CN101324909A - MEMS design optimizing method - Google Patents

Abstract

The invention discloses a novel MEMS design and optimization method and belongs to the technology field of MEMS CAD. The method comprises the following steps: constructing a system model of a new MEMS device based on a cell library under the condition that the MEMS device structure, the performance index and the optimized variable thereof to be tested are given; conducting a computer simulation experiment for the system model on the basis of the experimental design; conducting the analysis of regression for simulation experiment results to build the functional relationship between the performance index and the optimized variable; writing mathematical expression of an optimized target and constraint conditions; and optimizing by selecting optimization algorithm and obtaining the optimized result. Compared with the MEME design and optimization method based on the cell library and the genetic algorithm, the method maintains the advantage of realizing quick modeling for the MEMS device, and at the same time, has the advantages of reduced time of the entire optimization process and suitability for different optimization algorithms.

Description

A kind of MEMS design optimization method

Technical field

The present invention relates to a kind of MEMS design optimization method, belong to MEMS cad technique field.

Background technology

The fast development of MEMS technology needs the support of MEMS cad technique.The MEMS design optimization method is a major issue of MEMSCAD technical field, helps the researcher to find satisfactory solution rapidly under given restrictive condition, shortens time of product development.

The MEME design optimization method that people such as the Zhou of University of California Berkeley proposed in disclosed PhD dissertation " Simulation and synthesis ofMicro Electro Mechanical systems " based on cell library and genetic algorithm in 2002.This method resolves into many general elementary cells with the MEMS device, sets up the model of elementary cell, thereby forms cell library; According to the version of device, the elementary cell in the cell library is coupled together, make up the model of MEMS device; With the elementary cell model conversation is genetic algorithm encoding; Produce initial population based on genetic algorithm encoding, individual corresponding the one group of optimization variable value of MEMS device of each genetic algorithm encoding in the population; In the device model that every group of optimization variable value substitution elementary cell constituted, carry out emulation, with simulation result as fitness function; According to fitness function to genetic algorithm encoding select, intersect, operation such as variation, produce new genetic algorithm encoding population; Repeat emulation, select, intersect, processes such as variation, constantly circulation finishes when satisfying Rule of judgment, then obtains more excellent separating.

This method does not need the deviser to understand device physics mechanism in depth, only need the unit be coupled together according to the device form and just can set up device model, and is therefore very easy to be quick.Simultaneously, because model of element is parameterized, so model modification is very convenient.

But, because this method has a large amount of cyclic processes, and in each cyclic process, to carry out emulation and with simulation result as fitness function, need a large amount of simulation times, therefore have the long deficiency of global optimization process time.Simultaneously, for an optimization problem, different optimized Algorithm has considerable influence to optimizing the result, the MEMS deviser wishes to select flexibly proper optimization algorithm to realize the design optimization of MEMS, but this method can only realize optimizing by genetic algorithm, and the deficiency that can not select multiple optimized Algorithm flexibly for use is arranged.

Summary of the invention

Grow and the deficiency that can not be applicable to multiple optimized Algorithm in order to overcome existing MEME design optimization method global optimization process time based on cell library and genetic algorithm, the present invention proposes a kind of new MEMS design optimization method.

Technical scheme of the present invention is:

A kind of MEMS design optimization method may further comprise the steps:

1. given MEMS device architecture determines that it waits to investigate performance index y _m(m=1,2 ... M) with optimization variable x _i(i=1,2 ... n);

2. based on cell library, use the system model of elementary cell model construction MEMS device.Described cell library can be based on the cell library that Structured Design thought is set up, as (the patent " the core modeling method and the core kernel of mini inertial sensor spare " of the core kernel in " the core modeling method and the core kernel of mini inertial sensor spare ", number of patent application 200410025985.X, patent publication No. CN1673751), NODAS cell library (J.Qi.Modeling andSimulation for Design of Suspended MEMS.PhD Dissertation.Carnegie MellonUniversity.2003.), SUGAR cell library (Zhou, Ningning.Simulation and synthesis ofMicroElectroMechanical systems.PhD Dissertation.University of California, Berkeley.2002.), ARCHITECT cell library (G.Lorenz, A.Morris, I.Lakkis.A Top-Down Design Flowfor MOEMS.Proc.Design, Test, Integration, and Packaging of MEMS/MOEMS, DTIP2001.);

