CN104462018A - Similar case retrieval method based on multidimensional correlation function - Google Patents

Abstract

A similar case retrieval method based on a multidimensional correlation function includes the steps of firstly, improving the lateral spacing through a variable slope method, and establishing a multidimensional lateral spacing model based on the improved lateral spacing; secondly, establishing the multidimensional correlation function with a good dimensionality reduction effect under the relatively-complex multidimensional lateral spacing calculation; thirdly, putting forward a three-stage low-carbon product retrieval method based on the multidimensional correlation function. By means of the similar case retrieval method based on the multidimensional correlation function, the data dimensionality calculation can be reduced, the retrieval efficiency can be improved, and the more accurate and reliable result can be obtained.

Description

A kind of similar case retrieval method based on multidimensional correlation function

Technical field

The present invention relates to low-carbon (LC) design field, especially a kind of similar case retrieval method based on multidimensional correlation function.

Background technology

Low-carbon (LC) design is as towards one of energy-conservation Design For The Ecological technology, under the prerequisites such as the due function of guarantee product, quality and life-span, consider carbon emission and energy-efficient modern Design, and launching primary study in energy-saving ecological design, light-weight design and modular design etc.The cunalysis and calculation of product carbon footprint is the basis of low-carbon (LC) method for designing research, and the low-carbon (LC) demand of product is only concentrated on the quantum chemical method of product carbon footprint by current most research, and analytic process is comparatively numerous and diverse, and have ignored the impact of product resource consumption.

Green products is constantly updated in order to the demand meeting market and is regenerated in evolution, and kind and the quantity of product example also increase thereupon fast.Further, complex product has the multiple attributes of different dimension, and classic method first calculates single attribute similarity, the more integrated similarity solving global property, but cannot embody the difference of multidimensional property input and the input of one-dimensional attribute.The structure of multidimensional correlation function, can the quantitative distance of accurate and formal description low-carbon (LC) demand and product-derived example, and builds similarity model based on this, exports case similarity, for design knowledge reuse provides designing quality guarantee.

Summary of the invention

In order to the deficiency of " dimension is frightened " that the data dimension existed when overcoming prior art retrieval too much produces, the present invention builds similarity model by multidimensional correlation function, use Spatial Data Index Technology and dimensionality reduction technology, space is split, reduce space and solve dimension, high dimensional data is down to low-dimensional, provides a kind of similar case retrieval method based on multidimensional correlation function.

The technical solution adopted for the present invention to solve the technical problems is as following content:

Based on a similar case retrieval method for multidimensional correlation function, the method comprises the steps:

(1), towards the side distance of low-carbon (LC) design

Suppose the joint territory X=< c of product attribute, d >, x ₀for the optimum point value of this attribute, then the left side of x to interval X is apart from being expressed as:

${\mathrm{\&rho;}}_{\mathrm{Il}}(x,x_0,X)=\left\{\begin{array}{cc}c-x,& x\&Element;(-\&infin;,c]\\ \frac{d-x_0}{{(x_0-c)}^2}{(x-x_0)}^2+x_0-d,& x\&Element;[c,x_0]\mathrm{and}{x}_0\&NotEqual;c\\ \frac{4(d-x_0)}{{(2x_0-c-d)}^2}{(x-x_0)}^2+x_0-d,& x\&Element;[x_0,\frac{2x_0+c+d}{4}]\mathrm{and}{x}_0\&NotEqual;\mathrm{cand}{x}_0\&NotEqual;\frac{c+d}{2}\\ \frac{12(x_0-d)}{{(3d-2x_0-c)}^2}{(x-d)}^2,& x\&Element;[\frac{2x_0+c+d}{4},d]\mathrm{and}{x}_0\&NotEqual;c\\ x-d,& x\&Element;[d,+\&infin;)\\ -{(x-d)}^2,& x\&Element;[c,d]\&Element;\left[\mathrm{0,1}\right]\mathrm{and}{x}_0=c\\ -\frac{1}{{(x-d)}^2}& x\&Element;[c,d]\mathrm{andd}\&Element;[1,+\&infin;]\mathrm{and}{x}_0=c\end{array}\right.$

Right side apart from formula is:

${\mathrm{\&rho;}}_{\mathrm{Ir}}(x,x_0,X)=\left\{\begin{array}{cc}c-x,& x\&Element;(-\&infin;,c]\\ \frac{12(c-x_0)}{{({2x}_0-3c+d)}^2}{(x-x_0)}^2,& x\&Element;[c,\frac{2x_0+c+d}{4}]\mathrm{and}{x}_0\&NotEqual;d\\ \frac{4(x_0-c)}{{(c+d-2x_0)}^2}{(x-x_0)}^2+c-x_0,& x\&Element;[\frac{2x_0+c+d}{4},x_0]\mathrm{and}{x}_0\&NotEqual;\mathrm{dand}{x}_0\&NotEqual;\frac{c+d}{2}\\ \frac{x_0-c}{{(d-x_0)}^2}{(x-x_0)}^2+c-x_0,& x\&Element;[x_0,d]\mathrm{and}{x}_0\&NotEqual;c\\ x-d,& x\&Element;[d,+\&infin;)\\ -{(x-c)}^2& x\&Element;[c,d]\&Element;\left[\mathrm{0,1}\right]\mathrm{and}{x}_0=d\\ -\frac{1}{{(x-c)}^2}& x\&Element;[c,d]\mathrm{andd}\&Element;[1,+\&infin;]\mathrm{and}{x}_0=d\end{array}\right.$

