CN103984825A

CN103984825A - Three-dimensional plate shape dynamic simulation method

Info

Publication number: CN103984825A
Application number: CN201410214716.1A
Authority: CN
Inventors: 陆宁云; 姜斌; 曾水林
Original assignee: Nanjing University of Aeronautics and Astronautics
Current assignee: Nanjing University of Aeronautics and Astronautics
Priority date: 2014-05-20
Filing date: 2014-05-20
Publication date: 2014-08-13
Anticipated expiration: 2034-05-20
Also published as: CN103984825B

Abstract

The invention discloses a three-dimensional plate shape dynamic simulation method, which belongs to the technical field of three-dimensional visualization. The method is characterized in that a three-dimensional plate shape curved surface of a plate is constructed in real time by utilizing a tensor product uniform B-spline method according to plate shape data acquired in real time, and comprises the following steps of firstly constructing an initial three-dimensional plate shape curve surface by utilizing the tensor product uniform B-spline method according to initial cross section plate shape data of a plurality of groups of plates; then calculating a control point matrix by utilizing a recursive least-squares method or improved recursive least-squares method for cross section plate shape data of each group of subsequent plates, and further realizing real-time dynamic fitting of the three-dimensional plate shape curved surface. Compared with the prior art, the three-dimensional plate shape dynamic simulation method has the advantage of capability of accurately and dynamically representing the three-dimensional plate shape online in real time.

Description

Three dimensional panel shape dynamic emulation method

Technical field

The present invention relates to a kind of three dimensional panel shape dynamic emulation method, according to the board form data of Real-time Collection, utilize tensor product Uniform B-spline method to construct in real time the three dimensional panel shape curved surface of sheet material, belong to three-dimensional visualization technique field.

Background technology

In Strip production run (such as belt steel rolling, aluminum alloy plate materials production etc.), in order to ensure strip shape quality, site operation personnel need to pay close attention to the board form data that detecting instrument of flatness Real-time Collection arrives, therefrom tell valuable information, suitably regulate accordingly rolling mill technology parameter, reduce underproof plate product.How by Real-time Collection to board form data efficiently show intuitively site operation personnel so that operating personnel implement to control more reliably and decision-making, be an important need in production process of plate.Conventional panels graphic data dynamic display technology mostly dynamically shows board form data by two-dimensional histogram.Although this plate shape display technique has, speed is fast, real-time advantages of higher, and display frame is directly perceived not, and is difficult to reappear complicated flatness defect, has been difficult to meet the demand that site operation personnel controls plate shape at present.

Three dimensional panel shape visualization technique possesses stronger information representation ability, can be more efficiently and show intuitively the board form data that detecting instrument of flatness collects.Existing three dimensional panel shape visualization technique has: the plate shape display packing based on plane what comes into a driver's and three-dimension curved surface display packing.Plate shape figure based on plane what comes into a driver's increases color map on two dimensional surface, by color map, in two dimensional surface, different plate shape stress values is represented with different colours, to plane, carries out painted.Diagram of block is to utilize visual software directly to show each board form data that detecting instrument of flatness collects constantly.

Plate shape figure based on plane what comes into a driver's is the actual method adopting in producing, site operation personnel must just can identify flatness defect in conjunction with the two-dimensional histogram of dynamic display panels graphic data, this has not only increased operating personnel's work load, has also reduced the speed of identification flatness defect.Utilize diagram of block that visual software technology realizes can be fast and accurately direct display board shape curved surface, but it does not carry out necessary processing to data, therefore show that image quality is coarse, the unlifelike shortcoming of display effect, site operation personnel is difficult to identify fast flatness defect according to this three-dimension curved surface.

Summary of the invention

Technical matters to be solved by this invention is to overcome the existing deficiency of existing three dimensional panel shape visualization technique, and a kind of three dimensional panel shape dynamic emulation method is provided, and can dynamically reproduce online, in real time, exactly three dimensional panel shape.

