CN107609252A - A kind of hysteresis curve goodness of fit quantization method based on character pair point spacing - Google Patents

A kind of hysteresis curve goodness of fit quantization method based on character pair point spacing Download PDF

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CN107609252A
CN107609252A CN201710797552.3A CN201710797552A CN107609252A CN 107609252 A CN107609252 A CN 107609252A CN 201710797552 A CN201710797552 A CN 201710797552A CN 107609252 A CN107609252 A CN 107609252A
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mrow
msup
point
loop line
hysteresis curve
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鲁海亮
陈怀飞
蓝磊
文习山
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Wuhan University WHU
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Wuhan University WHU
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Abstract

It is that loop line overall length L is calculated by line integral the present invention relates to a kind of hysteresis curve goodness of fit quantization method based on character pair point spacing, starting point is made with an end points of loop line, it is point-by-point to carry out line integral, find all N number of characteristic points, apart from sum D between hysteresis curve characteristic point known to calculating and emulation loop line character pair point, the transverse and longitudinal coordinate scope of hysteresis curve is set to take quantizating index of the evaluation function f as the hysteresis curve goodness of fit between [1,1] by normalized.Have the advantages that：(1) the hysteresis curve goodness of fit quantizating index based on character pair point spacing is proposed, evaluation function f function value is non-negative, and when emulating loop line and known loop line and being completely superposed, f has maximum(2) normalized is solved in the calculating of loop line line integral, the length on H directions account for it is leading, cause equidistant points on loop line turn into the contribution of point equidistant on H directions and the distance on H directions to result much larger than on B directions apart from the problem of.

