CN118052127A - Circuit board residual life prediction method based on fault physics and data driving fusion - Google Patents
Circuit board residual life prediction method based on fault physics and data driving fusion Download PDFInfo
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Abstract
The invention provides a circuit board residual life prediction method based on fault physics and data driving fusion, which comprises the following steps: determining a fault physical model form; generating degradation data with uncertainty in the future by using a wiener process; and carrying the parameters obtained by the fault physical model into a data driving model for life fusion prediction, and converting the predicted parameter values into residual life values of the circuit board. The invention also provides a method for predicting the residual life of the circuit board by utilizing the fault physics and data driving fusion of the kernel function, which comprises the following steps: calculating the physical life of the fault; predicting the residual life of the product by using a data driving model; and carrying out fusion prediction on the residual life by using a kernel function constructed based on the exponential function. The two methods cover the electronic product with a single main failure mechanism and a multi-component multi-failure mechanism, and the prediction result of the physical model and the prediction result of the on-line monitoring data drive are mutually fused to obtain a more comprehensive and more accurate prediction result of the residual life.
Description
Technical Field
The invention belongs to the technical field of electronic product life prediction, relates to two electronic product circuit board residual life fusion prediction methods, and particularly relates to a circuit board residual life prediction method based on fault physics and data driving fusion.
Background
As a product integrated by various components according to different functions and use requirements, the electronic product has more and more abundant structures and functions, but is accompanied by more and more complex system structures and ever-increasing use and maintenance costs, and particularly for valuable electronic products, if early warning can be provided for impending faults and the residual service life of the product can be effectively estimated, the electronic product has important significance in improving the usability, reliability and safety of the product.
The life prediction method of the electronic product gradually develops to the prediction of a data driving algorithm based on degradation data from the prediction based on a fault physical model at the beginning along with the development of technology. The prediction method based on the fault physical model adopts physical models such as a Paris crack model, a vibration fatigue model and the like to conduct fault prediction; the prediction based on the data driving algorithm is performed by adopting a mathematical statistics method or an artificial intelligence and machine learning algorithm. The prediction method based on the fault physical model or the data driving algorithm has certain limitation, the prediction method based on the fault physical model needs less data information, but higher model accuracy can ensure higher prediction precision; the prediction method based on the data driving algorithm requires enough data to obtain better prediction precision through learning and training.
In recent years, many scholars consider fusing the prediction result based on the fault physical model with the prediction result based on the data driving algorithm, and combine the advantages of the two to improve the prediction performance. On one hand, the fusion method can expand the application range of the prediction method based on the physical model; on the other hand, interpretation of the data driven algorithm model may also be improved. Five key steps required for the fusion approach include data acquisition, feature extraction, diagnostics, degradation modeling, and residual life (RUL) prediction, where the hybrid approach has advantages in building structure and random dependencies between mold systems and components. The existing fusion method of the fault physical model and the data driving algorithm is mainly divided into four types: 1) Inferring a prediction model using the data-driven model and predicting using a physical model-based method; 2) Replacing a system model based on a physical model by using a data driving model; 3) Predicting a future degradation state using a data-driven model, and using a physical model-based RUL prediction; 4) And carrying out RUL prediction by using a data driving algorithm and a physical model-based method, and fusing the results. The first three types are prior to each other for data driven algorithms or fault physical models, i.e., the two methods work in series. The fourth class is to start the data driving model and the physical model at the same time and fuse the results, i.e. the two integration methods work in parallel.
In fact, in the above four types of fusion methods, the prediction method based on the physical model is mostly limited to particle filtering, markov chain, state equation and the like, and then the degradation trend of the performance parameter is taken as the prediction result, and the failure mechanism of the system and the application of the failure physical model are not considered, and fusion is still performed on the premise of acquiring corresponding data. The product is lack of data in the initial stage of design, and the life or the relation model of degradation parameters and internal factors and external factors provided by the fault physical model can make up for the condition of insufficient data in the initial stage, and the information for evaluating the residual life of the product is richer along with the increase of monitoring data in the later stage. In summary, at any stage, the method of fusing the fault physical model with the monitoring data is still imperfect.
Disclosure of Invention
The invention aims to solve the technical problems that a physical model prediction result and an on-line monitoring data driving prediction result are mutually fused based on a kernel function and a wiener process, and the fused algorithm is used for predicting the residual life of the circuit board of the electronic product to obtain a more comprehensive and more accurate residual life prediction result.
