CN111368457B - Semiconductor laser degradation prediction method based on wavelet density estimation model improvement - Google Patents

Semiconductor laser degradation prediction method based on wavelet density estimation model improvement Download PDF

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CN111368457B
CN111368457B CN202010197901.XA CN202010197901A CN111368457B CN 111368457 B CN111368457 B CN 111368457B CN 202010197901 A CN202010197901 A CN 202010197901A CN 111368457 B CN111368457 B CN 111368457B
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林焱辉
丁泽琦
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Beihang University
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Abstract

The invention provides a semiconductor laser degradation prediction method based on wavelet density estimation model improvement, which is characterized in that wavelet density estimation is carried out on probability distribution of degradation increment based on performance parameter degradation data of a semiconductor laser, which is obtained by monitoring at equal time intervals, and a plurality of random process models are established; based on wavelet transformation, linearly expressing the established degradation increment probability density function in various random processes by using wavelets; improving all wavelet linear representations based on the wavelet density estimate to obtain an improved model; and quantifying the similarity degree of all the improved models and the wavelet density estimation, and selecting the most similar model from the improved models for the degradation prediction of the semiconductor laser. The invention can improve the existing random process model for predicting the degradation of the semiconductor laser and select the optimal model from a plurality of improved models, thereby improving the accuracy of the degradation prediction.

Description

Semiconductor laser degradation prediction method based on wavelet density estimation model improvement
Technical Field
The invention relates to the technical field of device prediction, in particular to a semiconductor laser degradation prediction method based on wavelet density estimation model improvement.
Background
The semiconductor laser is widely applied to the aspects of laser communication, radar ranging and the like, and is an important engineering device. The service life of the semiconductor laser is accurately estimated, a maintenance plan of a product can be scientifically formulated, the accident risk caused by product failure is reduced, and economic waste caused by premature replacement is reduced. The semiconductor laser has the characteristics of high reliability and long service life, and the time cost and the economic cost are very high when the semiconductor laser is used for obtaining the service life data of the semiconductor laser through a failure test.
The degradation model of a type of semiconductor laser widely used at present is a random process model, such as a wiener process, a gamma process, an inverse gaussian process and the like. After the random process type is selected, on the basis of independent increment hypothesis, unknown parameters in the random process are estimated by using the degradation data obtained by monitoring, and then a random process model is established. Random process models are widely used because they can model the general trend and randomness of the degradation process, particularly the unexplainable randomness of the degradation process caused by unknown environmental factors or unknown effects. However, the stochastic process model makes more rigorous assumptions about the type of distribution of the degradation increments, such as: the degradation increment of the wiener process is subject to normal distribution, the degradation increment of the gamma process is subject to gamma distribution, and the degradation increment of the inverse Gaussian process is subject to inverse Gaussian distribution. In fact, due to the complicated variability and unpredictability of the external field degradation environment, the degradation increment does not follow a certain distribution, and the assumption of the degradation increment distribution type of the stochastic process model reduces the fitting effect of the stochastic process model on the data, so that when the degradation data is analyzed and predicted, after the stochastic process model is established, the established stochastic process model is improved based on the data. On the other hand, since various random process models (such as a wiener process, a gamma process, an inverse gaussian process, and the like) are currently used for the degradation data analysis of the semiconductor laser, after the random process models are improved, an optimal model should be selected from the multiple models for the degradation prediction.
Disclosure of Invention
The present invention provides the following technical solutions to overcome the above-mentioned drawbacks in the prior art.
A semiconductor laser degradation prediction method based on wavelet density estimation model improvement comprises the following steps:
an obtaining step, namely obtaining performance parameter degradation data of the semiconductor laser device obtained by monitoring of the monitoring equipment at equal time intervals, numbering all the monitored semiconductor laser devices, and counting I semi-like partsConductor laser devices, respectively denoted as I1, 2, …, I, where the performance parameters of the device degrade with time, and S data points, respectively numbered as S1, 2, …, S, are obtained in total from the time of putting into service to the last monitoring, and are numbered as tsThe time of s-th monitoring is represented by Δ t-t, because the degradation data of the device is obtained by monitoring at equal time intervals by the monitoring equipment2-t1＝…＝ts+1-ts＝…＝tS-tS；1By using
Figure BDA0002418283060000021
Denotes the ith device at tsThe performance parameter degradation amount of the moment is obtained to obtain a performance parameter degradation data set of the semiconductor laser
Figure BDA0002418283060000022
Figure BDA0002418283060000023
Through type
Figure BDA0002418283060000024
Calculating to obtain a degradation increment data set
Figure BDA0002418283060000025
Figure BDA0002418283060000026
A probability density estimation step based on the degradation increment data set of the semiconductor laser
Figure BDA0002418283060000027
Estimating a probability density function of the degradation increment by using a wavelet density estimation method;
establishing a random process model, namely modeling the degradation data of the semiconductor laser by using various random process models, and estimating unknown parameters in each random process model by using a maximum likelihood estimation method;
A transformation step, based on discrete wavelet transformation, transforming the degradation increment probability density function in the established various random process models into linear representation of wavelet function;
an improvement step, comparing the wavelet density estimation with the wavelet representation of the degradation increment probability density function of the random process, and improving the wavelet linear representation of the degradation increment probability density of various random process models by taking the wavelet density estimation as the standard to obtain improved models;
a selection step, namely quantifying the similarity of each improved model and the wavelet density estimation, and selecting the improved model most similar to the wavelet density estimation;
and a prediction step of predicting the degradation amount of the semiconductor laser by using the selected model to obtain a prediction result.
