Reliability evaluation method and system for collaborative robot PMSM servo system

Abstract

The invention discloses a reliability evaluation method and system for a collaborative robot PMSM servo system. Comprising the following steps: dividing a servo system into a permanent magnet, a winding and other key parts, and establishing a series reliability model; carrying out a high-temperature accelerated degradation test on the permanent magnet and the winding, and constructing a stochastic differential equation degradation model of a superimposed temperature-dependent diffusion term; a temperature condition neural generation model is introduced to generate and synthesize degradation track data; collecting a temperature sequence under a task spectrum and extracting a fusion temperature feature tensor; constructing a time sequence proxy model in which the one-dimensional dilated convolutional network and the long-short-term memory network are connected in series, and training the time sequence proxy model; recursion is carried out according to the agent model to obtain degradation variable statistics and condition failure probability, and instantaneous failure rate is determined; and substituting the instantaneous failure rate and the constant failure rate into the series model to obtain a system reliability curve. According to the method, the dynamic reliability of the collaborative robot PMSM servo system under the complex task spectrum can be accurately evaluated.

Description

Technical Field

[0001] This invention relates to the field of robot reliability engineering technology, and in particular to a reliability assessment method and system for a collaborative robot PMSM servo system. Background Technology

[0002] Collaborative robot joint drive systems typically employ high-power-density PMSM servo systems, which operate under complex and variable workloads for extended periods, facing severe challenges from thermal and mechanical stresses. Existing reliability assessment methods are mostly based on static life models, such as using exponential or Weibull distributions to statistically model component failure times and calculating system reliability through series-parallel system models. However, these methods struggle to reflect the cumulative impact of time-varying temperature histories on the degradation processes of critical components like permanent magnets and windings in actual task scenarios, and lack adaptability to complex motion patterns and multi-condition switching.

[0003] On the other hand, while isothermal degradation models based on thermal aging mechanisms such as Arrhenius can describe the aging behavior of materials at a single temperature, they are difficult to directly generalize to actual operating temperature processes with strong fluctuations and non-stationary characteristics. Simply extrapolating isothermal models to complex temperature paths introduces significant prediction bias. Furthermore, while purely data-driven deep learning models have strong fitting capabilities when degradation data is abundant, in emerging application scenarios such as collaborative robots, long-term degradation experiments are costly and lifetime data is scarce, leading to models that are prone to overfitting, have weak generalization ability, and lack clear physical interpretability.

[0004] Currently, there is a lack of a unified framework that can organically connect temperature-driven degradation mechanisms, temperature history within the task spectrum, and system-level dynamic reliability indicators, making it difficult to accurately assess the reliability and predict the lifespan of servo systems under time-varying operating conditions. Therefore, there is an urgent need for a dynamic reliability assessment method and system that can integrate physical mechanisms and data-driven approaches, is applicable to finite degradation data conditions, and can reflect the impact of the task spectrum. Summary of the Invention

[0005] To address at least one of the aforementioned technical problems, this invention proposes a reliability assessment method and system for PMSM servo systems of collaborative robots.

[0006] The first aspect of this invention provides a reliability assessment method for a PMSM servo system for collaborative robots, comprising: The PMSM servo system in the joint module of the collaborative robot is divided into several key components, including permanent magnets, windings, power devices, bearings and position sensors. The key components are established in series according to the functional links, and a series reliability model is established based on the series system structure. High-temperature accelerated degradation tests were conducted on the permanent magnet and winding to establish the Arrhenius relationship between degradation rate and temperature, and a stochastic differential equation degradation model was constructed based on the Arrhenius degradation trajectory with temperature-related diffusion terms superimposed. Based on the aforementioned stochastic differential equation degradation model, a temperature-conditional neural generation model with temperature and random noise as inputs is introduced to generate synthetic degradation trajectory data of permanent magnets and windings, thus obtaining a temperature-time-degradation mapping dataset of permanent magnets and windings. Under a representative task spectrum, the internal temperature sequence of the permanent magnet and winding during the operation of the servo system is collected. Statistical feature vectors and physical feature vectors are extracted from the temperature time sequence to form a fused temperature feature tensor. A time series proxy model consisting of a one-dimensional dilated convolutional network and a long short-term memory network is constructed, and the time series proxy model is trained based on the temperature-time-degradation mapping dataset and the fused temperature feature tensor. Under the preset task spectrum temperature history, the mean, standard deviation and several confidence level degradation quantiles of the permanent magnet and winding at each time node are obtained by recursion based on the time series proxy model. The conditional failure probability when the degradation variable exceeds the threshold is determined, and the instantaneous failure rate of the permanent magnet and winding over time is determined based on the conditional failure probability. Substituting the instantaneous failure rate of the permanent magnet and windings over time, along with the constant failure rate of the power devices, bearings, and position sensors, into the series reliability model, the system reliability curve of the PMSM servo system under the preset task spectrum is determined.

[0007] In this solution, the PMSM servo system in the collaborative robot's joint module is divided into several key components, including permanent magnets, windings, power devices, bearings, and position sensors. These key components are then organized into a series system structure according to their functional links. A series reliability model is then established based on this series system structure. Specifically: Based on the electromagnetic energy conversion link and functional output link of the collaborative robot joint PMSM servo system, key components on the path from electrical energy input to mechanical torque output are identified, including permanent magnets, windings, power devices, bearings, and position sensors. Based on the failure mechanism of key components, key components are divided into temperature-dominated degradation components and statistical lifetime components. The temperature-dominated degradation components include permanent magnets and windings, while the remaining key components are statistical lifetime components. Based on the functional dependencies of each key component in the functional link, the system is organized into a serial system structure. Under the serial system structure, the system reliability is defined as the product of the reliability of all key components at the same time point, and the system failure rate is the sum of the failure rates of all key components at the same time point. A series reliability model is established based on the system reliability and system failure rate.

[0008] In this scheme, the high-temperature accelerated degradation test is conducted on the permanent magnet and winding to establish the Arrhenius relationship between degradation rate and temperature. A stochastic differential equation degradation model is constructed based on the Arrhenius degradation trajectory and superimposed with temperature-related diffusion terms. Specifically: For the permanent magnet and winding, samples of permanent magnet and winding insulation consistent with the materials and structure of the PMSM servo system are prepared. The permanent magnet and winding insulation samples are placed at multiple constant temperature levels for high-temperature accelerated degradation tests. At each constant temperature level, the remanence density of the permanent magnet sample and the insulation resistance of the winding insulation sample are periodically measured at fixed time intervals. The degree of degradation of the permanent magnet and the winding assembly at different temperatures is determined based on the remanence density and insulation resistance, and degradation curves at multiple temperatures are constructed. The aging stages of the degradation curves at the multiple temperatures are identified, and the degradation curves of the aging stages are fitted exponentially to identify the degradation rate parameter at each constant temperature level. An Arrhenius relationship is established between the degradation rate parameter and temperature, expressed as: , in, Pre-exponential factor, To activate energy, Boltzmann's constant, Absolute temperature; Using the average degradation trajectory determined by the Arrhenius relation as the deterministic part, and superimposing a temperature-related stochastic diffusion term, a stochastic differential equation degradation model is constructed, which is expressed as: , in, As a degenerate variable, The degradation rate is determined by the Arrhenius relation. For temperature-dependent diffusion intensity, A weighting function to reflect the degree of fluctuation at different stages of degradation, For the standard Wiener process, This is the time increment.