In order to solve the problems, the invention provides a circuit board residual life prediction method based on fault physics and data driving fusion, which comprises the following steps:
S1, determining a fault physical model of a circuit board;
s11, describing the whole degradation of the product by adopting an acceleration degradation rate model, wherein the acceleration degradation rate model accelerates the degradation rate Expressed as:
Wherein M is the degradation amount of the parameter, T is time, S is the stress except the temperature stress T, K is Boltzmann constant, ea is activation energy, and C 0 and n are constants;
S12, modeling a circuit board by adopting a fault physical life model, and obtaining the following output voltage model:
Wherein V out is output voltage, V, T, S is electric stress, temperature stress and vibration stress of circuit operation, ea is activation energy, k is Boltzmann constant, t is time, and a, b, c, d is constant; unknown parameters Ea, a, b, c, d are obtained through experimental fitting;
S13, considering probability uncertainty aiming at a voltage model, performing discretization operation on stress parameters V, T, S, performing discretization by using normal distribution N (u, sigma), performing Monte Carlo simulation, using reliability to represent degradation of a circuit, and performing next prediction input by taking the reliability as a parameter of a fault physical model, wherein the reliability is expressed as follows:
Wherein, R is reliability, M Vout is margin of the performance parameter V out, and n is simulation times performed at the working time t; i (V out(t)∈MVout) is an oscillometric function, I (·) =1 when V out(t)∈MVout and I (·) =0 when V out(t)□MVou
S2, generating wiener degradation data; generating future degradation data with probability uncertainty by monitoring the working stress of the circuit board and the change condition of degradation parameters and utilizing a wiener process to describe the trend of the future degradation parameters; wherein the wiener degradation data generation process expression is:
dXt＝μXtdt+σXtdBt(4)
wherein, X t is a random variable, uX t is the mean value of the random variable X t, sigma X t is variance, bt is standard Brownian motion;
S3, carrying the degradation rate or reliability obtained by the fault physical model and the degraded performance parameters into a data driving model for fusion prediction to obtain a parameter prediction value;
S4, converting the parameter predicted value obtained by fusion prediction into the residual life of the circuit board, determining the expected value and the degradation threshold value of the degraded performance parameter, obtaining the real-time performance parameter degradation amount by the predicted performance parameter, and obtaining the residual life value of the circuit board through calculation of a residual life expression.
Further, in step S4, when the parameter predicted value obtained by fusion prediction is converted into the remaining life of the circuit board, the remaining life of the data drive at time t is represented by the following formula (5):
Wherein, delta theta (t) is the damage caused by the product working for time t, and can be obtained by theta (t) -theta (0), and theta (t) represents the performance parameter degraded with time; delta theta th is the margin of the performance parameter theta, and the initial value and the threshold value of the performance parameter are subtracted to obtain; ruldata (t) represents the remaining life of the data drive at time t.
Further, in step S2, the unknown parameters u and σ in the wiener degradation data generation process expression are obtained by fitting the distribution obtained by taking the difference of the logarithm to the Xt:
Δln X＝ln Xt-ln Xs＝(μ-1/2σ2)t+σBt～N((μ-1/22)d,σ2d) (6)
Where d=t-s (t > s) is the normal distribution with the mean value (μ - σ 2) d and the variance σ 2 d for the time interval N ((μ - σ 2)d,σ2 d) for time t and time s.
Further, the fusion prediction in step S3 includes a first fusion prediction algorithm that is selected when predicting the life of the circuit board at the next time, and a second fusion prediction algorithm that is selected when predicting the remaining life of the circuit board in the future time range.
Further, the first fusion prediction algorithm is a training neural network algorithm aiming at a data driving model by using real degradation data and monitoring stress as inputs, the training input of the first fusion prediction algorithm for obtaining the predicted value of the real data is the front x% of all the real data, wherein x is more than 70 and less than 90, the predicted input is the rear x% of all the data to 100%, and if the degradation trend is obvious, x takes a small value; if the degradation is not obvious, x takes a large value; and learning the neural network through the degradation parameters of the front x percent and the physical parameters of the faults, obtaining the neural network after learning, and predicting the degradation parameters and the physical parameters of the faults except the front x percent to obtain the predicted value of the degradation parameters.
Further, the second fusion prediction algorithm is used for training a data driving model by taking all the monitored degradation parameters and the monitored stress as input to a neural network algorithm, predicting by using the generated future degradation parameters, and predicting to obtain future performance parameter degradation values considering uncertainty; and the second fusion prediction algorithm inputs all real data, takes 100% of degradation parameters and fault physical parameters as training input of the neural network, acquires the trained neural network through the neural network learning, generates a certain number of data in the future through a wiener process, selects 10% -30% of all real data, takes the future data generated in the wiener process as prediction input, and acquires the predicted value of the future degradation parameters.
Further, in step S11, the activation energy Ea and the parameter C 0Sn in expression (1) can be obtained by:
The linear equation is: y=β 0+β1 x (8), let β0＝ln(C0Sn),β1＝-Ea；
Calculating the change rate of the monitoring parameter at different moments when the temperature stress is T by using the monitoring dataSubstituting the parameters into a linear equation and solving to obtain the activation energy Ea and the parameter C 0Sn of the fault physical model.
