CN1912539A - Method for precision measuring width of paper money - Google Patents

Abstract

A method for accurately detecting width of paper money includes using left and right infrared counting tubes to record infrared sensing signal and simultaneously using a pair of infrared transducers to collect infrared signal on evenly divided code wheel in the same center with rotation shaft to record synchronous code wheel number, obtaining value of four character points of paper money by calculating number of code wheel, using mathematic model to derive out an algebraic formula being used to calculate out width of various paper money accurately.

Description

Method for precision measuring width of paper money

1. technical field:

The present invention relates to a kind of accurate detecting method of width of paper money, particularly relate to the width of paper money detection method that becomes the angle of inclination with traffic direction in pick-up unit.

2. background technology:

In the paper money counter system, the calculated relationship of banknote width to accurate differentiation and half of bank note, the paper slip of the width of paper money of various nominal values, connect open, residual accurate differentiation.Therefore width of paper money detects and distinguishes in the identification very important at the bank note denomination.Cross in the paper money in reality, if bank note is that the value of four unique points of two pairs of infrared counter collections directly drew about the calculating of its width value can simply be used when passing through paper money counter with the detection traffic direction is nonangular; But all can pass through the left and right sides infrared counter of paper money counter in the banknote major part with inclination to a certain degree.The detection of the width of paper money that adopts at present all is the data of gathering number of characteristics point, rule of thumb data creating becomes numerical table, when realizing, program use the mode of tabling look-up that form is traveled through, adopt the mode of coupling, with the measured value table of logarithm of four unique points coupling of tabling look-up, draw the width of bank note.Because paper money counter electromechanics and sensor-based system parameter change, currency examine personnel's currency examine custom differs, the variation of surrounding environment humiture, paper money counter or checkout equipment system difference etc., the numerical table that is made into by empirical data often needs alignment; For the upgrading of paper money counter, the width form of making at a kind of paper money counter type is a thing that workload is bigger, and the accurate judgement of width that draws and actual banknote also is difficult to be guaranteed.

3. summary of the invention:

Technical matters to be solved by this invention provides a kind of method that width of paper money accurately can be detected.

By single-chip microcomputer handle by sensor acquisition to Renminbi or the spectral signal of other Currency Types, by bank note being twisted with the fingers the mathematics model analysis of paper money process, utilize the equal proportion character of the computational geometry of inclination bank note, adopt polynomial expression to approach, Pade approaches, least square approximation and non-linear optimized Algorithm work out an algebraic formula, this algebraic formula accurately approaches the width of paper money value of the run-off the straight of twisting with the fingers the paper money process.

Respectively the code-disc of the concentric branch hollow outs such as quilt of bank note and counting shaft is shone with the infrared light point source, use the sensor acquisition spectral signal, draw the absolute encoder value of four unique points that left and right sides counter tube collects, send single-chip microcomputer to, detect secund half coin earlier by rudimentary algorithm, then other data are stored.Transmit the data of entire paper coin at sensor after, again the data of storage are handled.Earlier the data of storage are classified during width algorithm in design,, again the data of detected four unique points are judged that simply the back uses algebraic formula calculating for satisfying half, paper slip, connecting and open and processings of reporting to the police of residual bank note or counterfeit money.Along with the growth of the term of life of paper money counter, the speed of motor can be slack-off, so adopt timer to count the method for measuring width of paper money, width value that calculates after machine ages and developed width value have bigger error.Physical characteristics according to paper money counter itself: the girth of counting shaft is fixed in paper money counter type of the same race; The value of left and right sides counter tube spacing is in the error range of being strict with below millimeter; On the code-disc lattice number of equidistant hollow out be certain and code-disc concentric with counting shaft, therefore the amplitude of the bank note that ground of counting shaft be with code-disc on the code-disc value that collects be fully one to one, so value and the code-disc value of bank note by resulting four unique points of left and right sides infrared counter also is one to one.The distance of actual bank note by left and right sides counter tube is that the value with two unique points of coming in and going out of the right and left is proportional fully.Still utilize the physical characteristics of machine, come the value of real-time tolerance bank note unique point with the code-disc value, adopt equal proportion character and computational geometry, polynomial expression to approach then to approach with Pade, non-linear optimization method and least square approximation algorithm set up mathematical model, draws algebraic expression from Analysis of Mathematical.The width value that algebraic expression is calculated classify handle after, the result passed to needs the false distinguishing of width data function, and passes to operations such as each real-time processing unit control warning, demonstration, motor by transmission line as required.