Description

A kind of hysteresis curve goodness of fit quantization method based on character pair point spacing
Technical field
The invention belongs to electrical engineering technical field, and in particular to a kind of hysteresis curve kiss based on character pair point spacing Right quantization method.
Background technology
JA models can preferably describe hysteresis, but its model is complex, by the different values of 5 parameters To distinguish the different hysteresis characteristics that different materials have.5 parameters of JA models determine the shape of hysteresis curve, different iron Magnetic material has different hysteresis curves, and the parameter for corresponding to JA models is different.Because 5 parameters of model are to hysteresis curve shape The influence part of shape is had any different, and is related again, is intercoupled between each parameter so that the determination of parameter is extremely difficult.
In the optimization of JA model parameters, the quality of one group of parameter be decided by hysteresis curve corresponding to this group of parameter with it is known " identical " degree of hysteresis curve, it is in the calculation using " identical " degree, it is necessary to quantify to it.Two groups of hysteresis curves " identical " is better, it is meant that " distance " is smaller between them, and based on this, the present invention is proposed with N number of point equidistant on hysteresis curve As " characteristic point " of loop line, retouched by character pair point between computer sim- ulation hysteresis curve and known hysteresis curve apart from sum The method for stating degree of agreement.
The content of the invention
The technical problem to be solved in the present invention is that equidistant N number of point leads to as " characteristic point " of loop line using on hysteresis curve Cross and calculate character pair point apart from sum to describe the method for emulating hysteresis curve and known hysteresis curve degree of agreement.
The present invention technical solution be：
A kind of hysteresis curve goodness of fit quantization method based on character pair point spacing, it is characterised in that including：
Step 1, by line integral calculate loop line overall length L, starting point is made with an end points of loop line, i.e. the 1st characteristic point, by Line integration is clicked through, when integration lengths corresponding to certain point i are more than L/N, note i points are the 2nd characteristic point；The rest may be inferred, when certain When integration lengths are more than nL/N corresponding to point j, note j points are (n+1)th characteristic point, until finding all N number of characteristic points, are write down each Coordinate (the H of pointm,Bm), m=1,2 ... N, Hm、BmIt is the abscissa and ordinate for emulating hysteresis curve characteristic point respectively；Calculate Know hysteresis curve characteristic point (H0 m,B0 m) (the H between emulation loop line character pair pointm,Bm) apart from sum：
H0 m、B0 mIt is the abscissa and ordinate of known hysteresis curve characteristic point respectively, the goodness of fit is got between two hysteresis curves Height, corresponding D values are smaller；
Step 2, H and B is normalized respectively, will two groups of H and B difference divided by corresponding maximum Hmax、 Bmax：
Step 3, line integral is carried out to the loop line after processing, and ask for key point, calculate loop line space D；In view of passing through After normalized, the transverse and longitudinal coordinate scope of hysteresis curve is between [- 1,1], so in shown planar range, any two Point the distance between maximum beNow evaluation function f function value is non-negative, and emulates loop line and known loop line When being completely superposed, f obtains maximum
It is right in a kind of above-mentioned hysteresis curve goodness of fit quantization method based on character pair point spacing, the step 2 For ferromagnetic material, numerically H is often bigger than B, B spans within (- 2,2) T, and H scopes can exceed (- 100, 100)A/m；So on the one hand in the calculating of loop line line integral, the length on H directions accounts for leading, causes equidistant points on loop line to turn into Equidistant point on H directions, as shown in Figure 1；In another aspect loop line distance computation result D, H componentsIt is often remote More than B componentContribution of the distance to result i.e. on H directions is much larger than the distance on B directions；Asked to solve this Topic, before line integral calculating is carried out to hysteresis curve, first H and B can be normalized respectively, will be two groups H and B points Other divided by corresponding maximum Hmax、Bmax：
