations, transient noise distribution, and impact on circuit performance of a power network under operating conditions through coupled modeling and co-simulation of electromagnetic and thermal fields. The invention aims to establish a high-precision power integrity assessment mechanism to ensure that the power network maintains a stable power supply state under different thermal and electromagnetic interference conditions. Through simulation, a comprehensive analysis of the power network impedance characteristics, noise transmission paths, and thermal stress effects can be achieved, thereby improving the design accuracy and reliability of electronic systems.

[0004] Existing multiphysics coupled simulation techniques, under a unified mathematical model and iterative solution framework, focus on the overall response of multiple field quantities such as electricity, heat, and force. They often use averaging and coarse-grained grid statistics to measure the power difference between nodes and energy transfer paths in power networks. This makes it difficult to clearly characterize local high-power-density and low-power-density regions in the board-level and interlayer structures. The boundaries of voltage drop locations and transient noise concentration areas are relatively vague in the numerical results, which is not conducive to targeted design constraints for critical areas. In the existing power integrity assessment process, impedance characteristic analysis, noise transmission path analysis, and thermal stress impact analysis are mostly completed in steps and by comparing results. The relationship between various physical quantities relies on human experience for comprehensive judgment, making it difficult to form a tight closed loop in a single simulation process. This prolongs the assessment cycle and leaves gaps in the coverage of potential failure risks of power networks. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of existing technologies by proposing a power integrity simulation method based on multi-physics coupling.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: a power integrity simulation method based on multi-physics coupling, comprising the following steps: S1: Using the power input current data, conductor geometry data, dielectric layering parameters and heat dissipation boundary conditions acquired by the sensor, discrete electric field strength, thermal conductivity and power dissipation nodes are used to compare the power difference between adjacent nodes and filter the path to generate a coupled energy transfer structure diagram. S2: Based on the coupled energy transfer structure diagram, calculate the electromagnetic energy density and temperature rise rate of the conductor layer, determine the power ratio between energy units and use the residual network to correct the deviation nodes, perform proportional balancing and numerical normalization on the multilayer conductor region, and construct an adaptive weight balancing matrix model. S3: Based on the adaptive weight balance matrix model, iterate and solve the electromagnetic field and thermal field, calculate the current distribution heat source within the time step and correct the node energy, continuously judge the temperature and current residuals and incorporate the Markov chain Monte Carlo method, recalculate the local until the residual is stable, and obtain the multi-field steady-state response distribution map. S4: Based on the adaptive weight balance matrix model and the multi-field steady-state response distribution map, the energy distribution value, temperature gradient and impedance difference of the conductor layer are jointly analyzed, high deviation nodes are counted and a parameter mapping index is established to obtain the multi-source coupling deviation feature set. S5: Based on the multi-source coupling deviation feature set, calculate the nodes with current distribution, thermal conductivity, and power density, determine the correction of interpolation by distance weighting and the ratio of adjacent nodes, compare the predicted output with the standard curve and update the interpolation coefficients, and establish a coupled field prediction model set.

[0007] As a further embodiment of the present invention, the coupled energy transfer structure diagram includes node power difference records, energy transfer direction markers, and node connection indexes; the adaptive weight balance matrix model includes conductor layer electromagnetic energy density proportional weights, temperature rise rate proportional coefficients, and normalized data of deviation node corrections; the multi-field steady-state response distribution diagram includes node current distribution steady-state values, node temperature distribution steady-state values, and residual stable region markers; the multi-source coupling deviation feature set includes conductor layer energy distribution deviations, temperature gradient offsets, and impedance difference parameter indexes; and the coupled field prediction model set includes interpolation correction parameters based on node current distribution, interpolation correction parameters based on thermal conductivity, and interpolation correction parameters based on power density.

[0008] As a further aspect of the present invention, the specific steps for generating the coupled energy transfer structure diagram are as follows: Based on the power current input data, conductor geometry data, dielectric layering parameters and heat dissipation boundary conditions obtained by the sensor, the cross section is converted after the node is located, the electric field strength, temperature gradient and power difference are calculated, and a node energy distribution mapping table is generated. Based on the node energy distribution mapping table, the power difference between adjacent nodes is compared and channels are filtered to determine the energy direction and continuous transmission, the path index is recorded, and a coupled energy transfer structure diagram is generated.

[0009] As a further aspect of the present invention, the specific steps for establishing the adaptive weight balancing matrix model are as follows: Based on the coupled energy transfer structure diagram, the current intensity of the conductor layer nodes is collected and the magnetic field direction is calculated. The magnetic energy concentration area is determined by superimposing the distance between nodes and the current direction. The magnetic energy values ​​of each node are weighted and statistically analyzed and accumulated in the region. The overall energy distribution of the conductor layer is calculated and an electromagnetic energy density distribution table is generated. Based on the electromagnetic energy density distribution table, the ratio of temperature rise rate to power output is calculated. The power imbalance region is determined by comparing the energy deviation of adjacent units. A residual network structure is introduced in the deviation calculation process. The accumulated deviation of the previous round is used as an additional input to superimpose and correct the current offset. The thermal power parameters of each node are re-recorded and organized to generate an energy deviation correction set. Based on the energy deviation correction set, the energy ratio balance of the multilayer conductor region is calculated and numerically normalized. By redistributing the node energy weights and updating the interlayer ratio, the energy sharing relationship between the conductor and the dielectric layer is adjusted to form a global energy allocation matrix and construct an adaptive weight balance matrix model.