[0009] In this scheme, based on the stochastic differential equation degradation model, a temperature-conditional neural generative model with temperature and random noise as input is introduced to generate synthetic degradation trajectory data of permanent magnets and windings, resulting in a temperature-time-degradation mapping dataset of permanent magnets and windings. Specifically: Using the isothermal Arrhenius mean degradation trajectory determined by the stochastic differential equation degradation model as the deterministic backbone, a temperature-conditional neural network generation model is constructed. The input of the temperature-conditional neural network generation model includes the target temperature Tc and a random noise vector, and the output is a degradation perturbation sequence superimposed on the mean trajectory. The temperature-conditional neural generation model employs a neural stochastic differential equation structure, with its drift term... and diffusion terms Even with temperature characteristics The relevant model is as follows: , The above model is discretized using the Euler-Maruyama scheme to obtain a discrete state sequence. : , The state vector is mapped using the linear projection operator LinProj. For temperature-related noise terms, For the first Points in time: , in, The temperature feature vector is provided by the temperature encoding module. This is the amplitude adjustment coefficient at temperature Tc. This is the intermediate hidden state vector obtained after a nonlinear transformation; The generated noise term is superimposed on the Arrhenius mean degradation trajectory to obtain the synthetic degradation trajectory: , The generative model is trained based on synthetic degradation trajectories at multiple isothermal points, and the training loss function includes adversarial loss. And multiple physical constraint losses: , Within the target operating temperature range, a preset fine temperature step size is used to input different random noise samples to generate a large number of synthetic degradation trajectories, which together with real experimental data form a dense temperature-time-degradation mapping dataset for permanent magnets and windings.

[0010] In this scheme, the step of collecting the internal temperature sequence of the permanent magnet and winding during the operation of the servo system under a representative task spectrum, and extracting statistical feature vectors and physical feature vectors based on the temperature time sequence to form a fused temperature feature tensor, specifically involves: Under a representative task spectrum, the internal temperature time series is collected in real time by temperature sensors arranged inside the permanent magnet and winding, and the task spectrum is repeated multiple times to obtain a set of temperature samples at each time sampling point. For each time sampling point, calculate the first to fourth moments of temperature across samples, calculate several low-order autocorrelation coefficients, and perform principal component analysis on the temperature sequence covariance matrix to extract several principal components. Combine the first to fourth moments, low-order autocorrelation coefficients, and principal component features to form a statistical feature vector. The physical features related to the thermal aging mechanism are calculated based on the temperature time series, including the cumulative thermal aging dose obtained by Arrhenius weighted integration of historical temperatures, the excess cumulative deviation relative to the reference temperature, the equivalent aging factor based on the Arrhenius rate, and the temperature gradient of adjacent sampling points. The physical features are then combined to form a physical feature vector. The statistical feature vector and physical feature vector of each time sampling point are concatenated to form the temperature feature vector of that time point. The temperature feature vectors of all time points in the entire task cycle are stacked in chronological order to form a fused temperature feature tensor.

[0011] In this scheme, the construction of a time-series proxy model consisting of a one-dimensional dilated convolutional network and a long short-term memory network, and the training of the time-series proxy model based on the temperature-time-degradation mapping dataset and the fused temperature feature tensor, specifically involves: A time series surrogate model is constructed by connecting a one-dimensional dilated convolutional network and a long short-term memory network. The one-dimensional dilated convolutional network is used to extract local patterns within a time window from the fused temperature feature tensor. By setting multiple convolutional layers with different dilation rates, a multi-scale receptive field is constructed to extract short-term fluctuations and periodic patterns in the temperature time series. The long short-term memory network is used to model the long-term dependency between temperature features and degradation increments. The temperature feature sequence in the temperature-time-degradation mapping dataset is used as the model input, and the corresponding degradation increment is used as the supervision label to construct a training sample set, wherein the length of the input sequence is the preset time window length, and the output is the degradation increment of the next time step; During model training, Gaussian negative log-likelihood loss is used as the data fitting loss function, and its expression is: , in, This represents the actual increase in degradation. and These are the conditional mean and log-variance of the degradation increment predicted by the model, respectively. By introducing physical constraint loss based on the Arrhenius mechanism, the difference between the average degradation rate predicted by the model under isothermal conditions and the theoretical degradation rate given by the Arrhenius model is calculated: , in, For the model at temperature The mean of the predicted degradation rate, The theoretical degradation rate determined for the Arrhenius relation; The weighted sum of the data fitting loss and the physical constraint loss constitutes a composite loss function: , Where λ is the physical constraint weight coefficient, the network parameters are optimized by the stochastic gradient descent algorithm so that the time series surrogate model can maintain the data fitting accuracy while conforming to the physical mechanism consistency; In the gating mechanism of the Long Short-Term Memory Network, physical feature vectors are explicitly introduced as additional inputs, so that physical features such as cumulative thermal aging dose and equivalent aging factor participate in memory unit update and forgetting gating calculation. After training, a time series surrogate model is obtained by mapping the temperature feature time series to the degradation increment probability distribution, which is used to predict the degradation trajectory of permanent magnets and windings under a given task spectrum temperature history.

[0012] In this scheme, under a preset task spectrum temperature history, the mean, standard deviation, and degradation quantiles of the permanent magnet and winding at each time node are recursively obtained according to the time series proxy model. The conditional failure probability when the degradation variable exceeds the threshold is determined, and the instantaneous failure rate of the permanent magnet and winding over time is determined based on the conditional failure probability. Specifically: Given a preset temperature history for the task spectrum, the collected temperature time series of the permanent magnet and winding are transformed into a fused temperature feature tensor, which is then input into a trained time series surrogate model. The conditional mean of the degradation variables of the permanent magnet and winding at discrete time nodes is obtained recursively through a sliding time window. ( ) and conditional standard deviation ; Based on the conditional mean and conditional standard deviation, at each time point The calculation of multiple pre-set confidence levels of degradation quantiles, including lower quantiles, is performed. ( ), median ( ) and upper quantile ( ); Linear interpolation is performed on the degenerate quantiles at the Probit scale to reconstruct any given time point. Degenerate variables ( Conditional cumulative distribution function Its reconstruction formula is: ; Where Φ(·) is the standard normal cumulative function, and q(·) is the Probit transform value of the corresponding quantile; The conditional failure probability when the degradation variable reaches a preset performance failure threshold is read from the conditional cumulative distribution function. Based on the ratio of the conditional failure probability increment to the probability of not yet failed at adjacent time steps, the instantaneous failure rate of the permanent magnet and winding at discrete time nodes is calculated. : ; By repeating the calculation process along the time axis, the failure rate curves of the permanent magnet and windings as a function of time under the preset task spectrum are obtained.

[0013] In this scheme, the instantaneous failure rate of the permanent magnet and windings over time, along with the constant failure rate of the power devices, bearings, and position sensors, are substituted into the series reliability model to determine the system reliability curve of the PMSM servo system under a preset task spectrum. Specifically: Based on the reliability model of the series system, the instantaneous failure rate of the permanent magnet and winding at each discrete time node is superimposed with the constant failure rate of the power device, bearing and position sensor obtained from historical fault data to obtain the time-varying system failure rate function of the PMSM servo system under the preset task spectrum. Based on the time-varying system failure rate function, the system reliability as a function curve of time is calculated by solving the differential relationship between system reliability and system failure rate, where the system reliability function is expressed as a negative exponential integral of the system failure rate function; Based on the system reliability function curve, calculate the reliability indicators in the task time, system median lifetime, and system mean time to failure corresponding to the first drop in system reliability to a predetermined threshold level.

