CN110096738A - Modeling method and device based on sensitivity analysis - Google Patents
Modeling method and device based on sensitivity analysis Download PDFInfo
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- G06F30/30—Circuit design
- G06F30/36—Circuit design at the analogue level
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Abstract
The invention discloses a kind of modeling method and device based on sensitivity analysis, wherein this method comprises: obtaining the state vector of circuit system according to the circuit system for meeting default equation form；Presetting method is determined to handle state vector according to the Parameter Conditions of default equation, obtains the sensitivity of state vector；Circuit model is established according to sensitivity.This method can use sensitivity building circuit behavior model or performance model, effectively reduce simulation times, improve model construction rate.
Description
Technical field
The present invention relates to EDA Technique field, in particular to a kind of modeling method based on sensitivity analysis
And device.
Background technique
Electric design automation (Electronics Design Automation, EDA) is used for using software as carrier
In the method that the design phase analyzes prediction performance of integrated circuits, common circuit simulation tools have the HSPICE of Synopsys company
With the Spectre of Cadence company etc..The targeted object of circuit simulation is the electricity described using circuit network list or other forms
The electrology characteristic of circuit is calculated by using certain device model for road.
Circuit simulation establishes equation by kirchhoffs law and solves equation, implementation step usually by
Two parts composition.First part is the foundation of circuit equation, and in the establishment stage of circuit equation, circuit simulation is according to circuit structure
And the voltage of circuit interior joint and the electric current of branch establish equation.Second part is the solution of circuit equation, is specifically solved
The type of equation is different according to different circuit emulation methods, including the differential equation, linear equation and nonlinear equation.
Transient analysis is a kind of circuit emulation method, mainly according to circuit structure, driving signal and simulation parameter (input
Information) calculate the curve (output result) that the voltage of each node in circuit changes over time.
The input of transient analysis generally comprises following information:
(1) circuit structure: the element composition and topological structure of circuit.
(2) driving signal: the external drive signal of circuit.
(3) simulation parameter: the attribute of the required emulation done, such as simulation type, total time, step-length, precision etc..
The output of transient analysis is usually the curve that the voltage of each node in circuit changes over time, also known as each section
The waveform of point voltage.It can carry out further post-processing using this waveform to obtain other desired information, such as circuit
Spectral characteristic etc..
In recent years, the significantly promotion of computer computation ability makes the dynamic response precision improvement of extensive dynamic circuit, this
Transient state sensitivity between a little dynamic responses and system parameter plays particularly significant in integrated circuit the Automation Design algorithm
Effect, ((Data Assimilation, DA) is considering that data spatial and temporal distributions and observation field and ambient field miss to data assimilation
On the basis of difference, the method that new observation data are merged in the dynamic running process of numerical model, in the dynamic of process model
In frame, constantly merged by data assimilation algorithm on space-time the separate sources of discrete distribution and the direct of different resolution or
Connect observation information and come self-optimizing model track, to improve the estimated accuracy of dynamic model state, improve model prediction ability),
Parameter Estimation, quantization uncertainty are widely used in stability analysis.In engineering, sensitivity is indispensable as algorithm
Gradient be also usually utilized to do circuit optimization.
Most important index is exactly the operating rate of circuit, that is, clock frequency for gate circuit.In statistics
In circuit analysis, it need to analyze also therefore attract attention when statistical.Statistical static timing analysis (Statistical static
Timing analysis, SSTA) application, so that statistical delay is propagated in sequence circuit figure as single number.
In the method, the distribution of delay is expressed as special format, the device parameters (or being its principal component) usually floated
Low order form, enable its be distributed presentation format compare as single number maximum value be added.Or it can direct basis
Final concern delay and the sensitivity of parameter are established low order and are contacted, and delay distribution is found, and this method is although have passed through global low
Rank is approximate, but extensive with its quick feature application prospect.No matter any method, transient state sensitivity all plays wherein
Indispensable important function.
