CN111046555A - Time-varying degradation quality characteristic compensation full life cycle quality robustness optimization method - Google Patents
Time-varying degradation quality characteristic compensation full life cycle quality robustness optimization method Download PDFInfo
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Abstract
A time-varying degradation quality characteristic compensation full-life cycle quality robustness optimization method belongs to the field of electromagnetic relay quality optimization design. Analyzing and determining key design parameters of the electromagnetic relay, carrying out linearity analysis, expanding the whole life cycle of the electromagnetic relay based on a K-L expansion method, dividing the whole life cycle of the electromagnetic relay into a plurality of sub-life intervals, modeling quality robustness characteristic parameters of the sub-life intervals by using a Kriging method, carrying out unified expression, establishing a quality robustness model of the whole life cycle of the electromagnetic relay, selecting an appropriate quality characteristic level for a quality robustness characteristic requirement level, calculating the quality robustness characteristic deviation degree of the electromagnetic relay under the action of time-varying degradation parameters, compensating the quality deviation to the requirement of the quality robustness of the whole life cycle, generating batch samples by using Monte Carlo, calculating output characteristics, and verifying and optimizing effects. A new method is provided for solving the design optimization of the quality robustness of the electromagnetic relay product in the whole life cycle.
Description
Technical Field
The invention relates to a quality robustness optimization method, in particular to a time-varying degradation quality characteristic compensation full-life cycle quality robustness optimization method, and belongs to the field of electromagnetic relay quality optimization design.
Background
The electromagnetic relay has the typical advantages of excellent universality, extremely high isolation strength, excellent interference resistance strength and the like, and is widely applied to modern equipment such as industrial operation and control systems, aerospace planes, space shuttles, manned and unmanned spacecrafts and the like to complete the functions of control signal transmission, function control execution, energy system power distribution and the like. With the development of modern equipment towards high sensitivity, high power consumption per unit volume and high reliability of the whole life cycle, especially the requirement of high robustness of the whole life cycle is obvious, and correspondingly, the requirement of robustness of the whole life cycle of the electromagnetic relay is improved to an unprecedented height. The development of the full-life-cycle robustness optimization of the electromagnetic relay is a necessary way for ensuring the application reliability of the electromagnetic relay and designing and optimizing the full-life-cycle robustness of the electromagnetic relay.
The robustness optimization design method with the aim of weakening the influence of parameter fluctuation on the product quality consistency can obviously improve the quality robustness in the industrial application process. The most common method for robust design optimization is to combine an experimental design method with a Taguchi method, which can only optimize in a limited range and has a large amount of calculation. In order to solve the problem of dimension and calculation of distribution of quality characteristic calculation and tolerance of the robust design, a substitution model is provided, the problem of quality output characteristic calculation in the robust design process is solved to a certain extent by introducing the substitution model, but the calculation accuracy of the substitution model and the accuracy of a training sample of the substitution model become the problems restricting the optimization development of the robust design. In addition, aiming at the problem that the Taguchi method is only suitable for single-target optimization, robust design optimization methods based on a sensitive domain, a multi-target interaction entropy, an intelligent algorithm and a hierarchical multi-target are provided, the methods better realize the requirements of multi-target robust design, but the methods mainly pay attention to the mutual influence among output characteristics and often ignore the influence of the correlation among input parameters on the optimal robust solution. It should be noted that under the comprehensive action of multiple parameters such as mechanical-electrical-magnetic-thermal-vibration-impact and the like in the actual working process, a large number of time-varying degradation parameters exist in the parameters of key parts of the product, and the time-varying performance degradation affects the whole life quality robustness of the product, so that the mean value and the variance of the quality robustness characteristic of the permanent magnet actuator are greatly changed. The robustness design method based on initial (time invariant) design is optimized aiming at initial quality design, and the analysis and design optimization of the time variant (dynamic) robustness of the whole life cycle of the permanent magnet actuator are rarely researched.
Aiming at the influence of the performance degradation of parts in the whole life cycle of the electromagnetic relay on the quality robustness, the invention provides a method for modeling the quality robustness characteristic of the whole life cycle of the electromagnetic relay based on K-L expansion and a Krigin model and optimizing the anti-degradation quality robustness of the whole life cycle of the electromagnetic relay based on time-varying degradation quality characteristic compensation, thereby realizing the optimization of the quality robustness of the whole life cycle of the electromagnetic relay.
