CN103487096A - Detection method of small flow based on gray correlation method - Google Patents

Abstract

The invention discloses a detection method of small flow based on a gray correlation method. The method includes: establishing mathematical model and restraint conditions for flow, frequency disturbance and water pressure change to form a mathematical model suitable for online detection of small flow; performing frequency small signal disturbance under the stable state, and detecting system flow by a gray correlation algorithm and gray correlation criterion; classifying the flow value detected online to determine whether a system is in the small-flow state or not. The method is high in detection speed, high in reliability, high in practicality and effective in protecting a motor and a converter from the failure low efficiency caused by operation under low frequency in the condition of small flow; the life of the system is prolonged, and the reliability of the system is improved; safe, efficient operation of the water pump motor is reliably guaranteed.

Description

A kind of low discharge detection method based on Grey Incidence

Technical field

The invention belongs to the electromechanical integration measurement and control area, be specifically related to a kind of low discharge based on Grey Incidence and operate in line detecting method, be particularly useful for the operation of air pressure tank constant pressure water supply device water pump low discharge and detect and protection.

Background technology

In the constant pressure frequency conversion water system, lift characteristic and pipe resistance characteristic have important impact to the performance of water system, when not closing fully with penstock or cause water system to run on low discharge due to the pipeline valve leakage, the now pipe of water system resistance and headloss increase, cause system energy consumption to increase, inefficiency.Wherein, " low discharge " refers to when the water swivel aperture is very little or water swivel is not closed fully and the pipeline water clock causes that its water consumption is very little or, close to zero, this situation is called frequency-conversion water supply system low discharge situation.Now, water pump moves under low discharge, can cause pump efficiency greatly to reduce, and can not reach energy-conservation purpose, and the larger electricity consumption of pump power is more.

Simultaneously, the low discharge operation causes pump motor and frequency converter in the low-frequency operation state, causes motor and converter low-frequency noise serious, reduces serviceable life and the performance of motor and frequency converter, and safe reliability and the production cost supplied water had a negative impact.

It is that the pump variable frequency constant pressure water supply system is realized one of key technical problem that efficient energy-saving, safe and reliable water supply need emphasis to solve that the low discharge of water pump constant pressure water supply system detects.At present, the low discharge that cuts out the pump detects the two kinds of modes that mainly contain:

One, flow sensor scheme: by the water outlet at water pump, flow sensor is installed, is realized that low discharge detects; Normally used flow sensor testing agency is mainly vane type and float-type structure.

(1) vane type detects and exists following three kinds of situations can cause flow detection precision and Reliability performance measure not high: 1. supply in the larger situation of water flow velocity, the solid sundries existed in water quality can be clashed into impeller, make impeller distortion and damaged, cause whole mechanism moment of inertia imbalance, cause flow detection inefficacy or precision and data reliability greatly to reduce; 2. water quality is subject to polluting while presenting acidity or alkalescence, and meeting heavy corrosion impeller mechanism, cause whole mechanism moment of inertia imbalance equally, and flow detection inefficacy or precision and data reliability reduce greatly; 3. the vane type flow detection is rotated by flowing liquid transmission impeller blade, thereby drives the action of associated electrical magnetic mechanism, the turn signal of impeller blade is converted into to the electric signal of different frequency.In the situation that pipeline section is long-pending constant, by the frequency of sampling electric signal, just can measure the flow of liquid.Owing to will considering the restraint conditions such as mechanism's intensity and machining precision and processing cost, the inertia of the rotatable parts such as impeller can not be very little, thereby have a Small flowrate measurement dead zone range, so can not detect such as the low discharge state such as dripping, leak.Simultaneously due to testing agency have certain inertia and signal convert nurse one's health and the routine processes process in, have a time delay, thereby mathematical model can be understood as the one order inertia system with delay component, so the flow detection response speed is slow.