[0014] A second aspect of the present invention also provides a reliability assessment system for a collaborative robot PMSM servo system. The system includes a memory and a processor. The memory includes a reliability assessment method program for a collaborative robot PMSM servo system. When the processor executes the reliability assessment method program for a collaborative robot PMSM servo system, it implements the steps of the reliability assessment method for a collaborative robot PMSM servo system as described in any of the preceding claims.

[0015] This invention discloses a reliability assessment method and system for PMSM servo systems of collaborative robots. The method includes: dividing the servo system into key components such as permanent magnets and windings, and establishing a series reliability model; conducting high-temperature accelerated degradation tests on the permanent magnets and windings, and constructing a stochastic differential equation degradation model with superimposed temperature-related diffusion terms; introducing a temperature-conditional neural network generation model to generate synthetic degradation trajectory data; collecting temperature sequences under the task spectrum and extracting fused temperature feature tensors; constructing and training a time-series surrogate model cascaded from a one-dimensional dilated convolutional network and a long short-term memory network; recursively obtaining degradation variable statistics and conditional failure probabilities based on the surrogate model to determine the instantaneous failure rate; and substituting the instantaneous failure rate and constant failure rate into the series model to obtain the system reliability curve. This invention can accurately assess the dynamic reliability of PMSM servo systems of collaborative robots under complex task spectra. Attached Figure Description

[0016] Figure 1 A flowchart of a reliability assessment method for a PMSM servo system for collaborative robots according to the present invention is shown. Figure 2 A block diagram of the serial system structure of the present invention is shown; Figure 3 The degradation curves of the permanent magnet of the present invention under multi-temperature degradation tests are shown; Figure 4 The degradation curves of the windings of the present invention under multi-temperature degradation tests are shown; Figure 5 The temperature-time-degradation mapping surface of the permanent magnet of the present invention is shown; Figure 6 The winding temperature-time-degradation mapping surface plot of the present invention is shown; Figure 7 The degradation trajectory diagram of the permanent magnet of the present invention is shown; Figure 8 The diagram shows the winding degradation trajectory of the present invention; Figure 9 A block diagram of a reliability assessment system for a collaborative robot PMSM servo system is shown. Detailed Implementation

[0017] To better understand the above-mentioned objectives, features, and advantages of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in these embodiments can be combined with each other.

[0018] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and therefore the scope of protection of the invention is not limited to the specific embodiments disclosed below.

[0019] Figure 1 A flowchart of a reliability assessment method for a collaborative robot PMSM servo system according to the present invention is shown.

[0020] like Figure 1 As shown, the first aspect of the present invention provides a reliability assessment method for a collaborative robot PMSM servo system, comprising: The PMSM servo system in the joint module of the collaborative robot is divided into several key components, including permanent magnets, windings, power devices, bearings and position sensors. The key components are established in series according to the functional links, and a series reliability model is established based on the series system structure. High-temperature accelerated degradation tests were conducted on the permanent magnet and winding to establish the Arrhenius relationship between degradation rate and temperature, and a stochastic differential equation degradation model was constructed based on the Arrhenius degradation trajectory with temperature-related diffusion terms superimposed. Based on the aforementioned stochastic differential equation degradation model, a temperature-conditional neural generation model with temperature and random noise as inputs is introduced to generate synthetic degradation trajectory data of permanent magnets and windings, thus obtaining a temperature-time-degradation mapping dataset of permanent magnets and windings. Under a representative task spectrum, the internal temperature sequence of the permanent magnet and winding during the operation of the servo system is collected. Statistical feature vectors and physical feature vectors are extracted from the temperature time sequence to form a fused temperature feature tensor. A time series proxy model consisting of a one-dimensional dilated convolutional network and a long short-term memory network is constructed, and the time series proxy model is trained based on the temperature-time-degradation mapping dataset and the fused temperature feature tensor. Under the preset task spectrum temperature history, the mean, standard deviation and several confidence level degradation quantiles of the permanent magnet and winding at each time node are obtained by recursion based on the time series proxy model. The conditional failure probability when the degradation variable exceeds the threshold is determined, and the instantaneous failure rate of the permanent magnet and winding over time is determined based on the conditional failure probability. Substituting the instantaneous failure rate of the permanent magnet and windings over time, along with the constant failure rate of the power devices, bearings, and position sensors, into the series reliability model, the system reliability curve of the PMSM servo system under the preset task spectrum is determined.

[0021] It should be noted that by dividing the servo system into key components and establishing a series reliability model, high-temperature accelerated degradation tests were conducted on temperature-sensitive components such as permanent magnets and windings. A degradation model integrating physical mechanisms and random diffusion was constructed, and a dense synthetic degradation data was generated using a temperature-conditional neural network generation model to compensate for the lack of measured data. Furthermore, by extracting the statistical and physical characteristics of temperature sequences under the task spectrum, a surrogate model of one-dimensional dilated convolution and long short-term memory network was constructed to accurately learn the complex mapping relationship between time-varying temperature history and degradation increment. Finally, based on the surrogate model, the dynamic statistical characteristics of degradation variables were recursively obtained, the time-varying failure rate of components was calculated, and combined with the constant failure rate of other components, a dynamic and accurate assessment of the reliability of the collaborative robot PMSM servo system under complex task spectrum was achieved. This effectively overcomes the limitations of traditional static models that cannot reflect the impact of actual working temperature fluctuations and the weak generalization ability of pure data-driven methods when data is scarce.

[0022] According to an embodiment of the present invention, the PMSM servo system in the joint module of the collaborative robot is divided into several key components, including permanent magnets, windings, power devices, bearings, and position sensors. The key components are then arranged in a series system structure according to their functional links. A series reliability model is established based on the series system structure. Specifically: The electromagnetic energy conversion link and functional output link of the collaborative robot joint PMSM servo system identify key components on the path from electrical energy input to mechanical torque output, including permanent magnets (PM), windings (W), power devices (e.g., MOSFET modules, denoted as power devices MOS), bearings (BR), and position sensors (PS). Based on the failure mechanism of key components, key components are divided into temperature-dominated degradation components and statistical lifetime components. The temperature-dominated degradation components include permanent magnets and windings, while the remaining key components are statistical lifetime components. like Figure 2 The system is organized into a serial system structure based on the functional dependencies of each key component along the functional chain. Under this serial system structure, the system reliability is defined as the product of the reliability of all key components at the same point in time. The system failure rate is the sum of the failure rates of all critical components at the same point in time; A series reliability model is established based on the system reliability and system failure rate.

[0023] It should be noted that the electromagnetic energy conversion link refers to the energy transfer path from electrical energy input to mechanical torque output in the PMSM servo system of a collaborative robot joint. Key components such as permanent magnets and windings achieve energy conversion through electromagnetic interaction. The functional output link describes the functional dependence of these components in the mechanical torque output process. The failure mechanism of permanent magnets and windings is mainly closely related to temperature. Permanent magnets will undergo irreversible demagnetization at high temperatures, while the insulation performance of windings will decline due to thermal aging of the insulation material. The failure mechanisms of other key components such as power devices, bearings, and position sensors are mostly random failures, and their failure rate can be considered constant over the life cycle. Since the performance degradation of permanent magnets and windings is directly affected by temperature and exhibits time-varying characteristics, degradation analysis is required to accurately predict their lifespan. For other components, since the failure rate is relatively stable, statistical lifetime models are usually used for reliability assessment.