Disclosure of Invention
The invention aims to solve the problem of missing of a full-life-cycle degradation-resistant optimization design method under the degradation action of an electromagnetic relay, provides a full-life-cycle quality robustness optimization method for time-varying degradation quality characteristic compensation, and particularly relates to how to perform quality robustness characteristic degradation-resistant optimization on the electromagnetic relay under the condition that the performance of parts of the electromagnetic relay is continuously degraded along with the working to obtain the electromagnetic relay with the full-life-cycle quality robustness so as to overcome the problems in the background technology.
In order to achieve the purpose, the invention adopts the following technical scheme: the method for optimizing the quality robustness of the full life cycle of the time-varying degradation quality characteristic compensation comprises the following steps:
the method comprises the following steps: analyzing and determining key design parameters of the electromagnetic relay, and recording the key design parameters as a set U-U (U)1,u2,…,un)；
Step two: carrying out linearity analysis on the key design parameters of the electromagnetic relay determined by analysis in the step one, and screening out key nonlinear designsThe parameter is expressed as the set V ═ V (V)1,v2,…,vm)；
Step three: the method comprises the steps that the whole life cycle of the electromagnetic relay is unfolded based on a K-L unfolding method, and the whole life cycle is divided into a plurality of sub-life intervals;
step four: modeling the quality robustness characteristic parameters of the sub-life intervals by using a Kriging method, carrying out unified expression on each sub-life interval, and establishing a quality robustness model of the whole life cycle of the electromagnetic relay;
step five: selecting a proper quality characteristic level according to the quality robustness characteristic requirement level of the whole life cycle of the electromagnetic relay;
step six: calculating the deviation degree of the electromagnetic relay quality robustness characteristic under the action of the time-varying degradation parameter based on the quality robustness level requirement obtained by the analysis in the fifth step
Wherein b is a quality robustness level;
step seven: compensation for quality robust feature bias using nonlinear parameter combinations, i.e., let
Thereby compensating the mass offset to the full life cycle mass robustness requirement;
step eight: and generating batch samples by using Monte Carlo according to the optimized parameter combination of the electromagnetic relay, calculating the output characteristics of the batch samples, performing statistical analysis on the multiple output characteristics, and verifying the optimization effect.
Compared with the prior art, the invention has the beneficial effects that: the method comprises the steps of determining key design parameters of the electromagnetic relay through analysis, carrying out linearity analysis, screening out key nonlinear design parameters, establishing a quality robustness characteristic parameter model of the whole life cycle by using a K-L expansion method and a Krigin method, selecting a proper quality characteristic level according to the quality robustness characteristic requirement level of the whole life cycle of the electromagnetic relay, calculating the quality robustness characteristic deviation degree of the electromagnetic relay under the action of time-varying degradation parameters, and compensating the quality robustness characteristic deviation degree by using a nonlinear parameter combination to realize the optimization requirement of the quality robustness of the whole life cycle.
Drawings
FIG. 1 is a flow chart of a time varying degradation quality feature compensated full life cycle quality robustness optimization method of the present invention;
fig. 2 is a schematic diagram of the compensation effect of the compensation performed in step seven in the embodiment of the present invention.
Detailed Description
The technical solutions in the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the invention, rather than all embodiments, and all other embodiments obtained by those skilled in the art without any creative work based on the embodiments of the present invention belong to the protection scope of the present invention.