(2), when float-type detects flow, the cavity and the float link device that due to its physical construction, mainly outer wall and inwall, consist of detect whether flow is arranged.The stroke size of ball float in cavity is a key factor that affects the type flow detection precision and reliability.Stroke is crossed conference and is caused the bulky of mechanism, and material cost is high, and complexity is installed, and measures inertia and time delay large, and sensitivity is low, causes detecting losing efficacy; Stroke is too small can cause the machining precision of mechanism and processing cost high, the accuracy requirement of magnetic cylinder is high and whole assembly precision is high, the defects such as poor anti jamming capability.

Two, nonshared control unit+Special water pump motor scheme: by the pump motor to special-purpose, carry out the test repeatedly of heat-capacity curve, draw the family curve of pump working in the low discharge situation, and using this curve and detect the reference value of flow as system, whether in low discharge characteristic interval, carry out the detection system low discharge by detecting the current operation characteristic of pump motor.

Nonshared control unit+Special water pump motor scheme, due to the test repeatedly that will carry out heat-capacity curve and hydraulic pressure resonse characteristic, show that the characteristic quantity of pump working in various low discharge situations is the reference value that system detects flow.Then by a large amount of online data collection and routine processes, actual characteristic amount under the current running status of the system that draws, by with the reference characteristic quantity, carrying out similarity analysis, thus the current flow value of the system that draws, and then judge whether system runs on low flow rate condition.But this method exists serious problem to be exactly:

To the hardware and software of control system require high.Because controller will gather a large amount of data and carry out the characteristic quantity of signal processing and solving system, and carries out similarity analysis with the reference characteristic amount be stored in internal memory, thereby requires high to controller;

(2) owing to will carrying out a large amount of data sampling and processings and the characteristic quantity of solving system, and carry out similarity analysis with the reference characteristic quantity, its procedure quantity is large, and the processing time is long, and detection speed is slow;

Due to system in During Process of Long-term Operation, the parameter of electric machine, converter parameter etc. are subject to such environmental effects and senile cause changes, the operation characteristic quantitative changeization that causes system is larger, causes precision and the poor reliability measured, and the erroneous judgement action appears in control system;

(4) because water system is long-time continuous operation, once thereby water pump break down, can only adopt and the motor of the strict coupling of controller, and can not use the pump motor of other types, thereby cause the operation expense of system high, practicality and poor for applicability.

Summary of the invention

The object of the invention is to overcome above-mentioned weak point, propose a kind of simple in structure, applicability is good based on Grey Incidence low discharge online test method.

A kind of low discharge online test method based on Grey Incidence, comprise the steps:

(1) with sampling period T _sfor being sampled in interval by hydraulic pressure value and the frequency converter output frequency of water system pipe network, sampled value is labeled as p (1) and f (1) for the first time; Current sampling number is k, makes k=1;

(2) set up the hydraulic pressure value array { p (i) } formed by M element, and frequency converter output frequency array { f (i) }, i={k-M+1 wherein, k-M+2 ... k}, M is the predefined positive integer that is greater than 1, k is current sampling number; P (i) | _i<=0=0, f (i) | _i<=0=0;

(3) judge that whether water system is in steady state (SS); If so, enter step (4); Otherwise water system plays pendulum, proceed to step (13);

(4) solve the mean value of hydraulic pressure value

and the mean value of frequency converter output frequency $\stackrel{\&OverBar;}{F}=\frac{1}{M}\underset{i=k-M+1}{\overset{k}{\mathrm{\&Sigma;}}}f\left(i\right);$

(5) the mark current time is the t=0 moment, gives fixing Arbitrary Perturbation Δ F of frequency converter output frequency;

(6) definition Q ^g[m] is t=mT _sflow estimated value constantly, definition Δ p ^g(m) be corresponding hydraulic pressure disturbance quantity estimated value; M=1 wherein, 2 ..., N,

t _dfor predefined observation interval; Order

wherein

initial value for any flow estimated value of setting;