The invention provides a fusion prediction method for the residual life of a circuit board based on a kernel function, which specifically comprises the following steps:
S1, calculating the fault physical life of a circuit board; obtaining a fault physical life value of the circuit board by using a fault physical life model of the circuit board;
s11, determining a life prediction model based on a fault physical model, wherein the life prediction model is specifically expressed as:
Wherein N f (x%) is the number of cycles corresponding to x% failure; epsilon is the plasticity of the welding spot, and 0.325 is taken; f is a stress experimental factor; h and LD are the solder joint height and effective length; Δa is the coefficient of thermal expansion coefficient difference between the component and the substrate; Δte is the effective thermal cycle temperature range; c is a constant related to the average temperature of the weld and the stress relaxation/creep time per cycle; beta is 4 when the lead-free installation is carried out;
S12, parameters F, h, LD, delta a, delta Te and c are obtained from the self parameters and working stress of the product;
S13, substituting the parameters into a life prediction model to obtain the thermal fatigue life N f of the welding spots of the circuit board;
s14, converting the thermal fatigue life into the residual life RUL_pof (t) of the product at time t, wherein the calculation method comprises the following steps:
RUL_pof(t)＝Nf-t (2)
S2, predicting the residual life of the circuit board by using a data driving model; determining degraded performance parameters, predicting degradation values of the performance parameters by using a data driving model, converting the performance parameter values into residual life values, and calculating by using the following Miner linear damage method:
s3, fusion of kernel functions; the residual life of the circuit board, which is obtained by respective prediction of the fault physical model and the data driving model, is fused by utilizing a kernel function, and the fused residual life is obtained;
S31, selecting a Logistic function as a kernel function for prediction, wherein the function form is as follows:
Kdata(t0,ti)＝1-Kpof(t0,ti)
Where K pof (t 0, ti) represents the kernel function coefficients of the fault physics, and K data (t 0, ti) represents the data driven kernel function; a is
The initial weight parameter of the kernel function, a is more than or equal to 0, namely the weight size allocated to the fault physical model at the initial 0 moment, kpof (t 0, ti) =1/(a+1), the initial weights of the fault physical and the data driving are allocated by adjusting the size of a, and the weights of 0.5 are allocated to the fault physical and the data driving when a=1; b is a constant parameter and b >0, controlling the changing shape of the kernel function; wherein t0 and ti are as follows:
t0＝RUL_pof0 (5)
ti＝RUL_pofi，i＝1,2，…m
Wherein RUL_ pofi is a residual life value obtained at the moment i based on the fault physical model;
S32, obtaining a fusion residual life predicted value RUL (theta) of the circuit board by using a kernel function fusion result:
RUL(θ)＝Kpof(t0,ti)·RUL_pofi+Kdata(t0,ti)·RUL_datai (6).
Compared with the prior art, the technical effect that this scheme produced is:
(1) The fusion method based on the kernel function is suitable for the conditions that the main failure mechanism of the electronic product is damage type, the physical model is failure time type, the degradation trend of performance parameters is obvious, the monotonicity is good and the certainty is strong, and degradation data is processed by adopting a long and short memory network.
(2) The fusion method based on the wiener process is applicable to a circuit module or a circuit board besides directly adopting a fault physical life model, wherein the internal fault mechanism crosslinking relation is complex, a definite fault time model cannot be obtained or is difficult to derive by using the fault physical method, the integral performance parameter has the conditions of insignificant degradation and strong uncertainty of future degradation trend, and an Arrhenius acceleration rate model is adopted at the moment; according to the method, actual measurement data is utilized for learning, future random data is generated by adopting a wiener process to predict, future uncertainty is fully considered, and therefore the change trend of the residual life is predicted in advance.
The two methods cover the electronic product with a single main failure mechanism or a multi-component multi-failure mechanism, and the prediction result of the physical model and the prediction result of the on-line monitoring data drive are mutually fused to obtain a more comprehensive and more accurate prediction result of the residual life.
Drawings
FIG. 1 is a block diagram of the overall flow of a circuit board life fusion prediction method of the present invention;
FIG. 2 is a frame diagram of a method for predicting the residual life of a circuit board based on the integration of fault physics and data driving;
FIG. 3 is a schematic diagram of specific input/output of the first fusion prediction algorithm and the second fusion prediction algorithm according to the present invention;
FIG. 4 is a framework diagram of a fusion prediction method for the residual life of a circuit board based on a kernel function;
FIG. 5 is a diagram of the original recorded data of the present invention;
FIG. 6 is a schematic diagram of the result of linear fitting of the generalized Arrhenius model of the present invention;
FIG. 7 is a diagram of data generated by the wiener process of the present invention;
FIG. 8 is a diagram of the prediction result of real data according to the present invention;
FIG. 9 is a diagram of the prediction error of real data according to the present invention;
FIG. 10 is a diagram of a wiener process prediction result according to the present invention;
FIG. 11 is a diagram of the prediction error of the wiener process of the present invention;
FIG. 12 is a graph showing predicted remaining life of real data according to the present invention;
FIG. 13 is a schematic diagram of the predicted remaining lifetime of the wiener process generated data of the present invention;
FIG. 14A is a schematic diagram of a chip daisy chain resistor sample of an experiment of the present invention;
FIG. 14B is a schematic diagram of a chip daisy chain resistor sample structure according to the present invention;
FIG. 15 is a schematic diagram of a stress profile of an experimental chip according to the present invention;
FIG. 16 is a graph showing the comparison of predicted values and actual values according to the present invention;
FIG. 17 is a diagram illustrating the predicted value and residual error size according to the present invention;
FIG. 18 is a graph showing the trend of the kernel coefficients according to the present invention;
FIG. 19 is a schematic diagram showing the variation of fusion lifetime according to the present invention.