Determine parameter transient state sensitivity, traditional violence method for solving (Brute-force Method) makes by micro- respectively
Each parameter of each device is disturbed to obtain the sensitivity of final all parameters, emulation complexity and number of parameters and device
Number product is in a linear relationship.In order to overcome this complexity, the device group of someone's use experience cluster variation, rather than by it
Be considered as it is incoherent.This method will emulate complexity and fall in a linear relationship with number of parameters, but need to circuit behavior
There is deep understanding, and is primarily adapted for use in sequential digital logic.Violence method for solving emulates several times due to needing to pass through,
Today that single simulation time can reach several hours, which just seems, is inconvenient benefit.
Summary of the invention
The present invention is directed to solve at least some of the technical problems in related technologies.
For this purpose, an object of the present invention is to provide a kind of modeling method based on sensitivity analysis, this method can be with
Circuit model is established using sensitivity, is applied to circuit optimization and other aspects.
It is another object of the present invention to propose a kind of model building device based on sensitivity analysis.
In order to achieve the above objectives, one aspect of the present invention embodiment proposes a kind of modeling method based on sensitivity analysis,
It include: that the state vector of the circuit system is obtained according to the circuit system for meeting default equation form；According to the default side
The Parameter Conditions of journey determine presetting method to handle the state vector, obtain the sensitivity of the state vector；Root
Circuit model is established according to the sensitivity.
The modeling method based on sensitivity analysis of the embodiment of the present invention, by with matrix calculate angle set out understand it is adjoint
The method that method calculates transient state sensitivity is understood backpropagation meter sensitivity using directed acyclic graph auxiliary, is built using sensitivity
Vertical circuit behavior model or performance model reduce simulation times, mitigate the complexity of modeling, improve model construction rate, can be with
It is applied in circuit optimization and other aspects.
In addition, the modeling method according to the above embodiment of the present invention based on sensitivity analysis can also have following add
Technical characteristic:
Further, in one embodiment of the invention, the default equation are as follows:
Wherein, f (x) is default equation, and x is the state vector of circuit system, and p is the sensitivity parameter of circuit system, and t is
Time, B (p, t) are the input vector of system.
Further, in one embodiment of the invention, further includes:
Calculate Jacobian matrix Jac:
The state vector x is iterated according to the Jacobian matrix so that the state vector x meets precision and wants
It asks, iterative formula are as follows:
Δ x=(Jac)-1·rhs
Wherein, Δ x is accurate state vector after iteration, and rhs indicates the residual error of default equation, (Jac)-1For Jacobi square
Battle array JacInverse matrix.
Further, in one embodiment of the invention, the sensitivity of the state vector passes through to the default side
Journey derivation obtains:
Wherein,It is led to ask default equation.
Further, in one embodiment of the invention, the presetting method includes direct method and adjoint method；
The Parameter Conditions according to the default equation determine presetting method to handle the state vector, have
Body includes:
P number of sensitivity parameter of circuit system be less than or equal to the first preset threshold, the default equation number be greater than etc.
When the second preset threshold, the state vector is handled using direct method；
P number of sensitivity parameter of circuit system is greater than the first preset threshold, and the default equation number is pre- less than second
If when threshold value, being handled using adjoint method the state vector.
In order to achieve the above objectives, another aspect of the present invention embodiment proposes a kind of modeling dress based on sensitivity analysis
It sets, comprising: first obtains module, for obtaining the shape of the circuit system according to the circuit system for meeting default equation form
State vector；Second obtain module, for according to the Parameter Conditions of the default equation determine presetting method with to the state to
Amount is handled, and the sensitivity of the state vector is obtained；Modeling module, for establishing circuit model according to the sensitivity.
The model building device based on sensitivity analysis of the embodiment of the present invention, by with matrix calculate angle set out understand it is adjoint
The method that method calculates transient state sensitivity is understood backpropagation meter sensitivity using directed acyclic graph auxiliary, is built using sensitivity
Vertical circuit behavior model or performance model reduce simulation times, mitigate the complexity of modeling, improve model construction rate, can be with
It is applied in circuit optimization and other aspects.