[0010] As a further aspect of the present invention, the residual network, based on the electromagnetic energy density distribution table, calculates the energy deviation of adjacent units in the order of calculation, takes the cumulative deviation of the previous time step as the residual input, adds the deviation to the energy offset of the current node item by item through superposition, and redetermines the offset node based on the superimposed offset result. After determining the offset node, the node thermal power parameters are compensated, recorded and data is organized, so that the updated thermal power parameters serve as the input source for the subsequent energy deviation correction set.

[0011] As a further aspect of the present invention, the specific steps for obtaining the multi-field steady-state response distribution map are as follows: Based on the adaptive weight balance matrix model, the electromagnetic field and thermal field coupling are initialized, the node heat source power is calculated by current density and thermal conductivity, the energy input and temperature change are recorded synchronously, the node potential and temperature gradient are updated, and the initial distribution set of electromagnetic thermal coupling is generated. Based on the initial distribution set of electromagnetic thermal coupling, node energy correction and residual calculation are performed. Offset nodes are determined by comparing the temperature and current difference in continuous time steps. In the offset determination process, the Markov chain Monte Carlo method is introduced to generate multiple possible energy correction sequences. The correction path with higher convergence is selected from the sequence. The energy of the offset node is compensated and the power is adjusted. The node temperature value and energy path are updated to generate a local energy correction table. Based on the local energy correction table, the residual is determined to be stable and converges iteratively. By cyclically updating the current density and temperature distribution and detecting the change amplitude, the unstable nodes are re-solved and the stable nodes are fixed to obtain the multi-field steady-state response distribution map.

[0012] As a further aspect of the present invention, the Markov chain Monte Carlo method, based on the initial distribution set of electromagnetic thermal coupling, compares the temperature and current differences of continuous time steps and determines the offset nodes. It uses the energy change corresponding to the offset node as the initial sampling quantity, generates multiple energy correction sequences, and constructs a node energy update chain based on the sequence's jump states. The energy correction results formed in each sequence are recorded as candidate correction paths according to the generation order. Then, a path with higher convergence is selected from the candidate paths as the basis for energy correction of the current offset node. Compensation recording and update operations are performed on the node thermal power and energy path, so that the updated node quantity is written to the corresponding position in the local energy correction table.

[0013] As a further aspect of the present invention, the determination of residual stability and iterative convergence is a set of states exhibiting stable characteristics in the residual changes formed by continuous comparison of node temperature difference and current difference. The set of states includes node regions where the residual maintains low amplitude fluctuations within a set range, node regions where the temperature and current change trends are consistent, and node regions that maintain stable output in continuous cycles. By merging the node regions to form an overall stable distribution, the temperature distribution, energy distribution, and current density distribution are made consistent in space, thereby constituting a steady-state data set for characterizing the stability of multi-field coupling, forming a multi-field steady-state response distribution that can be used as the final output.

[0014] As a further aspect of the present invention, the specific steps for generating the multi-source coupling deviation feature set are as follows: Based on the adaptive weight balance matrix model and the multi-field steady-state response distribution map, the energy distribution and temperature gradient of the conductor layer are extracted. The impedance difference is matched by the node index, the copper layer thickness and dielectric loss offset ratio are calculated, and the energy and temperature difference are normalized and statistically analyzed to generate the node deviation distribution matrix. Based on the node deviation distribution matrix, high deviation nodes are classified and screened according to energy range. Abnormal areas are judged by the correlation ratio between node energy and temperature. A mapping index and parameter value correspondence are established for abnormal nodes. Energy interlayer deviation data are integrated to obtain a multi-source coupling deviation feature set.

[0015] As a further aspect of the present invention, the specific steps for establishing the coupled field prediction model set are as follows: Based on the multi-source coupling deviation feature set, nodes with current distribution, thermal conductivity and power density are extracted. The weights are calculated by the node distance and the power ratio is compared. Interpolation correction and energy compensation are performed on the deviating nodes. The node energy transfer order and current direction are updated to generate the node interpolation correction matrix. Based on the node interpolation correction matrix, the predicted output is compared with the standard curve. The error ratio is used to determine the interpolation accuracy and adjust the weights. The corrected node parameters are recombined and recalculated to output the relationship between predicted impedance and temperature, and a set of coupled field prediction models is established.

[0016] Compared with the prior art, the advantages and positive effects of the present invention are as follows: 1. In this invention, by using a residual network to cumulatively correct deviation nodes during the calculation of electromagnetic energy density and temperature rise rate of the conductor layer, local power anomaly nodes are more easily highlighted numerically, and the power network simulation's ability to identify fine-grained deviations is significantly enhanced. 2. In this invention, by using the Markov chain Monte Carlo method to construct multiple energy correction sequences and selecting the path with higher convergence in the temperature and current residual judgment stage, the multi-field coupling solution presents a more stable current distribution and temperature distribution in the steady state stage, and the prediction of voltage fluctuation amplitude and noise peak position is closer to the actual operating conditions. 3. In this invention, by statistically analyzing high-deviation nodes based on steady-state response results and forming a multi-source coupling deviation feature set, the simulation process achieves higher accuracy and stronger extrapolation capability in impedance frequency response curve and temperature distribution prediction. The reliability of high-risk node location, power integrity assessment, and design parameter adjustment efficiency are all improved simultaneously. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the main steps of the present invention. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0019] Example 1 Please see Figure 1 This invention provides a technical solution: a power integrity simulation method based on multi-physics coupling, comprising the following steps: S1: Using the power input current data, conductor geometry data, dielectric layering parameters and heat dissipation boundary conditions acquired by the sensor, discrete electric field strength, thermal conductivity and power dissipation nodes are used to compare the power difference between adjacent nodes and filter the path to generate a coupled energy transfer structure diagram. S2: Based on the coupled energy transfer structure diagram, calculate the electromagnetic energy density and temperature rise rate of the conductor layer, determine the power ratio between energy units and use the residual network to correct the deviation nodes, perform proportional balancing and numerical normalization on the multilayer conductor region, and construct an adaptive weight balancing matrix model. S3: Based on the adaptive weight balance matrix model, iterate and solve the electromagnetic field and thermal field, calculate the current distribution heat source within the time step and then correct the node energy, continuously judge the temperature and current residuals and incorporate the Markov chain Monte Carlo method, recalculate the local until the residual is stable, and obtain the multi-field steady-state response distribution map. S4: Based on the adaptive weight balance matrix model and the multi-field steady-state response distribution map, the energy distribution value, temperature gradient and impedance difference of the conductor layer are jointly analyzed, high deviation nodes are counted and parameter mapping index is established to obtain the multi-source coupling deviation feature set; S5: Based on the multi-source coupling deviation feature set, calculate the nodes with current distribution, thermal conductivity, and power density. Use distance weighting and the ratio of adjacent nodes to determine and correct the interpolation. Compare the predicted output with the standard curve and update the interpolation coefficients to establish a coupled field prediction model set.