Make m=1, second level lowest difference Δ (min)=0, the maximum poor Δ (max)=1 in the second level, resolution ratio γ=0.5;

(7) judgement mT _s>T _dwhether set up, if set up, proceed to step (13); Otherwise, calculate $\mathrm{\&Delta;p}\left(m\right)=p\left(m\right)-\stackrel{\&OverBar;}{P};$

(8) judgement

whether set up, if be false, proceed to step (13); Otherwise, by flow estimated value Q ^g[m] and t=mT _s,

Δ F, P _b, V _b, T _bwith T substitution formula $\frac{\mathrm{\&Delta;}{p}^g\left(m\right)}{\stackrel{\&OverBar;}{P}}=\frac{2\stackrel{\&OverBar;}{F}\&times;\mathrm{\&Delta;F}+\mathrm{\&Delta;}{F}^2}{{\stackrel{\&OverBar;}{F}}^2}\frac{Q^g\left[m\right]\stackrel{\&OverBar;}{P}{T}_b}{P_b{V}_{b}T}m{T}_s,$ Solve and draw Δ p ^g(m);

Wherein, P _bfor water system air pressure tank rated pressure value, V _bfor water system air pressure tank air chamber nominal volume, T _bfor water system air pressure tank rated temperature; T is environment temperature;

(9) using Δ p (m) as with reference to sequence, Δ p ^g(m) sequence as a comparison, and to Δ p (m), Δ p ^g(m) carry out normalized and obtain corresponding normalization sequence Δ p ₁(m) and

(10) error of calculation sequence ${\mathrm{\&Delta;}}_0\left(m\right)=\left|\right|\mathrm{\&Delta;}{p}_1\left(m\right)-\mathrm{\&Delta;}{p}_1^g\left(m\right)\left|\right|;$

Solve Δ p ₁(m), correlation coefficient ξ ₀(m), ${\mathrm{\&xi;}}_0\left(m\right)=\frac{\mathrm{\&Delta;}\left(\min \right)+\mathrm{\&gamma;\&Delta;}\left(\max \right)}{{\mathrm{\&Delta;}}_0\left(m\right)+\mathrm{\&gamma;\&Delta;}\left(\max \right)};$

(11) solve degree of association r,

ξ wherein ₀(ψ) | _ψ<=0=0;

Judge whether r>=0.95 sets up; If set up, enter step (12); Otherwise more new variables, make m=m+1, $Q^g\left[m\right]=Q^g[m-1]+\frac{1}{r}\mathrm{sgn}\left(\mathrm{\&Delta;p}\right[m-1]-\mathrm{\&Delta;}{p}^g[m-1\left]\right),$ Return to step (7);

(12) judgement

whether set up; Wherein,

for peak flow values corresponding to predefined low discharge running status; If set up, Q ^g[m] is exactly the system flow value, exits; Otherwise, enter step (13).

(13) make k=k+1; After this sampling period finishes, sample, and the sampled value of mark hydraulic pressure value and frequency converter output frequency is p (k) and f (k) next time; Return to step (2).

The further setting of the present invention is, described steady state (SS) is defined as:

Calculate the standard deviation of array { p (i) } ${\mathrm{\&sigma;}}_p=\sqrt{\frac{M\underset{i=k-M+1}{\overset{k}{\mathrm{\&Sigma;}}}p{\left(i\right)}^2-{\left(\underset{i=k-M+1}{\overset{k}{\mathrm{\&Sigma;}}}p\left(i\right)\right)}^2}{M^2}},$ And the standard deviation of array { f (i) } ${\mathrm{\&sigma;}}_f=\sqrt{\frac{M\underset{i=k-M+1}{\overset{k}{\mathrm{\&Sigma;}}}f{\left(i\right)}^2-{\left(\underset{i=k-M+1}{\overset{k}{\mathrm{\&Sigma;}}}f\left(i\right)\right)}^2}{M^2}},$

Judge whether to meet: σ simultaneously _p<ε _pand σ _f<ε _f, wherein: ε _pand ε _ffor predefined on the occasion of; If meet, think that water system is in steady state (SS), otherwise, think that water system plays pendulum.