[0024] According to an embodiment of the present invention, the high-temperature accelerated degradation test is conducted on the permanent magnet and winding to establish the Arrhenius relationship between degradation rate and temperature, and a stochastic differential equation degradation model is constructed based on the Arrhenius degradation trajectory with a temperature-related diffusion term superimposed, specifically as follows: For the permanent magnet and winding, samples of permanent magnet and winding insulation consistent with the materials and structure of the PMSM servo system are prepared. The permanent magnet and winding insulation samples are placed at multiple constant temperature levels for high-temperature accelerated degradation tests. At each constant temperature level, the remanence density of the permanent magnet sample and the insulation resistance of the winding insulation sample are periodically measured at fixed time intervals. The degree of degradation of the permanent magnet and the winding assembly at different temperatures is determined based on the remanence density and insulation resistance, and degradation curves at multiple temperatures are constructed. It should be noted that during the permanent magnet test, sampling and measurement are performed at fixed time intervals Δt. For example, a sample can be taken out every two hours, cooled to room temperature, and then the remanence density B is measured using a gaussmeter before the sample is returned to the constant temperature chamber for continued aging. The duration can be set to approximately 500 hours. The results are as follows: Figure 3 The multi-temperature degradation curves are shown. During the main aging stage, the degradation curves at each temperature can be well fitted by an exponential function. The degradation rate parameter obtained by the fitting changes exponentially with temperature, conforming to an Arrhenius-type relationship. Therefore, the degradation of permanent magnets can be regarded as a temperature-driven first-order thermal activation process, and the form of degradation rate with temperature can be given by the Arrhenius equation.

[0025] For the winding test, the test temperature can be selected at multiple constant temperature levels, such as 230°C, 260°C, and 290°C. The samples are aged in the constant temperature chamber, removed at fixed time intervals, cooled, and then the insulation resistance R_s is measured using an insulation resistance meter. The time and resistance values ​​are used to construct degradation observation data. The samples are then returned to the chamber for continued aging until the predetermined total aging time is reached. The insulation degradation curves at different temperatures are shown below. Figure 4 As shown, within the main aging range, the degradation of insulation resistance at various temperatures can also be approximated as exponential, and its degradation rate parameter conforms to the Arrhenius relation with temperature. The variation of the degradation rate with temperature is given by the Arrhenius equation.

[0026] Let component i represent the permanent magnet or winding, and define the degenerate variable Zi(t,T): , The aging stages of the degradation curves at the multiple temperatures are identified, and the degradation curves of the aging stages are fitted exponentially, as follows: , Identify the degradation rate parameter at each constant temperature level, and establish the Arrhenius relation between the degradation rate parameter and temperature, which is expressed as: , in, Pre-exponential factor, To activate energy, Boltzmann's constant, Absolute temperature; Using the average degradation trajectory determined by the Arrhenius relation as the deterministic part, the deterministic average trajectory of the degradation variable Z(t,T) of the permanent magnet or winding at a constant temperature T is as follows: ; Considering factors such as material discreteness, manufacturing errors, environmental fluctuations, and measurement noise, a stochastic differential equation degradation model is constructed by superimposing temperature-related random perturbations, i.e., superimposing temperature-related random diffusion terms, on a deterministic average trajectory. This stochastic differential equation degradation model is expressed as follows: , in, As a degenerate variable, The degradation rate is determined by the Arrhenius relation. For temperature-dependent diffusion intensity, A weighting function to reflect the degree of fluctuation at different stages of degradation, For the standard Wiener process, This is the time increment.

[0027] It should be noted that this model identifies the temperature-related diffusion intensity and weighting function by fitting the average behavior and variance evolution of degradation curves at different temperatures, thus obtaining an Arrhenius-stochastic degradation model that reflects both the temperature acceleration effect and includes random fluctuation characteristics.

[0028] According to an embodiment of the present invention, based on the stochastic differential equation degradation model, a temperature-conditional neural generative model with temperature and random noise as input is introduced to generate synthetic degradation trajectory data of the permanent magnet and winding, thereby obtaining a temperature-time-degradation mapping dataset of the permanent magnet and winding, specifically: Using the isothermal Arrhenius mean degradation trajectory determined by the stochastic differential equation degradation model as the deterministic backbone, a temperature-conditional neural network generation model is constructed. The input of the temperature-conditional neural network generation model includes the target temperature Tc and a random noise vector, and the output is a degradation perturbation sequence superimposed on the mean trajectory. The temperature-conditional neural generation model employs a neural stochastic differential equation structure, with its drift term... and diffusion terms Even with temperature characteristics The relevant model is as follows: , It should be noted that, To match the temperature characteristic h T The relevant drift term describes the statistical change of the degradation rate over time at a given temperature; This is the diffusion term, used to describe the intensity of random fluctuations caused by external disturbances. The above model is discretized using the Euler-Maruyama scheme to obtain a discrete state sequence. : , The state vector is mapped using the linear projection operator LinProj. For temperature-related noise terms, For the first Points in time: , in, The temperature feature vector is provided by the temperature encoding module. This is the amplitude adjustment coefficient at temperature Tc. This is the intermediate hidden state vector obtained after a nonlinear transformation; The generated noise term is superimposed onto the Arrhenius mean degradation trajectory. The above yields the synthetic degenerate trajectory: , The generative model is trained based on synthetic degradation trajectories at multiple isothermal points, and the training loss function includes adversarial loss. And multiple physical constraint losses: , It should be noted that, among them Constraining the deviation of the local slope of the generated trajectory from the Arrhenius prediction rate ensures that the degradation is monotonic over time and has a reasonable decay rate; The variance of degradation increment increases with increasing temperature under different temperatures, reflecting the mechanism of increased degradation uncertainty under high temperature conditions; Ensure that the insulation resistance decreases as the temperature rises, constrain the winding insulation resistance at any given time section to decrease as the temperature rises, and avoid cross-curves that violate the thermal aging law; This suppresses abnormal correlations between adjacent time increments and weakens unreasonable short-period oscillations. This is achieved through the weighting coefficient λ. phy ,λ ind ,λ temp The adjustment can achieve a trade-off between approximating the measured statistical distribution and maintaining the consistency of the mechanism, as follows: ; ; ; Within the target operating temperature range, a preset fine temperature step size is used to input different random noise samples to generate a large number of synthetic degradation trajectories, which together with real experimental data form a dense temperature-time-degradation mapping dataset for permanent magnets and windings.

[0029] It should be noted that after training convergence, a detailed temperature grid is divided within the actual operating temperature range, for example, in steps of several degrees Celsius between 80 and 170 degrees Celsius. Multiple different random noises are input for each temperature point to generate a large number of degradation paths. During this process, the permanent magnet and windings are trained with their respective temperature condition generation models, ultimately resulting in a temperature-time-degradation three-dimensional mapping dataset covering the actual operating temperature range. As shown in the figure, this dataset has high resolution in both the time and temperature dimensions and provides the statistical distribution of the degradation process at each temperature level, providing sufficient samples for subsequent time-series surrogate model training.