3. carry out test design, based on test design method, with optimization variable x _i(i=1,2 ... n) as experimental factor, obtain the testing program of N test $\left[\begin{array}{c}{x}_{}\end{array}\right]$ $\left[\begin{array}{ccc}{}_{11}& \&CenterDot;\&CenterDot;\&CenterDot;& x_{1n}\\ \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;\\ x_{\mathrm{<figure-callout\; id="1"\; label="N"\; filenames="A20081015037600152.png,A20081015037600182.png"\; state="\{\{state\}\}">N</figure-callout>}1}& \&CenterDot;\&CenterDot;\&CenterDot;& x_{\mathrm{Nn}}\end{array}\right],$ X wherein _Ui(u=1,2 ... N, i=1,2 ... n) the u time test value of i optimization variable of expression.Described test design method can be the multivariate test design method, as the uniform Design method;

4. based on the testing program of step 3, will wait to investigate performance index y _m(m=1,2 ... M) as test findings, the MEMS device system model that step 2 is made up carries out computer simulation experiment N time, obtains test findings $\left[\begin{array}{ccc}{y}_{11}& \&CenterDot;\&CenterDot;\&CenterDot;& y_{1M}\\ \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;\\ {\mathrm{<figure-callout\; id="1"\; label="y\; N"\; filenames="A20081015037600152.png,A20081015037600182.png"\; state="\{\{state\}\}">y</figure-callout>}}_N& \&CenterDot;\&CenterDot;\&CenterDot;& y_{\mathrm{NM}}\end{array}\right],$ Y wherein _Um(u=1,2 ... N, m=1,2 ... M) m of expression waits to investigate the u time test findings of performance index;

5. set up by regretional analysis and wait to investigate performance index y _m(m=1,2 ... M) with optimization variable x _i(i=1,2 ... the funtcional relationship n).Described funtcional relationship is a quadratic regression equation:

${\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="A20081015037600152.png,A20081015037600182.png"\; state="\{\{state\}\}">y</figure-callout>}}_1={\mathrm{\&beta;}}_{01}+\underset{i=1}{\overset{k}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_{i1}{x}_i+\underset{i=1}{\overset{k}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_{\mathrm{ii}1}{x}_i^2+\underset{i\&NotEqual;j}{\overset{k}{\mathrm{\&Sigma;}}}\mathrm{\&Sigma;}{\mathrm{\&beta;}}_{\mathrm{ij}1}{x}_i{x}_j$

……

$y_M={\mathrm{\&beta;}}_{0M}+\underset{i=1}{\overset{k}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_{\mathrm{iM}}{x}_i+\underset{i=1}{\overset{k}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_{\mathrm{iiM}}{x}_i^2+\underset{i\&NotEqual;j}{\overset{k}{\mathrm{\&Sigma;}}}\mathrm{\&Sigma;}{\mathrm{\&beta;}}_{\mathrm{ijM}}{x}_i{x}_j$

Wherein, β _0m(m=1,2 ... M) expression m waits to investigate the constant term in the regression equation of variable, β _Im(i=1,2 ... n, m=1,2 ... M) expression m waits to investigate the once item coefficient of i optimization variable in the regression equation of variable, β _Iim(i=1,2 ... n, m=1,2 ... M) expression m waits to investigate the quadratic term coefficient of i optimization variable in the regression equation of variable, β _{Ijm, i ≠ j}(i=1,2 ... n, j=1,2 ... n, m=1,2 ... M) expression m waits to investigate in the regression equation of variable the cross term coefficient of i optimization variable with j optimization variable, and summation ∑ subscript k represents to have the k item factor to sue for peace;