Furthermore, the semiconductor laser is a gallium arsenide laser, a cadmium sulfide laser, an indium phosphide laser and a zinc sulfide laser.
Still further, the probability density estimating step includes:
a tightly supported wavelet sym7 is chosen by matching the mother function phi (x) of the scale of the sym7 wavelet with the mother function of the wavelet
Figure BDA0002418283060000029
Performing expansion and translation to obtain a series of scale functions and wavelet functions:
φj,k(x)＝2j/2φ(2jx-k)
Figure BDA0002418283060000028
wherein j is the resolution level of the wavelet and represents the expansion degree of the wavelet function, k is the translation coefficient of the wavelet function, and in a wavelet system, any wavelet function is uniquely determined by j and k. Linearly combining a series of wavelet functions to represent a probability density function of a degradation increment delta y, setting a minimum resolution level j 0With the highest resolution level j1(satisfy j)0，j1Is an integer and j1>j0) By using
Figure BDA0002418283060000031
Representing the integer set, the wavelet of the probability density function of the degradation increment Δ y is represented as:
Figure BDA0002418283060000032
wherein
Figure BDA0002418283060000033
And dj,kFor wavelet coefficients, semiconductor laser based degradation-augmented data sets
Figure BDA0002418283060000034
Estimating wavelet coefficients by
Figure BDA0002418283060000035
The estimation value of the wavelet coefficient is represented by the following wavelet coefficient estimation expression:
Figure BDA0002418283060000036
Figure BDA0002418283060000037
substituting the wavelet coefficient estimated value obtained by calculation into wavelet representation of the probability density function to obtain probability density estimation of degradation increment delta y:
Figure BDA0002418283060000038
further, the step of establishing a stochastic process model comprises:
three random process models were selected:
(1) the wiener process:
Δy～N(u·Δt,σ2·Δt)
Figure BDA0002418283060000039
(2) the gamma process:
Δy～Gamma(α,Δt)
Figure BDA00024182830600000310
wherein Γ (·) is a gamma function;
(3) the inverse Gaussian process:
Δy～IG(η·Δt,λ·(Δt)2)
Figure BDA00024182830600000311
in any of the random processes described above, the size of the degradation increment Δ y is independent of the start time of the increment, and is dependent on the size of the corresponding time interval Δ t; for degradation data (Δ t is a constant value) obtained by monitoring at equal time intervals, all degradation increments obey the same probability distribution, and the probability density expression of the probability distribution can be simplified as follows:
(1) the wiener process:
Δy～N(μ′,σ′2)
Figure BDA0002418283060000041
wherein, mu' is mu.delta t,
Figure BDA0002418283060000042
(2) the gamma process:
Δy～Gamma(α′,β′)
Figure BDA0002418283060000043
wherein α ═ α, β ═ Δ t;
(3) The inverse Gaussian process:
Δy～IG(η′,λ′)
Figure BDA0002418283060000044
wherein η ═ η · Δ t, λ ═ λ · (Δ t)2；
Degradation-based incremental data set
Figure BDA0002418283060000045
Estimating unknown parameter values in three random processes by using a maximum likelihood method, wherein the unknown parameters in the three random processes are as follows: mu 'in wiener process, alpha' in gamma process, beta 'in gamma process, and eta' in inverse Gaussian process, using
Figure BDA0002418283060000046
Representing the maximum likelihood estimated value of the parameter, wherein the estimated expression of the parameter in each random process is as follows:
the parameter estimation expression of the wiener process is as follows:
Figure BDA0002418283060000047
the gamma process has the parameter estimation expression:
Figure BDA0002418283060000048
the parameter estimation expression of the inverse gaussian process is:
Figure BDA0002418283060000049
in the process of obtaining wiener through the above formula
Figure BDA00024182830600000410
And
Figure BDA00024182830600000411
value, in gamma process
Figure BDA00024182830600000412
And
Figure BDA00024182830600000413
value, in inverse Gaussian process
Figure BDA00024182830600000414
And
Figure BDA00024182830600000415
a value;
substituting the calculated parameter values into each random process model to obtain:
(1) wiener process model
Figure BDA00024182830600000416
(2) Gamma process model
Figure BDA0002418283060000051
(3) Inverse Gaussian process model
Figure BDA0002418283060000052
Still further, the transforming step comprises:
according to a set maximum resolution level j1And a minimum resolution level j0Probability density function f of degenerated increment in three random process models to be establishedWi(Δy),fG(Δ y) and fIG(Δ y) performing a discrete wavelet transform, transformed into a linear representation of a wavelet function:
A wiener process:
Figure BDA0002418283060000053
wherein the wavelet coefficients
Figure BDA0002418283060000054
The calculation formula of (c) is:
Figure BDA0002418283060000055
Figure BDA0002418283060000056
and (3) gamma process:
Figure BDA0002418283060000057
wherein the wavelet coefficients
Figure BDA0002418283060000058
The calculation formula of (A) is as follows:
Figure BDA0002418283060000059
Figure BDA00024182830600000510
the inverse Gaussian process:
Figure BDA00024182830600000511
wherein the wavelet coefficients
Figure BDA00024182830600000512
The calculation formula of (A) is as follows:
Figure BDA00024182830600000513
Figure BDA00024182830600000514
still further, the improving step comprises:
comparing the wavelet representations of the obtained degradation increment probability density functions of the three random processes with wavelet density estimation respectively; due to the functional orthonormal of wavelet functions, it is the wavelet coefficients that are essentially compared; calculating the absolute difference value between the wavelet coefficient in the wavelet representation and the wavelet coefficient in the wavelet density estimation, selecting the wavelet coefficient in the wavelet representation with the maximum absolute difference value, and replacing the wavelet coefficient with the corresponding wavelet coefficient in the wavelet density estimation, thereby realizing model improvement; the wavelet representation of the degenerate delta probability density function of the three random processes is improved once according to the steps, and the formula is as follows:
if it is not
Figure BDA0002418283060000061
Then
Figure BDA0002418283060000062
If it is not
Figure BDA0002418283060000063
Then
Figure BDA0002418283060000064
Wherein (·) refers to the corner marks Wi, G and IG of the three models; through the steps, the improved model f is obtained(Wi)′(Δy)，f(G)′(Δ y) and f(IG)′(Δy)。
Still further, the selecting step includes:
the degree of similarity of the improved model and the wavelet density estimate is quantified using the 2-norm of the wavelet coefficients, and the calculation formula is:
Figure BDA0002418283060000065
Wherein (·) refers to the corner marks Wi, G, IG of the three models;
Figure BDA0002418283060000066
and
Figure BDA0002418283060000067
is the wavelet coefficient in the wavelet density estimation;
Figure BDA0002418283060000068
and
Figure BDA0002418283060000069
wavelet coefficients in the improved model; the smaller the 2-norm is, the higher the similarity degree of the corresponding wavelet representation and the wavelet density estimation is, and the probability density function f (delta y) of the semiconductor laser degradation quantity is selected to be linearly represented by the improved wavelet which is most similar to the wavelet density estimation;
furthermore, based on the improved and selected model, the degradation of the semiconductor laser device is predicted, and the degradation prediction quantity of the ith semiconductor laser device at the next monitoring time is as follows:
Figure BDA0002418283060000071
wherein
Figure BDA0002418283060000072
For degenerate data sets
Figure BDA0002418283060000073
The amount of degradation obtained from the last monitoring of the ith device in (i), Δ y, is a random variable, and the probability density function describing its randomness is f (Δ y).
Further, I is 15, S is 17, j0＝0，j1＝5。
The invention has the technical effects that:
the invention provides a semiconductor laser degradation prediction method based on wavelet density estimation model improvement, which is characterized in that wavelet density estimation is carried out on probability distribution of degradation increment based on performance parameter degradation data of a semiconductor laser, which is obtained by monitoring at equal time intervals, and a plurality of random process models are established; based on wavelet transform, linearly expressing the established degradation increment probability density function in various random processes by using wavelets; improving all wavelet linear representations based on the wavelet density estimate to obtain an improved model; and for optimization, quantifying the similarity of all the improved models and the wavelet density estimation, and selecting the most similar model for the degradation prediction of the semiconductor laser. The invention provides a model improvement method based on wavelet density estimation, which can improve the existing random process model for predicting the degradation of a semiconductor laser and select the optimal model from a plurality of improved models, thereby improving the accuracy of degradation prediction.
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FIG. 1 is a flow chart of a semiconductor laser degradation prediction method based on wavelet density estimation model improvement.
Detailed Description
The present application will be described in further detail with reference to the drawings and examples. It is to be understood that the specific embodiments described herein are merely illustrative of the relevant invention and not restrictive of the invention. It should be noted that, for convenience of description, only the portions related to the related invention are shown in the drawings.
It should be noted that the embodiments and features of the embodiments in the present application may be combined with each other without conflict. The present application will be described in detail below with reference to the embodiments with reference to the attached drawings.
The core idea of the invention is to utilize the following relationship of the wavelet density estimation and the degenerate delta probability density function in the stochastic process: wavelet density estimation can approximate all square multiplicative functions, while the probability density function of the degradation increment in the random process model can only be the probability density function of a certain specific distribution (for example, the degradation increment of the wiener process can only be a normal distribution, the degradation increment of the gamma process can only be a gamma distribution, and the degradation increment of the inverse gaussian process can only be an inverse gaussian distribution). Therefore, wavelet density estimates tend to have a better fit to the data. On the other hand, the result of the wavelet density estimation is a linear representation of a group of wavelet functions, the probability density function of the degradation increment in the random process can also be converted into the linear representation of the wavelet functions through wavelet transformation, when the same wavelet function is selected for the two wavelet functions, the comparison between the probability density function of the degradation increment in the random process and the wavelet density estimation is simplified into the comparison of the wavelet coefficients of the two wavelet functions, and the model improvement of the random process is simplified into the wavelet coefficient replacement of the wavelet representation of the probability density function of the degradation increment in the random process. This effectively reduces computational complexity and increases engineering feasibility.