Three dimensional panel shape dynamic emulation method of the present invention, according to the board form data of Real-time Collection, utilizes tensor product Uniform B-spline method to construct in real time the three dimensional panel shape curved surface of sheet material, and described structure three dimensional panel shape curved surface comprises the following steps:

Step 1, according to initial k ₀group sheet material xsect template data, k ₀for being more than or equal to 3 integer, utilize tensor product Uniform B-spline method to construct initial three dimensional panel shape curved surface;

Step 2, for the k group sheet material xsect template data that after this gather, k=k ₀+ 1, k ₀+ 2 ..., calculate the reference mark vector d on sheet material Width _kand the knot vector t of the Uniform B-Spline Curve of sheet material direct of travel _y:

If y _k<t _y(n), knot vector t _yremain unchanged, n is the reference mark number on sheet material direct of travel, dimension, t _y(n) be knot vector t _yin meet t _y(n-1)≤y _k-1<t _y(n) node;

If y _k>=t _y(n), make n=n+1, t _y(n+l ₂)=t _y(n+l ₂-1)+b, makes t _y(n-1)≤y _k-1<t _y(n);

Wherein, b-spline surface reference mark Matrix C for front k-1 group board form data _k-1i column vector, y _kbe that k organizes sheet material xsect board form data at the coordinate figure with on steel direct of travel, b is knot vector t _ynodal pitch, l ₂number of times for B spline base function on sheet material direct of travel;

Step 3, according to reference mark d _k, knot vector t _y, and reference mark Matrix C _k-1, recursion is calculated the curved surface reference mark Matrix C of front k group sheet data _k:

According to t in step 2 _ywhether there is increase node, be divided into following two kinds of situations and calculate reference mark Matrix C _k:

The first situation: t _ywhile not increasing node, the number at curved surface reference mark remains unchanged, and adopts least square method of recursion to calculate respectively curved surface reference mark Matrix C _keach column vector

c_{i}^{k} = c_{i}^{k - 1} + P_{k} b_{k} (d_{i, k} b_{k} c_{i}^{k - 1})

Wherein, d _i,kfor reference mark vector d _ki reference mark, P _kfor recursion intermediate quantity, its expression formula is

P_{k} = {[B_{k}^{T} B_{k}]}^{- 1} = {[B_{k - 1}^{T} B_{k - 1} + b_{k}^{T} b_{k}]}^{- 1} = P_{k - 1} - P_{k - 1} b_{k}^{T} {(1 + b_{k} P_{k - 1} b_{k}^{T})}^{- 1} b_{k}^{T} P_{k - 1}

B _kfor the l on sheet material direct of travel ₂inferior B spline base function is at y _j(j=1 ..., matrix that value forms k), its expression formula is

B_{k} = [\begin{matrix} B_{k - 1} \\ b_{k} \end{matrix}], B_{k - 1} = [\begin{matrix} B_{0, l_{2}} (y_{1}) & B_{1, l_{2}} (y_{1}) & \cdot \cdot \cdot & B_{n - 1, l_{2}} (y_{1}) \\ B_{0, l_{2}} (y_{2}) & B_{1, l_{2}} (y_{2}) & \cdot \cdot \cdot & B_{n - 1, l_{2}} (y_{2}) \\ \cdot & \cdot & \cdot & \cdot \\ \cdot & \cdot & \cdot & \cdot \\ \cdot & \cdot & \cdot & \cdot \\ B_{0, l_{2}} (y_{k - 1}) & B_{1, l_{2}} (y_{k - 1}) & \cdot \cdot \cdot & B_{n - 1, l_{2}} (y_{k - 1}) \end{matrix}]

B _kit is matrix B _kk capable, its expression formula is

b_{k} = [\begin{matrix} B_{0, l_{2}} (y_{k}) & B_{1, l_{2}} (y_{k}) & \cdot \cdot \cdot & B_{n - 1, l_{2}} (y_{k}) \end{matrix}];

The second situation: t _ywhile having the node of increasing, the number at curved surface reference mark need correspondingly increase, order

C_{k - 1} = (\begin{matrix} C_{k - 1} \\ 0 \end{matrix})

Or

c_{i}^{k - 1} = (\begin{matrix} c_{i}^{k - 1} \\ 0 \end{matrix})

Now, adopt following methods to calculate reference mark Matrix C _keach column vector

Matrix B _kk capable

b_{k} = [\begin{matrix} B_{0, l_{2}} (y_{k}) & B_{1, l_{2}} (y_{k}) & \cdot \cdot \cdot & B_{n - 2, l_{2}} (y_{k}) & B_{n - 1, l_{2}} (y_{k}) \end{matrix}],

Matrix B _kexpression formula be

B_{k}^{*} = [\begin{matrix} B_{k - 1} & 0 \\ b_{k} \end{matrix}]

Recursion intermediate quantity P _kfor

P_{k} = {[{(B_{k}^{*})}^{T} B_{k}^{*}]}^{- 1} = [[\begin{matrix} B_{k - 1}^{T} B_{k - 1} & 0 \\ 0 & 0 \end{matrix}] + b_{k}^{T} b_{k}]^{- 1}