As shown in FIGS. 1-2, the invention discloses a time-varying degradation quality characteristic compensation full life cycle quality robustness optimization method, which comprises
The method comprises the following steps: analyzing the electromagnetic relay according to the working principle, the composition and the manufacturing process parameters of the electromagnetic relay, determining key design parameters (such as armature length, armature thickness, yoke length, yoke thickness and the like) of the electromagnetic relay, and recording the key design parameters as a set of U-U (U-U)1,u2,…,un) Wherein: n is the number of key design parameters;
step two: and (3) carrying out linearity analysis on the key design parameters of the electromagnetic relay analyzed and determined in the step one by using a single parameter or contribution rate analysis method, screening out key nonlinear design parameters from the parameters, and recording the parameters as a set V (V-V)1,v2,…,vm) Wherein: m is the number of non-linear design parameters;
step three: the method comprises the following steps of unfolding the whole life cycle of the electromagnetic relay based on a K-L unfolding method, dividing the whole life cycle into a plurality of sub-life intervals, determining the sub-life intervals to lay a foundation for determining the unity expression of the whole life cycle of the electromagnetic relay, wherein the unfolding process is as follows:
wherein: xm(t) and Xr(t) is the life cycle interval process { X (t) epsilon XI(T), T ∈ T } and a radius function, ζj∈ζI＝[-1,1]J is 1,2, and K is a standard interval variable which should satisfy
λjE [0, ∞) and
is composed of
According to the Mercer theorem, the characteristic value and the characteristic function of the autocorrelation coefficient can obtain that the correlation coefficient is expressed by the following spectral decomposition:
wherein: t, t' are any two moments in the life cycle, the characteristic value lambdajAnd a characteristic function
The solution can be solved by Fredholm integration:
wherein: the characteristic function should satisfy
δijCan be obtained by a Kronecker-delta function;
step four: modeling the quality robustness characteristic parameters of the sub-life intervals by using a Krigin method, carrying out unified expression on each sub-life interval, and establishing an electromagnetic relay full-life cycle quality robustness model, wherein the calculation process is as follows:
the full-life-cycle quality robustness model includes both output characteristic statistics (mean and variance) and a multivariate spatio-temporal model of output characteristic time series relationship, assuming that the full-life-cycle output characteristic is a model including a magnitude of Ns×NtThe matrix of (a) is a regionalized variable in the same time series and space domainWherein
Is an Euclidean space dimension plus a time dimension, is a multivariate space-time random field, and:
U(s,t)＝[U1(s,t),U2(s,t),K,Up(s,t)]T,p≥3 (4)
wherein: s is as large as NsRepresenting spatial field coordinates, t ∈ NtRepresenting the coordinates of a time field, improving the interpolation precision of a main variable by adding a related covariate,
the interpolation formula of the space-time synergetic kriging is as follows:
wherein:
is (s, t)0Is output as a characteristic estimate, U11(s,t)1iFor output characteristics being principal variables, U12(s,t)2iIs a co-variable, M1And M2Is the number of interpolation points and M1＜M2，ν1iV and v2iThe weight coefficient corresponding to the main variable and the cooperative variable can be determined by a space-time variation functionAnd then the step of determining the number of the first time,
the space-time variation function can be obtained by introducing Lagrange factor
And (3) solving:
wherein η (g) is a space-time variation function which can be solved by the formula (4),
assuming spatio-temporal random fields
Space-time distance d of two positions (d ═ d)s,dt)，dsFor vectors that can represent sample spatial distance and direction information, dtThe temporal distance between samples is expressed, so the spatio-temporal variation function can be expressed as:
the average value and the variance of the key index output characteristics of the stability of the full life cycle can be obtained through a Kriging model according to the formulas (6) and (7), for the establishment and optimization of the subsequent stable design optimization model of the full life cycle, the converted output characteristics are recorded as f (·), and the average value and the variance are respectively recorded as muf(·)And σf(·)；
Step five: selecting a proper quality characteristic level according to the quality robustness characteristic requirement level of the whole life cycle of the electromagnetic relay, wherein the relationship between the quality robustness level and the reliability and the number of the invalid products is shown in the following table;
TABLE I relationship between robust design level and DPMO and reliability
Step six: calculating time-varying degradation based on quality robustness level requirements obtained from step five analysisCharacteristic deviation degree of electromagnetic relay quality robustness under parameter action
Wherein b is a quality robustness level;
step seven: compensation for quality robust feature bias using nonlinear parameter combinations, i.e., let
Thereby compensating the mass shift to the full life cycle mass robustness requirement, the compensation effect is shown in fig. 2;
step eight: and generating batch samples by using Monte Carlo according to the optimized parameter combination of the electromagnetic relay, calculating the output characteristics of the batch samples, performing statistical analysis on the multiple output characteristics, and verifying the optimization effect.
It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential attributes thereof. The present embodiments are therefore to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned.
Furthermore, it should be understood that although the present description refers to embodiments, not every embodiment may contain only a single embodiment, and such description is for clarity only, and those skilled in the art should integrate the description, and the embodiments may be combined as appropriate to form other embodiments understood by those skilled in the art.