Fig. 1 shows a semiconductor laser degradation prediction method based on wavelet density estimation model improvement, which comprises the following steps:
step S101 of acquiring performance parameter degradation data of the semiconductor laser device obtained by the monitoring device, numbering all the monitored semiconductor laser devices, and counting I semiconductor laser devices, which are respectively marked as I1, 2, …, I, and the performance parameter of the device degrades with the use time, and counting S data points, which are respectively numbered as S1, 2, …, S, and t 1,2, …, S, obtained from the time of putting into use to the last monitoringsIndicating the time of the s-th monitoring, in engineering, the monitoring instrument is often set to monitor the degradation of the performance parameter at equal time intervals, which results in a constant time span of adjacent degradation data points, i.e. Δ t ═ t2-t1＝…＝ts+1-ts＝…＝tS-tS-1By using
Figure BDA0002418283060000081
Denotes the ith device at tsThe performance parameter degradation amount of the moment is obtained to obtain a performance parameter degradation data set of the semiconductor laser
Figure BDA0002418283060000082
Through type
Figure BDA0002418283060000083
Calculating to obtain a degradation increment data set
Figure BDA0002418283060000084
Figure BDA0002418283060000085
Denotes the ith device from tsTime ts+1An incremental degradation of the amount of degradation of the performance parameter at the time. Preferably, I-15 and S-17.
A probability density estimation step S102, based on the performance parameter degradation data of the semiconductor, obtains a wavelet density estimation regarding the degradation increment distribution according to the prior art.
The wavelet density estimation is a non-parameter probability density estimation method, after a statistical sample of random variables is obtained, the wavelet density estimation is used for approximating the probability density function of the random variables by using a group of linear representation of wavelet functions, and wavelet coefficients in the wavelet linear representation are estimated from the statistical sample in an unbiased mode. Let X denote the continuous random variable, p (X) the probability density function of the random variable X, X1,x2,…,xn,…,xNRepresenting the statistical samples of the observed random variables, where N is the number of statistical samples of the observed random variables, the wavelet of the probability density function of the random variable X is represented as:
Figure BDA0002418283060000086
statistical sample x with random variables1,x2,…,xn,…,xNCalculating wavelet coefficients
Figure BDA0002418283060000087
And dj,kThe unbiased estimate of (c) is as follows:
Figure BDA0002418283060000088
Figure BDA0002418283060000089
substituting the estimated value into a wavelet table formula to obtain the wavelet density estimation as follows:
Figure BDA0002418283060000091
wherein the content of the first and second substances,
Figure BDA0002418283060000092
and dj,kThe wavelet coefficients are represented by a number of wavelet coefficients,
Figure BDA0002418283060000093
the function of the scale is represented by,
Figure BDA0002418283060000094
the function of a wavelet is represented by,
Figure BDA0002418283060000095
the wavelet density estimate is represented as a function of,
Figure BDA0002418283060000096
a wavelet density estimate representing a probability density function p (x),
Figure BDA0002418283060000097
representing unbiased estimates of wavelet coefficients, j0Represents the lowest resolution level, j1Represents the highest resolution level and satisfies j0，j1Is an integerAnd j is1>j0And k is a positive integer.
Step S103 of establishing a random process model, modeling the degradation data of the semiconductor laser by using various existing random process models, and estimating unknown parameters in each random process model by using a maximum likelihood estimation method;
A transformation step S104, based on discrete wavelet transformation, transforming the degradation increment probability density function in the established multiple random process models into linear representation of wavelet function;
an improvement step S105, comparing the wavelet density estimation with the wavelet representation of the degradation increment probability density function of the random process, and improving the wavelet linear representation of the degradation increment probability density of various random process models by taking the wavelet density estimation as the standard to obtain improved models;
a selecting step S106, which quantifies the similarity degree of each improved model and the wavelet density estimation and selects the improved model which is most similar to the wavelet density estimation;
in the prediction step S107, the amount of degradation of the semiconductor laser is predicted using the selected model, and a prediction result is obtained.
The method of the invention can predict the performance parameter degradation of the following semiconductor lasers: gallium arsenide laser, cadmium sulfide laser, indium phosphide laser, zinc sulfide laser. The semiconductor laser degradation prediction method based on the wavelet density estimation model improvement is specifically realized as follows:
firstly, according to the obtaining step S101, obtaining the performance parameter degradation data of the semiconductor laser obtained by the monitoring device.
The probability density estimating step S102 includes:
the tightly-supported wavelet sym7 is selected by combining the mother function phi (x) of the scale of sym7 wavelet with the mother function of the wavelet
Figure BDA0002418283060000099
Performing stretching and translation to obtain a series of scale functions and wavelet functions:
φj，k(x)＝2j/2φ(2jx-k)
Figure BDA0002418283060000098
linearly combining a series of wavelet functions to represent a probability density function of a degradation increment Δ y, setting a minimum resolution level j0With the highest resolution level j1(satisfy j)0，j1Is an integer and j1>j0) By using
Figure BDA00024182830600000910
Representing the integer set, the wavelet of the probability density function of the degradation increment Δ y is represented as:
Figure BDA0002418283060000101
where p (Δ y) is a wavelet representation of a probability density function of the degradation increment Δ y,
Figure BDA0002418283060000102
and dj，kFor wavelet coefficients, semiconductor laser based degradation-augmented data sets
Figure BDA00024182830600001013
Estimating wavelet coefficients by
Figure BDA0002418283060000103
The estimation value of the wavelet coefficient is represented by the following wavelet coefficient estimation expression:
Figure BDA0002418283060000104
Figure BDA0002418283060000105
wherein the wavelet function
Figure BDA0002418283060000106
And scale function
Figure BDA0002418283060000107
In that
Figure BDA0002418283060000108
The value of the position can be calculated by a Cascade function in matlab. Substituting the wavelet coefficient estimated value obtained by calculation into wavelet representation of the probability density function to obtain the wavelet density estimation of the degradation increment delta y:
Figure BDA0002418283060000109
preferably, j0＝0，j1＝5。
In one embodiment of the present invention, the operation of the step S103 of establishing a stochastic process model is:
selecting the existing three random process models:
(1) The wiener process:
Δy～N(μ·Δt，σ2·Δt)
Figure BDA00024182830600001010
(2) the gamma process:
Δy～Gamma(α，Δt)
Figure BDA00024182830600001011
(3) the inverse Gaussian process:
Δy～IG(η·Δt，λ·(Δt)2)
Figure BDA00024182830600001012
wherein f isWiRepresenting the wiener process function, mu and sigma being coefficients of the wiener process function, fGRepresenting a gamma process function, gamma (·) being the gamma function, alpha being a coefficient of the gamma process function, fIGRepresenting an inverse gaussian process function, η and λ are coefficients of the inverse gaussian process function, and Δ t represents degradation data (constant values) obtained by monitoring at equal time intervals.