6. based on waiting to investigate performance y _m(m=1,2 ... M) with optimization variable x _i(i=1,2 ... the funtcional relationship n), write out the mathematic(al) representation of optimization aim and constraint condition.The common version that the mathematic(al) representation of described optimization aim and constraint condition can be expressed as:

Optimization aim:

min?f(x _i，y _m)

Constraint condition:

g _i(x _i，y _m)≤0(i＝1，2，...I)

h _j(x _i，y _m)＝0(j＝1，2，...J)

Wherein, f (x _i, y _m) represent and wait to investigate performance y _m(m=1,2 ... M) with optimization variable x _i(i=1,2 ... n) relevant functional form, min f (x _i, y _m) represent to ask function minimum, general optimization problem can be converted to the problem of asking function minimum.g _i(x _i, y _m)≤0 (i=1,2 ... I) one group of inequality constrain condition of expression, h _j(x _i, y _m)=0 (j=1,2 ... J) one group of equality constraint of expression;

7. based on the mathematic(al) representation of optimization aim and constraint condition, select optimized Algorithm to be optimized, the result is optimized.Described optimized Algorithm can be global optimization approach such as genetic algorithm, or Local Optimization Algorithm such as seqential quadratic programming algorithm.

The invention has the beneficial effects as follows: the MEMS design optimization method that the present invention proposes, reduce than existing MEME design optimization method global optimization process time based on cell library and genetic algorithm, and applicable to different optimized Algorithm, make the deviser to select the effective optimization algorithm flexibly for use, and when new more effective optimized Algorithm occurs, still can be suitable for according to the needs of practical problems.

The present invention is further described below in conjunction with drawings and Examples.

Description of drawings:

Fig. 1 is the process flow diagram of the MEMS design optimization method that proposes of the present invention.

Fig. 2 is the little gyro structural representation of embodiment of the invention 1MEMS.

Fig. 3 is the little gyro optimization variable of an embodiment of the invention 1MEMS synoptic diagram.

Fig. 4 is the little gyro optimization variable of an embodiment of the invention 1MEMS span.

Fig. 5 is the little gyrosystem model of MEMS that the embodiment of the invention 1 is set up based on cell library.

Fig. 6 is the testing program of the embodiment of the invention 1 based on the uniform Design method.

Fig. 7 is the embodiment of the invention 1 amplitude-versus-frequency curve figure.

Fig. 8 is the embodiment of the invention 1 computer simulation experiment result.

Fig. 9 is that the embodiment of the invention 1 is used seqential quadratic programming optimization Algorithm result.

Figure 10 is an embodiment of the invention 2MEMS micro-resonator structural representation.

Figure 11 is an embodiment of the invention 2MEMS micro-resonator optimization variable synoptic diagram.

Figure 12 is an embodiment of the invention 2MEMS micro-resonator optimization variable span.

Figure 13 is the little gyrosystem model of MEMS that the embodiment of the invention 2 is set up based on cell library.

Figure 14 is the testing program of the embodiment of the invention 2 based on the uniform Design method.

Figure 15 is the embodiment of the invention 2 amplitude-versus-frequency curve figure.

Figure 16 is the embodiment of the invention 2 computer simulation experiment results.

Figure 17 is the optimization result that the invention process 2 examples are used genetic algorithm.

Embodiment 1:

The design optimization method of the little gyro of a kind of MEMS may further comprise the steps:

1. given MEMS device architecture determines that it waits to investigate performance index y _m(m=1,2 ... M) with optimization variable x _i(i=1,2 ... n).Present embodiment is the design optimization object with the little gyro of MEMS.The structural representation of the little gyro of MEMS is referring to Fig. 2.Performance index to be investigated are the resonance frequency fx and the resonance frequency fy that detects mode that drive mode.Optimization variable is a thickness t, beam width w, beam 1 length l ₁, beam 2 length l ₂, beam 3 length l ₃The optimization variable synoptic diagram is referring to Fig. 3.The optimization variable span is referring to Fig. 4.