Making A is that n * n ties up non-null matrix, as order

A = [\begin{matrix} 0 & 0 \\ 0 & \frac{3}{4} b_{k} (n) \cdot b_{k} (n) \end{matrix}],

Make matrix

{(P_{k - 1}^{*})}^{- 1} = [\begin{matrix} B_{k - 1}^{T} B_{k - 1} & 0 \\ 0 & 0 \end{matrix}] + A

Full rank and

{(b_{k}^{*})}^{T} b_{k}^{*} = b_{k}^{T} b_{k} - A,

B _k(n) be vectorial b _kn element,

Thereby

P_{k} = {[{(B_{k}^{*})}^{T} B_{k}^{*}]}^{- 1} = {[{(P_{k - 1}^{*})}^{- 1} + {(b_{k}^{*})}^{T} b_{k}^{*}]}^{- 1}

Decompose and be converted to recursion intermediate quantity

P_{k} = P_{k - 1}^{*} - P_{k - 1}^{*} {(b_{k}^{*})}^{T} {(1 + b_{k}^{*} P_{k - 1}^{*} {(b_{k}^{*})}^{T})}^{- 1} {(b_{k}^{*})}^{T} P_{k - 1}^{*}

By formula recursion calculates the curved surface reference mark Matrix C of front k group sheet data _keach column vector

Step 4, according to curved surface reference mark Matrix C _k, the three dimensional panel shape curved surface of reconstruct k group xsect template data.

In order to improve visual effect, further, three dimensional panel shape dynamic emulation method of the present invention also comprises:

Step 5, according to the difference of xsect template data, the three dimensional panel shape curved surface reconstructing is carried out to the filling of different colours.

Compared to existing technology, technical solution of the present invention has following beneficial effect:

(1) the present invention adopts recursive algorithm to guarantee the rapidity that three dimensional panel shape dynamically shows, makes this visualization technique can realize online dynamically demonstration, is applicable to again the analysis that off-line plate shape is reproduced.

(2) in fit procedure, the knot vector on sheet material direct of travel and reference mark do not need to pre-determine, and it can upgrade along with the increase of data volume.

(3) the present invention can significantly improve the visual effect that three dimensional panel shape dynamically shows.

Accompanying drawing explanation

Fig. 1 is the schematic flow sheet of three dimensional panel shape dynamic emulation method of the present invention;

Fig. 2 is the matching B-spline curves figure of a certain moment strip width direction;

Fig. 3 is the plate shape Dynamic Simulation Results of different sampling instants.

Embodiment

Below in conjunction with accompanying drawing, technical scheme of the present invention is elaborated:

Three dimensional panel shape dynamic emulation method of the present invention can be used for the online or visual demonstration of off-line in all kinds of production process of plates, can present the plate product in production run visual pattern, make site operation personnel can analyze rapidly flatness defect, and adjusting process parameter suitably, thereby improve the quality of plate product.The belt steel rolling process of take is below described in detail technical solution of the present invention as example, and the flow process of three dimensional panel shape dynamic simulation as shown in Figure 1, specifically comprises the following steps:

Set strip width direction and be respectively l with the B spline base function number of times on steel direct of travel ₁and l ₂.Measurement point sum according to detecting instrument of flatness, adopts genetic Optimization Algorithm to determine the nodal pitch a of the Uniform B-Spline Curve in strip width direction, and according to the nodal pitch b on rolling mill technology setting parameter band steel direct of travel.Knot vector t in strip width direction _xand with the start node vector t on steel direct of travel _ybe respectively:

t _x＝{t _x(i)}(i＝0,…,m+l ₁)，t _x(l ₁)＝x ₁，t _x(i+1)＝t _x(i)+a，t _x(m-1)≤x _M<t _x(m)

t _y＝{t _y(j)}(j＝0,…,n+l ₂)，t _y(l ₂)＝y ₁，t _y(j+1)＝t _y(j)+b，t _y(n-1)≤y _k-1<t _y(n)

Wherein, m is the reference mark number in strip width direction, and n is with the initial control point number on steel direct of travel, x _i(i=1 ..., M) be detecting instrument of flatness measurement point coordinate figure in strip width direction, y _j(j=1 ..., be k-1) that i group sheet material xsect board form data is at the coordinate figure with on steel direct of travel.