In any of the random processes described above, the size of the degradation increment Δ y is independent of the start time of the increment, and is dependent on the size of the corresponding time interval Δ t; for degradation data (Δ t is a constant value) obtained by monitoring at equal time intervals, all degradation increments obey the same probability distribution, and the probability density expression of the probability distribution can be simplified as follows:
(1) the wiener process:
Δy～N(μ′，σ′2)
Figure BDA0002418283060000111
wherein, mu' is mu.delta t,
Figure BDA0002418283060000112
(2) the gamma process:
Δy～Gamma(α′,β′)
Figure BDA0002418283060000113
where α 'α, β' Δ t.
(3) The inverse Gaussian process:
Δy～IG(η′,λ′)
Figure BDA0002418283060000114
wherein η ═ η · Δ t, λ ═ λ · (Δ t)2。
Degradation-based incremental data set
Figure BDA0002418283060000115
Estimating unknown parameter values in three random processes by using a maximum likelihood method, wherein the unknown parameters in the three random processes are as follows: mu 'in wiener process, alpha' in gamma process, beta 'in gamma process, and eta' in inverse Gaussian process, using
Figure BDA0002418283060000116
Representing the maximum likelihood estimated value of the parameter, wherein the estimated expression of the parameter in each random process is as follows:
the parameter estimation expression of the wiener process is as follows:
Figure BDA0002418283060000117
the gamma process parameter estimation expression is:
Figure BDA0002418283060000118
the parameter estimation expression of the inverse gaussian process is:
Figure BDA0002418283060000119
in the process of obtaining wiener through the above formula
Figure BDA0002418283060000121
And
Figure BDA0002418283060000122
value, in gamma process
Figure BDA0002418283060000123
And
Figure BDA0002418283060000124
value, in inverse Gaussian process
Figure BDA0002418283060000125
And
Figure BDA0002418283060000126
a value;
substituting the calculated parameter values into each random process model to obtain:
(1) wiener process model
Figure BDA0002418283060000127
(2) Gamma process model
Figure BDA0002418283060000128
(3) Inverse Gaussian process model
Figure BDA0002418283060000129
In this embodiment, the wiener process is obtained by the above formula
Figure BDA00024182830600001210
In the gamma process
Figure BDA00024182830600001211
In the inverse Gaussian process
Figure BDA00024182830600001212
Substituting the calculated parameter values into each random process model to obtain:
(1) wiener process model
Figure BDA00024182830600001213
(2) Gamma process model
Figure BDA00024182830600001214
(3) Inverse Gaussian process model
Figure BDA00024182830600001215
The operation of the transformation step S104 of the present invention is:
according to a set maximum resolution level j1And a minimum resolution level j0Probability density function f of degenerated increment in three random process models to be establishedWi(Δy),fG(Δ y) and fIG(Δ y) performing a discrete wavelet transform, transformed into a linear representation of a wavelet function:
(1) the wiener process:
Figure BDA00024182830600001216
wherein the wavelet coefficients
Figure BDA00024182830600001217
The calculation formula of (A) is as follows:
Figure BDA00024182830600001218
Figure BDA00024182830600001219
(2) the gamma process:
Figure BDA0002418283060000131
Wherein the wavelet coefficients
Figure BDA0002418283060000132
The calculation formula of (A) is as follows:
Figure BDA0002418283060000133
Figure BDA0002418283060000134
(3) the inverse Gaussian process:
Figure BDA0002418283060000135
wherein the wavelet coefficients
Figure BDA0002418283060000136
The calculation formula of (A) is as follows:
Figure BDA0002418283060000137
Figure BDA0002418283060000138
preferably, j0＝0，j1＝5。
The operation of the modified step S105 of the present invention is:
comparing the wavelet representations of the obtained degradation increment probability density functions of the three random processes with wavelet density estimation respectively; due to the functional orthonormal of wavelet functions, it is the wavelet coefficients that are essentially compared; calculating the absolute difference value between the wavelet coefficient in the wavelet representation and the wavelet coefficient in the wavelet density estimation, selecting the wavelet coefficient in the wavelet representation with the maximum absolute difference value, and replacing the wavelet coefficient with the corresponding wavelet coefficient in the wavelet density estimation, thereby realizing model improvement; the wavelet representation of the degenerate delta probability density function of the three random processes is improved once according to the steps, and the formula is as follows:
if it is used
Figure BDA0002418283060000139
Then
Figure BDA00024182830600001310
If it is not
Figure BDA0002418283060000141
Then
Figure BDA0002418283060000142
Wherein (·) refers to the corner marks Wi, G and IG of the three models; through the steps, the improved model f is obtained(Wi)′(Δy)，f(G)′(Δ y) and f(IG)′(Δy)。
It should be noted that the above steps replace a certain wavelet coefficient in the wavelet representation of the degraded incremental probability density functions of the three random process models (for brevity, the wavelet coefficient of the random process is referred to below) with a corresponding wavelet coefficient in the wavelet density estimation, thereby achieving model improvement. As described above, because wavelet density estimates can approximate all squared integrable functions, rather than some particular type of probability density function, wavelet density estimates tend to fit data better; because the wavelet density estimation can better fit data, the wavelet coefficient of the random process is replaced by the wavelet coefficient of the wavelet density estimation, the fitting effect of a model on the data can be improved, and the model improvement is realized. On the other hand, as a non-parametric density estimation method, when the data volume is small, the wavelet density estimation tends to be overfitting to the obtained data, so in the invention, the calculated wavelet density estimation is only used as a reference for model improvement, and is not directly used as a probability density function for predicting degradation increment.