In addition, the model building device according to the above embodiment of the present invention based on sensitivity analysis can also have following add
Technical characteristic:
Further, in one embodiment of the invention, the default equation are as follows:
Wherein, f (x) is default equation, and x is the state vector of circuit system, and p is the sensitivity parameter of circuit system, and t is
Time, B (p, t) are the input vector of system.
Further, in one embodiment of the invention, further includes: computing module and iteration module；
The computing module, for calculating Jacobian matrix Jac:
The iteration module is iterated so that described the state vector x with about according to the Jacobian matrix
State vector x meets required precision, iterative formula are as follows:
Δ x=(Jac)-1·rhs
Wherein, Δ x is accurately state vector, rhs indicate the residual error of default equation, (J after iterationac)-1For Jacobi square
Battle array JacInverse matrix.
Further, in one embodiment of the invention, the sensitivity of the state vector passes through to the default side
Journey derivation obtains:
Wherein,It is led to ask default equation.
Further, in one embodiment of the invention, the presetting method includes direct method and adjoint method；
The Parameter Conditions according to the default equation determine presetting method, specifically include:
P number of sensitivity parameter of circuit system be less than or equal to the first preset threshold, the default equation number be greater than etc.
When the second preset threshold, using direct method；
P number of sensitivity parameter of circuit system is greater than the first preset threshold, and the default equation number is pre- less than second
If when threshold value, using adjoint method.
The additional aspect of the present invention and advantage will be set forth in part in the description, and will partially become from the following description
Obviously, or practice through the invention is recognized.
Detailed description of the invention
Above-mentioned and/or additional aspect and advantage of the invention will become from the following description of the accompanying drawings of embodiments
Obviously and it is readily appreciated that, in which:
Fig. 1 is the modeling method flow chart based on sensitivity analysis according to one embodiment of the invention；
Fig. 2 is the fit solution figure according to one embodiment of the invention；
Fig. 3 is to understand schematic diagram according to the matrix method of one embodiment of the invention；
Fig. 4 is the directed acyclic graph according to one embodiment of the invention；
Fig. 5 is the model building device structural schematic diagram based on sensitivity analysis according to one embodiment of the invention.
Specific embodiment
The embodiment of the present invention is described below in detail, examples of the embodiments are shown in the accompanying drawings, wherein from beginning to end
Same or similar label indicates same or similar element or element with the same or similar functions.Below with reference to attached
The embodiment of figure description is exemplary, it is intended to is used to explain the present invention, and is not considered as limiting the invention.
The modeling method and device based on sensitivity analysis proposed according to embodiments of the present invention is described with reference to the accompanying drawings.
The modeling method based on sensitivity analysis proposed according to embodiments of the present invention is described with reference to the accompanying drawings first.
Fig. 1 is the modeling method flow chart based on sensitivity analysis according to one embodiment of the invention.
As shown in Figure 1, should modeling method based on sensitivity analysis the following steps are included:
In step s101, according to the circuit system for meeting default equation form, the state vector of circuit system is obtained.
Further, in one embodiment of the invention, equation is preset are as follows:
Wherein, f (x) is default equation, and x is the state vector of circuit system, and p is the sensitivity parameter of circuit system, and t is
Time, B (p, t) are the input vector of system, and F is amount relevant with time-derivative to state, and F (p, x) is state and time phase
The amount of pass.
Further, in one embodiment of the invention, further includes:
Calculate Jacobian matrix Jac:
State vector x is iterated so that state vector x meets required precision, iterative formula according to Jacobian matrix
Are as follows:
Δ x=(Jac)-1·rhs
Wherein, Δ x is accurate state vector after iteration, and rhs indicates the residual error of default equation, (Jac)-1For Jacobi square
Battle array JacInverse matrix.