Detailed Description
The application is described in further detail below with reference to the drawings and examples. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the application. It should be noted that, for convenience of description, only the portions related to the present application are shown in the drawings. Embodiments of the application and features of the embodiments may be combined with each other without conflict.
The flow of the two methods for predicting the residual life of the circuit board based on the wiener process and the kernel function disclosed by the invention is shown in figure 1, the wiener process method is selected when the residual life of the multi-fault mechanism and the data-driven fusion is predicted, and the kernel function method is selected when the residual life of the single-fault mechanism and the data-driven fusion is predicted.
As shown in fig. 2, the invention discloses a circuit board residual life prediction method based on fault physics and data driving fusion, which comprises the following steps:
S1, determining a fault physical model of a circuit board;
s11, describing the whole degradation of the product by adopting an acceleration degradation rate model, wherein the acceleration degradation rate model accelerates the degradation rate Expressed as:
Wherein M is the degradation amount of the parameter, T is time, S is the stress except the temperature stress T, K is Boltzmann constant, ea is activation energy, and C 0 and n are constants;
S12, modeling a circuit board by adopting a fault physical life model, and obtaining the following output voltage model:
Wherein V out is output voltage, V, T, S is electric stress, temperature stress and vibration stress of circuit operation, ea is activation energy, k is Boltzmann constant, t is time, and a, b, c, d is constant; unknown parameters Ea, a, b, c, d are obtained through experimental fitting;
S13, considering probability uncertainty aiming at a voltage model, performing discretization operation on stress parameters V, T, S, performing discretization by using normal distribution N (u, sigma), performing Monte Carlo simulation, using reliability to represent degradation of a circuit, and performing next prediction input by taking the reliability as a parameter of a fault physical model, wherein the reliability is expressed as follows:
Wherein, R is reliability, M Vout is margin of the performance parameter V out, and n is simulation times performed at the working time t; i (V out(t)∈MVout) is an oscillometric function, I (·) =1 when V out(t)∈MVout and I (·) =0 when V out(t)□MVou
S2, generating wiener degradation data; generating future degradation data with probability uncertainty by monitoring the working stress of the circuit board and the change condition of degradation parameters and utilizing a wiener process to describe the trend of the future degradation parameters; wherein the wiener degradation data generation process expression is:
dXt×μXtdt+σXtdBt(4)
wherein, X t is a random variable, uX t is the mean value of the random variable X t, sigma X t is variance, bt is standard Brownian motion;
S3, carrying the degradation rate or reliability obtained by the fault physical model and the degraded performance parameters into a data driving model for fusion prediction to obtain a parameter prediction value;
The first fusion prediction algorithm is a training neural network algorithm aiming at a data driving model by using real degradation data and monitoring stress as inputs, and a predicted value of the real data is obtained; the training input of the first method is the front x% of all real data, the recommendation is 70 < x < 90, the prediction input is the data of the rear x% -100% of all data, and if the degradation trend is obvious, x takes a smaller value; if the degradation is not obvious, x takes a larger value; and learning the neural network through the degradation parameters of the front x percent and the physical parameters of the faults, obtaining the neural network after learning, and predicting the degradation parameters and the physical parameters of the faults except the front x percent to obtain the predicted value of the degradation parameters.
The second fusion prediction algorithm is aimed at a data driving model, all the monitored degradation parameters and the monitored stress are used as inputs to the neural network algorithm for training, the generated future degradation parameters are used for prediction, and the future performance parameter degradation values considering uncertainty are obtained through prediction; the second method inputs all real data, takes 100% degradation parameters and fault physical parameters as training input of a neural network, acquires the trained neural network through the neural network learning, generates a certain number of data in the future through a wiener process, selects 10% -30% of all real data, takes the future data generated in the wiener process as prediction input, and acquires the prediction value of the future degradation parameters. The specific inputs and outputs of the two methods are shown in fig. 3.
S4, converting the parameter predicted value obtained by fusion prediction into the residual life of the circuit board, determining the expected value and the degradation threshold value of the degraded performance parameter, obtaining the real-time performance parameter degradation amount by the predicted performance parameter, and obtaining the residual life value of the circuit board through calculation of a residual life expression.
Further, in step S4, when the parameter predicted value obtained by fusion prediction is converted into the remaining life of the circuit board, the remaining life of the data drive at time t is represented by the following formula (5):
Wherein, delta theta (t) is the damage caused by the product working for time t, and can be obtained by theta (t) -theta (0), and theta (t) represents the performance parameter degraded with time; delta theta th is the margin of the performance parameter theta, and the initial value and the threshold value of the performance parameter are subtracted to obtain; ruldata (t) represents the remaining life of the data drive at time t.