When $x_0=\frac{c+d}{2}$ Time, curve minimum point is ${\mathrm{\&rho;}}_{\mathrm{Il}}(x,x_0,X)=\frac{c-d}{2};$ When $x_0\&RightArrow;\frac{c+d}{2}$ In approach procedure, left side distance curve, right side distance curve are respectively at interval [c, x ₀], [x ₀, d] on concaved, its formula is:

${\mathrm{\&rho;}}_I(x,x_0,X)=\left\{\begin{array}{c}{\mathrm{\&rho;}}_{\mathrm{Il}}(x,x_0,X)=-{(x-c)}^2\\ {\mathrm{\&rho;}}_{\mathrm{Ir}}(x,x_0,X)=-{(x-d)}^2\end{array}\right.$

(2) the multidimensional side distance, based on low-carbon (LC) example builds

Postulated point P falls within a certain region of n dimensional plane, crosses the straight line l of optimum point O and some P _oPthe frame intersection point tieing up enclosure space with n is P ₁and P ₂, it is known, $\frac{P_1+P_2}{2}\&le;O\&le;P_2$ And $\{\frac{P_1+P_2}{2},O,P_1,P_2\}\&Element;l_{\mathrm{OP}},$ Then n dimension right side is apart from being expressed as:

$\begin{array}{c}{\mathrm{\&rho;}}_{3-D}^{\mathrm{Ir}}(P,O,S_1)=\\ \left\{\begin{array}{cc}d(P_1,P),& P_1\left|\mathrm{OP}\right|,O\&NotEqual;\mathrm{Fr}\left(S_1\right),P\&Element;l_{\mathrm{OP}}\\ d(P_2,P),& P_2\&Element;\left|\mathrm{OP}\right|,O\&NotEqual;\mathrm{Fr}\left(S_1\right),P\&Element;l_{\mathrm{OP}}\\ \frac{-12d}{{(2d(P_1,O)+d(P_1,P_2))}^2}{\left[d(P_1,P)\right]}^2,& P\&Element;{[P}_1,\frac{2O+P_1+P_2}{4}],O\&NotEqual;\mathrm{Fr}\left(S_1\right),O\&NotEqual;\frac{P_1+P_2}{2}\\ \frac{4d(P_1,O)}{{(d(P_1,O)+d(O,P_2))}^2}{\left[d(O,P)\right]}^2-d(P_1,O),& P\&Element;[\frac{2O+P_1+P_2}{4},O]O\&NotEqual;\mathrm{Fr}\left(S_1\right),O\&NotEqual;\frac{P_1+P_2}{2}\\ \frac{d(P_1,O)}{{\left[d(O,P_2)\right]}^2}{\left[d(O,P)\right]}^2-d(P_1,O),& P\&Element;[O,P_2],O\&NotEqual;\mathrm{Fr}\left(S_1\right),O\&NotEqual;\frac{P_1+P_2}{2}\\ -{\left[d(P_1,P)\right]}^2,& P\&Element;[P_1,P_2]\&Element;[0,e],O=\mathrm{Fr}\left(S_1\right)\\ -\frac{1}{{\left[d(P_1,P)\right]}^2},& P\&Element;[P_1,P_2]\&cup;P_2\&Element;[e,+\&infin;],O=\mathrm{Fr}\left(S_1\right),P\&NotEqual;O\\ -d(O,P_2),& P=[P_1,P_2],O=\frac{P_1+P_2}{2},P\&NotEqual;O\\ -d(O,P_1),& P=O\end{array}\right.\end{array}$

Wherein:

S ₁the multidimensional being expressed as an actual product demand is interval, namely be expressed as the length of i-th dimension;

Fr (S ₁) be expressed as the length end points of each dimension to the vertical border mapping the multidimensional interval closed formed of other dimensions;

P ₁be expressed as the some O in multidimensional interval and P place straight line and Fr (S ₁) intersection point;

D (P, P ₁) be expressed as a P and put P ₁linear range;

(3) the multidimensional correlation function, based on low-carbon (LC) design builds

Suppose the interval X of existence two ₀=< a, b >, X=< c, d >, and the geometric center in space overlaps with input multi-Dimensional parameters optimal value O, then multidimensional correlation function is expressed as:

$K_{n-D}\left(P\right)=\left\{\begin{array}{cc}\frac{\left|{\mathrm{PP}}_2\right|}{|P_1{P}_2},& {\mathrm{\&rho;}}_{n-D}(P,S_2)\&NotEqual;{\mathrm{\&rho;}}_{n-D}(P,S_1)\&cap;P\&Element;S_2\\ -\frac{\left|{\mathrm{PP}}_2\right|}{\left|P_1{P}_2\right|},& {\mathrm{\&rho;}}_{n-D}(P,S_2)\&NotEqual;{\mathrm{\&rho;}}_{n-D}(P,S_1)\&cap;P\&Element;R-S_2\\ \left|{\mathrm{PP}}_1\right|+1,& {\mathrm{\&rho;}}_{n-D}(P,S_2)={\mathrm{\&rho;}}_{n-D}(P,S_1)\&cap;P\&Element;S_1\\ \left|{\mathrm{PP}}_2\right|,& {\mathrm{\&rho;}}_{n-D}(P,S_2)={\mathrm{\&rho;}}_{n-D}(P,S_1)\&cap;P\&Element;S_2-S_1\\ -\left|{\mathrm{PP}}_2\right|,& {\mathrm{\&rho;}}_{n-D}(P,S_2)={\mathrm{\&rho;}}_{n-D}(P,S_1)\&cap;P\&Element;R-S_2\\ \min d(x_0,\mathrm{Fr}\left(S_1\right)),& P=x_0\end{array}\right.$