[0020] The coupled energy transfer structure diagram includes node power difference records, energy transfer direction markers, and node connection indexes. The adaptive weight balance matrix model includes conductor layer electromagnetic energy density proportional weights, temperature rise rate proportional coefficients, and normalized data of deviation node corrections. The multi-field steady-state response distribution diagram includes steady-state values ​​of node current distribution, steady-state values ​​of node temperature distribution, and residual stable region markers. The multi-source coupling deviation feature set includes conductor layer energy distribution deviations, temperature gradient offsets, and impedance difference parameter indexes. The coupled field prediction model set includes interpolation correction parameters based on node current distribution, interpolation correction parameters based on thermal conductivity, and interpolation correction parameters based on power density.

[0021] The specific steps for generating the coupled energy transfer structure diagram are as follows: Based on the power current input data, conductor geometry data, dielectric layering parameters and heat dissipation boundary conditions obtained by the sensor, the cross section is converted after the node is located, the electric field strength, temperature gradient and power difference are calculated, and a node energy distribution mapping table is generated. Based on the node energy distribution mapping table, the power difference between adjacent nodes is compared and channels are filtered to determine the energy direction and continuous transmission, the path index is recorded, and a coupled energy transfer structure diagram is generated. Based on the power current input data, conductor geometry data, dielectric layering parameters, and heat dissipation boundary conditions acquired by sensors, the power current input data is discretized. The current density is segmented in 0.1 mm increments along both the horizontal and vertical directions and numbered from 1 to 500 with fixed node numbers. Using the cross-sectional width of 2 mm and thickness of 35 μm given in the conductor geometry, the effective cross-sectional area of ​​each node is converted into a two-dimensional discrete area value using a forward differential method. The dielectric constant recorded in the dielectric layering parameters is sequentially assigned to the corresponding layer of the node. The node electric field strength is numerically approximated, with a fixed difference of 0.05 V / mm between adjacent nodes to calculate the local intensity increment. The obtained temperature gradient is linearly approximated based on the convective heat transfer coefficient of 12 W / m² / Kelvin given in the heat dissipation boundary conditions. The power difference of each node is calculated using a power difference coefficient of 1.0, and the node energy value is recorded. The node number, node cross-sectional area, local electric field strength difference, temperature gradient difference, and power difference data are combined to form a complete node record. Finally, the node energy distribution mapping table is formed by organizing the data in node order. Based on the node energy distribution mapping table, the power difference between adjacent nodes is compared. Each pair of adjacent nodes in the mapping table is read in numerical order, and a fixed threshold of 0.2 watts is used as the power difference judgment criterion. Node pairs exceeding the threshold are marked as candidate channel node pairs. The energy direction is derived based on the node coordinate difference, where the lateral increment is calculated with a discrete spacing of 0.1 mm and the longitudinal increment is calculated with the synchronous spacing. The direction is recorded according to four categories: right, left, up, and down. The nodes marked as candidate channels are connected in adjacent order. The node chains that continuously satisfy the direction consistency are integrated into path units, and each path is assigned a fixed number from P1 to P80. By organizing and archiving the path numbers, direction categories, and node order, the path set constitutes a path index structure. Finally, the path index structure and node energy information are combined in a graph-like relationship to generate a complete coupled energy transfer structure diagram.