It should also be noted that in the improvement step of the embodiment of the present invention, only one wavelet coefficient of a random process is replaced, because the amount of degraded data in the embodiment is small, and replacing more wavelet coefficients will cause the problem of overfitting. The number of wavelet coefficients that are replaced may also be further increased as the amount of data increases, and the present invention includes, but is not limited to, replacing one wavelet coefficient.
The operation of the selection step S106 of the present invention is:
the degree of similarity of the improved model and the wavelet density estimate is quantified using the 2-norm of the wavelet coefficients, and the calculation formula is:
Figure BDA0002418283060000143
wherein (·) refers to the corner marks Wi, G and IG of the three models;
Figure BDA0002418283060000144
and
Figure BDA0002418283060000145
is the wavelet coefficient in the wavelet density estimation;
Figure BDA0002418283060000146
and
Figure BDA0002418283060000147
are wavelet coefficients in the improved model. The smaller the 2-Norm, the greater the degree of similarity of the corresponding wavelet representation to the wavelet density estimate, and the improved wavelet linear representation, which is selected to be most similar to the wavelet density estimate, is selected to represent the probability density function f (Δ y) representing the amount of semiconductor laser degradation, which, in this example, is calculated to be Norm(IG)<Norm(G)<Norm(Wi)Therefore f isIG′(Δ y) is selected as a probability density function f (Δ y) of the semiconductor laser degradation amount, i.e., f (Δ y) ═ fIG′(Δy)。
The operation of the prediction step S107 of the present invention is:
Predicting the degradation of the semiconductor laser based on the improved and selected model, wherein the degradation prediction of the ith semiconductor laser at the next monitoring moment is as follows:
Figure BDA0002418283060000151
wherein
Figure BDA0002418283060000152
As a degraded data set
Figure BDA0002418283060000153
The amount of degradation obtained from the last monitoring of the ith device, Δ y, is a random variable, and the probability density function describing its randomness is f (Δ y), i.e., fIG′(Δy)。
In one embodiment of the invention, the percentage increase of the working current of the semiconductor laser along with time is used as the degradation amount of a performance parameter, the degradation processes of 15 gallium arsenide semiconductor lasers are monitored, 17 data points are monitored in each degradation process, a random process model is established and is improved and selected based on monitoring data, and the improved and selected model is used for predicting the degradation process to obtain a prediction result.
The innovation points and the rationality of the invention are as follows: (1) based on the wavelet density estimate improved model, the wavelet density estimate can approximate all square multiplicative functions, which makes it possible to better fit the data and improve the stochastic process model commonly used in engineering as a reference. (2) The functional standard orthogonality of the wavelet function is utilized, the comparison of two probability density estimation in the improvement step is simplified into the comparison of wavelet coefficients, and the application complexity is reduced. (3) Due to the diversity of the wavelet functions, the engineering application of the invention has great flexibility, and the most suitable wavelet function can be selected according to the degradation data of different types of semiconductor lasers.
The invention provides a semiconductor laser degradation prediction method based on wavelet density estimation model improvement, which is characterized in that wavelet density estimation is carried out on probability distribution of degradation increment based on performance parameter degradation data of a semiconductor laser, which is obtained by monitoring at equal time intervals, and a plurality of random process models are established; based on wavelet transformation, linearly expressing the established degradation increment probability density function in various random processes by using wavelets; improving all wavelet linear representations based on the wavelet density estimate to obtain an improved model; and for optimization, quantifying the similarity of all the improved models and the wavelet density estimation, and selecting the most similar model for the degradation prediction of the semiconductor laser. The invention provides a model improvement method based on wavelet density estimation, which can improve the existing random process model for predicting the degradation of a semiconductor laser and select the optimal model from a plurality of improved models, thereby improving the accuracy of degradation prediction.
Finally, it should be noted that: although the present invention has been described in detail with reference to the above embodiments, it should be understood by those skilled in the art that: modifications and equivalents may be made thereto without departing from the spirit and scope of the invention and it is intended to cover in the claims the invention as defined in the appended claims.