Described width computational mathematics model be to form like this: according to the physical property of paper money counter machine, the optimum solution that width calculates is preferably utilized the computational geometry character of machine, separates it with approximate algorithm.We know two kinds of main types in approximation of function: pointwise approaches and least square approximation.Be divided into polynomial expression in every type again and approach with Pade and approach (being that the fraction polynomial expression approaches), so just have four kinds of selections that approach.We do not consider that interpolation approaches in this calculates, because its amount of calculation is bigger and whole precision of approaching may not be fine.People's common mathematical function launches to do pointwise at the Taylor of certain point and approaches, but its shortcoming is high excessively in the precision of breaking up point, and greatly reduces away from the precision of breaking up point, is not fit to do numerical evaluation.We launch to formulate numerical table with Taylor, and this numerical table is carried out actual computation, and experimental result has proved our conclusion.

We unite the three kinds of technology of having used here: fraction polynomial expression, optimal approximation, non-linear optimization method.

We consider general fraction polynomial expression earlier

G(x)＝P _m(x)/Q _n(x)，e＝f(x)-G(x).

Here P _m(x)=a ₀+ a ₁X+a ₂x ²+ ... + a _mx ^m, Q _n(x)=1+b ₁X+b ₂x ²+ ... + b _nx ⁿBe respectively m, polynomial of degree n, its coefficient a=(a ₀, a ₁..., a _m) and b=(b, b ₂..., b _n) be undetermined, total m+n+1.Be exactly that common polynomial expression approaches when getting n=0.If ρ (x)＞the 0th, interval L=(a, β) the known weight function on (in common situation, people often get ρ=1).We propose the least square approximation problem of cum rights ρ＞0 of function f (x)

$E(a,b)=\frac{1}{2}{\∫}_L\mathrm{\ρ}\left(x\right){(G\left(x\right)-f\left(x\right))}^2\mathrm{dx}=\min ---\left(1\right)$

Function E (a, b) getting minimum necessary condition is that its all single order partial derivatives are zero, they can be divided into two prescription formulas of simultaneous:

$\frac{\mathrm{DE}}{{\mathrm{Da}}_i}={\∫}_L\mathrm{\ρ}(G\left(x\right)-f\left(x\right))Q_n^{-1}\left(x\right)x^i\mathrm{dx}=0,i=\mathrm{0,1,2},...,m;---\left(2\right)$

$\frac{\mathrm{DE}}{{\mathrm{Db}}_j}={\∫}_L\mathrm{\ρ}(f\left(x\right)-G\left(x\right))G\left(x\right)Q_n^{-1}\left(x\right)x^j\mathrm{dx}=0,j=\mathrm{1,2},...,n;---\left(3\right)$

(a b), has promptly obtained required approaching to obtain coefficient from this Simultaneous Equations.

In order to find the solution this system of equations with the Newton method, calculate all second-order partial differential coefficients earlier, they can be divided into three groups as follows

$\frac{D^{2}E}{{\mathrm{Da}}_i{\mathrm{Da}}_j}={\∫}_L\mathrm{\ρ}{Q}_n^{-2}{x}^{i+j}\mathrm{dx},i,j\≤m,$

$\frac{D^{2}E}{{\mathrm{Db}}_l{\mathrm{Db}}_k}={\∫}_L\mathrm{\ρ}(3G-2f){\mathrm{GQ}}_n^{-2}{x}^{l+k}\mathrm{dx},l,k\≤n,$

$\frac{D^{2}E}{{\mathrm{Db}}_i{\mathrm{Db}}_l}={\∫}_L\mathrm{\ρ}(3G-f)Q_n^{-2}{x}^{i+l}\mathrm{dx},i\≤m,l\≤n.$

But (2), (3) are very complicated nonlinear equation groups, have only given better initial after, just can use the process of iteration numerical solution.And obtain a better initial itself is exactly very difficult thing.In order to obtain a good initial value, we can find the solution the problem of simplifying as the next one earlier.Get this power for this reason $\mathrm{\&rho;}={\mathrm{<figure-callout\; id="2"\; label="Q\; n"\; filenames="A20051003199700171.png"\; state="\{\{state\}\}">Q</figure-callout>}}_n^{},$ Former problem (1) just turns to

$E^{*}(a,b)=\frac{1}{2}{\&Integral;}_L{(Q_n\left(x\right)f\left(x\right)-P_m\left(x\right))}^2\mathrm{dx}=\min .---\left(4\right)$