[0022] The specific steps for establishing an adaptive weight balancing matrix model are as follows: Based on the coupled energy transfer structure diagram, the node current intensity of the conductor layer is collected and the magnetic field direction is calculated. The magnetic energy concentration area is determined by superimposing the distance between nodes and the current direction. The magnetic energy values ​​of each node are weighted and statistically accumulated in the region to calculate the overall energy distribution of the conductor layer and generate an electromagnetic energy density distribution table. Based on the electromagnetic energy density distribution table, the ratio of temperature rise rate to power output is calculated. The power imbalance region is judged by comparing the energy deviation of adjacent units. A residual network structure is introduced in the deviation calculation process. The accumulated deviation of the previous round is used as an additional input to superimpose and correct the current offset. The thermal power parameters of each node are re-recorded and organized to generate an energy deviation correction set. Based on the energy deviation correction set, the energy ratio balance of the multilayer conductor region is calculated and numerically normalized. By redistributing the node energy weights and updating the interlayer ratio, the energy sharing relationship between the conductor and the dielectric layer is adjusted to form a global energy allocation matrix and construct an adaptive weight balance matrix model. Based on the coupled energy transfer structure diagram, the current intensity of the conductor layer nodes is collected. In the method, the distance between nodes is set to a fixed value of 0.1 mm and the data is read in the order of node number. The direction of the node current is recorded as a unit vector and split into values ​​1, 0, 0 and 0, 1, 0 according to the three-axis direction to determine the direction component. When calculating the magnetic field direction, the distance vector between nodes and the current direction vector are superimposed with a fixed step size of 0.05. The magnetic energy value of each node is weighted by setting the magnetic energy coefficient to 2.0 and multiplying the magnetic energy coefficient with the current intensity. The magnetic energy values ​​of nodes of the same direction category are accumulated in sequence and formed into a regional accumulation unit with every ten nodes. The accumulated data of each group are sorted in the order of nodes to form the overall energy distribution data column of the conductor layer. The current intensity column, direction component column, magnetic energy weighting column and regional accumulation column are combined in sequence to generate an electromagnetic energy density distribution table. Based on the electromagnetic energy density distribution table, the ratio of temperature rise rate to power output is calculated. In this method, the temperature rise rate is fixed at 0.2 Kelvin per second according to the node sequence, and the power output is fixed at 0.5 watts per node according to the sequence. The ratio of the two is recorded as the corresponding ratio sequence by division. The power imbalance region is determined by comparing the energy deviation of adjacent units. In the deviation calculation process, a residual network structure is introduced, and the cumulative deviation of the previous round is added to the current offset by a fixed input value of 0.1 to complete the superposition correction. Through superposition correction, the node thermal power parameters are rewritten into the parameter column according to the node order and sorted according to the node number order. The offset sequence, ratio sequence, deviation accumulation sequence and thermal power parameter sequence are combined to form an energy deviation correction set. Based on the energy deviation correction set, the energy ratio of the multilayer conductor region is calculated. In this method, the energy values ​​of each layer are proportionally allocated according to fixed proportional coefficients of 1.0, 0.8, and 0.6. The energy values ​​after proportional processing are normalized to values ​​within the range of 0 to 1 by summing them. The interlayer ratio is updated by redistributing the node energy weights and updating them in a fixed order. During the interlayer ratio update process, the weight of the conductor layer is set to 0.7 and the weight of the dielectric layer is set to 0.3, so that the energy sharing relationship is adjusted according to the weights. By arranging the normalized node energy values ​​according to matrix rules and filling the energy values ​​of each layer into the matrix row and column structure in sequence, a global energy allocation matrix is ​​formed to represent the overall energy relationship, and an adaptive weight balance matrix model is constructed.

[0023] The residual network, based on the electromagnetic energy density distribution table, calculates the energy deviation of adjacent units in the order of calculation. It takes the cumulative deviation of the previous time step as the residual input, adds the deviation to the energy offset of the current node one by one through the superposition method, and redetermines the offset node based on the superimposed offset result. After determining the offset node, it performs compensation recording and data processing on the node thermal power parameters, so that the updated thermal power parameters can be used as the input source of the subsequent energy deviation correction set. Residual networks, according to the formula: ; in: For node index At time step The cumulative residual amount, For node index At time step The cumulative residual amount, For node index At time step Thermal power parameters For node index Reference thermal power parameters, For node index At time step electromagnetic energy density, For time steps The average electromagnetic energy density of all nodes in the conductor layer. For node index At time step Temperature value, For time step Average temperature of all nodes in the conductor layer For residual inheritance weighting coefficients, This is the weighting coefficient for thermal power deviation. This is the electromagnetic energy deviation weighting coefficient. This is the temperature deviation weighting coefficient. For node indexing, This is the current time step; Execution process: Node indexing on the conductor layer At time step Perform residual update processing, and read the cumulative residual of the nodes from the calculation results of the previous time step. Then, the current thermal power parameters of the nodes are read from the multi-field coupling solution process. Compared with reference thermal power parameters Current electromagnetic energy density and the current temperature value And average the electromagnetic energy density of all nodes within the same time step to obtain The average temperature of all nodes is obtained. During the weight setting phase, , , , The values ​​are given according to preset rules and normalized from a set of candidate coefficients. After satisfying fixed constraints, the cumulative residual of the previous time step and the thermal power deviation are calculated. Electromagnetic energy density deviation Temperature deviation Multiply by the corresponding weighting coefficients respectively , , , The four results are summed according to the formula structure to obtain the cumulative residual at the current time step. .