Claims (5)

1. A semiconductor laser degradation prediction method based on wavelet density estimation model improvement is characterized in that: the method comprises the following steps:
the method comprises the steps of obtaining performance parameter degradation data of the semiconductor laser device obtained by monitoring equipment at equal time intervals, numbering all monitored semiconductor laser devices, wherein the number of the semiconductor laser devices is I, the number of the semiconductor laser devices is respectively recorded as I-1, 2,sthe time of s-th monitoring is represented by Δ t-t, because the degradation data of the device is obtained by monitoring at equal time intervals by the monitoring equipment2-t1＝…＝ts+1-ts＝…＝tS-tS-1By using
Figure FDA0003498628960000011
Denotes the ith device at tsThe degradation amount of the performance parameter at the moment is obtainedPerformance parameter degradation data set to semiconductor laser
Figure FDA0003498628960000012
Figure FDA0003498628960000013
Through type
Figure FDA0003498628960000014
Calculating to obtain a degradation increment data set
Figure FDA0003498628960000015
Figure FDA0003498628960000016
A probability density estimation step based on the degradation increment data set of the semiconductor laser
Figure FDA0003498628960000017
Estimating a probability density function of the degradation increment by using a wavelet density estimation method;
establishing a random process model, namely modeling the degradation data of the semiconductor laser by using various random process models, and estimating unknown parameters in each random process model by using a maximum likelihood estimation method;
A transformation step based on discrete wavelet transformation according to a set highest resolution level j1And a minimum resolution level j0Transforming the degradation increment probability density function in the built random process models into linear representation of a wavelet function;
an improvement step, which takes wavelet density estimation as a standard, improves wavelet linear representation of the degradation increment probability density of various random process models to obtain improved models; due to the functional orthonormal of wavelet functions, it is the wavelet coefficients that are essentially compared; calculating the absolute difference value between the wavelet coefficient in the wavelet representation and the wavelet coefficient in the wavelet density estimation, selecting the wavelet coefficient in the wavelet representation with the maximum absolute difference value, and replacing the wavelet coefficient with the corresponding wavelet coefficient in the wavelet density estimation, thereby realizing model improvement;
a selection step of quantifying the similarity of each improved model and the wavelet density estimation, and selecting the improved model most similar to the wavelet density estimation; the method specifically comprises the following steps: quantifying the degree of similarity of the improved model and the wavelet density estimate using the 2-norm of the wavelet coefficients;
predicting, namely predicting the degradation amount of the semiconductor laser by using the selected model to obtain a prediction result;
The step of establishing the stochastic process model comprises the following steps:
three random process models were selected:
(1) a wiener process:
Δy～N(μ·Δt，σ2·Δt)
Figure FDA0003498628960000018
(2) and (3) gamma process:
Δy～Gamma(α，Δt)
Figure FDA0003498628960000021
wherein Γ (·) is a gamma function;
(3) the inverse Gaussian process:
Δy～IG(η·Δt，λ·(Δt)2)
Figure FDA0003498628960000022
wherein f isWiRepresenting the wiener process function, mu and sigma being coefficients of the wiener process function, fGRepresenting a gamma process function, gamma (·) being the gamma function, alpha being a coefficient of the gamma process function, fIGRepresenting an inverse Gaussian process function, eta and lambda being coefficients of the inverse Gaussian process function, Δ t tableIndicating degradation data obtained by monitoring at equal time intervals, wherein the degradation data is a constant value;
in any of the random processes described above, the size of the degradation increment Δ y is independent of the start time of the increment, and is dependent on the size of the corresponding time interval Δ t; for degradation data obtained by monitoring at equal time intervals, namely Δ t is a constant value, all degradation increments obey the same probability distribution, and the probability density expression of the probability distribution can be simplified as follows:
(1) the wiener process:
Δy～N(μ′，σ′2)
Figure FDA0003498628960000023
wherein, mu' is mu.delta t,
Figure FDA0003498628960000024
(2) the gamma process:
Δy～Gamma(α′，β′)
Figure FDA0003498628960000025
wherein α ═ α, β ═ Δ t;
(3) the inverse Gaussian process:
Δy～IG(η′，λ′)
Figure FDA0003498628960000026
wherein η ═ η · Δ t, λ ═ λ · (Δ t)2；
Degradation-based incremental data set
Figure FDA0003498628960000027
Estimating unknown parameter values in three random processes by using maximum likelihood method, wherein the unknown parameter values in the three random processes are unknown The parameters are as follows: mu 'in wiener process, alpha' in gamma process, beta 'in gamma process, and eta' in inverse Gaussian process, using
Figure FDA0003498628960000031
Representing the maximum likelihood estimated value of the parameter, wherein the estimated expression of the parameter in each random process is as follows:
the parameter estimation expression of the wiener process is as follows:
Figure FDA0003498628960000032
the gamma process has the parameter estimation expression:
Figure FDA0003498628960000033
the parameter estimation expression of the inverse gaussian process is:
Figure FDA0003498628960000034
in the process of obtaining wiener through the above formula
Figure FDA0003498628960000035
And
Figure FDA0003498628960000036
value, in gamma process
Figure FDA0003498628960000037
And
Figure FDA0003498628960000038
value, in inverse Gaussian process
Figure FDA0003498628960000039
And
Figure FDA00034986289600000310
a value;
substituting the calculated parameter values into each random process model to obtain:
(1) wiener process model
Figure FDA00034986289600000311
(2) Gamma process model