Wherein S ₂for product design requires multidimensional property space, $S_2=(\mathrm{\&Delta;}{x}_1^{1^{\&prime;}},\mathrm{\&Delta;}{x}_2^{2^{\&prime;}},...,\mathrm{\&Delta;}{x}_m^{m^{\&prime;}}),\mathrm{\&Delta;}{x}_j^{j^{\&prime;}}\&GreaterEqual;\mathrm{\&Delta;}{x}_j^j;$

(4) the low-carbon (LC) case similarity, based on multidimensional correlation function is retrieved

Low-carbon (LC) and cost needs extraction are carried out to product demand, first both is done to the one-level retrieval of two dimension, determine in low-carbon (LC) and cost to have a product example mated at least, as the example source of 2-level search, such object is that unnecessary data calculate in order to reduce, the output of null result, highlight the importance of low-carbon (LC) design; Input product performance requirement again, does the 2-level search of multidimensional data, calculates the Similarity value based on multidimensional correlation function, and example source is divided into again the full up foot of product performance demands and these two example domains of the not full up foot of product performance demands; Finally input multidimensional product component demand, again divide the low-carbon (LC) example domains on upper strata, output products parts demand coupling and unmatched product example collection;

The similarity of one-level retrieval is: ${\mathrm{sim}}_{i,t}^1({\mathrm{PR}}_i,P_t)=\left\{\begin{array}{cc}1,& K_{m_1-D}\left(P_t\right)\&GreaterEqual;0\\ e^{K_{m_1-D}\left(P_t\right)},& K_{m_1-D}\left(P_t\right)<0\end{array}\right.;$

The similarity of 2-level search is: ${\mathrm{sim}}_{i,t}^2({\mathrm{PR}}_i,P_t)=\left\{\begin{array}{cc}1,& K_{m_2-D}\left(P_t\right)\&GreaterEqual;0\\ e^{K_{m_2-D}\left(P_t\right)},& K_{m_2-D}\left(P_t\right)<0\end{array}\right.;$

The similarity of three－stagesearch is: ${\mathrm{sim}}_{i,t}^3({\mathrm{PR}}_i,P_t)=1-\underset{l=1}{\overset{n-m_1-m_2}{\mathrm{\&Sigma;}}}{d}_l({\mathrm{PR}}_i^l,P_i^l);$

Then, product demand and product example similarity are:

${\mathrm{sim}}_{i,t}({\mathrm{PR}}_i,P_t)=\underset{j=1}{\overset{3}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_j{\mathrm{sim}}_i^j({\mathrm{PR}}_i,P_t).$

Further, in described step (4), the process based on the similarity retrieval method of multidimensional correlation function is as follows:

4.1) product demand point value and conversion acquisition demand interval value: judge product demand type, is determined;

4.2): build multidimensional Classical field space S according to product demand interval value ₁with multidimensional extension range space S ₂;

4.3): combination product instance properties point P _twith optimum point x ₀, build straight line l _oPwith n-D dimension space;

4.4): according to putting P _tsolving equation provides P _taffiliated area;

4.5): dimensionality reduction calculating K _n-D(P _t);

4.6): judge K _n-D(P _t), calculate sim (PR _i, P _t);

4.7): the sim (PR recording this product example retrieval rank _i, P _t);

4.8): terminate.

Principle of work of the present invention: the present invention is by improving the computing method of side distance, build multidimensional correlation function, utilize when the geometric space center by different attribute demand composition overlaps with optimal value, high dimensional data can be down to the feature that low-dimensional calculates, greatly reduce calculated amount, and by using multilevel retrieval mechanism, highlighted the importance of complex product different attribute, also improve effectiveness of retrieval simultaneously.

Beneficial effect of the present invention shows as: 1, side distance improved, make design parameter more accurate to the skewed popularity of design parameter optimum point; 2, build multidimensional correlation function, high dimensional data can be down to low-dimensional, reduce calculated amount; 3, multilevel retrieval mechanism is set up, the primacy of low-carbon (LC) in more outstanding product design process.; 4, make the result that retrieves more accurately and reliably, scientific and reasonable.

Accompanying drawing explanation

Fig. 1 is that three-dimensional side is apart from schematic diagram calculation.

Fig. 2 is multilevel retrieval mechanism choice.

Embodiment

Below the present invention is described further.

See figures.1.and.2, a kind of similar case retrieval method based on multidimensional correlation function, the method comprises the steps:

(1), towards the side distance of low-carbon (LC) design

Side is apart from the distance computing formula of skewed popularity and the design parameter point that accurately provides and design object interval that mainly to consider product design parameter optimal value position.Therefore, when considering design parameter optimal value, design parameter point is not obviously static constant relative to the distance counting yield of optimal value, is that the curve of variable slope is formed.

Suppose the joint territory X=< c of product attribute, d >, x ₀for the optimum point value of this attribute, then the left side of x to interval X is apart from being expressed as:

${\mathrm{\&rho;}}_{\mathrm{Il}}(x,x_0,X)=\left\{\begin{array}{cc}c-x,& x\&Element;(-\&infin;,c]\\ \frac{d-x_0}{{(x_0-c)}^2}{(x-x_0)}^2+x_0-d,& x\&Element;[c,x_0]\mathrm{and}{x}_0\&NotEqual;c\\ \frac{4(d-x_0)}{{(2x_0-c-d)}^2}{(x-x_0)}^2+x_0-d,& x\&Element;[x_0,\frac{2x_0+c+d}{4}]\mathrm{and}{x}_0\&NotEqual;\mathrm{cand}{x}_0\&NotEqual;\frac{c+d}{2}\\ \frac{12(x_0-d)}{{(3d-2x_0-c)}^2}{(x-d)}^2,& x\&Element;[\frac{2x_0+c+d}{4},d]\mathrm{and}{x}_0\&NotEqual;c\\ x-d,& x\&Element;[d,+\&infin;)\\ -{(x-d)}^2,& x\&Element;[c,d]\&Element;\left[\mathrm{0,1}\right]\mathrm{and}{x}_0=c\\ -\frac{1}{{(x-d)}^2}& x\&Element;[c,d]\mathrm{andd}\&Element;[1,+\&infin;]\mathrm{and}{x}_0=c\end{array}\right.$