[0030] According to an embodiment of the present invention, the step of acquiring the internal temperature sequence of the permanent magnet and winding during the operation of the servo system under a representative task spectrum, and extracting statistical feature vectors and physical feature vectors based on the temperature time sequence to construct a fused temperature feature tensor, specifically involves: Under a representative task spectrum, the internal temperature time series is collected in real time by temperature sensors arranged inside the permanent magnet and winding, and the task spectrum is repeated multiple times to obtain a set of temperature samples at each time sampling point. For each time sampling point, calculate the first to fourth moments of temperature across samples, calculate several low-order autocorrelation coefficients, and perform principal component analysis on the temperature sequence covariance matrix to extract several principal components. Combine the first to fourth moments, low-order autocorrelation coefficients, and principal component features to form a statistical feature vector. It should be noted that, based on typical collaborative robot movements, a representative task spectrum is designed, including acceleration segments, constant speed segments, deceleration segments, and intermittent stationary segments, forming a task cycle. The specific statistical feature vector of temperature is as follows: For component i (permanent magnet or winding), at each time sampling point The temperature observations corresponding to the M repeated executions are considered as a set of samples: Calculate the first to fourth moments of this sample set, representing the temperature mean, variance, skewness, and kurtosis, respectively, to describe the shape of the temperature distribution. ; ; ; ; For each temperature time series, a low-order autocorrelation coefficient is calculated and averaged across samples to characterize the short-term temporal correlation of the temperature series. ; A temperature sample matrix is ​​constructed, the covariance matrix across time is calculated, and several principal components are extracted through principal component analysis to represent the dominant modes of temperature fluctuation.

[0031] ; ; The above statistics are organized into a statistical feature vector u at each time point. T( t j This vector comprehensively reflects the temporal structure of temperature under operational uncertainty and mission spectrum.

[0032] ; The physical features related to the thermal aging mechanism are calculated based on the temperature time series, including the cumulative thermal aging dose obtained by Arrhenius weighted integration of historical temperatures, the excess cumulative deviation relative to the reference temperature, the equivalent aging factor based on the Arrhenius rate, and the temperature gradient of adjacent sampling points. The physical features are then combined to form a physical feature vector. It should be noted that the physical feature vector of temperature is specifically implemented as follows: Arrhenius-type thermal aging dose: The cutoff time t is obtained by performing an Arrhenius-weighted integral over historical temperatures. j The cumulative thermal aging index; ; Cumulative deviation from reference temperature: The comprehensive index of over-limit time and over-limit magnitude is obtained by integrating the portion of the temperature that is higher than a certain reference temperature. ; Equivalent aging factor: Equivalent to a complex temperature curve as an equivalent lifespan consumption ratio under constant temperature. ; Temperature gradient and fluctuation intensity indicators: These indicators characterize rapid temperature changes in the form of temperature differences between adjacent time points and the rate of temperature change.

[0033] ; The above physical quantities are organized into a physical feature vector V. T (t j This vector directly reflects the cumulative driving effect of temperature on the degradation process.

[0034] ; The statistical feature vector and physical feature vector of each time sampling point are concatenated to form the temperature feature vector of that time point. The temperature feature vectors of all time points in the entire task cycle are stacked in chronological order to form a fused temperature feature tensor.

[0035] It should be noted that at each time point t j , to statistical feature vector u T (t j ) and physical eigenvector V T (t j The temperature feature vectors at all time points within the entire task cycle are concatenated to obtain the "temperature feature vector" for that time point. The temperature feature vectors at all time points within the entire task cycle are stacked in chronological order to form a temperature feature time series, which is then input into the subsequent time series surrogate model in the form of a fixed-length sliding window.

[0036] .

[0037] According to an embodiment of the present invention, the construction of a time-series proxy model consisting of a one-dimensional dilated convolutional network and a long short-term memory network, and the training of the time-series proxy model based on the temperature-time-degradation mapping dataset and the fused temperature feature tensor, specifically involves: A time series surrogate model is constructed by connecting a one-dimensional dilated convolutional network and a long short-term memory network. The one-dimensional dilated convolutional network is used to extract local patterns within a time window from the fused temperature feature tensor. By setting multiple convolutional layers with different dilation rates, a multi-scale receptive field is constructed to extract short-term fluctuations and periodic patterns in the temperature time series. The long short-term memory network is used to model the long-term dependency between temperature features and degradation increments. It should be noted that the time series surrogate model mainly consists of two parts: One-dimensional temporal convolutional network (TCN) module is used to extract local temporal patterns from temperature history windows; physically constrained long short-term memory network (LSTM) module is used to combine statistical and physical features to model long-term dependencies and nonlinear dynamics.

[0038] Specifically, the temperature sequence within each time window is input into the TCN module, which extracts local temperature change patterns over time through multi-layer one-dimensional convolution, dilated convolution, and appropriate pooling operations, and outputs intermediate features. It can identify temperature steps, plateaus, rapid heating and rapid cooling modes.

[0039] At each time step, Compared with the aforementioned statistical feature vectors ( The inputs are then combined to form a combined input. The data is then fed into a multi-layer LSTM network. The LSTM network's gating equations explicitly incorporate physical feature vectors. ( As an additional input, physical features are used to participate in memory unit updates and gating variable calculations, thereby characterizing the cumulative thermal aging effect within the network.

[0040] ; After the LSTM outputs the hidden state, an output layer maps the hidden state to the conditional mean and logarithmic variance of the degradation increment, in order to characterize the uncertainty of the degradation process.

[0041] ; The temperature feature sequence in the temperature-time-degradation mapping dataset is used as the model input, and the corresponding degradation increment is used as the supervision label to construct a training sample set, wherein the length of the input sequence is the preset time window length, and the output is the degradation increment of the next time step; During model training, Gaussian negative log-likelihood loss is used as the data fitting loss function, and its expression is: , in, This represents the actual increase in degradation. and These are the conditional mean and log-variance of the degradation increment predicted by the model, respectively. By introducing physical constraint loss based on the Arrhenius mechanism, the difference between the average degradation rate predicted by the model under isothermal conditions and the theoretical degradation rate given by the Arrhenius model is calculated: , in, For the model at temperature The mean of the predicted degradation rate, The theoretical degradation rate determined for the Arrhenius relation; The weighted sum of the data fitting loss and the physical constraint loss constitutes a composite loss function: +λ , Where λ is the physical constraint weight coefficient, the network parameters are optimized by the stochastic gradient descent algorithm so that the time series surrogate model can maintain the data fitting accuracy while conforming to the physical mechanism consistency; In the gating mechanism of Long Short-Term Memory (LSTM) networks, physical feature vectors are explicitly introduced as additional inputs, allowing physical features such as cumulative thermal aging dose and equivalent aging factor to participate in memory unit updates and forgetting gating calculations. After training, a time-series surrogate model is obtained, mapping the temperature feature time series to the degradation increment probability distribution. This model is used to predict the degradation trajectory of permanent magnets and windings under a given task spectrum temperature history. Figure 7 , Figure 8 As stated above.