2. based on cell library, use the system model of elementary cell model construction MEMS device.Present embodiment is based on the ARCHITECT cell library, uses elementary cell models such as mass in the cell library, beam, anchor point, made up the system model of the little gyro of MEMS in the COVENTWARE emulation platform, referring to Fig. 5.

3. carry out test design, based on test design method, with optimization variable x _i(i=1,2 ... n) as experimental factor, obtain the testing program of N test $\left[\begin{array}{ccc}{x}_{11}& \&CenterDot;\&CenterDot;\&CenterDot;& x_{1n}\\ \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;\\ {\mathrm{<figure-callout\; id="1"\; label="x\; N"\; filenames="A20081015037600152.png,A20081015037600182.png"\; state="\{\{state\}\}">x</figure-callout>}}_N& \&CenterDot;\&CenterDot;\&CenterDot;& x_{\mathrm{Nn}}\end{array}\right].$ In order to make test number (TN) less, simultaneously can warranty test validity, present embodiment selects for use the uniform Design method to carry out test design.Present embodiment is the optimization variable thickness t, beam width w, beam 1 length l ₁, beam 2 length l ₂, beam 3 length l ₃As experimental factor.Owing to 5 optimization variable are arranged, select uniform designs table U ₁₅(15 ⁵), i.e. 5 experimental factors, No. 15 computing machine tests.Optimization variable equidistantly is divided into 15 values as the experimental factor level in span, chooses the varying level combination according to uniform designs table, the testing program that obtains 15 tests is seen Fig. 6.

4. based on the testing program of step 3, will wait to investigate performance index y _m(m=1,2 ... M) as test findings, the MEMS device system model that step 2 is made up carries out computer simulation experiment N time, obtains test findings $\left[\begin{array}{c}{y}_{}\end{array}\right]$ $\left[\begin{array}{ccc}{}_{11}& \&CenterDot;\&CenterDot;\&CenterDot;& y_{1M}\\ \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;\\ {\mathrm{<figure-callout\; id="1"\; label="y\; N"\; filenames="A20081015037600152.png,A20081015037600182.png"\; state="\{\{state\}\}">y</figure-callout>}}_N& \&CenterDot;\&CenterDot;\&CenterDot;& y_{\mathrm{NM}}\end{array}\right].$ Present embodiment will need the performance index investigated resonance frequency fx that drives mode and the resonance frequency fy that detects mode as test findings.First class value in getting testing program, i.e. thickness t=7.9 μ m, beam width w=6.3 μ m, beam 1 length l ₁=1500 μ m, beam 2 length l ₂=720 μ m, beam 3 length l ₃=580 μ m, in the SABER emulation platform, carry out the emulation of small-signal frequency domain, can obtain amplitude-versus-frequency curve, referring to Fig. 7, can read the value of test findings x direction resonance frequency fx and y direction resonance frequency fy from amplitude-versus-frequency curve figure, be respectively 1261Hz and 585Hz.Based on testing program, MEMS device system model is carried out computer simulation experiment 15 times, obtain test findings, referring to Fig. 8.

5. set up by regretional analysis and wait to investigate performance index y _m(m=1,2 ... M) with optimization variable x _i(i=1,2 ... the funtcional relationship n).Use the Matlab software programming to carry out regretional analysis, obtain waiting to investigate the quadratic regression equation between performance x direction resonance frequency fx and y direction resonance frequency fy and the optimization variable respectively, following fy=10500000-3920000*w-1310000*t+69000*l ₂+ 41.1*w*w+464000*w*t-1120*w*l ₃+ 1070*w*l ₁-8820*t*l ₂+ 12.4*l ₃* l ₃-5.68*l ₁* l ₁

fx＝4600000-12.2*l ₁-11000*w*w-384*w*l ₂-1.7*w*l ₁-1.44*t*l ₁-0.0295*l ₃*l ₃+0.0299*l ₃*l ₂-3.35*l ₂*l ₂+0.0219*l ₁*l ₁

* represents multiplication sign in the top formula.From the regression result coefficient of determination R of two equations as can be known ²Be respectively 0.9838 and 0.9819,, illustrate that quadratic regression model can be explained to wait to investigate performance and optimization variable influencing each other and concern more than 90%, so quadratic regression model be believable all greater than 0.9.