Right side apart from formula is:

${\mathrm{\&rho;}}_{\mathrm{Ir}}(x,x_0,X)=\left\{\begin{array}{cc}c-x,& x\&Element;(-\&infin;,c]\\ \frac{12(c-x_0)}{{({2x}_0-3c+d)}^2}{(x-x_0)}^2,& x\&Element;[c,\frac{2x_0+c+d}{4}]\mathrm{and}{x}_0\&NotEqual;d\\ \frac{4(x_0-c)}{{(c+d-2x_0)}^2}{(x-x_0)}^2+c-x_0,& x\&Element;[\frac{2x_0+c+d}{4},x_0]\mathrm{and}{x}_0\&NotEqual;\mathrm{dand}{x}_0\&NotEqual;\frac{c+d}{2}\\ \frac{x_0-c}{{(d-x_0)}^2}{(x-x_0)}^2+c-x_0,& x\&Element;[x_0,d]\mathrm{and}{x}_0\&NotEqual;c\\ x-d,& x\&Element;[d,+\&infin;)\\ -{(x-c)}^2& x\&Element;[c,d]\&Element;\left[\mathrm{0,1}\right]\mathrm{and}{x}_0=d\\ -\frac{1}{{(x-c)}^2}& x\&Element;[c,d]\mathrm{andd}\&Element;[1,+\&infin;]\mathrm{and}{x}_0=d\end{array}\right.$

When $x_0=\frac{c+d}{2}$ Time, curve minimum point is ${\mathrm{\&rho;}}_{\mathrm{Il}}(x,x_0,X)=\frac{c-d}{2};$ When $x_0\&RightArrow;\frac{c+d}{2}$ In approach procedure, left and right side distance curve is respectively at interval [c, x ₀], [x ₀, d] on concaved, its formula is:

${\mathrm{\&rho;}}_I(x,x_0,X)=\left\{\begin{array}{c}{\mathrm{\&rho;}}_{\mathrm{Il}}(x,x_0,X)=-{(x-c)}^2\\ {\mathrm{\&rho;}}_{\mathrm{Ir}}(x,x_0,X)=-{(x-d)}^2\end{array}\right.$

(2) the multidimensional side distance, based on low-carbon (LC) example builds

In order to respond product design requirement fast, method retrieves product example storehouse exactly the most efficiently, by retrieving the input of demand properties, provides satisfactory product example or most like product example, as the reference design basis that final plan exports.Due to the multi-dimensional nature of product attribute, in order to solve the inclined subjectivity of multidimensional retrieval middle distance assignment, build the multidimensional side distance based on improving side distance.

, namely postulated point P falls within a certain region of n-dimensional space, crosses the straight line l of optimum point O and some P _oPthe frame intersection point tieing up enclosure space with n is P ₁and P ₂, it is known, and then n dimension right side is apart from being expressed as:

$\begin{array}{c}{\mathrm{\&rho;}}_{3-D}^{\mathrm{Ir}}(P,O,S_1)=\\ \left\{\begin{array}{cc}d(P_1,P),& P_1\left|\mathrm{OP}\right|,O\&NotEqual;\mathrm{Fr}\left(S_1\right),P\&Element;l_{\mathrm{OP}}\\ d(P_2,P),& P_2\&Element;\left|\mathrm{OP}\right|,O\&NotEqual;\mathrm{Fr}\left(S_1\right),P\&Element;l_{\mathrm{OP}}\\ \frac{-12d}{{(2d(P_1,O)+d(P_1,P_2))}^2}{\left[d(P_1,P)\right]}^2,& P\&Element;{[P}_1,\frac{2O+P_1+P_2}{4}],O\&NotEqual;\mathrm{Fr}\left(S_1\right),O\&NotEqual;\frac{P_1+P_2}{2}\\ \frac{4d(P_1,O)}{{(d(P_1,O)+d(O,P_2))}^2}{\left[d(O,P)\right]}^2-d(P_1,O),& P\&Element;[\frac{2O+P_1+P_2}{4},O]O\&NotEqual;\mathrm{Fr}\left(S_1\right),O\&NotEqual;\frac{P_1+P_2}{2}\\ \frac{d(P_1,O)}{{\left[d(O,P_2)\right]}^2}{\left[d(O,P)\right]}^2-d(P_1,O),& P\&Element;[O,P_2],O\&NotEqual;\mathrm{Fr}\left(S_1\right),O\&NotEqual;\frac{P_1+P_2}{2}\\ -{\left[d(P_1,P)\right]}^2,& P\&Element;[P_1,P_2]\&Element;[0,e],O=\mathrm{Fr}\left(S_1\right)\\ -\frac{1}{{\left[d(P_1,P)\right]}^2},& P\&Element;[P_1,P_2]\&cup;P_2\&Element;[e,+\&infin;],O=\mathrm{Fr}\left(S_1\right),P\&NotEqual;O\\ -d(O,P_2),& P=[P_1,P_2],O=\frac{P_1+P_2}{2},P\&NotEqual;O\\ -d(O,P_1),& P=O\end{array}\right.\end{array}$

Wherein:

S ₁the multidimensional being expressed as an actual product demand is interval, namely be expressed as the length of i-th dimension;