[0042] According to an embodiment of the present invention, under a preset task spectrum temperature history, the mean, standard deviation, and degradation quantiles of the permanent magnet and winding at each time node are recursively obtained according to the time series surrogate model. The conditional failure probability when the degradation variable exceeds a threshold is determined, and the instantaneous failure rate of the permanent magnet and winding over time is determined based on the conditional failure probability. Specifically: Given a preset temperature history for the task spectrum, the collected temperature time series of the permanent magnet and winding are transformed into a fused temperature feature tensor, which is then input into a trained time series surrogate model. The conditional mean of the degradation variables of the permanent magnet and winding at discrete time nodes is obtained recursively through a sliding time window. ( ) and conditional standard deviation ; Based on the conditional mean and conditional standard deviation, at each time point The calculation of multiple pre-set confidence levels of degradation quantiles, including lower quantiles, is performed. ( ), median ( ) and upper quantile ( ); Linear interpolation is performed on the degenerate quantiles at the Probit scale to reconstruct any given time point. Degenerate variables ( Conditional cumulative distribution function Its reconstruction formula is: ; Where Φ(·) is the standard normal cumulative function, and q(·) is the Probit transform value of the corresponding quantile; The conditional failure probability when the degradation variable reaches a preset performance failure threshold is read from the conditional cumulative distribution function. Based on the ratio of the conditional failure probability increment to the probability of not yet failed at adjacent time steps, the instantaneous failure rate of the permanent magnet and winding at discrete time nodes is calculated. : ; By repeating the calculation process along the time axis, the failure rate curves of the permanent magnet and windings as a function of time under the preset task spectrum are obtained.

[0043] According to an embodiment of the present invention, the step of substituting the instantaneous failure rate of the permanent magnet and windings over time with the constant failure rate of the power devices, bearings, and position sensors into the series reliability model to determine the system reliability curve of the PMSM servo system under a preset task spectrum is as follows: Based on the reliability model of the series system, the instantaneous failure rate of the permanent magnet and winding at each discrete time node is superimposed with the constant failure rate of the power device, bearing and position sensor obtained from historical fault data to obtain the time-varying system failure rate function of the PMSM servo system under the preset task spectrum. Based on the time-varying system failure rate function, the system reliability as a function curve of time is calculated by solving the differential relationship between system reliability and system failure rate, where the system reliability function is expressed as a negative exponential integral of the system failure rate function; Based on the system reliability function curve, calculate the reliability indicators in the task time, system median lifetime, and system mean time to failure corresponding to the first drop in system reliability to a predetermined threshold level.

[0044] It should be noted that for power devices, bearings, and position sensors, since the main reliability information is historical failure records or life manual data, an exponential life model is used to estimate their constant failure rate. By constructing a dynamic reliability assessment framework that integrates physical guidance and data-driven approaches, the problems of traditional static life models being insensitive to complex task spectra, isothermal mechanism models being unable to adapt to non-stationary temperature processes, and pure data-driven methods having weak generalization ability when degradation data is scarce are effectively addressed. This method first decomposes the servo system into temperature-dominated degradation components and statistical lifetime components, establishing a unified reliability model within a cascaded system structure. An Arrhenius-stochastic differential equation degradation model is established through multi-temperature accelerated degradation experiments, and a temperature-conditional neural network generation model is used to generate dense degradation data covering actual operating conditions, significantly alleviating the limitation of insufficient experimental data. Furthermore, statistical and physical characteristics of the task spectrum temperature sequence are extracted, and a surrogate model composed of a one-dimensional dilated convolutional network and a long short-term memory network is constructed. A mechanistic constraint loss function ensures that the model conforms to Arrhenius physical laws while maintaining data fitting accuracy. Finally, based on the degradation distribution predicted by the surrogate model, the conditional cumulative distribution function is reconstructed through Probit-scale interpolation to calculate the time-varying failure rate of the components. This result is then combined with the constant failure rate of the statistical lifetime components to achieve system-level dynamic reliability assessment. This method can more sensitively reflect the impact of task spectrum temperature fluctuations on reliability, and the obtained lifetime indicators are more conservative and have greater engineering guidance value, providing a quantitative basis for the reliability design, load management, and maintenance strategies of collaborative robot joint servo systems.

[0045] According to an embodiment of the present invention, it further includes: Based on the electromagnetic-thermal finite element simulation model of the joint module of the collaborative robot, a three-dimensional temperature field distribution database of permanent magnets and windings under different working conditions is constructed. Based on the three-dimensional temperature field distribution database, the spatial heat transfer function relationship between the theoretical optimal placement position of temperature sensors and the key areas of each component is extracted. During the actual operation of the servo system, auxiliary temperature sequences are collected by auxiliary temperature sensors built into the power devices and bearings. The abnormal sensor contact state is identified based on the dynamic temperature difference pattern between the auxiliary temperature sequence and the readings of the main temperature sensors of the permanent magnet and winding. When the dynamic temperature difference pattern is detected to continuously deviate from the theoretical temperature difference range predicted by the spatial heat transfer function relationship, it is determined that the main temperature sensor has a placement deviation and a distortion flag signal is generated. The sensor reading correction algorithm based on Kalman filtering is triggered by the distortion flag signal. The auxiliary temperature sequence is used as the observation variable, and the spatial heat transfer function relationship is used as the state transition matrix. The estimated temperature sequence of the key area of ​​the permanent magnet and winding is obtained by data fusion calculation. The estimated temperature sequence is used to replace the distorted main sensor reading and input into the fusion temperature feature tensor construction process.

[0046] According to an embodiment of the present invention, the step of triggering a sensor reading correction algorithm based on Kalman filtering according to the distortion flag signal, using the auxiliary temperature sequence as the observed variable and the spatial heat transfer function relationship as the state transition matrix, and obtaining the estimated temperature sequence of the key region of the permanent magnet and winding through data fusion calculation, specifically involves: Based on the aforementioned spatial heat transfer function relationship, a system state-space equation is established with the actual temperature of the key area of ​​the component as the state vector and the readings of the auxiliary sensors as the observation vector. Initialize the state covariance matrix of the Kalman filter, and use the covariance of the difference between the historical readings of the main temperature sensor before the first deviation and the readings of the auxiliary sensor as the basis for estimating the process noise covariance matrix. At each sampling time, state prediction is performed based on the system state space equation. The predicted state vector is then weighted and fused with the current auxiliary temperature sequence using Kalman gain to obtain the optimal estimate of the temperature in the key area. The optimal estimates at consecutive sampling times are combined in chronological order to form an estimated temperature sequence, and the posterior error covariance of each estimate is calculated to assess the estimation uncertainty. The estimated temperature sequence and its corresponding estimation uncertainty index are input into the time series surrogate model, so that the surrogate model can simultaneously consider the error propagation effect caused by the uncertainty of temperature measurement when predicting the degradation trajectory.

[0047] It should be noted that the mechanical vibrations generated during robot operation may cause slight misalignment or poor contact of the temperature sensors in the permanent magnets and windings inside the joints, resulting in a systematic deviation of the measured temperature sequence from the true value. This distorted input directly affects the subsequent fusion feature tensor extracted based on the temperature sequence. A three-dimensional temperature field database is constructed to establish the theoretical placement of sensors and the heat transfer relationship in key areas, and real-time cross-validation is performed using power devices and auxiliary sensors on bearings. When a continuous abnormality in the dynamic temperature difference pattern of the main and auxiliary sensors is detected, a Kalman filter-based data fusion algorithm is triggered, using the spatial heat transfer function as the state transition basis to correct the distorted readings. The final output estimated temperature sequence and its uncertainty index are injected into the degradation prediction process. The technical effect is a significant improvement in the reliability of temperature monitoring data and an assurance of accurate degradation trajectory prediction, enabling the collaborative robot servo system to achieve more accurate lifespan prediction and fault warning under complex working conditions.