As shown in fig. 4, the method for predicting the remaining life of a circuit board based on a kernel function disclosed by the invention specifically comprises the following steps:
S1, calculating the fault physical life of a circuit board; obtaining a fault physical life value of the circuit board by using a fault physical life model of the circuit board;
s11, determining a life prediction model based on a fault physical model, wherein the life prediction model is specifically expressed as:
Wherein N f (x%) is the number of cycles corresponding to x% failure; epsilon is the plasticity of the welding spot, and 0.325 is taken; f is a stress experimental factor; h and LD are the solder joint height and effective length; Δa is the coefficient of thermal expansion coefficient difference between the component and the substrate; Δte is the effective thermal cycle temperature range; c is a constant related to the average temperature of the weld and the stress relaxation/creep time per cycle; beta is 4 when the lead-free installation is carried out;
S12, parameters F, h, LD, delta a, delta Te and c are obtained from the self parameters and working stress of the product;
S13, substituting the parameters into a life prediction model to obtain the thermal fatigue life N f of the welding spots of the circuit board;
s14, converting the thermal fatigue life into the residual life RUL_pof (t) of the product at time t, wherein the calculation method comprises the following steps:
RUL_pof(t)＝Nf-t (2)
S2, predicting the residual life of the circuit board by using a data driving model; determining degraded performance parameters, predicting degradation values of the performance parameters by using a data driving model, converting the performance parameter values into residual life values, and calculating by using the following Miner linear damage method:
s3, fusion of kernel functions; the residual life of the circuit board, which is obtained by respective prediction of the fault physical model and the data driving model, is fused by utilizing a kernel function, and the fused residual life is obtained;
S31, selecting a Logistic function as a kernel function for prediction, wherein the function form is as follows:
Kdata(t0,ti)＝1-Kpof(t0,ti)
Where K pof (t 0, ti) represents the kernel function coefficients of the fault physics, and K data (t 0, ti) represents the data driven kernel function; a is
The initial weight parameter of the kernel function, a is more than or equal to 0, namely the weight size allocated to the fault physical model at the initial 0 moment, kpof (t 0, ti) =1/(a+1), the initial weights of the fault physical and the data driving are allocated by adjusting the size of a, and the weights of 0.5 are allocated to the fault physical and the data driving when a=1; b is a constant parameter and b >0, controlling the changing shape of the kernel function; wherein t0 and ti are as follows:
t0＝RUL_pof0 (5)
ti＝RUL_pofi，i＝1,2，…n
Wherein RUL_ pofi is a residual life value obtained at the moment i based on the fault physical model;
S32, obtaining a fusion residual life predicted value RUL (theta) of the circuit board by using a kernel function fusion result:
RUL(θ)＝Kpof(t0,ti)·RUL_pofi+Kdata(t0,ti)·RUL_datai (6).
the technical scheme of the invention is further described below by using fusion cases based on the wiener process and considering probability uncertainty and fusion cases based on a kernel function.
Fusion prediction cases based on the wiener process considering probability uncertainty.
The case is illustrated by taking a DC-DC device of a certain board module as an example, the experiment is carried out for continuously measuring the board for four months, the output voltage and the monitoring temperature of the DC-DC device are obtained, the original data are simply processed, as shown in fig. 5, and the output voltage has obvious degradation condition in the latter half section. The output voltage of the DC-DC is obtained through fault analysis and is also a key performance parameter of the whole circuit, so that the case analysis takes the degradation of the output voltage as a degraded performance parameter.
S1, determining a fault physical model form; it is known from fig. 5 that the recorded temperature has no obvious change rule or is constant, and is difficult to directly calculate by using a fault physical model and difficult to model, so that a generalized alennis model is used as a physical parameter.
Using experimental data, from which data with more significant temperature and voltage gradients were selected, fitting results are shown in fig. 6, and regression yields the following linear equation:
y＝6.023-0.2525x (1)
The parameters of the linear equation can be derived from: activation energy ea=0.2525, parameter CS n = 412.82.
S2, generating wiener degradation data; after the mean and variance are obtained by fitting the data distribution by using the wiener function, voltage degradation data of a certain period of time in the future is generated by using the wiener process, as shown in fig. 7, the data is degradation data of the last 30% of all the voltage data, and future degradation data of 20% of all the degradation data are generated.
S3, a first fusion prediction algorithm; and fusing the predicted result, and adopting an LSTM (long and short memory neural network prediction) algorithm. Uncertainty is introduced in order to realize verification of modeling by adopting a wiener process, and reasonability of future performance parameter degradation trend is predicted. The data-driven fusion prediction method 1 predicts real data by using an algorithm, the data-driven fusion prediction method 2 predicts data generated by a wiener process, and the rationality of adopting the wiener process can be illustrated by comparing the prediction results of the data-driven fusion prediction methods 1 and 2.
Fig. 8 and 9 are graphs showing the prediction results of real data predicted by LSTM algorithm, and it can be seen from the graphs that the error of prediction using real data is only 0.025V, and the error is very small.
S4, a second fusion prediction algorithm; fig. 10 and 11 are graphs of the prediction results of the future wiener process predicted by using the LSTM algorithm, and it can be seen from the graphs that the data generated by the wiener process has strong stationarity, while the neural network obtained by learning the real data is used to predict the future wiener process, so that the correlation is still strong, the overall maximum error is 0.03V, and the random data generated by the wiener process can be accepted to predict the value of the future voltage compared with the error 0.025V predicted by using the real data.