Fr (S ₁) be expressed as the length end points of each dimension to the vertical border mapping the multidimensional interval closed formed of other dimensions;

P ₁be expressed as the some O in multidimensional interval and P place straight line and Fr (S ₁) intersection point;

D (P, P ₁) be expressed as a P and put P ₁linear range;

(3) the multidimensional correlation function, based on low-carbon (LC) design builds

Suppose the interval X of existence two ₀=< a, b >, X=< c, d >, and the geometric center in space overlaps with input multi-Dimensional parameters optimal value O, then multidimensional correlation function can be expressed as:

$K_{n-D}\left(P\right)=\left\{\begin{array}{cc}\frac{\left|{\mathrm{PP}}_2\right|}{|P_1{P}_2},& {\mathrm{\&rho;}}_{n-D}(P,S_2)\&NotEqual;{\mathrm{\&rho;}}_{n-D}(P,S_1)\&cap;P\&Element;S_2\\ -\frac{\left|{\mathrm{PP}}_2\right|}{\left|P_1{P}_2\right|},& {\mathrm{\&rho;}}_{n-D}(P,S_2)\&NotEqual;{\mathrm{\&rho;}}_{n-D}(P,S_1)\&cap;P\&Element;R-S_2\\ \left|{\mathrm{PP}}_1\right|+1,& {\mathrm{\&rho;}}_{n-D}(P,S_2)={\mathrm{\&rho;}}_{n-D}(P,S_1)\&cap;P\&Element;S_1\\ \left|{\mathrm{PP}}_2\right|,& {\mathrm{\&rho;}}_{n-D}(P,S_2)={\mathrm{\&rho;}}_{n-D}(P,S_1)\&cap;P\&Element;S_2-S_1\\ -\left|{\mathrm{PP}}_2\right|,& {\mathrm{\&rho;}}_{n-D}(P,S_2)={\mathrm{\&rho;}}_{n-D}(P,S_1)\&cap;P\&Element;R-S_2\\ \min d(x_0,\mathrm{Fr}\left(S_1\right)),& P=x_0\end{array}\right.$

Wherein S ₂for product design requires multidimensional property space, $S_2=(\mathrm{\&Delta;}{x}_1^{1^{\&prime;}},\mathrm{\&Delta;}{x}_2^{2^{\&prime;}},...,\mathrm{\&Delta;}{x}_m^{m^{\&prime;}}),\mathrm{\&Delta;}{x}_j^{j^{\&prime;}}\&GreaterEqual;\mathrm{\&Delta;}{x}_j^j.$

(4), based on the low-carbon (LC) case similarity searching algorithm of multidimensional correlation function

For the primacy analysis under current environment, as energy-saving and emission-reduction, low-carbon (LC), green etc. have been transformed into particular/special requirement by General Requirements to the constraint of product, therefore in this case, grading search process must be done to product demand.Its multilevel retrieval mechanism is as shown in Figure 2:

Low-carbon (LC) and cost needs extraction are carried out to product demand, first both is done to the one-level retrieval of two dimension, determine in low-carbon (LC) and cost to have a product example mated at least, as the example source of 2-level search, such object is that unnecessary data calculate in order to reduce, the output of null result, highlight the importance of low-carbon (LC) design; Input product performance requirement again, does the 2-level search of multidimensional data, calculates the Similarity value based on multidimensional correlation function, and example source is divided into again the full up foot of product performance demands and these two example domains of the not full up foot of product performance demands; Finally input multidimensional product component demand, again divide the low-carbon (LC) example domains on upper strata, output products parts demand coupling and unmatched product example collection.

Similarity retrieval algorithm based on multidimensional correlation function can be expressed as:

The first step: judge product demand type, determines product demand point value and conversion acquisition demand interval value.

Second step: build multidimensional Classical field space S according to product demand interval value ₁with multidimensional extension range space S ₂.

3rd step: combination product instance properties point P _twith optimum point x ₀, build straight line l _oPwith n-D dimension space.

4th step: according to putting P _tsolving equation provides P _taffiliated area.

5th step: dimensionality reduction calculating K _n-D(P _t).

6th step: judge K _n-D(P _t), calculate sim (PR _i, P _t).

7th step: the sim (PR recording this product example retrieval rank _i, P _t).

8th step: terminate.

Calculating formula of similarity wherein at different levels is:

The similarity of level retrieval is: ${\mathrm{sim}}_{i,t}^1({\mathrm{PR}}_i,P_t)=\left\{\begin{array}{cc}1,& K_{m_1-D}\left(P_t\right)\&GreaterEqual;0\\ e^{K_{m_1-D}\left(P_t\right)},& K_{m_1-D}\left(P_t\right)<0\end{array}\right.;$

The similarity of 2-level search is: ${\mathrm{sim}}_{i,t}^2({\mathrm{PR}}_i,P_t)=\left\{\begin{array}{cc}1,& K_{m_2-D}\left(P_t\right)\&GreaterEqual;0\\ e^{K_{m_2-D}\left(P_t\right)},& K_{m_2-D}\left(P_t\right)<0\end{array}\right.;$

The similarity of three－stagesearch is: ${\mathrm{sim}}_{i,t}^3({\mathrm{PR}}_i,P_t)=1-\underset{l=1}{\overset{n-m_1-m_2}{\mathrm{\&Sigma;}}}{d}_l({\mathrm{PR}}_i^l,P_i^l);$

Then, product demand and product example similarity are:

${\mathrm{sim}}_{i,t}({\mathrm{PR}}_i,P_t)=\underset{j=1}{\overset{3}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_j{\mathrm{sim}}_i^j({\mathrm{PR}}_i,P_t)$

In the present embodiment, case-base reasoning has significant effect for the degree of reusing promoting design knowledge.By the retrieval to product example storehouse, match the example or maximal phase seemingly product example that meet product parameters demand, utilize similar case structure and do not meet product parameters analysis, find out the relevance of product parameters and product module, structure, by to design activities such as the knowledge reuse between module or structure, principle improvement, structure innovations, realize the whole of product parameters and meet.