[0048] Figure 9 A block diagram of a reliability assessment system for a collaborative robot PMSM servo system is shown.

[0049] A second aspect of the present invention also provides a reliability assessment system for a collaborative robot PMSM servo system. The system includes a memory 901, a processor 902, and a communication interface 903. The memory includes a reliability assessment method program for a collaborative robot PMSM servo system. The communication interface is used for data connection and communication between the memory and the processor. When the processor executes the reliability assessment method program for a collaborative robot PMSM servo system, it implements the steps of the reliability assessment method for a collaborative robot PMSM servo system as described in any of the above claims.

[0050] This invention discloses a reliability assessment method and system for PMSM servo systems of collaborative robots. The method includes: dividing the servo system into key components such as permanent magnets and windings, and establishing a series reliability model; conducting high-temperature accelerated degradation tests on the permanent magnets and windings, and constructing a stochastic differential equation degradation model with superimposed temperature-related diffusion terms; introducing a temperature-conditional neural network generation model to generate synthetic degradation trajectory data; collecting temperature sequences under the task spectrum and extracting fused temperature feature tensors; constructing and training a time-series surrogate model cascaded from a one-dimensional dilated convolutional network and a long short-term memory network; recursively obtaining degradation variable statistics and conditional failure probabilities based on the surrogate model to determine the instantaneous failure rate; and substituting the instantaneous failure rate and constant failure rate into the series model to obtain the system reliability curve. This invention can accurately assess the dynamic reliability of PMSM servo systems of collaborative robots under complex task spectra.

[0051] Those skilled in the art will understand that all or part of the steps of the above method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When the program is executed, it performs the steps of the above method embodiments. The aforementioned storage medium includes various media capable of storing program code, such as mobile storage devices, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0052] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A reliability assessment method for a PMSM servo system for collaborative robots, characterized in that, Includes the following steps: The PMSM servo system in the joint module of the collaborative robot is divided into several key components, including permanent magnets, windings, power devices, bearings and position sensors. The key components are established in series according to the functional links, and a series reliability model is established based on the series system structure. High-temperature accelerated degradation tests were conducted on the permanent magnet and winding to establish the Arrhenius relationship between degradation rate and temperature, and a stochastic differential equation degradation model was constructed based on the Arrhenius degradation trajectory with temperature-related diffusion terms superimposed. Based on the aforementioned stochastic differential equation degradation model, a temperature-conditional neural generation model with temperature and random noise as inputs is introduced to generate synthetic degradation trajectory data of permanent magnets and windings, thus obtaining a temperature-time-degradation mapping dataset of permanent magnets and windings. Under a representative task spectrum, the internal temperature sequence of the permanent magnet and winding during the operation of the servo system is collected. Statistical feature vectors and physical feature vectors are extracted from the temperature time sequence to form a fused temperature feature tensor. A time series proxy model consisting of a one-dimensional dilated convolutional network and a long short-term memory network is constructed, and the time series proxy model is trained based on the temperature-time-degradation mapping dataset and the fused temperature feature tensor. Under the preset task spectrum temperature history, the mean, standard deviation and several confidence level degradation quantiles of the permanent magnet and winding at each time node are obtained by recursion based on the time series proxy model. The conditional failure probability when the degradation variable exceeds the threshold is determined, and the instantaneous failure rate of the permanent magnet and winding over time is determined based on the conditional failure probability. Substituting the instantaneous failure rate of the permanent magnet and windings over time, along with the constant failure rate of the power devices, bearings, and position sensors, into the series reliability model, the system reliability curve of the PMSM servo system under the preset task spectrum is determined.

2. The reliability assessment method for a PMSM servo system for collaborative robots according to claim 1, characterized in that, The PMSM servo system in the collaborative robot's joint module is divided into several key components, including permanent magnets, windings, power devices, bearings, and position sensors. These key components are then arranged in a series system structure according to their functional links. A series reliability model is then established based on this series system structure. Specifically: Based on the electromagnetic energy conversion link and functional output link of the collaborative robot joint PMSM servo system, key components on the path from electrical energy input to mechanical torque output are identified, including permanent magnets, windings, power devices, bearings, and position sensors. Based on the failure mechanism of key components, key components are divided into temperature-dominated degradation components and statistical lifetime components. The temperature-dominated degradation components include permanent magnets and windings, while the remaining key components are statistical lifetime components. Based on the functional dependencies of each key component in the functional link, the system is organized into a serial system structure. Under the serial system structure, the system reliability is defined as the product of the reliability of all key components at the same time point, and the system failure rate is the sum of the failure rates of all key components at the same time point. A series reliability model is established based on the system reliability and system failure rate.

3. The reliability assessment method for a PMSM servo system for collaborative robots according to claim 1, characterized in that, The high-temperature accelerated degradation test was conducted on the permanent magnet and winding to establish the Arrhenius relationship between degradation rate and temperature. A stochastic differential equation degradation model was constructed based on the Arrhenius degradation trajectory with added temperature-related diffusion terms. Specifically: For the permanent magnet and winding, samples of permanent magnet and winding insulation consistent with the materials and structure of the PMSM servo system are prepared. The permanent magnet and winding insulation samples are placed at multiple constant temperature levels for high-temperature accelerated degradation tests. At each constant temperature level, the remanence density of the permanent magnet sample and the insulation resistance of the winding insulation sample are periodically measured at fixed time intervals. The degree of degradation of the permanent magnet and the winding assembly at different temperatures is determined based on the remanence density and insulation resistance, and degradation curves at multiple temperatures are constructed. The aging stages of the degradation curves at the multiple temperatures are identified, and the degradation curves of the aging stages are fitted exponentially to identify the degradation rate parameter at each constant temperature level. An Arrhenius relationship is established between the degradation rate parameter and temperature, expressed as: ， in, Pre-exponential factor, To activate energy, Boltzmann's constant, Absolute temperature; Using the average degradation trajectory determined by the Arrhenius relation as the deterministic part, and superimposing a temperature-related stochastic diffusion term, a stochastic differential equation degradation model is constructed, which is expressed as: ， in, As a degenerate variable, The degradation rate is determined by the Arrhenius relation. For temperature-dependent diffusion intensity, A weighting function to reflect the degree of fluctuation at different stages of degradation, For the standard Wiener process, This is the time increment.

4. The reliability assessment method for a PMSM servo system for collaborative robots according to claim 1, characterized in that, Based on the stochastic differential equation degradation model, a temperature-conditional neural generative model with temperature and random noise as inputs is introduced to generate synthetic degradation trajectory data of the permanent magnet and winding, resulting in a temperature-time-degradation mapping dataset of the permanent magnet and winding, specifically: Using the isothermal Arrhenius mean degradation trajectory determined by the stochastic differential equation degradation model as the deterministic backbone, a temperature-conditional neural network generation model is constructed. The input of the temperature-conditional neural network generation model includes the target temperature Tc and a random noise vector, and the output is a degradation perturbation sequence superimposed on the mean trajectory. The temperature-conditional neural generation model employs a neural stochastic differential equation structure, with its drift term... and diffusion terms Even with temperature characteristics The relevant model is as follows: ， The above model is discretized using the Euler-Maruyama scheme to obtain a discrete state sequence. : ， The state vector is mapped using the linear projection operator LinProj. For temperature-related noise terms, For the first Points in time: ， in, The temperature feature vector is provided by the temperature encoding module. This is the amplitude adjustment coefficient at temperature Tc. This is the intermediate hidden state vector obtained after a nonlinear transformation; The generated noise term is superimposed on the Arrhenius mean degradation trajectory to obtain the synthetic degradation trajectory: ， The generative model is trained based on synthetic degradation trajectories at multiple isothermal points, and the training loss function includes adversarial loss. And multiple physical constraint losses: ， Within the target operating temperature range, a preset fine temperature step size is used to input different random noise samples to generate a large number of synthetic degradation trajectories, which together with real experimental data form a dense temperature-time-degradation mapping dataset for permanent magnets and windings.