[0024] The specific steps to obtain the multi-field steady-state response distribution map are as follows: Based on the adaptive weighted balance matrix model, the electromagnetic field and thermal field coupling are initialized, the node heat source power is calculated by current density and thermal conductivity, the energy input and temperature change are recorded synchronously, the node potential and temperature gradient are updated, and the initial distribution set of electromagnetic thermal coupling is generated. Based on the initial distribution set of electromagnetic thermal coupling, node energy correction and residual calculation are performed. Offset nodes are determined by comparing the temperature and current difference in continuous time steps. In the offset determination process, the Markov chain Monte Carlo method is introduced to generate multiple possible energy correction sequences. The correction path with higher convergence is selected from the sequence. The energy of the offset node is compensated and the power is adjusted. The node temperature value and energy path are updated to generate a local energy correction table. Based on the local energy correction table, the residual is determined to be stable and iteratively converged. By cyclically updating the current density and temperature distribution and detecting the change amplitude, the unstable nodes are re-solved and the stable nodes are fixed to obtain the multi-field steady-state response distribution map. Based on an adaptive weighted balance matrix model, the electromagnetic and thermal fields are initialized and coupled. The discrete step size of the spatial grid is set to 0.1 mm and the time step to 0.01 s. When processing the current density, the current density values ​​of each node are directly read from the input data as fixed values ​​ranging from 1 A / m² to 3 A / m², and arranged in order of node number. When processing the thermal conductivity, the thermal conductivity is specified as two fixed values ​​of 180 W / m / Kelvin and 0.3 W / m / Kelvin respectively, and directly assigned according to the layer where the node is located. When calculating the node heat source power, the heat source power value is recorded as the node current density multiplied by the thermal conductivity node by node, and the result is expressed in watts. The sequence is stored in a grid. When recording energy input and temperature changes synchronously, the energy input is written node by node in a fixed value between 2 and 5 joules, and the temperature change is written in a fixed increment between 0.1 and 0.4 Kelvin per node. When updating the node potential, the node potential is set to a reading value between 0.5 and 1.2 volts according to a fixed distribution and written in grid order. When updating the temperature gradient, the gradient is filled in with a fixed gradient of 0.02 Kelvin per millimeter according to the difference between nodes. The current density sequence, thermal conductivity sequence, heat source power sequence, energy input sequence, temperature change sequence, potential sequence and temperature gradient sequence of the nodes are combined and organized to generate an initial distribution set for electromagnetic thermal coupling. Based on the initial distribution set of electromagnetic thermal coupling, node energy correction and residual calculation are performed. Temperature differences across continuous time steps are read in the range of 0.05 Kelvin to 0.2 Kelvin, and current differences are collected in the range of 0.1 A to 0.3 A. These are combined into a difference sequence according to node order and compared in a fixed order to determine the offset node. In the offset determination process, a Markov chain Monte Carlo method is introduced, and the offset of the previous time step is added as an additional input to the current energy change sequence at a fixed value of 0.1 Joules. When generating the energy correction sequence, the energy offset of each node is recorded in a fixed increment of 0.05 Joules and arranged sequentially in the sequence. Multiple possible energy correction sequences are constructed. In the process of listing, each sequence is set to a length of 20 nodes and arranged in ascending order of node number. When comparing different offset paths in the sequence, the path with the smallest change in offset is taken as the convergent path. The nodes in the path are recorded in order as a correction node group. When compensating for the energy of the deviation node, the compensation value is written in a fixed increment of 0.02 joules. When adjusting the power of the deviation node, the power is written in a fixed adjustment value of 0.1 watts. The node temperature value is rewritten according to the updated temperature sequence and the node arrangement order is updated in the energy path. Finally, the above offset node group, energy offset sequence, compensation energy sequence, adjustment power sequence and updated temperature sequence are combined to generate a local energy correction table. Based on the local energy correction table, residual stability is determined and iterative convergence is achieved. The residual stability threshold is set to 0.01, and the allowable variation range is set to 0.005. The temperature change of the node in continuous cycles is read according to a fixed difference sequence of 0.02 Kelvin to 0.05 Kelvin. The node current density change is recorded according to 0.05 A to 0.15 A and compared with the residual threshold. When updating the current density in each cycle, the current density corresponding to the node in each update is written into the new cycle sequence, and the sequence length is kept consistent with the number of nodes. When updating the temperature... During distribution, the temperature is written sequentially at a fixed step size of 0.1 Kelvin. When detecting the change amplitude, the temperature change and current change are recorded as a difference sequence according to the node order. When resolving unstable nodes, the unstable nodes are directly recorded as a numbered list and rewritten into the solution sequence in ascending order of the numbers. When fixing the output stable nodes, the stable nodes are removed from the solution sequence and written into the stable node table separately. The node temperature sequence, node current density sequence, stable node list and unstable node list after the cycle are combined to obtain the multi-field steady-state response distribution map.

[0025] The Markov chain Monte Carlo method, based on the initial distribution set of electromagnetic thermal coupling, compares the temperature and current differences of continuous time steps to determine the offset node. It uses the energy change corresponding to the offset node as the sampling start quantity, generates multiple energy correction sequences, and constructs the node energy update chain with the jump state of the sequence. The energy correction results formed in each sequence are recorded as candidate correction paths in the order of generation. Then, the path with higher convergence is selected from the candidate paths as the basis for the energy correction of the current offset node. Compensation recording and update operations are performed on the node thermal power and energy path, so that the updated node quantity is written into the corresponding position of the local energy correction table. The Markov chain Monte Carlo method, according to the formula: ; in: The step index is The time node index is Energy-corrected acceptance probability, The step index is The time node index is The change in energy, The step index is The time node index is The change in heat source power. The step index is The time node index is The change in current density, The step index is The time node index is The amount of impedance change. For the change in energy The weighting coefficients, For the change in power of the heat source The weighting coefficients, For the change in current density The weighting coefficients, For the amount of impedance change The weighting coefficients, The constant coefficient is used to unify the dimensions of the changes in the numerator and the temperature parameter in the denominator. The step index is The time node index is The effective temperature parameter, For node indexing, For step indexing; Execution process: Index of each step and indexes of each node Read the node's energy value, heat source power, current density, and impedance value under the current step and the previous reference step from the initial distribution set and local energy correction table of electromagnetic thermal coupling, and obtain them sequentially according to the difference calculation. , , and Simultaneously, the current node temperature is read from the multi-field steady-state response distribution map and combined with the temperature of all nodes in the same conductor layer to calculate the average layer temperature. The node temperature and the average layer temperature are then combined according to a preset ratio to form the effective temperature parameter. During the weighting coefficient determination stage, for all nodes within a sampling window... , , , Calculate the variance and variance percentage separately, and use the variance percentage as the initial weight ratio and set it. , , , The initial values ​​are then normalized for the four weights. The initial value is 1. When weight adjustment is needed, the four weights are fine-tuned within a given value set by comparing the acceptance rates under a series of calibration conditions until the acceptance rate falls within a predetermined range. Then, the current weight combination is fixed. After the weights are determined, [the following steps are performed]. , , , With corresponding weights , , , Substitute the constant coefficient into the numerator of the exponent term. With effective temperature Substitute the terms into the denominator to calculate the exponent, and then calculate the result using the formula. .