Claims (3)
1. The method for optimizing the quality robustness of the time-varying degradation quality characteristic compensation in the whole life cycle is characterized by comprising the following steps: the method comprises the following steps:
the method comprises the following steps: analyzing and determining key design parameters of the electromagnetic relay, and recording the key design parameters as a set U-U (U)1,u2,…,un)；
Step two: carrying out linearity analysis on the key design parameters of the electromagnetic relay determined by the analysis in the step one, screening out key nonlinear design parameters from the key nonlinear design parameters, and recording the key nonlinear design parameters as a set V (V ═ V)1,v2,…,vm)；
Step three: the method comprises the steps that the whole life cycle of the electromagnetic relay is unfolded based on a K-L unfolding method, and the whole life cycle is divided into a plurality of sub-life intervals;
step four: modeling the quality robustness characteristic parameters of the sub-life intervals by using a Kriging method, carrying out unified expression on each sub-life interval, and establishing a quality robustness model of the whole life cycle of the electromagnetic relay;
step five: selecting a proper quality characteristic level according to the quality robustness characteristic requirement level of the whole life cycle of the electromagnetic relay;
step six: calculating the deviation degree of the electromagnetic relay quality robustness characteristic under the action of the time-varying degradation parameter based on the quality robustness level requirement obtained by the analysis in the fifth step
Wherein b is a quality robustness level;
step seven: compensation for quality robust feature bias using nonlinear parameter combinations, i.e., let
Thereby compensating the mass offset to the full life cycle mass robustness requirement;
step eight: and generating batch samples by using Monte Carlo according to the optimized parameter combination of the electromagnetic relay, calculating the output characteristics of the batch samples, performing statistical analysis on the multiple output characteristics, and verifying the optimization effect.
2. The time-varying degradation quality feature compensated full-life cycle quality robustness optimization method of claim 1, wherein: the unfolding process of the third step is as follows:
wherein: xm(t) and Xr(t) is the life cycle interval process { X (t) epsilon XI(T), T ∈ T } and a radius function, ζj∈ζI＝[-1,1]J is 1,2, and K is a standard interval variable which should satisfy
λjE [0, ∞) and
is composed of
According to the Mercer theorem, the characteristic value and the characteristic function of the autocorrelation coefficient can obtain that the correlation coefficient is expressed by the following spectral decomposition:
wherein: t, t' are any two moments in the life cycle, the characteristic value lambdajAnd a characteristic function
The solution can be solved by Fredholm integration:
wherein: the characteristic function should satisfy
δijFrom KroneThe cker-delta function.
3. The time-varying degradation quality feature compensated full-life cycle quality robustness optimization method of claim 1, wherein: the calculation process of the step four is as follows:
assume that the full life cycle output characteristic is one including a magnitude of Ns×NtThe matrix of (a) is a regionalized variable in the same time series and space domain
Wherein
Is an Euclidean space dimension plus a time dimension, is a multivariate space-time random field, and:
U(s,t)＝[U1(s,t),U2(s,t),K,Up(s,t)]T,p≥3 (4)
wherein: s is as large as NsRepresenting spatial field coordinates, t ∈ NtRepresenting the coordinates of a time field, improving the interpolation precision of a main variable by adding a related covariate,
the interpolation formula of the space-time synergetic kriging is as follows:
wherein:
is (s, t)0Is output as a characteristic estimate, U11(s,t)1iFor output characteristics being principal variables, U12(s,t)2iIs a co-variable, M1And M2Is the number of interpolation points and M1＜M2，ν1iV and v2iThe weight coefficient corresponding to the main variable and the cooperative variable can be determined by a space-time variation function,
the spatio-temporal variation function can be obtained by introducing lagsLangeri factor
And (3) solving:
wherein η (g) is a space-time variation function which can be solved by the formula (4),
assuming spatio-temporal random fields
Space-time distance d of two positions (d ═ d)s,dt)，dsFor vectors that can represent sample spatial distance and direction information, dtThe temporal distance between samples is expressed, so the spatio-temporal variation function can be expressed as:
the average value and the variance of the key index output characteristics of the stability of the full life cycle can be obtained through a Kriging model according to the formulas (6) and (7), for the establishment and optimization of the subsequent stable design optimization model of the full life cycle, the converted output characteristics are recorded as f (·), and the average value and the variance are respectively recorded as muf(·)And σf(·)。
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