Specifically, for a nonlinear circuit, it can be assumed that the system to be solved meets the differential algebra of following form
Equation (Differential-Algebraic Equation, DAE):
Wherein, x is the state vector of system, such as the node voltage or branch current of circuit；P is intended to the wink solved
State sensitivity parameter, such as the threshold voltage vt h of MOSFET, saturated velocity Vsat, u；T is the time, and q and f are charge/ respectively
Flue and current.Under the conditions of given original state x (t0), for the dynamic response for calculating stiff DAE system, it is based on
The estimation of Local Truncation Error (LTE) determines time step, and continuous track is carried out time discretization.Transient state
In analysis, carry out solving state x using the methods of Newton method or the newton of upgrading blocking.
In order to calculate state vector x, calculating Jacobian matrix Jac first obtains formula (1) derivation:
Then continuous iteration updates x:
Δ x=(Jac)-1·rhs
Wherein, rhs indicates the residual error of current formula (1).By being iterated to x for each, be the precision of x increasingly
Height, usual 3 iteration can reach required state x required precision.
In step s 102, according to the Parameter Conditions of default equation determine presetting method to handle state vector,
Obtain the sensitivity of state vector.
Further, in one embodiment of the invention, the sensitivity of state vector is by obtaining default equation derivation
Out:
Wherein,It is led to ask default equation.
Further, in one embodiment of the invention, presetting method includes direct method and adjoint method；
Presetting method is determined to handle state vector according to the Parameter Conditions of default equation, is specifically included:
P number of sensitivity parameter of circuit system is less than or equal to the first preset threshold, presets equation number and is more than or equal to the
When two preset thresholds, direct method handles state vector；
P number of sensitivity parameter of circuit system is greater than the first preset threshold, presets equation number less than the second default threshold
When value, state vector is handled using adjoint method.
Specifically, the sensitivity of state vector x is that dx/dp can seek the p of default equation (1) to calculate dx/dp
It leads:
To solveThe problem of numerical value, solves final result by way of solving linear multi step equation.Linear
In multistep processes, the calculated result of a certain step is not only related with current solution, also related with the solution of several steps in front, that is, utilizes front
The information of multistep predicts next step result.
In an embodiment of the present invention, it solvesThe problem of numerical value, there are two types of calculation methods, respectively direct method and companion
With method.
Direct method and adjoint method are considered as being to solve for different from the direction of exhaustion.Illustrate that O is mesh below with an example
Equation is marked, i.e., the default equation in above example, p is the transient state sensitivity parameter to be solved.
Direct method:
Adjoint method:
In static circuit, when parameter p is less, df/dp is the less matrix of a columns, first by the inverse square of df/dx
Battle array is multiplied to obtain dx/dp with df/dp, then the calculation amount that is multiplied with dO/dx is smaller, so direct method calculates all intermediate variables pair
The sensitivity of system parameter, until finally searching out target equation.
As shown in Fig. 2, dO/dx is the less matrix of a line number, first by df/ when the objective function O to be solved is less
The inverse matrix of dx is multiplied to obtain dO/df with dO/dx, then the calculation amount that is multiplied with df/dp is smaller.
It is compared with direct method, adjoint method calculates sensitivity of the target equation to all intermediate variables, until finally finding
To system parameter.As shown in Fig. 2, so when objective function O is more, being suitble to solve using direct method when parameter p is less.Work as ginseng
Number p is more, when objective function O is less, is suitble to solve using adjoint method.
In dynamic circuit, as shown in figure 3, deriving O to the derivative of p, between parameter p and target equation O by chain rule
There are the state x (tn) at many time points, the sum for the path derivative product that O is all p to O to the derivative of p, the area of two methods
The difference for enumerating path direction has not just been evolved into.Direct method is calculated along time step sequence until being pushed into from parameter p
Target equation O.With rule after all time step states determine, from target equation O, it is pushed into along time step inverted sequence
Parameter p.