This is common least square problem, and the sufficient and necessary condition of getting minimum value is

$\frac{{\mathrm{DE}}^{\&times;}}{{\mathrm{Da}}_i}={\&Integral;}_L(Q_n\left(x\right)f\left(x\right)-P_n\left(x\right))x^i\mathrm{dx}=0,i=\mathrm{0,1,2},...,m;---\left(5\right)$

$\frac{{\mathrm{DE}}^{*}}{{\mathrm{Db}}_j}={\&Integral;}_L(Q_n\left(x\right)f\left(x\right)-P_m\left(x\right))f\left(x\right)x^j\mathrm{dx}=0,j=\mathrm{1,2},...,n;---\left(6\right)$

Obviously, it is a linear equations group, solves easily with conventional method, therefore can obtain an approximate value (a ⁰, b ⁰), solve the initial value of (1) after, just separating of equation (1) can be asked it.

4. description of drawings:

Fig. 1 is the nonangular planimetric map by paper money counter of bank note;

Fig. 2 is that bank note tilts by the planimetric map of paper money counter;

Fig. 3 is the Error Graph of directly launching with the Taylor formula;

Fig. 4 is the Error Graph of approaching calculating with least square Pade;

Fig. 5 is the process flow diagram that width calculates.

Among Fig. 6,2.-the code-disc sensor, 3.-code-disc

Among Fig. 7,1.-twist with the fingers paper money to take turns, 2.-code-disc, 3.-the code-disc sensor, 4. left infrared counter, 5.-banknote feeding frame, 6.-right infrared counter, 7.-impeller

5. specific implementation method:

Shown in (Fig. 1), be that a banknote does not have and tilts to enter paper money counter, to LSP to LEP and RSP to REP, be respectively about the positions of two infrared counter scannings, whether have the information of paper money to write down the width value on banknote both sides under the infrared counter timing acquiring acquisition counter tube.

Shown in (Fig. 2), be the banknote of an inclination by counter tube.

Be recorded to the distance of LSP to LEP and RSP to REP by timing acquiring left and right sides infrared counter, wherein LSP is that a left side is gone into a little, and LEP is that a left side goes out a little, and RSP is that the right side is gone into a little, and REP is that the right side goes out a little.Cross in the paper money in reality, the banknote major part all can be passed through left and right sides infrared counter with inclination to a certain degree.Therefore the width that calculates oblique paper money fast and accurately is very necessary.

In the design of paper money counter in the past, utilize empirical data to make numerical table, adopt the mode of tabling look-up to obtain in the width value.We remember that the developed width of banknote is L in this process, and the 5th edition Renminbi width used in everyday is: 100 yuan of denomination 77CM, 50 yuan of denomination 70CM, 5 yuan of denomination 63CM; According to the distance of hardware design standard left and right sides infrared counter be 68 (± 0.5) mm. we be that 100 yuan of denomination Renminbi of 77cm are the formula that approaches that example derives width with the width.

Designing requirement is: designed algorithm can calculate the exact value of L fast when calculating, and according to the single-chip microcomputer computing velocity, evolution, number of times is not arranged than higher function and sine and cosine, positive cotangent function in the algorithm.

Because of being measurement unit with the code-disc number, we are converted to the code-disc units to the width value data in counting process.Suppose that machine code-disc one circle is 100 measurement units, a circle 120mm, then to be converted to the code-disc value be 65 to 77mm, 68mm is 57 code-disc units.As (Fig. 1), consider the physical deformation of banknote, the width L=(LEP+REP-LSP-RSP)/2 of banknote, we remember a=(REP-LEP+RSP-LSP)/2 in (Fig. 2), b=(LEP+REP-LSP-RSP)/2, and the inclination angle of banknote is X (0＜x＜60), utilize leg-of-mutton definition and theorem $\mathrm{tgx}=\frac{a}{d},L=b\cos x,$ A here, b, d are known numbers, and a in formula, b are stochastic variables, and d is a definite value.