Hmax=max (H0,H),Bmax=max (B0,B)
It is right in a kind of above-mentioned hysteresis curve goodness of fit quantization method based on character pair point spacing, the step 3 Loop line after processing carries out line integral, and asks for key point, calculates the specific method of loop line space D and is：
In view of after normalized, the transverse and longitudinal coordinate scope of hysteresis curve is between [- 1,1], so in institute Show in planar range, the distance between any two points maximum isThe evaluation function f is taken to be
Evaluation function value is non-negative, and when emulating loop line and known loop line and being completely superposed, f obtains maximum
The technological core of the present invention is to calculate loop line overall length L by line integral, makees starting point with an end points of loop line, point by point Line integral is carried out, finds all N number of characteristic points, distance between hysteresis curve characteristic point known to calculating and emulation loop line character pair point Sum D, the transverse and longitudinal coordinate scope of hysteresis curve is set to take evaluation function f as magnetic between [- 1,1] by normalized The quantizating index of the hysteresis curves goodness of fit.
The beneficial effects of the invention are as follows：(1) the identical metrization of the hysteresis curve based on character pair point spacing is proposed to refer to Mark, evaluation function f function value is non-negative, and emulates loop line and when known loop line is completely superposed, f has maximum(2) Normalized is solved in the calculating of loop line line integral, and the length on H directions accounts for leading, causes equidistant points on loop line to turn into H side Upwards the contribution of equidistant point and the distance on H directions to result much larger than on B directions apart from the problem of.
Brief description of the drawings
Fig. 1 is original hysteresis curve.
Fig. 2 is normalization hysteresis curve.
Embodiment
Loop line overall length L is calculated by line integral, starting point is made with an end points of loop line, i.e. the 1st characteristic point, it is point-by-point to carry out Line integral, when integration lengths corresponding to certain point i are more than L/N, note i points are the 2nd characteristic point；The rest may be inferred, when certain point j is corresponding Integration lengths when being more than nL/N, note j points be (n+1)th characteristic point, until finding the N number of characteristic points of whole, write down the seat of each point Mark (Hm,Bm), m=1,2 ... N, Hm、BmIt is the abscissa and ordinate for emulating hysteresis curve characteristic point respectively.Magnetic hysteresis known to calculating Loop line characteristic point (H0 m,B0 m) (the H between emulation loop line character pair pointm,Bm) apart from sum：
H0 m、B0 mIt is the abscissa and ordinate of known hysteresis curve characteristic point respectively, the goodness of fit is got between two hysteresis curves Height, corresponding D values are smaller.
For most ferromagnetic materials, numerically H is often more much bigger than B, and general B spans are in (- 2,2) Within T, and H scopes can exceed (- 100,100) A/m.So on the one hand in the calculating of loop line line integral, the length on H directions accounts for It is leading, cause equidistant points on loop line to turn into point equidistant on H directions, as shown in Figure 1；Another aspect loop line distance computation result In D, H componentsOften it is much larger than B componentContribution of the distance to result i.e. on H directions is much larger than Distance on B directions.To solve this problem, before line integral calculating is carried out to hysteresis curve, first H and B can be carried out respectively Normalized, will two groups of H and B difference divided by corresponding maximum Hmax、Bmax：
Hmax=max (H0,H),Bmax=max (B0,B)
Line integral is carried out to the loop line after processing again, and asks for key point, as shown in Figure 2, calculates loop line space D.
Select probability is determined on the basis of individual fitness sequence, it is desirable to which calculating the evaluation function of adaptive value has following property Matter：
1. functional value is non-negative
2. optimal solution corresponds to maximum
In view of after normalized, the transverse and longitudinal coordinate scope of hysteresis curve is between [- 1,1], so in institute Show in planar range, the distance between any two points maximum isThe evaluation function f is taken to be
Evaluation function value is non-negative, and when emulating loop line and known loop line and being completely superposed, f obtains maximum