Circuit transient state sensitivity emulation is carried out in the case of extensive parameter, small-scale target equation, adjoint method solves
Transient state sensitivity.For large-scale circuit, parameter is many and diverse, and circuit simulation is advisable using adjoint method, shortens circuit-simulation time.
In step s 103, circuit model is established according to sensitivity.
Further, it after finding out sensitivity through the above steps, can be modeled according to sensitivity, construct circuit behavior mould
Type or performance model.
Circuit model, that is, people assume that there are certain mapping relations y between design parameter x and circuit behavior or circuit performance y
=f (x) obtains sample data by sampling, model is made to be fitted data with existing as far as possible.Obviously, the given data of acquisition is more,
The model established more may be close to truth (excluding over-fitting situation).
According to above-mentioned introduction, the analytic value and its sensitivity of circuit state and its function can be obtained by emulation,
The analytic value and its sensitivity of available event triggering type target equation, i.e., data needed for obtaining modeling in primary emulation
The derivative of f (x) and f (x).The case where this known sample point and its derivative is to compare in the regression problem that regular machinery learns
Rare.But the presence of derivative provides additional information to modeling, can be reduced using this partial information to sampled point quantity
Requirement, the demand to sampled point quantity of modeling can be effectively reduced using the gradient information of sampled point, that is, complete identical
Modeling accuracy can use less simulation times now, reduce simulation time, accelerate circuit design speed.
Over-fitting can also be effectively controlled using the gradient information of sampled point.
Application of the sensitivity in terms of reducing sampled point is introduced by taking linear regression model (LRM) as an example.
For the non-linear relation between description X and Y, dimension is carried out to X and extends to obtain (X, X2,X3,X4,X5).Y=w0+w1*
X+w2*X2+w3*X3+w4*X4+w5*X5S
It is once emulated, one group of corresponding relationship x can be obtained0,y0,y0’。
Equation can be obtained:
y0=w0*1+w1*x0+w2*x0 2+w3*x0 3+w4*x0 4+w5*x0 5y0?
=w0*0+w1*1+w2*(2*x0)+w3 *(3*x0 2)+w4 *(4*x0 3)+w5 *(5*x0 4)
In such a process, by derivative expressions as w0Coefficient is 0, other coordinate points accordingly reduce power and multiplied by original
The new coordinate data of secondary exponential is brought into the calculating of modeling, can so reduce the need to sampled point quantity to a certain extent
It asks.In addition it is also possible to first unify to model derivative, w is obtained1To w5Solving result, recycle original data return to obtain w0。
If not reducing sample point data, the introducing of derivative can also reduce over-fitting to a certain extent.As Fig. 4 (a) is
Non- over-fitting situation, Fig. 4 (b) are over-fitting situation.The introducing of derivative limits the tendency of curve, would not also occur inputting again
Decline when about 0.78, constrains over-fitting.
It is understood that the method for the embodiment of the present invention can not only be modeled in the hope of the sensitivity in circuit system,
Further, it can be constructed circuit performance model (such as circuit delay model) in the hope of the sensitivity of target component in target side journey,
It is illustrated below with an example.
In transient analysis, some events (delay of such as phase inverter) only occurred under certain specific condition are defined, for
The sensitivity analysis of these events continues discussing on the basis of non-practice above triggers.
Trigger event is defined to need to meet equation:
Target equation:
Solution can obtain, event triggering type sensitivity:
Wherein,
The modeling method based on sensitivity analysis proposed according to embodiments of the present invention is set out by calculating angle with matrix
Understand the method that adjoint method calculates transient state sensitivity, understands backpropagation meter sensitivity using directed acyclic graph auxiliary, utilize
Circuit behavior model or performance model are established in sensitivity, reduce simulation times, mitigate the complexity of modeling, improve model construction speed
Rate, can be applied in circuit optimization and other aspects.