5. The reliability assessment method for a PMSM servo system for collaborative robots according to claim 1, characterized in that, The process involves collecting temperature sequences of the permanent magnet and windings during servo system operation under a representative task spectrum, and extracting statistical and physical feature vectors from these temperature time sequences to construct a fused temperature feature tensor. Specifically: Under a representative task spectrum, the internal temperature time series is collected in real time by temperature sensors arranged inside the permanent magnet and winding, and the task spectrum is repeated multiple times to obtain a set of temperature samples at each time sampling point. For each time sampling point, calculate the first to fourth moments of temperature across samples, calculate several low-order autocorrelation coefficients, and perform principal component analysis on the temperature sequence covariance matrix to extract several principal components. Combine the first to fourth moments, low-order autocorrelation coefficients, and principal component features to form a statistical feature vector. The physical features related to the thermal aging mechanism are calculated based on the temperature time series, including the cumulative thermal aging dose obtained by Arrhenius weighted integration of historical temperatures, the excess cumulative deviation relative to the reference temperature, the equivalent aging factor based on the Arrhenius rate, and the temperature gradient of adjacent sampling points. The physical features are then combined to form a physical feature vector. The statistical feature vector and physical feature vector of each time sampling point are concatenated to form the temperature feature vector of that time point. The temperature feature vectors of all time points in the entire task cycle are stacked in chronological order to form a fused temperature feature tensor.

6. The reliability assessment method for a PMSM servo system for collaborative robots according to claim 1, characterized in that, The construction of the time-series proxy model, which consists of a one-dimensional dilated convolutional network and a long short-term memory network, is carried out by training the time-series proxy model based on the temperature-time-degradation mapping dataset and the fused temperature feature tensor. Specifically: A time series surrogate model is constructed by connecting a one-dimensional dilated convolutional network and a long short-term memory network. The one-dimensional dilated convolutional network is used to extract local patterns within a time window from the fused temperature feature tensor. By setting multiple convolutional layers with different dilation rates, a multi-scale receptive field is constructed to extract short-term fluctuations and periodic patterns in the temperature time series. The long short-term memory network is used to model the long-term dependency between temperature features and degradation increments. The temperature feature sequence in the temperature-time-degradation mapping dataset is used as the model input, and the corresponding degradation increment is used as the supervision label to construct a training sample set, wherein the length of the input sequence is the preset time window length, and the output is the degradation increment of the next time step; During model training, Gaussian negative log-likelihood loss is used as the data fitting loss function, and its expression is: ， in, This represents the actual increase in degradation. and These are the conditional mean and log-variance of the degradation increment predicted by the model, respectively. By introducing physical constraint loss based on the Arrhenius mechanism, the difference between the average degradation rate predicted by the model under isothermal conditions and the theoretical degradation rate given by the Arrhenius model is calculated: ， in, For the model at temperature The mean of the predicted degradation rate, The theoretical degradation rate determined for the Arrhenius relation; The weighted sum of the data fitting loss and the physical constraint loss constitutes a composite loss function: +λ , Where λ is the physical constraint weight coefficient, the network parameters are optimized by the stochastic gradient descent algorithm so that the time series surrogate model can maintain the data fitting accuracy while conforming to the physical mechanism consistency; In the gating mechanism of the Long Short-Term Memory Network, physical feature vectors are explicitly introduced as additional inputs, so that physical features such as cumulative thermal aging dose and equivalent aging factor participate in memory unit update and forgetting gating calculation. After training, a time series surrogate model is obtained by mapping the temperature feature time series to the degradation increment probability distribution, which is used to predict the degradation trajectory of permanent magnets and windings under a given task spectrum temperature history.

7. The reliability assessment method for a PMSM servo system for collaborative robots according to claim 1, characterized in that, Under the preset task spectrum temperature history, the mean, standard deviation, and degradation quantiles of the permanent magnet and winding at each time node are recursively obtained according to the time series proxy model. The conditional failure probability when the degradation variable exceeds the threshold is determined, and the instantaneous failure rate of the permanent magnet and winding over time is determined based on the conditional failure probability. Specifically: Given a preset temperature history for the task spectrum, the collected temperature time series of the permanent magnet and winding are transformed into a fused temperature feature tensor, which is then input into a trained time series surrogate model. The conditional mean of the degradation variables of the permanent magnet and winding at discrete time nodes is obtained recursively through a sliding time window. ( ) and conditional standard deviation ; Based on the conditional mean and conditional standard deviation, at each time point The calculation of multiple pre-set confidence levels of degradation quantiles, including lower quantiles, is performed. ( ), median ( ) and upper quantile ( ); Linear interpolation is performed on the degenerate quantiles at the Probit scale to reconstruct any given time point. Degenerate variables ( Conditional cumulative distribution function Its reconstruction formula is: ； Where Φ(·) is the standard normal cumulative function, and q(·) is the Probit transform value of the corresponding quantile; The conditional failure probability when the degradation variable reaches a preset performance failure threshold is read from the conditional cumulative distribution function. Based on the ratio of the conditional failure probability increment to the probability of not yet failed at adjacent time steps, the instantaneous failure rate of the permanent magnet and winding at discrete time nodes is calculated. : ； By repeating the calculation process along the time axis, the failure rate curves of the permanent magnet and windings as a function of time under the preset task spectrum are obtained.

8. The reliability assessment method for a PMSM servo system for collaborative robots according to claim 1, characterized in that, The instantaneous failure rate of the permanent magnet and windings over time, along with the constant failure rate of the power devices, bearings, and position sensors, are substituted into the series reliability model to determine the system reliability curve of the PMSM servo system under a preset task spectrum. Specifically: Based on the reliability model of the series system, the instantaneous failure rate of the permanent magnet and winding at each discrete time node is superimposed with the constant failure rate of the power device, bearing and position sensor obtained from historical fault data to obtain the time-varying system failure rate function of the PMSM servo system under the preset task spectrum. Based on the time-varying system failure rate function, the system reliability as a function curve of time is calculated by solving the differential relationship between system reliability and system failure rate, where the system reliability function is expressed as a negative exponential integral of the system failure rate function; Based on the system reliability function curve, calculate the reliability indicators in the task time, system median lifetime, and system mean time to failure corresponding to the first drop in system reliability to a predetermined threshold level.

9. A reliability assessment system for a PMSM servo system for collaborative robots, characterized in that, The reliability assessment system for a collaborative robot PMSM servo system includes a storage device and a processor. The storage device includes a reliability assessment method program for a collaborative robot PMSM servo system. When the processor executes the reliability assessment method program for a collaborative robot PMSM servo system, it implements the steps of the reliability assessment method for a collaborative robot PMSM servo system as described in any one of claims 1 to 8.

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