Tensor product uniform B-spline surfaces model is

z = Σ_{i = 0}^{m - 1} Σ_{j = 0}^{n - 1} B_{i, l_{1}} (x) c_{i, j} B_{j, l_{2}} (y) + e

Wherein, c _i,jfor curved surface reference mark, e is surface fitting error, with represent respectively strip width direction and with the l of steel direct of travel ₁and l ₂inferior B spline base function.Given knot vector t, l time B spline base function can obtain according to following formula

B_{i, l} (x) = \frac{x - t_{i}}{t_{i + 1} - t_{i}} B_{i, l - 1} (x) + \frac{t_{i + l + 1} - x}{t_{i + l + 1} - t_{i + 1}} B_{i + 1, i - 1} (x), (t_{i} \leq x < t_{i + 1})

Convert tensor product uniform B-spline surfaces model dimensionality reduction to following two Uniform B-Spline Curve models.

Uniform B-Spline Curve model in strip width direction:

z = Σ_{i = 0}^{m - 1} B_{i, l_{1}} (x) d_{i} + e

With the Uniform B-Spline Curve model on steel direct of travel:

d_{i} = Σ_{j = 0}^{n - 1} c_{j, l} B_{j, l_{2}} (y) + e^{*}

Wherein, e* is the error of fitting with the Uniform B-Spline Curve on steel direct of travel.

Therefore, initial three dimensional panel shape curved surface reference mark Matrix C _k, k=k ₀, can following process try to achieve.

(1) the k group board form data z recording according to detecting instrument of flatness _k=[z _{1, k}..., z _m,k], k=1 ..., k ₀, calculate the reference mark vector d on sheet material Width _k

d_{k}^{T} = {(B_{M}^{T} B_{M})}^{- 1} B_{M}^{T} z_{k}^{T}

Wherein, matrix B _mfor

B_{M} = [\begin{matrix} B_{0, l_{1}} (x_{1}) & B_{1, l_{1}} (x_{1}) & \cdot \cdot \cdot & B_{m - 1, l_{1}} (x_{1}) \\ B_{0, l_{1}} (x_{2}) & B_{1, l_{1}} (x_{2}) & \cdot \cdot \cdot & B_{m - 1, l_{1}} (x_{2}) \\ \cdot & \cdot & \cdot & \cdot \\ \cdot & \cdot & \cdot & \cdot \\ \cdot & \cdot & \cdot & \cdot \\ B_{0, l_{1}} (x_{M}) & B_{1, l_{1}} (x_{M}) & \cdot \cdot \cdot & B_{m - 1, l_{1}} (x_{M}) \end{matrix}]

(2) with by reference mark

[\begin{matrix} d_{1} \\ \cdot \\ \cdot \\ \cdot \\ d_{k_{0}} \end{matrix}]

The k forming ₀* m dimension matrix, as data point, calculates the reference mark vector on sheet material direct of travel

c_{i}^{k} = {(B_{k}^{T} B_{k})}^{- 1} B_{k}^{T} \times [\begin{matrix} d_{i, 1} \\ \cdot \\ \cdot \\ \cdot \\ d_{i, k} \end{matrix}]

Wherein, k=k ₀, d _i,kfor reference mark vector d _ki reference mark, matrix B _kfor

B_{k} = [\begin{matrix} B_{0, l_{2}} (y_{1}) & B_{1, l_{2}} (y_{1}) & \cdot \cdot \cdot & B_{n - 1, l_{2}} (y_{1}) \\ B_{0, l_{2}} (y_{2}) & B_{1, l_{2}} (y_{2}) & \cdot \cdot \cdot & B_{n - 1, l_{2}} (y_{2}) \\ \cdot & \cdot & \cdot & \cdot \\ \cdot & \cdot & \cdot & \cdot \\ \cdot & \cdot & \cdot & \cdot \\ B_{0, l_{2}} (y_{k}) & B_{1, l_{2}} (y_{k}) & \cdot \cdot \cdot & B_{n - 1, l_{2}} (y_{k}) \end{matrix}]

By reference mark vector the matrix forming is required initial control C _k, k=k ₀.

By reference mark Matrix C _k, k=k ₀, according to formula the k that reconstruct is initial ₀the three dimensional panel shape curved surface of group xsect template data.