Claims (3)

  1. A kind of 1. hysteresis curve goodness of fit quantization method based on character pair point spacing, it is characterised in that including：
    Step 1, by line integral calculate loop line overall length L, starting point is made with an end points of loop line, i.e. the 1st characteristic point, entered point by point Line integrates, and when integration lengths corresponding to certain point i are more than L/N, note i points are the 2nd characteristic point；The rest may be inferred, when certain j pairs of point When the integration lengths answered are more than nL/N, note j points are (n+1)th characteristic point, until finding all N number of characteristic points, write down each point Coordinate (Hm,Bm), m=1,2 ... N, Hm、BmIt is the abscissa and ordinate for emulating hysteresis curve characteristic point respectively；Magnetic known to calculating Hysteresis line feature point (H0 m,B0 m) (the H between emulation loop line character pair pointm,Bm) apart from sum：
    <mrow> <mi>D</mi> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>m</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <msubsup> <mi>H</mi> <mn>0</mn> <mi>m</mi> </msubsup> <mo>-</mo> <msup> <mi>H</mi> <mi>m</mi> </msup> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msubsup> <mi>B</mi> <mn>0</mn> <mi>m</mi> </msubsup> <mo>-</mo> <msup> <mi>B</mi> <mi>m</mi> </msup> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mrow>
    H0 m、B0 mIt is the abscissa and ordinate of known hysteresis curve characteristic point respectively, the goodness of fit is higher between two hysteresis curves, right Answer D values smaller；
    Step 2, H and B is normalized respectively, will two groups of H and B difference divided by corresponding maximum Hmax、Bmax：
    Step 3, line integral is carried out to the loop line after processing, and ask for key point, calculate loop line space D；In view of by normalizing Change processing after, the transverse and longitudinal coordinate scope of hysteresis curve is between [- 1,1], so in shown planar range, any two points it Between be apart from maximumNow evaluation function f function value is non-negative, and emulates loop line and known loop line is complete During coincidence, f obtains maximum
  2. 2. a kind of hysteresis curve goodness of fit quantization method based on character pair point spacing according to claim 1, it is special Sign is, in the step 2, for ferromagnetic material, numerically H is often bigger than B, B spans (- 2,2) T with It is interior, and H scopes can exceed (- 100,100) A/m；So on the one hand in the calculating of loop line line integral, the length on H directions accounts for master Lead, cause equidistant points on loop line to turn into point equidistant on H directions, as shown in Figure 1；Another aspect loop line distance computation result D In, H componentsOften it is much larger than B componentContribution of the distance to result i.e. on H directions is much larger than B Distance on direction；To solve this problem, before line integral calculating is carried out to hysteresis curve, first H and B can be returned respectively One change is handled, will two groups of H and B difference divided by corresponding maximum Hmax、Bmax：
    Hmax=max (H0,H),Bmax=max (B0,B)
    <mrow> <msubsup> <mi>h</mi> <mn>0</mn> <mi>m</mi> </msubsup> <mo>=</mo> <mfrac> <msubsup> <mi>H</mi> <mn>0</mn> <mi>m</mi> </msubsup> <msub> <mi>H</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </mfrac> <mo>,</mo> <msubsup> <mi>b</mi> <mn>0</mn> <mi>m</mi> </msubsup> <mo>=</mo> <mfrac> <msubsup> <mi>B</mi> <mn>0</mn> <mi>m</mi> </msubsup> <msub> <mi>B</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </mfrac> <mo>,</mo> <mi>m</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mi>N</mi> </mrow>
    <mrow> <msup> <mi>h</mi> <mi>m</mi> </msup> <mo>=</mo> <mfrac> <msup> <mi>H</mi> <mi>m</mi> </msup> <msub> <mi>H</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </mfrac> <mo>,</mo> <msup> <mi>b</mi> <mi>m</mi> </msup> <mo>=</mo> <mfrac> <msup> <mi>B</mi> <mi>m</mi> </msup> <msub> <mi>B</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </mfrac> <mo>,</mo> <mi>m</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mi>N</mi> <mo>.</mo> </mrow>
  3. 3. a kind of hysteresis curve goodness of fit quantization method based on character pair point spacing according to claim 1, it is special Sign is, in the step 3, line integral is carried out to the loop line after processing, and asks for key point, calculates the specific of loop line space D Method is：
    In view of after normalized, the transverse and longitudinal coordinate scope of hysteresis curve is between [- 1,1], so shown flat In the range of face, the distance between any two points maximum isThe evaluation function f is taken to be
    <mrow> <mi>f</mi> <mo>=</mo> <mi>N</mi> <mo>&amp;times;</mo> <mn>2</mn> <msqrt> <mn>2</mn> </msqrt> <mo>-</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>m</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <msubsup> <mi>h</mi> <mn>0</mn> <mi>m</mi> </msubsup> <mo>-</mo> <msup> <mi>h</mi> <mi>m</mi> </msup> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msubsup> <mi>b</mi> <mn>0</mn> <mi>m</mi> </msubsup> <mo>-</mo> <msup> <mi>b</mi> <mi>m</mi> </msup> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mrow>
    Evaluation function value is non-negative, and when emulating loop line and known loop line and being completely superposed, f obtains maximum
CN201710797552.3A 2017-09-06 2017-09-06 A kind of hysteresis curve goodness of fit quantization method based on character pair point spacing Withdrawn CN107609252A (en)

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Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102916421A (en) * 2012-10-22 2013-02-06 深圳供电局有限公司 Transformer protection mechanism
US8483019B2 (en) * 2010-03-01 2013-07-09 Esfir Z. Katsnelson Magneto-optical device with an optically induced magnetization
CN107122518A (en) * 2017-03-23 2017-09-01 中国人民解放军海军工程大学 Magnetic field method for measuring similarity

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US8483019B2 (en) * 2010-03-01 2013-07-09 Esfir Z. Katsnelson Magneto-optical device with an optically induced magnetization
CN102916421A (en) * 2012-10-22 2013-02-06 深圳供电局有限公司 Transformer protection mechanism
CN107122518A (en) * 2017-03-23 2017-09-01 中国人民解放军海军工程大学 Magnetic field method for measuring similarity

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
鲁海亮等: "A self-adaptive genetic algorithm to estimate JA model parameters considering minor loops", 《JOURNAL OF MAGNETISM AND MAGNETIC MATERIALS》 *

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