Now for part screw air compressor case library, as following table 1:

The some parameter data of table 1 part screw air compressor example

Suppose that the screw air compressor low-carbon (LC) demand basic-element model of jth time is:

Choose these 6 the screw machine low-carbon (LC) demand characteristics listed ( with ) as research parameters input, according to multilevel retrieval mechanism flow process, known: with for the feature of one-level retrieval; with for 2-level search feature; And in this demand, do not comprise the retrieval character of the third level.Then, corresponding solution procedure is as follows:

1) the screw machine example source acquisition process under one-level search mechanism

with these three one-level retrieval characters, screw air compressor example in associative list 4 and the character of multidimensional correlation function, known, under this state, the maximal value of valid dimension is 3, minimum value is 1, according to the search rule that screw air compressor example source generates, therefore, as long as calculate valid dimension (to comprise: a characteristic parameter meets (2 for having at least a characteristic parameter to meet,-), two characteristic parameters meet (1,-) and three characteristic parameters all meet the screw air compressor example multidimensional correlation function value of (3 ,+).

According to these three demand characteristics, interval and characteristic parameter is expected, determine corresponding to these three features optimal value, calculate optimal value in conjunction with normal distribution and be respectively: $x_0^{j,4}=45800,x_0^{j,n_j-1}=148361.5$ And $x_0^{j,n_j}=18895.7;$ Each characteristic parameter subspace forming extension range space is respectively: $S_1^{j,4}=\left[\mathrm{28600,63000}\right],S_1^{j,n_j-1}=\left[\mathrm{136723,160000}\right]$ With apply the similar to search algorithm based on multidimensional correlation function, then corresponding multidimensional correlation function calculates, retrieval calculates and example source (CASE1) obtains result as shown in the 1-4 row in table 2, n-D|0 and K in table _n-D| the valid dimension during the 0 example source acquisition process being expressed as Case-based Reasoning storehouse calculates and the computing of multidimensional correlation function thereof.

2) the screw machine example domains acquisition process under 2-level search mechanism

According to 2-level search feature with and the CASE1 obtained, then, and the max under this state _n-D=3 and min _n-D=1.The search and output flow process in this stage is: first determine this 3 features with optimal value, in conjunction with the normal distribution method of screw machine example aspects, be followed successively by: with determine that the subspace of each structural feature extension range is respectively again, be respectively $S_1^{j,1}=\left[\mathrm{0.9,1.3}\right],S_1^{j,2}=\left[\mathrm{3.8,6.4}\right]$ And

Calculate as long as same in screw machine example source and there is a characteristic parameter satisfied (2,-), two characteristic parameters meet (1,-) and three characteristic parameters all meet (3, +) example, and application is based on the similar to search algorithm of multidimensional correlation function, then this stage multidimensional correlation function calculate, retrieval calculate and example domains (CASE2) obtain result as in table 2 5-7 row shown in, n-D|1 and K in table _n-D| the valid dimension during the 1 example domains acquisition process being expressed as Case-based Reasoning source calculates and the computing of multidimensional correlation function thereof.

3) the screw machine example set acquisition process under three－stagesearch mechanism

Due to PR _jin do not have the 3rd class retrieval demand characteristic, therefore, valid dimension and the multidimensional correlation function value of each screw machine example aspects of this stage are defaulted as 0 and 1 respectively.Visible, the example set (CASE3) that the reasoning of this stage retrieval obtains just equals screw machine example domains (CASE2), and the 7-9 specifically in table 2 arranges, n-D|2 and K in table _n-D| the valid dimension during the 2 example set acquisition processs being expressed as Case-based Reasoning territory calculate and the computing of multidimensional correlation function thereof.

Application screw machine low-carbon (LC) demand and with screw machine case similarity computing formula, the similarity in each stage of COMPREHENSIVE CALCULATING and total demand and case similarity value, as shown in Table 2, final output screw machine example is 20, the existing Similarity Measure exporting the 10# screw machine example SAL37 in example for these 20:

Screw machine demand and the case similarity of one-level retrieval are:

The screw machine demand of 2-level search and case similarity are:

The screw machine demand of three－stagesearch and case similarity are:

Then, total similarity is: sim _{i, 10}(PR _i, P ₁₀) ≈ 0.9305.

As example, the comprehensive similarity value of remaining 19 screw machine example is in last row in table 2.

Screw machine case similarity value from table 2:

1) example 2#JN37-10 and 17#KHE37 meets the characteristic parameter demand of screw machine completely, can directly export; And remaining example at least exists a characteristic parameter and do not meet screw machine low-carbon (LC) demand, suitable conversion can be done, make it all meet to reach example directly to export target.

2) sim _{i, 10}(PR _i, P ₁₀) < 1 screw machine example in, 1,3,6,10 and 13# screw machine there is higher similarity, the operability implementing conversion is easy, easily meets screw machine low-carbon (LC) demand; 5,8,9,12 and 15# screw machine example there is medium similarity, implement conversion operability easier; Remaining 4,7,14,18,19 and 20# screw machine case similarity are lower, and the operability difficulty implementing conversion is comparatively large, particularly 18,19 and 20# screw machine example reach low-carbon (LC) demand by converting there is very large difficulty.

Table 2 is based on the similar to search result of part screw air compressor example.