S5, converting the predicted performance parameter value into the residual life; and after the predicted value of the voltage is obtained by fusion prediction in the step S3 and the step S4, calculating the value of the residual life by adopting a method for calculating the performance parameter to the residual life. The predicted performance parameter of the voltage was expected to be 24V, the degradation threshold was defined to be 22V, and the degradation amount was 2V, and the predicted performance parameter was converted into the remaining life using the following equation, and the change of the remaining life with time was obtained as shown in fig. 12 and 13.
It can be seen from fig. 12 that the resulting remaining life degradation is not significant when the data is temporarily less significant in the degradation trend. After data with a certain degradation rule is generated by adopting the wiener process, the residual life is predicted to have a better degradation result, as shown in fig. 13.
Fusion prediction cases based on kernel functions.
Take the data of the solder joint fatigue test of the BGA package chip on a certain circuit board as an example. The test sample is a 16×16 BGA package chip carrier, the PCB flame-retardant material grade is FR4, the solder joint material is Sn96.5Ag3Cu0.5, the diameter of the solder joint is 0.5mm, the test uses the resistance of the daisy chain as the performance degradation parameter by connecting the daisy chain as shown in fig. 14A and 14B on the solder holes of the PCB, the circuit board fault is judged when the resistance degradation reaches 21%, and the test is ended.
The experimental stress environment profile is shown in FIG. 15, with high and low stress cycles between 20℃and 100 ℃.
The failure criterion of the experiment is that the chip is considered to be invalid when the resistance value exceeds 21% of the initial value of the device, and the experiment is ended.
Experimental data are shown in table 1, where N represents the number of stress cycles of the experiment and R represents the resistance between the measured performance parameter welds.
TABLE 1 thermal fatigue test data for solder joints
S1, calculating fault physical life; as the data of the thermal fatigue test of the welding spots are obtained by the case, and the resistance value is degraded by 21 percent
As a performance parameter threshold, the following ENGELMAIRE welding spot fatigue life model with fault proportion can be selected for life prediction;
Where N f (x%) is the number of cycles corresponding to x% failure, epsilon is the solder joint plasticity, F is the stress experimental factor, h and LD are the solder joint attachment point dimensions, Δa is the coefficient of thermal expansion difference (stress generation) between the component and the substrate, Δte is the effective thermal cycling temperature range, c is a constant related to the solder joint average temperature and the stress relaxation/creep time per cycle, and β=4 when mounting the accessory on a lead-free surface.
The case shows that the experimental non-working environment temperature T0 is 20 ℃, and the device case temperature TC and the substrate temperature TS are 100 ℃ in the stress profile since no electrical stress is applied to the device. The failure proportion x% is 21% and the plasticity epsilon of the welding spot is 0.325. The daisy chain resistor on the experimental circuit board is directly exposed to the circuit board, and can be approximated as a ceramic package stress test factor F of 1. Solder joint attachment spot size h=0.5, ld=16. The effective thermal cycle temperature range Δte=100-20=80K.
The coefficient of difference (stress generation) between the daisy chain resistance and the thermal expansion coefficient of the substrate:
Δa＝2.5×10-6 -2.3×10-8＝2.477×10-6 (4)
The constant c can be calculated from parameters of the first weld fatigue model:
Ts＝100+273.15
T0＝20+273.15
TSJ＝0.25*(TC+TS+2T0)
＝0.25*(TC+373.15+586.3)＝333.15
c＝c0+c1In(1+360/d)Tc
＝-0.442-7.5×10-4×TSJ+1.74×10-2×In(1+360/15)
＝-06359
Substituting all known parameters and parameter values calculated by the two formulas into ENGE LMAI RE welding spot fatigue life model welding spots with fault proportion to obtain the cycle number which can be achieved by the fatigue life of the welding spots is Nf (21%) =950 times.
S2, predicting residual life by data driving; the LSTM algorithm is used herein as a data-driven predictive algorithm, and as is known from table 1, the input data to the LSTM algorithm is a single-column time series of resistance values with a lifetime of 12 cyclic stresses for each interval between data points. Substituting the data in table 1 into the LSTM algorithm yields the predicted results.
As shown in fig. 16, the neural network prediction results show that the red curve represents the predicted actual value and the blue curve represents the predicted value. The learning rate of the neural network is 0.80, and the resistance values of the predicted values from 0 to 396 cycles are all the predicted results by using the true values. The trend is predicted from the number of loops 396 and then using the predicted data. The predicted value in fig. 16 is obtained by substituting the input data into the neural network to perform a new prediction, and it can be seen from the graph that the neural network has a good prediction effect, the data before 396 cycles is used as the learned data, the fitting effect is good, the data after 396 cycles is used for the prediction, and the prediction result has a small difference from the actual value.
The result of trend prediction using the prediction data and the residual are shown in fig. 17. From the 408 th cycle, the actual value is used to predict the resistance trend at the next moment, and the difference between the predicted value and the actual value is small as can be seen from the residual result.