6. based on waiting to investigate performance y _m(m=1,2 ... M) with optimization variable x _i(i=1,2 ... the funtcional relationship n), write out the mathematic(al) representation of optimization aim and constraint condition.As follows

Optimization aim:

Min(fy-fx)+abs(fx-3000)/fx

Constraint condition:

g1：l ₃-l ₁＜＝0

g2：Xlow＜＝X＜＝Xup

X＝[t?w?l ₃?l ₂?l ₁]’

Optimization aim comprises two parts, the difference that fy-fx represents to drive the resonance frequency fx of mode and detects the resonance frequency fy of mode, abs (fx-3000)/fx represents to drive the difference of the resonance frequency fx and the desired value 3000Hz of mode, optimization aim is to make this two-part and minimum, just make fx and fy difference minimum, fx is about 3000Hz simultaneously.Constraint condition g1 represents to require beam 3 length l ₃Less than beam 1 length.The g2 expression requires optimization variable X in span, wherein X=[t w l ₃l ₂l ₁] ' representing optimized variable thickness t, beam width w, beam 3 length l ₃, beam 2 length l ₂, beam 1 length l ₁, Xlow and Xup represent minimum value of optimization variable and maximum occurrences.

7. based on the mathematic(al) representation of optimization aim and constraint condition, select optimized Algorithm to be optimized, the result is optimized.Present embodiment is selected local optimization methods for use--the seqential quadratic programming algorithm.Use the Matlab software programming to realize.Optimize the result referring to Fig. 9, thickness t=3 μ m wherein, beam width w=12 μ m, beam 3 length l ₃=50 μ m, beam 2 length l ₂=999 μ m, beam 1 length l ₁=50 μ m, the resonance frequency fx=3074Hz of driving mode, the resonance frequency fy=2998Hz of detection mode.

Embodiment 2:

A kind of design optimization method of MEMS micro-resonator may further comprise the steps:

1. given MEMS device architecture determines that it waits to investigate performance index y _m(m=1,2 ... M) with optimization variable x _i(i=1,2 ... n).Present embodiment is the design optimization object with the MEMS micro-resonator.The structural representation of MEMS micro-resonator is referring to Figure 10.Performance index to be investigated are the resonance frequency fy that make the y direction.Optimization variable is horizontal beam length l b, horizontal beam width wb, vertical beam length l t, vertical beam width wt, the mass length l sy that links to each other with static broach, the mass width wsy that links to each other with static broach, middle part mass width wsa.The optimization variable synoptic diagram is referring to Figure 11.The optimization variable span is referring to Figure 12.

2. based on cell library, use the system model of elementary cell model construction MEMS device.The present embodiment cell library uses the core kernel in " the core modeling method and the core kernel of mini inertial sensor spare ".Present embodiment uses the static broach in the core kernel, mass, and beam, elementary cell models such as environmental variance and global variable have made up the system model of the little gyro of MEMS, referring to Figure 13 in the SABER emulation platform.