Figure FDA00034986289600000312
(3) Inverse Gaussian process model
Figure FDA00034986289600000313
The transforming step includes:
according to a set maximum resolution level j1And a minimum resolution level j0Probability density function f of degenerated increment in three random process models to be establishedWi(Δy)，fG(Δ y) and fIG(Δ y) performing a discrete wavelet transform, transformed into a linear representation of a wavelet function:
(1) the wiener process:
Figure FDA00034986289600000314
wherein the wavelet coefficients
Figure FDA00034986289600000315
The calculation formula of (A) is as follows:
Figure FDA00034986289600000316
Figure FDA00034986289600000317
(2) the gamma process:
Figure FDA0003498628960000041
wherein the wavelet coefficients
Figure FDA0003498628960000042
The calculation formula of (A) is as follows:
Figure FDA0003498628960000043
Figure FDA0003498628960000044
(3) the inverse Gaussian process:
Figure FDA0003498628960000045
wherein the wavelet coefficients
Figure FDA0003498628960000046
The calculation formula of (A) is as follows:
Figure FDA0003498628960000047
Figure FDA0003498628960000048
the improvement step comprises:
Comparing the wavelet representations of the obtained degradation increment probability density functions of the three random processes with wavelet density estimation respectively; due to the functional orthonormal of wavelet functions, it is the wavelet coefficients that are essentially compared; calculating the absolute difference value between the wavelet coefficient in the wavelet representation and the wavelet coefficient in the wavelet density estimation, selecting the wavelet coefficient in the wavelet representation with the maximum absolute difference value, and replacing the wavelet coefficient with the corresponding wavelet coefficient in the wavelet density estimation, thereby realizing model improvement; the wavelet representation of the degenerate delta probability density function of the three random processes is improved once according to the steps, and the formula is as follows:
if it is used
Figure FDA0003498628960000049
Then
Figure FDA00034986289600000410
If it is not
Figure FDA00034986289600000411
Figure FDA0003498628960000051
Then
Figure FDA0003498628960000052
Wherein (·) refers to the corner marks Wi, G and IG of the three models; through the steps, the improved model f is obtained(Wi)′(Δy)，f(G)′(Δ y) and f(IG)′(Δy)；
In the selecting step, the similarity between the improved model and the wavelet density estimation is quantified by using the 2-norm of the wavelet coefficient, and the specific calculation formula is as follows:
Figure FDA0003498628960000053
wherein (·) refers to the corner marks Wi, G and IG of the three models;
Figure FDA0003498628960000054
and
Figure FDA0003498628960000055
is the wavelet coefficient in the wavelet density estimation;
Figure FDA0003498628960000056
and
Figure FDA0003498628960000057
the wavelet coefficients in the improved model are obtained; the smaller the 2-norm, the higher the degree of similarity of the corresponding wavelet representation to the wavelet density estimate, and the improved wavelet linear representation most similar to the wavelet density estimate is selected as the probability density function f (Δ y) of the semiconductor laser degradation amount.
2. The improved semiconductor laser degradation prediction method based on wavelet density estimation model according to claim 1, characterized in that: the semiconductor laser is a gallium arsenide laser, a cadmium sulfide laser, an indium phosphide laser or a zinc sulfide laser.
3. The improved semiconductor laser degradation prediction method based on wavelet density estimation model according to claim 1, characterized in that: the probability density estimating step includes:
the tightly-supported wavelet sym7 is selected by combining the mother function phi (x) of the scale of sym7 wavelet with the mother function of the wavelet
Figure FDA0003498628960000058
Performing stretching and translation to obtain a series of scale functions and wavelet functions:
φj，k(x)＝2j/2φ(2jx-k)
Figure FDA0003498628960000059
wherein j is the resolution level of the wavelet and represents the expansion degree of the wavelet function, k is the translation coefficient of the wavelet function, and in a wavelet system, any wavelet function is uniquely determined by j and k; setting the lowest resolution level j using a probability density function that linearly combines the series of wavelet functions to represent the degradation increment Δ y0With the highest resolution level j1Satisfy j0，j1Is an integer and j1＞j0By using
Figure FDA00034986289600000510
Representing the integer set, the wavelet of the probability density function of the degradation increment Δ y is represented as:
Figure FDA0003498628960000061
wherein
Figure FDA0003498628960000062
And dj，kFor wavelet coefficients, semiconductor laser based degradation-augmented data sets
Figure FDA0003498628960000063
Estimating wavelet coefficients by
Figure FDA0003498628960000064
The estimation value of the wavelet coefficient is represented by the following wavelet coefficient estimation expression:
Figure FDA0003498628960000065
Figure FDA0003498628960000066
substituting the wavelet coefficient estimated value obtained by calculation into wavelet representation of the probability density function to obtain probability density estimation of degradation increment delta y:
Figure FDA0003498628960000067
4. the wavelet density estimation model based improved semiconductor laser degradation prediction method of claim 1, wherein: predicting the degradation of the semiconductor laser based on the improved and selected model, wherein the degradation prediction of the ith semiconductor laser at the next monitoring moment is as follows:
Figure FDA0003498628960000068
wherein
Figure FDA0003498628960000069
For degenerate data sets
Figure FDA00034986289600000610
The amount of degradation obtained from the last monitoring of the ith device in (i), Δ y, is a random variable, and the probability density function describing its randomness is f (Δ y).
5. The semiconductor laser degradation prediction method based on wavelet density estimation model improvement according to claim 1, 3 or 4, characterized by: i15, S17, j0＝0，j1＝5。
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