The model building device based on sensitivity analysis proposed according to embodiments of the present invention is described referring next to attached drawing.
Fig. 5 is the model building device structural schematic diagram based on sensitivity analysis according to one embodiment of the invention.
As shown in figure 5, being somebody's turn to do the model building device based on sensitivity analysis includes: that the first acquisition module 100, second obtains module
200 and modeling module 300.
Wherein, first the circuit system that module 100 is used to preset equation form according to satisfaction is obtained, obtains circuit system
State vector.Second acquisition module 200 be used for according to preset equation Parameter Conditions determine presetting method with to state vector into
Row processing, obtains the sensitivity of state vector.Modeling module 300 is used to establish circuit model according to sensitivity.
The model building device based on sensitivity analysis can use sensitivity and establish circuit model, use circuit optimization and
Other aspects.
Further, in one embodiment of the invention, equation is preset are as follows:
Wherein, f (x) is default equation, and x is the state vector of circuit system, and p is the sensitivity parameter of circuit system, and t is
Time, B (p, t) are the input vector of system.
Further, in one embodiment of the invention, further includes: computing module and iteration module；
Computing module, for calculating Jacobian matrix Jac:
Iteration module is iterated so that state vector x meets precision state vector x with about according to Jacobian matrix
It is required that iterative formula are as follows:
Δ x=(Jac)-1·rhs
Wherein, Δ x is accurately state vector, rhs indicate the residual error of default equation, (J after iterationac)-1For Jacobi square
Battle array JacInverse matrix.
Further, in one embodiment of the invention, the sensitivity of state vector is by obtaining default equation derivation
Out:
Wherein,It is led to ask default equation.
Further, in one embodiment of the invention, presetting method includes direct method and adjoint method；
Presetting method is determined according to the Parameter Conditions of default equation, is specifically included:
P number of sensitivity parameter of circuit system is less than or equal to the first preset threshold, presets equation number and is more than or equal to the
When two preset thresholds, using direct method；
P number of sensitivity parameter of circuit system is greater than the first preset threshold, presets equation number less than the second default threshold
When value, using adjoint method.
It should be noted that the aforementioned explanation to the modeling method embodiment based on sensitivity analysis is also applied for this
The device of embodiment, details are not described herein again.
The model building device based on sensitivity analysis proposed according to embodiments of the present invention is set out by calculating angle with matrix
Understand the method that adjoint method calculates transient state sensitivity, understands backpropagation meter sensitivity using directed acyclic graph auxiliary, utilize
Circuit behavior model or performance model are established in sensitivity, reduce simulation times, mitigate the complexity of modeling, improve model construction speed
Rate, can be applied in circuit optimization and other aspects.
In addition, term " first ", " second " are used for descriptive purposes only and cannot be understood as indicating or suggesting relative importance
Or implicitly indicate the quantity of indicated technical characteristic.Define " first " as a result, the feature of " second " can be expressed or
Implicitly include at least one this feature.In the description of the present invention, the meaning of " plurality " is at least two, such as two, three
It is a etc., unless otherwise specifically defined.
In the description of this specification, reference term " one embodiment ", " some embodiments ", " example ", " specifically show
The description of example " or " some examples " etc. means specific features, structure, material or spy described in conjunction with this embodiment or example
Point is included at least one embodiment or example of the invention.In the present specification, schematic expression of the above terms are not
It must be directed to identical embodiment or example.Moreover, particular features, structures, materials, or characteristics described can be in office
It can be combined in any suitable manner in one or more embodiment or examples.In addition, without conflicting with each other, the skill of this field
Art personnel can tie the feature of different embodiments or examples described in this specification and different embodiments or examples
It closes and combines.
Although the embodiments of the present invention has been shown and described above, it is to be understood that above-described embodiment is example
Property, it is not considered as limiting the invention, those skilled in the art within the scope of the invention can be to above-mentioned
Embodiment is changed, modifies, replacement and variant.