S3, fusion of kernel functions; the change of the kernel function coefficient of the fatigue of the welding spot is shown in fig. 18, and the adopted exponential form kernel function leads the kernel function coefficient of fault physics to gradually decrease along with the increase of the experimental time of the chip and the degradation amount of the resistance value, namely the weight of life prediction is biased to the prediction result of data driving as much as possible.
The resulting fusion lifetime change is shown in fig. 19, from which it can be seen that the change in the physical lifetime of the fault is a linear degradation trend with increasing resistance degradation. When the measured resistance data reach the fault criteria (resistance value + -21%) and the experiment is finished, the residual life of the fault physics remains very large. The residual life of the data drive in fig. 19 has larger fluctuation at the beginning, the prediction has extremely large uncertainty, the mutation is obvious, and the kernel function is adopted to fuse the better comprehensive fault physics and the respective prediction results of the data drive, so as to obtain a relatively-affirmative residual life. With the increase of time operation and data quantity, an intersection point exists between the data-driven prediction and the fault physical prediction, the data-driven prediction accuracy is also continuously increased, and the kernel function prediction is adopted, so that the fault physical and data-driven prediction results can be well integrated.
Finally, what should be said is: the above embodiments are merely for illustrating the technical aspects of the present invention, and it should be understood by those skilled in the art that although the present invention has been described in detail with reference to the above embodiments: modifications and equivalents may be made thereto without departing from the spirit and scope of the invention, which is intended to be encompassed by the claims.
Claims (8)
1. The method for predicting the residual life of the circuit board based on fault physics and data driving fusion is characterized by comprising the following steps of:
S1, determining a fault physical model of a circuit board;
s11, describing the whole degradation of the product by adopting an acceleration degradation rate model, wherein the acceleration degradation rate model accelerates the degradation rate Expressed as:
Wherein M is the degradation amount of the parameter, T is time, S is the stress except the temperature stress T, K is Boltzmann constant, ea is activation energy, and C 0 and n are constants;
S12, modeling a circuit board by adopting a fault physical life model, and obtaining the following output voltage model:
Wherein V out is output voltage, V, T, S is electric stress, temperature stress and vibration stress of circuit operation, ea is activation energy, k is Boltzmann constant, t is time, and a, b, c, d is constant; unknown parameters Ea, a, b, c, d are obtained through experimental fitting;
S13, considering probability uncertainty aiming at a voltage model, performing discretization operation on stress parameters V, T, S, performing discretization by using normal distribution N (u, sigma), performing Monte Carlo simulation, using reliability to represent degradation of a circuit, and performing next prediction input by taking the reliability as a parameter of a fault physical model, wherein the reliability is expressed as follows:
Wherein R is reliability, M Vout is margin of the performance parameter V out, and n is simulation times performed at the working time t; i (V out(t)∈MVout) is an oscillometric function, I (·) =1 when V out(t)∈MVout, when Time I (·) =0;
S2, generating wiener degradation data; generating future degradation data with probability uncertainty by monitoring the working stress of the circuit board and the change condition of degradation parameters and utilizing a wiener process to describe the trend of the future degradation parameters; wherein the wiener degradation data generation process expression is:
dXt＝μXtdt+σXtdBt (4)
wherein, X t is a random variable, uX t is the mean value of the random variable X t, sigma X t is variance, bt is standard Brownian motion;
S3, carrying the degradation rate or reliability obtained by the fault physical model and the degraded performance parameters into a data driving model for fusion prediction to obtain a parameter prediction value;
S4, converting the parameter predicted value obtained by fusion prediction into the residual life of the circuit board, determining the expected value and the degradation threshold value of the degraded performance parameter, obtaining the real-time performance parameter degradation amount by the predicted performance parameter, and obtaining the residual life value of the circuit board through calculation of a residual life expression.
2. The method for predicting the remaining life of a circuit board based on fusion of failed physics and data driving according to claim 1, wherein in step S4, when the parameter predicted value obtained by fusion prediction is converted into the remaining life of the circuit board, the remaining life of the data driving at time t is represented by the following formula (5):
Wherein, delta theta (t) is the damage caused by the product working for time t, and can be obtained by theta (t) -theta (0), and theta (t) represents the performance parameter degraded with time; delta theta th is the margin of the performance parameter theta, and the initial value and the threshold value of the performance parameter are subtracted to obtain; ruldata (t) represents the remaining life of the data drive at time t.
3. The method for predicting the remaining life of a circuit board based on the fusion of fault physics and data driving according to claim 1, wherein in step S2, unknown parameters u and σ in the wiener degradation data generating process expression are obtained by fitting a distribution obtained by taking the difference of the logarithm of Xt:
ΔlnX＝lnXt-lnXs＝(μ-1/2σ2)t+σBt～N((μ-1/2σ2)d,σ2d) (6)
Where d=t-s (t > s) is the normal distribution with the mean value (μ - σ 2) d and the variance σ 2 d for the time interval N ((μ - σ 2)d,σ2 d) for time t and time s.