3. carry out test design, based on test design method, with optimization variable x _i(i=1,2 ... n) as experimental factor, obtain the testing program of N test $\left[\begin{array}{ccc}{x}_{11}& \&CenterDot;\&CenterDot;\&CenterDot;& x_{1n}\\ \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;\\ {\mathrm{<figure-callout\; id="1"\; label="x\; N"\; filenames="A20081015037600152.png,A20081015037600182.png"\; state="\{\{state\}\}">x</figure-callout>}}_N& \&CenterDot;\&CenterDot;\&CenterDot;& x_{\mathrm{Nn}}\end{array}\right].$ In order to make test number (TN) less, simultaneously can warranty test validity, present embodiment selects for use the uniform Design method to carry out test design.Present embodiment is with optimization variable horizontal beam length l b, horizontal beam width wb, vertical beam length l t, vertical beam width wt, the mass length l sy that links to each other with static broach, the mass width wsy that links to each other with static broach, middle part mass width wsa is as experimental factor.Owing to 7 optimization variable are arranged, select uniform designs table U ₁₈(18 ⁷), i.e. 7 experimental factors, No. 18 computing machine tests.Optimization variable equidistantly is divided into 18 values as the experimental factor level in span, chooses the varying level combination, obtain testing program and see Figure 14 according to uniform designs table.

4. based on the testing program of step 3, will wait to investigate performance index y _m(m=1,2 ... M) as test findings, the MEMS device system model that step 2 is made up carries out computer simulation experiment N time, obtains test findings $\left[\begin{array}{c}{y}_{}\end{array}\right]$ $\left[\begin{array}{ccc}{}_{11}& \&CenterDot;\&CenterDot;\&CenterDot;& y_{1M}\\ \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;\\ {\mathrm{<figure-callout\; id="1"\; label="y\; N"\; filenames="A20081015037600152.png,A20081015037600182.png"\; state="\{\{state\}\}">y</figure-callout>}}_N& \&CenterDot;\&CenterDot;\&CenterDot;& y_{\mathrm{NM}}\end{array}\right].$ Present embodiment will need the resonance frequency fy of the performance index y direction investigated as test findings.First class value in getting testing program, be horizontal beam length l b=2 μ m, horizontal beam width wb=6.2 μ m, vertical beam length l t=119 μ m, vertical beam width wt=8.4 μ m, the mass length l sy=189 μ m that links to each other with static broach, the mass width wsy=239 μ m that links to each other with static broach, middle part mass width wsa=354 μ m, in the SABER emulation platform, carry out the emulation of small-signal frequency domain, can obtain amplitude-versus-frequency curve, referring to Figure 15, can read the value of test findings y direction resonance frequency fy from amplitude-versus-frequency curve figure, be 84191Hz.Based on testing program, MEMS device system model is carried out computer simulation experiment 18 times, obtain test findings, referring to Figure 16.

5. set up by regretional analysis and wait to investigate performance index y _m(m=1,2 ... M) with optimization variable x _i(i=1,2 ... the funtcional relationship n).Use the Matlab software programming to carry out regretional analysis, obtain waiting to investigate the quadratic regression equation between performance y direction resonance frequency fy and the optimization variable, as follows

fy＝46956-0.9206*lb*wsa-12.754*wb*lt+183.49*wb*wt+14.948*wb*wsa-0.42201*lsy*wsa-0.23947*wsy*wsa+0.41053*wsa*wsa

* represents multiplication sign in the top formula.From regression result coefficient of determination R as can be known ²Be 0.9336,, illustrate that quadratic regression model can be explained to wait to investigate performance and optimization variable influencing each other and concern more than 90%, so quadratic regression model be believable greater than 0.9.

6. based on waiting to investigate performance y _m(m=1,2 ... M) with optimization variable x _i(i=1,2 ... the funtcional relationship n), write out the mathematic(al) representation of optimization aim and constraint condition.As follows

Optimization aim:

Minimize

F＝abs(fy-20000)/fy+area

area＝(2*lb+lsy)*2*(2*(166.68-88.56)+wsy+3*1t/2)；

Constraint condition:

g1＝lb-wb＞＝0；

g2＝lt-wt＞＝0；

g3＝lsy-wsy＞＝0；

g4＝lsy-wsa＞＝0；

Wherein, optimization aim comprises two parts, and abs (fy-20000)/fy represents the difference of y direction resonance frequency fy and desired value 20000Hz, area represents the area of micro-resonator, optimization aim is to make both and minimum, just makes y direction resonance frequency fy near desired value, simultaneously the area minimum.