Wherein, b-spline surface reference mark Matrix C for front k-1 group board form data _k-1i column vector, y _kbe that k group sheet material xsect board form data is at the coordinate figure with on steel direct of travel;

c_{i}^{k} = c_{i}^{k - 1} + P_{k} b_{k} (d_{i, k} b_{k} c_{i}^{k - 1})

P_{k} = {[B_{k}^{T} B_{k}]}^{- 1} = {[B_{k - 1}^{T} B_{k - 1} + b_{k}^{T} b_{k}]}^{- 1} = P_{k - 1} - P_{k - 1} b_{k}^{T} {(1 + b_{k} P_{k - 1} b_{k}^{T})}^{- 1} b_{k}^{T} P_{k - 1}

B_{k} = [\begin{matrix} B_{k - 1} \\ b_{k} \end{matrix}], B_{k - 1} = [\begin{matrix} B_{0, l_{2}} (y_{1}) & B_{1, l_{2}} (y_{1}) & \cdot \cdot \cdot & B_{n - 1, l_{2}} (y_{1}) \\ B_{0, l_{2}} (y_{2}) & B_{1, l_{2}} (y_{2}) & \cdot \cdot \cdot & B_{n - 1, l_{2}} (y_{2}) \\ \cdot & \cdot & \cdot & \cdot \\ \cdot & \cdot & \cdot & \cdot \\ \cdot & \cdot & \cdot & \cdot \\ B_{0, l_{2}} (y_{k - 1}) & B_{1, l_{2}} (y_{k - 1}) & \cdot \cdot \cdot & B_{n - 1, l_{2}} (y_{k - 1}) \end{matrix}]

B _kit is matrix B _kk capable, its expression formula is

b_{k} = [\begin{matrix} B_{0, l_{2}} (y_{k}) & B_{1, l_{2}} (y_{k}) & \cdot \cdot \cdot & B_{n - 1, l_{2}} (y_{k}) \end{matrix}];

C_{k - 1} = (\begin{matrix} C_{k - 1} \\ 0 \end{matrix})

Or

c_{i}^{k - 1} = (\begin{matrix} c_{i}^{k - 1} \\ 0 \end{matrix})

Now, adopt following improved least square method of recursion to calculate reference mark Matrix C _keach column vector

Matrix B _kk capable

b_{k} = [\begin{matrix} B_{0, l_{2}} (y_{k}) & B_{1, l_{2}} (y_{k}) & \cdot \cdot \cdot & B_{n - 2, l_{2}} (y_{k}) & B_{n - 1, l_{2}} (y_{k}) \end{matrix}],

Matrix B _kexpression formula be

B_{k}^{*} = [\begin{matrix} B_{k - 1} & 0 \\ b_{k} \end{matrix}]

Recursion intermediate quantity P _kfor

P_{k} = {[{(B_{k}^{*})}^{T} B_{k}^{*}]}^{- 1} = [[\begin{matrix} B_{k - 1}^{T} B_{k - 1} & 0 \\ 0 & 0 \end{matrix}] + b_{k}^{T} b_{k}]^{- 1}

Making A is that n * n ties up non-null matrix, as order

A = [\begin{matrix} 0 & 0 \\ 0 & \frac{3}{4} b_{k} (n) \cdot b_{k} (n) \end{matrix}],

Make matrix

{(P_{k - 1}^{*})}^{- 1} = [\begin{matrix} B_{k - 1}^{T} B_{k - 1} & 0 \\ 0 & 0 \end{matrix}] + A

Full rank and

{(b_{k}^{*})}^{T} b_{k}^{*} = b_{k}^{T} b_{k} - A,

B _k(n) be vectorial b _kn element,

Thereby

P_{k} = {[{(B_{k}^{*})}^{T} B_{k}^{*}]}^{- 1} = {[{(P_{k - 1}^{*})}^{- 1} + {(b_{k}^{*})}^{T} b_{k}^{*}]}^{- 1}

Decompose and be converted to recursion intermediate quantity

P_{k} = P_{k - 1}^{*} - P_{k - 1}^{*} {(b_{k}^{*})}^{T} {(1 + b_{k}^{*} P_{k - 1}^{*} {(b_{k}^{*})}^{T})}^{- 1} {(b_{k}^{*})}^{T} P_{k - 1}^{*}

Finally, by formula recursion calculates the curved surface reference mark Matrix C of front k group sheet data _keach column vector

Step 4, according to curved surface reference mark Matrix C _k, according to formula the three dimensional panel shape curved surface of reconstruct k group xsect template data.Fig. 2 has shown the matching B-spline curves figure of a certain moment strip width direction.