By sec ²X=1+tan ²X, promptly $\cos x=\frac{1}{\sqrt{1+{\tan }^{2}x}},$ Following formula is then arranged

$L=b\&times;\frac{1}{\sqrt{1+{\tan }^{2}x}},$

1) Taylor expansion, non-linear optimization method calculate and utilize Taylor expansion to get $\cos x\&ap;1-\frac{a^{2^{\&prime;}}}{{2d}^2}$ (we only get two for the calculated amount that reduces single-chip microcomputer).Make t=tanx again, then $L=b*(1-0.5t^2)=b*(1-\frac{a^2}{{2d}^2}),$ According to actual conditions when banknote surpasses the magnetic signal of 45 banknotes when spending can distortion, have a strong impact on the bank note false distinguishing, we consider that this formula can not surpass the situations of 45 degree in the degree of tilt of banknote so, i.e. the situation of t=tgx≤1 o'clock.

The formula angle is a step-length value table (unit: cm) with 2.5 degree thus

Number of degrees x	The value of b	0.5t 2	The approximate value of L	Number of degrees x	The value of b	0.5t 2	The approximate value of L
								5	7.72941	0.00383	7.69981	7.5	7.76644	0.00867	7.69911
10	7.81823	0.01555	7.69667	12.5	7.88695	0.02457	7.69317
								15	7.97163	0.03590	7.68545	17.5	8.07367	0.04971	7.67235
20	8.19417	0.06624	7.65138	22.5	8.33442	0.08579	7.61941
								25	8.49610	0.10872	7.57241	27.5	8.68085	0.13560	7.50377
30	8.89119	0.16667	7.40929	32.5	9.12981	0.20293	7.27710
								35	9.39996	0.24515	7.09556	37.5	9.70564
40	10.05164			42.5	10.4438
								45	10.88945

7.7cm both had been " just " deviation point as can be seen from the above table, was again " bearing " deviation point.Its error is just greater than 0.5cm when the number of degrees are spent greater than 35, the stability that is antiderivative Taylor expansion can not reach actual requirement, in order to obtain better result of calculation, just must revise former expression formula, we use method least square approximation commonly used earlier, and obtaining the best uniform approximating polynomial is polynomial of best approximation.

2) least square approximation algorithm, non-linear optimization method calculate

The coefficient that order requires is β, has again $L/b=\cos x\&ap;1-\frac{a^{2^{\&prime;}}}{{2\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="A20051003199700171.png"\; state="\{\{state\}\}">d</figure-callout>}}^2},$ Then problem is converted into calculating

$\cos x=1-\mathrm{\&beta;}\&times;{\tan }^2{x}_i=1-\mathrm{\&beta;}\&times;{\left(\frac{a}{d}\right)}^2=1-\mathrm{\&beta;}\&times;{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="A20051003199700171.png"\; state="\{\{state\}\}">t</figure-callout>}}^2$

We know cosx _i, tgx _iAll, therefore obtain interpolation knot x in limited area, being continuous and stable function _iThe value of corresponding β also is a continuous and stable value, then can find a reasonably number in limited zone, and (*) formula is set up.Through calculating, can draw the value of a series of β by equation, following numerical table:

x i	cosx i	1-cosx i	tan 2x i	β	x i	cosx i	1-cosx i	tan 2x i	β
										5	0.9962	0.0038	0.0077	0.4935	27.5	0.8870	0.1130	0.2710	0.4170
7.5	0.9915	0.0085	0.0173	0.4913	30	0.8660	0.1340	0.3333	0.4021
										10	0.9848	0.0152	0.0311	0.4887	32.5	0.8434	0.1566	0.4059	0.3858
12.5	0.9763	0.0237	0.0492	0.4817	35	0.8192	0.1808	0.4903	0.3588
										15	0.9659	0.0341	0.0718	0.4749	37.5	0.7934	0.2066	0.5888	0.3509
17.5	0.9537	0.0463	0.0994	0.4658	40	0.7661	0.2339	0.7041	0.3322
										20	0.9397	0.0603	0.1325	0.4551	42.5	0.7373	0.2627	0.8397	0.3128
22.5	0.9239	0.0761	0.1716	0.4435	45	0.7071	0.2929	1.0000	0.2929
										25	0.9063	0.0937	0.2174	0.4310

Press the weights analysis, calculate by matlab $\cos x=1-\mathrm{\&beta;}\&times;{\left(\frac{a}{d}\right)}^2=1-\mathrm{\&beta;}\&times;{\tan }^2{x}_i$ Can get the best stationary point of best, be about-0.33456672828279, and be that 0.5054 radian is promptly obtained maximal value 28.9573 ° the time at x.

Its minimum mean-square error:

errsqu＝0.01624839141554

The error that t=1 (degree of tilt is 45 °) locates:

error2＝0.04167350946933

Its error figure is shown in Figure 3.