Constraint condition requires to determine according to geometric configuration.G1 represents to require micro-resonator horizontal beam length 1b greater than horizontal beam width wb, g2 represents to require micro-resonator vertical beam length l t greater than vertical beam width wt, g3 represents to require mass length l sy that micro-resonator links to each other with static broach greater than the mass width wsy that links to each other with static broach, and g4 represents to require mass length l sy that micro-resonator links to each other with static broach greater than middle part mass width wsa.

7. based on the mathematic(al) representation of optimization aim and constraint condition, select optimized Algorithm to be optimized, the result is optimized.Present embodiment selects for use genetic algorithm to be optimized.Use the Matlab software programming to realize.The initial population of genetic algorithm is taken as 100, and maximum evolutionary generation was taken as for 25 generations, and crossover probability is taken as 0.6, and the variation probability is taken as 0.05.Optimize the result referring to Figure 17, horizontal beam length l b=340.4 μ m wherein, horizontal beam width wb=17 μ m, vertical beam length l t=237.3 μ m, vertical beam width wt=11.2 μ m, the mass length l sy=344.4 μ m that links to each other with static broach, the mass width wsy=64.9 μ m that links to each other with static broach, middle part mass width wsa=161.6 μ m, y direction resonance frequency fy=20771Hz.

Among the embodiment 1, the system model that makes up little gyro only needs 4 fens clock times, and among the embodiment 2, the system model that makes up micro-resonator only needs 5 fens clock times, two embodiment explanations, and the present invention can realize the rapid modeling of dissimilar MEMS devices.Among the embodiment 2, use the bright method of we, on the computing machine of single microprocessor Pentium 3.4GHz, the global optimization requirements of process of micro-resonator is time half an hour approximately; And based on the MEME design optimization method of cell library and genetic algorithm, on the computing machine of the Pentium2.40GHz that 4 microprocessors are arranged, about 3.5 hours (Y Zhang of the global optimization requirements of process of micro-resonator, MEMS Design Synthesis Based on Hybrid EvolutionaryComputation, PhD Dissertation.University of California, Berkeley.2006.), illustrate that the existing MEME design optimization method global optimization flow process time based on cell library and genetic algorithm of our bright ratio significantly reduces.Embodiment 1 has selected the seqential quadratic programming algorithm for use, and embodiment 2 has selected genetic algorithm for use, illustrates that we are bright applicable to different optimized Algorithm.

Claims (8)

1. MEMS design optimization method is characterized in that: may further comprise the steps:

Step 1: given MEMS device architecture, determine that it waits to investigate performance index y _m(m=1,2 ... M) with optimization variable x _i(i=1,2 ... n);

Step 2:, use the system model of elementary cell model construction MEMS device based on cell library;

Step 3: carry out test design, based on test design method, with optimization variable x _i(i=1,2 ... n) as experimental factor, obtain the testing program of N test $\left[\begin{array}{ccc}{x}_{11}& ...& x_{1n}\\ ...& ...& ...\\ x_{N1}& ...& x_{\mathrm{Nn}}\end{array}\right],$ X wherein _Ui(u=1,2 ... N, i=1,2 ... n) the u time test value of i optimization variable of expression;

Step 4:, will wait to investigate performance index y based on the testing program of step 3 _m(m=1,2 ... M) as test findings, the MEMS device system model that step 2 is made up carries out computer simulation experiment N time, obtains test findings $\left[\begin{array}{ccc}{y}_{11}& ...& y_{1M}\\ ...& ...& ...\\ y_{N1}& ...& y_{\mathrm{NM}}\end{array}\right],$ Y wherein _Um(u=1,2 ... N, m=1,2 ... M) m of expression waits to investigate the u time test findings of performance index;