Step 5, according to the difference of xsect template data, the three dimensional panel shape curved surface reconstructing is carried out to the filling of different colours:

In order to strengthen effect of visualization, can each region of three dimensional panel shape curved surface be composed with different colors according to the difference of flatness, for example can to each region of three dimensional panel shape curved surface, carry out stepping according to following stepping rule:

-5I～5I is a step shape;-10I～-5I or 5I～10I are two step shapes;-15I～-10I or 10I～15I are three step shapes; Be less than-15I or to be greater than 15I be level Four plate shape (wherein I is flatness unit); Each step shape is composed with a kind of color.

In order to verify the effect of the inventive method, the board form data that Yi Mou steel mill 2030 tandem mills detecting instrument of flatness collect is example, and the three dimensional panel shape that adopts said method to carry out off-line to it shows checking.100 groups of off-line board form datas that adopted a certain coiled strip steel product in this experiment, the width of this coiled strip steel is 1248mm, and length is 100 measurement sample points (being K=100), and effective measurement point sum of sheet shape measurer is 24, i.e. M=24.

Fig. 3 shows the plate shape Dynamic Simulation Results of different sampling instants, wherein (a)～(d) be followed successively by plate shape simulation result of the 5th, 25,75,100 sampling instants.As can be seen from Figure 3, the inventive method has good precision and Visual Performance, is of very high actual application value.

Claims

1. a three dimensional panel shape dynamic emulation method, according to the board form data of Real-time Collection, utilizes tensor product Uniform B-spline method to construct in real time the three dimensional panel shape curved surface of sheet material, it is characterized in that, described structure three dimensional panel shape curved surface comprises the following steps:

Step 1, according to initial group sheet material xsect template data, for being more than or equal to 3 integer, utilize tensor product Uniform B-spline method to construct initial three dimensional panel shape curved surface;

Step 2, for after this gather the kgroup sheet material xsect template data, , calculate the reference mark vector on sheet material Width and the knot vector of the Uniform B-Spline Curve of sheet material direct of travel t _y:

If y _k< t _y( n), knot vector t _yremain unchanged, nfor the reference mark number on sheet material direct of travel, dimension, t _y( n) be knot vector t _yin meet t _y( n-1)≤ y _k-1< t _y( n) node;

If y _k>= t _y( n), order n=n+1, t _y( n+l ₂)= t _y( n+l ₂ -1)+ b, make t _y( n-1)≤ y _k-1< t _y( n);

Wherein, for front kthe B-spline surface reference mark matrix of-1 group of board form data c _k-1? iindividual column vector, y _kbe korganize sheet material xsect board form data at the coordinate figure with on steel direct of travel, bfor knot vector t _ynodal pitch, l ₂number of times for B spline base function on sheet material direct of travel;

Step 3, according to reference mark d _k, knot vector t _y, and reference mark matrix c _k-1, before recursion is calculated kthe curved surface reference mark matrix of group sheet data c _k:

According in step 2 t _ywhether there is increase node, be divided into following two kinds of situations and calculate reference mark matrix c _k:

The first situation: t _ywhile not increasing node, the number at curved surface reference mark remains unchanged, and adopts least square method of recursion to calculate respectively curved surface reference mark matrix c _keach column vector :

Wherein, d _i,kfor reference mark vector d _k? iindividual reference mark, p _kfor recursion intermediate quantity, its expression formula is

b _kfor on sheet material direct of travel l ₂inferior B spline base function exists y _j( j=1 ..., k) matrix that value forms, its expression formula is

，

b _kit is matrix b _k? koK, its expression formula is b _k=[ b _{0, l2}( y _k), b _{1
, l2}( y _k) ..., b _n,l2( y _k)];

or

Now, adopt following methods to calculate reference mark matrix c _keach column vector :

Matrix b _k? koK b _k=[ b _{0, l2}( y _k), b _{1
, l2}( y _k) ..., b _{n-1
, l2}( y _k), b _n,l2( y _k)],

Matrix b _kexpression formula be

Recursion intermediate quantity p _kfor

Make A be ( n+1) * ( n+1) tie up non-null matrix, as order , make matrix full rank and ,

Thereby

Decompose and be converted to recursion intermediate quantity ,

By formula before recursion calculates kthe curved surface reference mark matrix of group sheet data c _keach column vector ;

Step 4, according to curved surface reference mark matrix c _k, reconstruct kthe three dimensional panel shape curved surface of group xsect template data.

2. three dimensional panel shape dynamic emulation method as claimed in claim 1, is characterized in that, the method also comprises:

3. three dimensional panel shape dynamic emulation method as claimed in claim 1 or 2, is characterized in that, described sheet material is band steel.