[0026] The residual is determined to be stable and converged iteratively. The state set exhibits stable characteristics in the residual changes formed by continuous comparison of the temperature difference and current difference of the nodes. The state set includes node regions where the residual maintains low amplitude fluctuation within a set range, node regions where the temperature and current change trends are consistent, and node regions that maintain stable output in continuous cycles. By merging the node regions to form an overall stable distribution, the temperature distribution, energy distribution and current density distribution are made consistent in space, thereby forming a steady-state data set used to characterize the stability of multi-field coupling, forming a multi-field steady-state response distribution that can be used as the final output.

[0027] The specific steps for generating the multi-source coupling deviation feature set are as follows: Based on the adaptive weight balance matrix model and multi-field steady-state response distribution map, the energy distribution and temperature gradient of the conductor layer are extracted. The impedance difference is matched by the node index, the copper layer thickness and dielectric loss offset ratio are calculated, and the energy and temperature difference are normalized and statistically analyzed to generate the node offset distribution matrix. Based on the node deviation distribution matrix, high deviation nodes are classified and screened according to energy range. Abnormal areas are judged by the correlation ratio between node energy and temperature. A mapping index and parameter value correspondence are established for abnormal nodes. Energy interlayer deviation data are integrated to obtain a multi-source coupling deviation feature set. Based on the adaptive weighted balance matrix model and multi-field steady-state response distribution map, the energy distribution and temperature gradient of the conductor layer are extracted. The energy distribution of the conductor layer is read in the order of nodes, grouped by each node, and linearly divided with a fixed step size of 0.1. The temperature gradient is read in according to the gradient values ​​recorded at a distance of 0.1 mm between nodes and written into the sequence in the original order. In the process of matching impedance difference through node index, the impedance difference is divided into three fixed intervals from 0.05 ohms to 0.15 ohms. The node number and the impedance difference value are arranged according to the interval index. When calculating the copper layer thickness and dielectric loss offset ratio, the copper layer thickness is set to a fixed value of 35 micrometers. The dielectric loss is written with a fixed loss coefficient in the range of 0.002 to 0.01 and the offset ratio is calculated by the ratio of 0.7 and 0.3. The energy difference and temperature difference are linearly normalized according to their respective maximum values ​​and written into the normalized sequence in the range of 0 to 1. The energy normalized sequence, temperature normalized sequence, impedance difference interval sequence and offset ratio sequence are combined in the order of nodes to generate the node offset distribution matrix. Based on the node deviation distribution matrix, high-deviation nodes are classified and screened, and energy ranges are divided. A high-deviation zone is defined with a fixed threshold of 0.6, and nodes with deviation values ​​less than 0.6 are classified into the normal zone. The energy range is fixedly divided into three segments: 0 to 0.3, 0.3 to 0.6, and 0.6 to 1. When judging abnormal areas by the correlation ratio between node energy and temperature, the correlation ratio is formed by dividing the node energy value by the temperature value and recorded within a fixed range of 0 to 10. Nodes with a correlation ratio exceeding 3 are recorded as abnormal nodes and arranged in order of node number. When establishing the mapping index and parameter value correspondence for abnormal nodes, the mapping index is directly arranged by node number, and the corresponding parameter values ​​are arranged and recorded in order of node energy, node temperature, and node impedance difference. When integrating the energy interlayer deviation data, a fixed-order interlayer superposition method is used, and the deviation values ​​of each layer are superimposed and arranged in the order of conductor layer deviation first and dielectric layer deviation last. The high-deviation node sequence, energy range sequence, correlation ratio sequence, abnormal node index sequence, and interlayer deviation sequence are combined to obtain the multi-source coupling deviation feature set.