Claims (2)

1., based on a similar case retrieval method for multidimensional correlation function, it is characterized in that: the method comprises the steps:

(1), towards the side distance of low-carbon (LC) design

Suppose the joint territory X=< c of product attribute, d >, x ₀for the optimum point value of this attribute, then the left side of any point x to interval X is apart from being expressed as:

${\mathrm{\&rho;}}_{\mathrm{Il}}(x,x_0,X)=\left\{\begin{array}{cc}c-x,& x\&Element;(-\&infin;,c]\\ \frac{d-x_0}{{(x_0-c)}^2}{(x-x_0)}^2+x_0-d,& x\&Element;[c,x_0]\mathrm{and}{x}_0\&NotEqual;c\\ \frac{4(d-x_0)}{{(2x_0-c-d)}^2}{(x-x_0)}^2+x_0-d,& x\&Element;[x_0,\frac{2x_0+c+d}{4}]\mathrm{and}{x}_0\&NotEqual;\mathrm{cand}{x}_0\&NotEqual;\frac{c+d}{2}\\ \frac{12(x_0-d)}{{(3d-2x_0-c)}^2}{(x-d)}^2,& x\&Element;[\frac{2x_0+c+d}{4},d]\mathrm{and}{x}_0\&NotEqual;c\\ x-d,& x\&Element;[d,+\&infin;)\\ -{(x-d)}^2,& x\&Element;[c,d]\&Element;\left[\mathrm{0,1}\right]\mathrm{and}{x}_0=c\\ \frac{1}{{(x-d)}^2}& x\&Element;[c,d]\mathrm{andd}\&Element;[1,+\&infin;]\mathrm{and}{x}_0=c\end{array}\right.$

Right side apart from formula is:

${\mathrm{\&rho;}}_{\mathrm{Ir}}(x,x_0,X)=\left\{\begin{array}{cc}c-x,& x\&Element;(-\&infin;,c]\\ \frac{12(c-x_0)}{{(2x_0-3c+d)}^2}{(x-c)}^2,& x\&Element;[c,\frac{2x_0+c+d}{4}]\mathrm{and}{x}_0\&NotEqual;d\\ \frac{4(x_0-c)}{{(c+d-2x_0)}^2}{(x-x_0)}^2+{c-x}_0,& x\&Element;[\frac{2x_0+c+d}{4},x_0]\mathrm{and}{x}_0\&NotEqual;\mathrm{dand}{x}_0\&NotEqual;\frac{c+d}{2}\\ \frac{x_0-c}{{(d-x_0)}^2}{(x-x_0)}^2+c-x_0,& x\&Element;[x_0,d]\mathrm{and}{x}_0\&NotEqual;d\\ x-d,& x\&Element;[d,+\&infin;)\\ -{(x-c)}^2,& x\&Element;[c,d]\&Element;\left[\mathrm{0,1}\right]\mathrm{and}{x}_0=d\\ \frac{1}{{(x-c)}^2}& x\&Element;[c,d]\mathrm{andd}\&Element;[1,+\&infin;]\mathrm{and}{x}_0=d\end{array}\right.$

When $x_0=\frac{c+d}{2}$ Time, curve minimum point is ${\mathrm{\&rho;}}_{\mathrm{Il}}(x,x_0,X)=\frac{c-d}{2};$ When $x_0\&RightArrow;\frac{c+d}{2}$ In approach procedure, left side distance curve, right side distance curve are respectively at interval [c, x ₀], [x ₀, d] on concaved, its formula is:

${\mathrm{\&rho;}}_I(x,x_0,X)=\left\{\begin{array}{c}{\mathrm{\&rho;}}_{\mathrm{Il}}(x,x_0,X)=-{(x-c)}^2\\ {\mathrm{\&rho;}}_{\mathrm{Ir}}(x,x_0,X)=-{(x-d)}^2\end{array}\right.$

(2) the three-dimensional side distance, based on low-carbon (LC) example builds

Postulated point P falls within a certain region of n-dimensional space, crosses the straight line l of optimum point O and some P _oPthe frame intersection point tieing up enclosure space with n is P ₁and P ₂, it is known, and then n dimension right side is apart from being expressed as:

$\begin{array}{c}{\mathrm{\&rho;}}_{3-D}^{\mathrm{Ir}}(P,O,S_1)=\\ \left\{\begin{array}{cc}d(P_1,P),& P_1\&Element;\left|\mathrm{OP}\right|,O\&NotEqual;\mathrm{Fr}\left(S_1\right),P\&Element;l_{\mathrm{OP}}\\ d(P_2,P),& P_2\&Element;\left|\mathrm{OP}\right|,O\&NotEqual;\mathrm{Fr}\left(S_1\right),P\&Element;l_{\mathrm{OP}}\\ \frac{-12d(P_1,O)}{{(2d(P_1,O)+d(P_1,P_2))}^2}{\left[d(P_1,P)\right]}^2,& P\&Element;[P_1,\frac{2O+P_1+P_1}{4}],O\&NotEqual;\mathrm{Fr}\left(S_1\right),O\&NotEqual;\frac{P_1+P_2}{2}\\ \frac{4d(P_1,O)}{{(d(P_1,O)+d(O,P_2))}^2}{\left[d(O,P)\right]}^2-d(P_1,O),& P\&Element;[\frac{2O+P_1+P_2}{4},O],O\&NotEqual;\mathrm{Fr}\left(S_1\right),O\&NotEqual;\frac{P_1+P_2}{2}\\ \frac{d(P_1,O)}{{\left[d(O,P_2)\right]}^2}{\left[d(O,P)\right]}^2-d(P_1,O),& P\&Element;[O,P_2],O\&NotEqual;\mathrm{Fr}\left(S_1\right),O\&NotEqual;\frac{P_1+P_2}{2}\\ -{\left[d(P_1,P)\right]}^2,& P\&Element;[P_1,P_2]\&Element;[0,e],O=\mathrm{Fr}\left(S_1\right)\\ -\frac{1}{{\left[d(P_1,P)\right]}^2},& P\&Element;[P_1,P_2]\&cup;P_2\&Element;[e,+\&infin;],O=\mathrm{Fr}\left(S_1\right),P\&NotEqual;O\\ -d(O,P_2),& P=[P_1,P_2],O=\frac{P_1+P_2}{2},P\&NotEqual;O\\ -d(O,P_1),& P=O\end{array}\right.\end{array}$