3) in conjunction with the handkerchief moral approach, least square approximation, non-linear optimization method calculate

In conjunction with the performance of single-chip microcomputer, we get ${\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="A20051003199700171.png"\; state="\{\{state\}\}">G</figure-callout>}}_{\mathrm{2,1}}=\frac{a+b{x}^2}{1+{\mathrm{<figure-callout\; id="2"\; label="cx"\; filenames="A20051003199700171.png"\; state="\{\{state\}\}">cx</figure-callout>}}^2}$ And investigating span is $x=[0,\sqrt{3}]$ Situation, promptly the situation of degree of tilt in [0,60 °] utilizes matlab to calculate

a＝0.99733491363080

b＝0.14057649312032

c＝0.60914643815697

The error that least square Pade approaches:

errsqu＝0.00175495388742，

Take advantage of power $\mathrm{\&rho;}={\mathrm{<figure-callout\; id="2"\; label="Q\; n"\; filenames="A20051003199700171.png"\; state="\{\{state\}\}">Q</figure-callout>}}_n^{}$ After error:

errsqu1＝0.00253288871550，

Error when the banknote degree of tilt is 60 °:

error2＝-0.00189030962714

Error when the banknote degree of tilt is 0 °:

error3＝0.00266508636920

Degree of tilt in 1000 subdivision graphs of [0,60 °] as shown in Figure 3.

The error minimum that the algebraic expression that comprehensive three kinds of situations above relatively, the third method adopt promptly also that the handkerchief moral is approached, least square approximation, non-linear optimization method calculate is approached actual width value.

Claims (4)

1, a kind of method for precision measuring width of paper money, it is characterized in that: when bank note passes through left and right sides infrared counter, with infrared light point source irradiation bank note, with the spectral signal of sensor acquisition bank note papery and be sent in the single-chip microcomputer and store, meanwhile wait the code-disc of branch hollow out with the concentric quilt of irradiation of infrared light point source and counting shaft, gather infrared ray variation on the code-disc with sensor, store after the synchronous code-disc signal that collects is sent to single-chip microcomputer, when bank note leaves counter tube fully, be that paper money counter is when finishing the data acquisition of bank note, we distinguish the data that are converted to magnitude of voltage by infrared spectrum that obtain, understanding, classification, and the come in and go out value of unique point of counter tube of the bank note the right and left that calculates left and right sides counter tube record, utilize equal proportion character that bank note is carried out simple half, paper slip, connect and open, after residual the judgement, directly simply calculate the width of bank note less than its value that can change the width developed width to tilting according to simple judgement and analysis; Pass through bank note is twisted with the fingers the Analysis of Mathematical of paper money process for the bigger bank note of degree of tilt, utilize the equal proportion character of the computational geometry of inclination bank note, adopt polynomial expression to approach, Pade approaches, least square approximation and non-linear optimized Algorithm work out an algebraic formula, this algebraic formula accurately approaches the width of paper money value of the run-off the straight of twisting with the fingers the paper money process, the result passed to needs the false distinguishing of width data function and task, passes to operations such as each real-time processing unit control warning, demonstration, motor as required by transmission line.

2, method for precision measuring width of paper money according to claim 1, it is characterized in that: utilize equal proportion character to bank note carry out simple half, paper slip, connect open, after residual the judgement, to directly calculating the width of bank note less than 10 ° of bank note with the traffic direction inclination angle; Inclination is passed through bank note is twisted with the fingers the mathematics model analysis of paper money process greater than 10 ° bank note, utilize the equal proportion character of the computational geometry of inclination bank note, adopt polynomial expression to approach, Pade approaches, least square approximation and non-linear optimized Algorithm work out an algebraic formula, this algebraic formula accurately approaches the width of paper money value of the run-off the straight of twisting with the fingers the paper money process.

3, method for precision measuring width of paper money according to claim 1, it is characterized in that: the absolute coordinate that will gather four unique points of bank note is converted to relative code-disc lattice number, calculate width of paper money with this substitution algebraic expression, promptly measure width of paper money with the physical characteristics of hardware itself rather than the revolution speed and the time relation of malleable.

4, according to the accurate detecting method of claim 1,2 or 3 described width of paper money, it is characterized in that: described sensor comprises multinomial functions such as collection, location, state output, the spacing of described paper money counter left and right sides computer tube should be according to the hardware design requirement, and fabric width is not more than the breadth extreme that will put bank note.

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