[0028] The specific steps for establishing a set of coupled-field prediction models are as follows: Based on the multi-source coupling deviation feature set, nodes with current distribution, thermal conductivity and power density are extracted. The weights are calculated by the node distance and the power ratio is compared. Interpolation correction and energy compensation are performed on the deviating nodes, the node energy transfer order and current direction are updated, and the node interpolation correction matrix is ​​generated. Based on the nodal interpolation correction matrix, the predicted output is compared with the standard curve. The error ratio is used to judge the interpolation accuracy and adjust the weights. The corrected nodal parameters are recombined and back-calculated to output the relationship between predicted impedance and temperature, and a set of coupled field prediction models is established. Based on the multi-source coupling deviation feature set, current distribution, thermal conductivity, and power density nodes are extracted. The current distribution is written in ascending order of node number within the range of 1 A / mm² to 3 A / mm². The thermal conductivity is read as two fixed values ​​based on the node's layer: 180 W / m / Kelvin and 0.3 W / m / Kelvin. The power density is read as a fixed value within the range of 0.4 W / mm² to 1.2 W / mm² based on node number. When calculating weights based on node distance, the distance is resolved into five distance values ​​in 0.1 mm increments, with corresponding weights set to 1.0, 0.8, 0.6, 0.4, and 0.2. The power ratio of each node is recorded as the power density divided by the base power of 0.5 W. The sequence is as follows: When performing interpolation correction on the off-node, the interpolation coefficient is set to three fixed coefficients of 0.3, 0.5, and 0.7. The energy of the interpolated node is written into the interpolation sequence by adding the interpolation coefficient to the average value of the sequence before and after the node and multiplying by the difference. When performing energy compensation, the compensation amount is set to a fixed value of 0.02 joules and added to the compensation list according to the node order. When updating the node energy transfer order, the node numbers are rearranged in ascending order of the interpolated energy value and written into the order list. When updating the current direction, the direction analysis comparison method is used and the direction is recorded as discrete direction labels according to the coordinate difference between nodes in four categories: up, down, left, and right. The interpolation sequence, compensation sequence, power ratio sequence, node order list and direction label sequence are combined to generate the node interpolation correction matrix. Based on the node interpolation correction matrix, the predicted output is compared with the standard curve. The predicted output is read sequentially by node number as an impedance value sequence and a temperature value sequence. The standard curve is read in the same order as the corresponding reference impedance and reference temperature. The error ratio is recorded as a fixed error ratio sequence by dividing the difference between the predicted value and the reference value by the reference value, and arranged sequentially by node. When using the error ratio to determine the interpolation accuracy and adjust the weights, the weight adjustment step size is set to 0.1. The weights of nodes with an error ratio greater than 0.2 are reduced by 0.1, and the weights of nodes with an error ratio less than 0.2 are increased by 0.1, and so on, node by node. The weight sequence is re-recorded in order. When recombining the corrected node parameters, the impedance value, temperature value and updated weight of the node are arranged in a fixed order as a three-column structure and written into the combination list according to the node number. When back-calculating the parameters, the back-calculation coefficient is set to 0.5 and the back-calculation result is written by multiplying the predicted impedance by 0.5 and adding it to the updated parameter. When outputting the correspondence between the predicted impedance and temperature, the two sequences are filled into the mapping table according to the node number. Finally, the corrected node mapping table, error ratio sequence, weight sequence and impedance-temperature mapping table are combined to establish the coupled field prediction model set.

[0029] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments that can be applied to other fields. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A power integrity simulation method based on multiphysics coupling, characterized in that, Includes the following steps: S1: Using the power input current data, conductor geometry data, dielectric layering parameters and heat dissipation boundary conditions acquired by the sensor, discrete electric field strength, thermal conductivity and power dissipation nodes are used to compare the power difference between adjacent nodes and filter the path to generate a coupled energy transfer structure diagram. S2: Based on the coupled energy transfer structure diagram, calculate the electromagnetic energy density and temperature rise rate of the conductor layer, determine the power ratio between energy units and use the residual network to correct the deviation nodes, perform proportional balancing and numerical normalization on the multilayer conductor region, and construct an adaptive weight balancing matrix model. S3: Based on the adaptive weight balance matrix model, iterate and solve the electromagnetic field and thermal field, calculate the current distribution heat source within the time step and correct the node energy, continuously judge the temperature and current residuals and incorporate the Markov chain Monte Carlo method, recalculate the local until the residual is stable, and obtain the multi-field steady-state response distribution map. S4: Based on the adaptive weight balance matrix model and the multi-field steady-state response distribution map, the energy distribution value, temperature gradient and impedance difference of the conductor layer are jointly analyzed, high deviation nodes are counted and a parameter mapping index is established to obtain the multi-source coupling deviation feature set. S5: Based on the multi-source coupling deviation feature set, calculate the nodes with current distribution, thermal conductivity, and power density, determine the correction of interpolation by distance weighting and the ratio of adjacent nodes, compare the predicted output with the standard curve and update the interpolation coefficients, and establish a coupled field prediction model set.

2. The power integrity simulation method based on multiphysics coupling according to claim 1, characterized in that, The coupled energy transfer structure diagram includes node power difference records, energy transfer direction markers, and node connection indexes. The adaptive weight balance matrix model includes conductor layer electromagnetic energy density proportional weights, temperature rise rate proportional coefficients, and normalized data of deviation node corrections. The multi-field steady-state response distribution diagram includes node current distribution steady-state values, node temperature distribution steady-state values, and residual stable region markers. The multi-source coupling deviation feature set includes conductor layer energy distribution deviation, temperature gradient offset, and impedance difference parameter indexes. The coupled field prediction model set includes interpolation correction parameters based on node current distribution, interpolation correction parameters based on thermal conductivity, and interpolation correction parameters based on power density.

3. The power integrity simulation method based on multiphysics coupling according to claim 1, characterized in that, The specific steps for generating the coupled energy transfer structure diagram are as follows: Based on the power current input data, conductor geometry data, dielectric layering parameters and heat dissipation boundary conditions obtained by the sensor, the cross section is converted after the node is located, the electric field strength, temperature gradient and power difference are calculated, and a node energy distribution mapping table is generated. Based on the node energy distribution mapping table, the power difference between adjacent nodes is compared and channels are filtered to determine the energy direction and continuous transmission, the path index is recorded, and a coupled energy transfer structure diagram is generated.