Step 5: wait to investigate performance index y by regretional analysis foundation _m(m=1,2 ... M) with optimization variable x _i(i=1,2 ... the funtcional relationship n), this funtcional relationship are quadratic regression equation:

$y_1={\mathrm{\&beta;}}_{01}+\underset{i=1}{\overset{k}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_{i1}{x}_i+\underset{i=1}{\overset{k}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_{\mathrm{ii}1}{x}_i^2+\underset{i\&NotEqual;j}{\overset{k}{\mathrm{\&Sigma;}}}\mathrm{\&Sigma;}{\mathrm{\&beta;}}_{\mathrm{ij}1}{x}_i{x}_j$

......

$y_M={\mathrm{\&beta;}}_{0M}+\underset{i=1}{\overset{k}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_{\mathrm{iM}}{x}_i+\underset{i=1}{\overset{k}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_{\mathrm{iiM}}{x}_i^2+\underset{i\&NotEqual;j}{\overset{k}{\mathrm{\&Sigma;}}}\mathrm{\&Sigma;}{\mathrm{\&beta;}}_{\mathrm{ijM}}{x}_i{x}_j$

In the formula, β _0m(m=1,2 ... M) expression m waits to investigate the constant term in the regression equation of variable, β _Im(i=1,2 ... n, m=1,2 ... M) expression m waits to investigate the once item coefficient of i optimization variable in the regression equation of variable, β _Iim(i=1,2 ... n, m=1,2 ... M) expression m waits to investigate the quadratic term coefficient of i optimization variable in the regression equation of variable, β _{Ijm, i ≠ j}(i=1,2 ... n, j=1,2 ... n, m=1,2 ... M) expression m waits to investigate in the regression equation of variable the cross term coefficient of i optimization variable with j optimization variable, and summation ∑ subscript k represents to have the k item factor to sue for peace;

Step 6: based on waiting to investigate performance y _m(m=1,2 ... M) with optimization variable x _i(i=1,2 ... the funtcional relationship n), write out the mathematic(al) representation of optimization aim and constraint condition, its common version is:

Optimization aim:

min f(x _i，y _m)

Constraint condition:

g _i(x _i，y _m)≤0(i＝1，2，...I)

h _j(x _i，y _m)＝0(j＝1，2，...J)

Wherein, f (x _i, y _m) represent and wait to investigate performance y _m(m=1,2 ... M) with optimization variable x _i(i=1,2 ... n) relevant functional form, min f (x _i, y _m) expression asks function minimum, g _i(x _i, y _m)≤0 (i=1,2 ... I) one group of inequality constrain condition of expression, h _j(x _i, y _m)=0 (j=1,2 ... J) one group of equality constraint of expression;

Step 7: based on the mathematic(al) representation of optimization aim and constraint condition, select optimized Algorithm to be optimized, the result is optimized.

2. MEMS design optimization method as claimed in claim 1 is characterized in that: the cell library described in the step 2 is based on the cell library that Structured Design thought is set up.

3. MEMS design optimization method as claimed in claim 1, it is characterized in that: the cell library described in the step 2 is core kernel, NODAS cell library, SUGAR cell library or ARCHITECT cell library.

4. MEMS design optimization method as claimed in claim 1, it is characterized in that: the test design method described in the step 3 is the multivariate test design method.

5. MEMS design optimization method as claimed in claim 1, it is characterized in that: the test design method described in the step 3 is the uniform Design method.

6. MEMS design optimization method as claimed in claim 1, it is characterized in that: the optimized Algorithm described in the step 7 is global optimization approach or Local Optimization Algorithm.

7. MEMS design optimization method as claimed in claim 6, it is characterized in that: described global optimization approach is a genetic algorithm.

8. MEMS design optimization method as claimed in claim 6, it is characterized in that: described Local Optimization Algorithm is the seqential quadratic programming algorithm.

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