4. The method for predicting the remaining life of a circuit board based on failed physics and data driven fusion according to claim 1, wherein the fusion prediction in step S3 comprises a first fusion prediction algorithm selected when predicting the life of the circuit board at the next time and a second fusion prediction algorithm selected when predicting the remaining life of the circuit board in a future time range.
5. The method for predicting the residual life of the circuit board based on the fault physics and the data driving fusion according to claim 4, wherein the first fusion prediction algorithm is a training neural network algorithm aiming at a data driving model by using real degradation data and monitoring stress as inputs, the training input of the first fusion prediction algorithm for obtaining the predicted value of the real data is the front x% of all the real data, wherein x is more than 70 and less than 90, the predicted input is the rear x% to 100% of all the data, and if the degradation trend is obvious, x takes a small value; if the degradation is not obvious, x takes a large value; and learning the neural network through the degradation parameters of the front x percent and the physical parameters of the faults, obtaining the neural network after learning, and predicting the degradation parameters and the physical parameters of the faults except the front x percent to obtain the predicted value of the degradation parameters.
6. The method for predicting the residual life of the circuit board based on the combination of fault physics and data driving according to claim 4, wherein the second combination prediction algorithm is a model for data driving, and uses all the monitored degradation parameters and the monitored stress as inputs to the neural network algorithm for training, and uses the generated future degradation parameters for prediction, so as to obtain a future performance parameter degradation value considering uncertainty; and the second fusion prediction algorithm inputs all real data, takes 100% of degradation parameters and fault physical parameters as training input of the neural network, acquires the trained neural network through the neural network learning, generates a certain number of data in the future through a wiener process, selects 10% -30% of all real data, takes the future data generated in the wiener process as prediction input, and acquires the predicted value of the future degradation parameters.
7. The method for predicting remaining life of a circuit board based on failed physical and data driving fusion according to claim 1 or 4, wherein in step S11, the activation energy Ea and the parameter C 0Sn in expression (1) can be obtained by:
The linear equation is: y=β 0+β1 x (8), let β0＝ln(C0Sn),β1＝-Ea；
Calculating the change rate of the monitoring parameter at different moments when the temperature stress is T by using the monitoring dataSubstituting the parameters into a linear equation and solving to obtain the activation energy Ea and the parameter C 0Sn of the fault physical model.
8. The method for predicting the residual life of the circuit board based on fault physics and data driving fusion is characterized by comprising the following steps of:
S1, calculating the fault physical life of a circuit board; obtaining a fault physical life value of the circuit board by using a fault physical life model of the circuit board;
s11, determining a life prediction model based on a fault physical model, wherein the life prediction model is specifically expressed as:
Wherein N f (x%) is the number of cycles corresponding to x% failure; epsilon is the plasticity of the welding spot, and 0.325 is taken; f is a stress experimental factor; h and LD are the solder joint height and effective length; Δa is the coefficient of thermal expansion coefficient difference between the component and the substrate; Δte is the effective thermal cycle temperature range; c is a constant related to the average temperature of the weld and the stress relaxation/creep time per cycle; beta is 4 when the lead-free installation is carried out;
S12, parameters F, h, LD, delta a, delta Te and c are obtained from the self parameters and working stress of the product;
S13, substituting the parameters into a life prediction model to obtain the thermal fatigue life N f of the welding spots of the circuit board;
s14, converting the thermal fatigue life into the residual life RUL_pof (t) of the product at time t, wherein the calculation method comprises the following steps:
RUL_pof(t)＝Nf-t (2)
S2, predicting the residual life of the circuit board by using a data driving model; determining degraded performance parameters, predicting degradation values of the performance parameters by using a data driving model, converting the performance parameter values into residual life values, and calculating by using the following Miner linear damage method:
s3, fusion of kernel functions; the residual life of the circuit board, which is obtained by respective prediction of the fault physical model and the data driving model, is fused by utilizing a kernel function, and the fused residual life is obtained;
S31, selecting a Logistic function as a kernel function for prediction, wherein the function form is as follows:
Kdata(t0,ti)＝1-Kpof(t0,ti)
where K pof (t 0, ti) represents the kernel function coefficients of the fault physics, kdata (t 0, ti) represents the data driven kernel function; a is
The initial weight parameter of the kernel function, a is more than or equal to 0, namely the weight size allocated to the fault physical model at the initial 0 moment, kpof (t 0, ti) =1/(a+1), the initial weights of the fault physical and the data driving are allocated by adjusting the size of a, and the weights of 0.5 are allocated to the fault physical and the data driving when a=1; b is a constant parameter, b is more than 0, and the changing shape of the kernel function is controlled; wherein t0 and ti are as follows:
t0＝RUL_pob0 (5)
ti＝RUL_pofi，i＝1，2，…n
Wherein RUL_ pofi is a residual life value obtained at the moment i based on the fault physical model;
S32, obtaining a fusion residual life predicted value RUL (theta) of the circuit board by using a kernel function fusion result:
RUL(θ)＝Kpof(t0,ti)·RUL_pofi+Kdata(t0,ti)·RUL_datai(6).
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