Claims (10)
1. a kind of modeling method based on sensitivity analysis, which comprises the following steps:
According to the circuit system for meeting default equation form, the state vector of the circuit system is obtained；
Presetting method is determined to handle the state vector according to the Parameter Conditions of the default equation, obtains the shape
The sensitivity of state vector；
Circuit model is established according to the sensitivity.
2. the modeling method according to claim 1 based on sensitivity analysis, which is characterized in that the default equation are as follows:
Wherein, f (x) is default equation, and x is the state vector of circuit system, and p is the sensitivity parameter of circuit system, when t is
Between, B (p, t) is the input vector of system.
3. the modeling method according to claim 2 based on sensitivity analysis, which is characterized in that further include:
Calculate Jacobian matrix Jac:
The state vector x is iterated according to the Jacobian matrix so that the state vector x meets required precision, repeatedly
For formula are as follows:
Δ x=(Jac)-1·rhs
Wherein, Δ x is accurately state vector, rhs indicate the residual error of default equation, (J after iterationac)-1For Jacobian matrix Jac
Inverse matrix.
4. the modeling method according to claim 2 based on sensitivity analysis, which is characterized in that the spirit of the state vector
Sensitivity is by obtaining the default equation derivation:
Wherein,It is led to ask default equation.
5. the modeling method according to claim 1 based on sensitivity analysis, which is characterized in that the presetting method includes
Direct method and adjoint method；
The Parameter Conditions according to the default equation determine that presetting method to handle the state vector, specifically wraps
It includes:
P number of sensitivity parameter of circuit system is less than or equal to the first preset threshold, and the default equation number is more than or equal to the
When two preset thresholds, the state vector is handled using direct method；
P number of sensitivity parameter of circuit system is greater than the first preset threshold, and the default equation number is less than the second default threshold
When value, the state vector is handled using adjoint method.
6. a kind of model building device based on sensitivity analysis characterized by comprising
First obtains module, for according to the circuit system for meeting default equation form, obtain the state of the circuit system to
Amount；
Second obtain module, for according to the Parameter Conditions of the default equation determine presetting method with to the state vector into
Row processing, obtains the sensitivity of the state vector；
Modeling module, for establishing circuit model according to the sensitivity.
7. the model building device according to claim 6 based on sensitivity analysis, which is characterized in that the default equation are as follows:
Wherein, f (x) is default equation, and x is the state vector of circuit system, and p is the sensitivity parameter of circuit system, when t is
Between, B (p, t) is the input vector of system.
8. the model building device according to claim 7 based on sensitivity analysis, it is characterised in that further include: computing module and
Iteration module；
The computing module, for calculating Jacobian matrix Jac:
The iteration module, for the state vector x is iterated according to the Jacobian matrix so that the state to
Amount x meets required precision, iterative formula are as follows:
Δ x=(Jac)-1·rhs
Wherein, Δ x is accurately state vector, rhs indicate the residual error of default equation, (J after iterationac)-1For Jacobian matrix Jac
Inverse matrix.
9. the model building device according to claim 7 based on sensitivity analysis, which is characterized in that the spirit of the state vector
Sensitivity is by obtaining the default equation derivation:
Wherein,It is led to ask default equation.
10. the model building device according to claim 6 based on sensitivity analysis, which is characterized in that the presetting method packet
Include direct method and adjoint method；
The Parameter Conditions according to the default equation determine that presetting method to handle the state vector, specifically wraps
It includes:
P number of sensitivity parameter of circuit system is less than or equal to the first preset threshold, and the default equation number is more than or equal to the
When two preset thresholds, the state vector is handled using direct method；
P number of sensitivity parameter of circuit system is greater than the first preset threshold, and the default equation number is less than the second default threshold
When value, the state vector is handled using adjoint method.
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| CN113032722A (en) * | 2021-03-29 | 2021-06-25 | 北京华大九天科技股份有限公司 | Method for reducing matrix decomposition in circuit simulation |
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