4. The power integrity simulation method based on multiphysics coupling according to claim 1, characterized in that, The specific steps for establishing the adaptive weight balancing matrix model are as follows: Based on the coupled energy transfer structure diagram, the current intensity of the conductor layer nodes is collected and the magnetic field direction is calculated. The magnetic energy concentration area is determined by superimposing the distance between nodes and the current direction. The magnetic energy values ​​of each node are weighted and statistically analyzed and accumulated in the region. The overall energy distribution of the conductor layer is calculated and an electromagnetic energy density distribution table is generated. Based on the electromagnetic energy density distribution table, the ratio of temperature rise rate to power output is calculated. The power imbalance region is determined by comparing the energy deviation of adjacent units. A residual network structure is introduced in the deviation calculation process. The accumulated deviation of the previous round is used as an additional input to superimpose and correct the current offset. The thermal power parameters of each node are re-recorded and organized to generate an energy deviation correction set. Based on the energy deviation correction set, the energy ratio balance of the multilayer conductor region is calculated and numerically normalized. By redistributing the node energy weights and updating the interlayer ratio, the energy sharing relationship between the conductor and the dielectric layer is adjusted to form a global energy allocation matrix and construct an adaptive weight balance matrix model.

5. The power integrity simulation method based on multiphysics coupling according to claim 1, characterized in that, The residual network, based on the electromagnetic energy density distribution table, calculates the energy deviation of adjacent units in the order of calculation, takes the cumulative deviation of the previous time step as the residual input, and adds the deviation to the energy offset of the current node item by item through superposition. Based on the superimposed offset result, the offset node is re-determined. After determining the offset node, the node thermal power parameters are compensated, recorded and data is organized, so that the updated thermal power parameters serve as the input source for the subsequent energy deviation correction set.

6. The power integrity simulation method based on multiphysics coupling according to claim 1, characterized in that, The specific steps to obtain the multi-field steady-state response distribution map are as follows: Based on the adaptive weight balance matrix model, the electromagnetic field and thermal field coupling are initialized, the node heat source power is calculated by current density and thermal conductivity, the energy input and temperature change are recorded synchronously, the node potential and temperature gradient are updated, and the initial distribution set of electromagnetic thermal coupling is generated. Based on the initial distribution set of electromagnetic thermal coupling, node energy correction and residual calculation are performed. Offset nodes are determined by comparing the temperature and current difference in continuous time steps. In the offset determination process, the Markov chain Monte Carlo method is introduced to generate multiple possible energy correction sequences. The correction path with higher convergence is selected from the sequence. The energy of the offset node is compensated and the power is adjusted. The node temperature value and energy path are updated to generate a local energy correction table. Based on the local energy correction table, the residual is determined to be stable and converges iteratively. By cyclically updating the current density and temperature distribution and detecting the change amplitude, the unstable nodes are re-solved and the stable nodes are fixed to obtain the multi-field steady-state response distribution map.

7. The power integrity simulation method based on multiphysics coupling according to claim 1, characterized in that, The Markov chain Monte Carlo method, based on the initial distribution set of electromagnetic thermal coupling, compares the temperature and current differences at continuous time steps to determine the offset nodes. It uses the energy change corresponding to the offset node as the initial sampling quantity, generates multiple energy correction sequences, and constructs a node energy update chain based on the sequence's jump states. The energy correction results formed in each sequence are recorded as candidate correction paths according to their generation order. Then, a path with higher convergence is selected from the candidate paths as the basis for energy correction of the current offset node. Compensation recording and update operations are performed on the node's thermal power and energy path, so that the updated node quantity is written to the corresponding position in the local energy correction table.

8. The power integrity simulation method based on multiphysics coupling according to claim 6, characterized in that, The determination of residual stability and iterative convergence involves a set of states exhibiting stable characteristics in the residual changes formed by continuous comparison of node temperature differences and current differences. The set of states includes node regions where the residual maintains low-amplitude fluctuations within a set range, node regions where the temperature and current change trends are consistent, and node regions that maintain stable output in continuous cycles. By merging the node regions to form an overall stable distribution, the temperature distribution, energy distribution, and current density distribution are made spatially consistent, thereby constituting a steady-state data set used to characterize the stability of multi-field coupling, forming a multi-field steady-state response distribution that can serve as the final output.

9. The power integrity simulation method based on multiphysics coupling according to claim 1, characterized in that, The specific steps for generating the multi-source coupling deviation feature set are as follows: Based on the adaptive weight balance matrix model and the multi-field steady-state response distribution map, the energy distribution and temperature gradient of the conductor layer are extracted. The impedance difference is matched by the node index, the copper layer thickness and dielectric loss offset ratio are calculated, and the energy and temperature difference are normalized and statistically analyzed to generate the node deviation distribution matrix. Based on the node deviation distribution matrix, high deviation nodes are classified and screened according to energy range. Abnormal areas are judged by the correlation ratio between node energy and temperature. A mapping index and parameter value correspondence are established for abnormal nodes. Energy interlayer deviation data are integrated to obtain a multi-source coupling deviation feature set.

10. The power integrity simulation method based on multiphysics coupling according to claim 1, characterized in that, The specific steps for establishing the coupled field prediction model set are as follows: Based on the multi-source coupling deviation feature set, nodes with current distribution, thermal conductivity and power density are extracted. The weights are calculated by the node distance and the power ratio is compared. Interpolation correction and energy compensation are performed on the deviating nodes. The node energy transfer order and current direction are updated to generate the node interpolation correction matrix. Based on the node interpolation correction matrix, the predicted output is compared with the standard curve. The error ratio is used to determine the interpolation accuracy and adjust the weights. The corrected node parameters are recombined and recalculated to output the relationship between predicted impedance and temperature, and a set of coupled field prediction models is established.

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