Wherein:

S ₁the multidimensional being expressed as an actual product demand is interval, namely be expressed as the length of i-th dimension;

Fr (S ₁) be expressed as the length end points of each dimension to the vertical border mapping the multidimensional interval closed formed of other dimensions;

P ₁be expressed as the some O in multidimensional interval and P place straight line and Fr (S ₁) intersection point;

D (P, P ₁) be expressed as a P and put P ₁linear range;

(3) the multidimensional correlation function, based on low-carbon (LC) design builds

Suppose the interval X of existence two ₀=< a, b >, X=< c, d >, and the geometric center in space overlaps with input multi-Dimensional parameters optimal value O, then multidimensional correlation function is expressed as:

$K_{n-D}\left(P\right)=\left\{\begin{array}{cc}\frac{\left|P{P}_2\right|}{\left|P_1{P}_2\right|},& {\mathrm{\&rho;}}_{n-D}(P,S_2)\&NotEqual;{\mathrm{\&rho;}}_{n-D}(P,S_1)\&cap;P\&Element;S_2\\ -\frac{\left|P{P}_1\right|}{\left|P_1{P}_2\right|},& {\mathrm{\&rho;}}_{n-D}(P,S_2)\&NotEqual;{\mathrm{\&rho;}}_{n-D}(P,S_1)\&cap;P\&Element;R-S_2\\ \left|P{P}_1\right|+1,& {\mathrm{\&rho;}}_{n-D}(P,S_2)={\mathrm{\&rho;}}_{n-D}(P,S_1)\&cap;P\&Element;S_1\\ \left|P{P}_2\right|,& {\mathrm{\&rho;}}_{n-D}(P,S_2)={\mathrm{\&rho;}}_{n-D}(P,S_1)\&cap;P\&Element;S_2-S_1\\ -\left|P{P}_2\right|,& {\mathrm{\&rho;}}_{n-D}(P,S_2)={\mathrm{\&rho;}}_{n-D}(P,S_1)\&cap;P\&Element;R-S_2\\ \min d(x_0,\mathrm{Fr}\left(S_1\right)),& P=x_0\end{array}\right.$

Wherein S ₂for product design requires multidimensional property space,

(4) the low-carbon (LC) case similarity, based on multidimensional correlation function is retrieved

Low-carbon (LC) and cost needs extraction are carried out to product demand, first both is done to the one-level retrieval of two dimension, determine in low-carbon (LC) and cost to have a product example mated at least, as the example source of 2-level search, such object is that unnecessary data calculate in order to reduce, the output of null result, highlight the importance of low-carbon (LC) design; Input product performance requirement again, does the 2-level search of multidimensional data, calculates the Similarity value based on multidimensional correlation function, and example source is divided into again the full up foot of product performance demands and these two example domains of the not full up foot of product performance demands; Finally input multidimensional product component demand, again divide the low-carbon (LC) example domains on upper strata, output products parts demand coupling and unmatched product example collection;

The similarity of one-level retrieval is: ${\mathrm{sim}}_{i,t}^1(P{R}_i,P_t)=\left\{\begin{array}{cc}1,& K_{m_1-D}\left(P_t\right)\&GreaterEqual;0\\ e^{K_{m_1-D}\left(P_t\right)},& K_{m_1-D}\left(P_t\right)<0\end{array}\right.;$

The similarity of 2-level search is: ${\mathrm{sim}}_{i,t}^2(P{R}_i,P_t)=\left\{\begin{array}{cc}1,& K_{m_2-D}\left(P_t\right)\&GreaterEqual;0\\ e^{K_{m_2-D}\left(P_t\right)},& K_{m_2-D}\left(P_t\right)<0\end{array}\right.;$

The similarity of three－stagesearch is: ${\mathrm{sim}}_{i,t}^3(P{R}_i,P_t)=1-\underset{l=1}{\overset{n-m_1-m_2}{\mathrm{\&Sigma;}}}{d}_l(P{R}_i^l,P_i^l);$

Then, product demand and product example similarity are:

${\mathrm{sim}}_{i,t}(P{R}_i,P_t)=\underset{j=1}{\overset{3}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_j{\mathrm{sim}}_i^j(P{R}_i,P_t).$

2. a kind of similar case retrieval method based on multidimensional correlation function as claimed in claim 1, it is characterized in that: in described step (4), the process based on the similarity retrieval method of multidimensional correlation function is as follows:

The first step: judge product demand type, determines product demand point value and conversion acquisition demand interval value;

Second step: build multidimensional Classical field space S according to product demand interval value ₁with multidimensional extension range space S ₂;

3rd step: combination product instance properties point P _twith optimum point x ₀, build straight line l _oPwith n-D dimension space;

4th step: according to putting P _tsolving equation provides P _taffiliated area;

5th step: dimensionality reduction calculating K _n-D(P _t);

6th step: judge K _n-D(P _t), calculate sim (PR _i, P _t);

7th step: the sim (PR recording this product example retrieval rank _i, P _t);

8th step: terminate.