Low discharge online test method based on Grey Incidence of the present invention has following beneficial effect:

One, with existing, by being installed, the flow sensor scheme compares, the present invention can realize that without flow detection sensor and auxiliary circuit low discharge detects, Installation and Debugging required time and the cost of flow sensor and auxiliary process circuit have been saved, make system architecture simpler, system cost is lower;

Two, with existing nonshared control unit+Special water pump motor scheme, compare, the present invention detects applicable to the low discharge of the three-phase alternating current pump motor water supply of various models, has versatility widely.Because when system is moved under low flow rate condition, its flow mathematical model is

wherein: hydraulic pressure value when P is water system stable operation, variation in water pressure amount when Δ p (t) moves for disturbance, electric machine frequency value when F is water system stable operation, frequency variation when Δ F is operation, flow value when Q is water system stable operation, P _b, V _band T _bfor air pressure tank nominal working conditions downforce value, air chamber bulking value and temperature value, T is the system current temperature value, and t is time quantum.As shown from the above formula, flow when wish detects current system stable operation, variation in water pressure amount Δ p (t), air pressure tank parameter P when frequency variation delta F, disturbance operation when electric machine frequency value F, disturbance operation when hydraulic pressure value P, stable operation in the time of only need to obtaining water system stable operation _b, V _b, T _bflow Q in the time of can measuring stable operation with parameters such as current environmental temperature T, and without the model of knowing pump motor and design parameter.Thereby the method can be widely used in meeting being connected with controller of three-phase alternating current pump motor of the various models of voltage and power index, realizes that low discharge detects online.

The characteristics such as it is fast that three, low discharge online test method of the present invention has detection speed, and reliability is high, practical; Can effectively protect the inefficiency fault that under motor and frequency converter low flow rate condition, low-frequency operation causes, improve the life and reliability of system, for pump motor safety, efficient operation provide Reliable guarantee.

Embodiment

Low discharge threshold value (being peak flow values corresponding to low discharge running status) size is different because of varying in size of water supply rated flow, such as 10 water swivels and 2 water swivels are arranged respectively in two family resident families, its situation of dripping of all leaking, obviously this situation all belongs to low discharge.But the rill value of 10 water swivels is greater than the rill value of 2 water swivels.Meanwhile, the threshold value of rill value is also relevant with lift, and in high-lift situation, the low discharge threshold value is usually large than the threshold value in little lift situation.Such as, the water swivel of same two models is and shuts, and its aperture is the same, and the flow value that to set lift be 20m is greater than the flow value that lift is 10m certainly.Thereby the size of low discharge threshold value is restricted by several factors, can not determine without exception, can artificially set up on their own as required.Such as, it has 10 water swivels certain resident, and lift is 20m, and can set: water consumption Q≤10L/min is the low discharge threshold value.Equally, it has 2 water swivels certain resident, and lift is 10m, and can set: water consumption Q≤1L/min is the low discharge threshold value.

The invention provides a kind of low discharge online test method based on Grey Incidence, mainly based on the water system mathematical model.The water system sketch as shown in Figure 1, mainly comprises water intaking water source, non-return valve 2, pump motor M, air pressure tank 4, device for detecting water pressure 5, ambient temperature detection device 6, outlet water control valve 3, frequency converter 7 and controller 8 etc.The water intaking water source is mainly tap water pipe network or deep-well, pool, rivers and lakes etc.; Non-return valve 2 major functions are while preventing that water pump is out of service, the aqueous reflux backwater source in user's webmaster; Pump motor M carries the water in water source by the impeller blade High Rotation Speed to the user; Air pressure tank 4 is mainly the function of stablizing hydraulic pressure, prevents the harm of water hammer accident to pipe network; Device for detecting water pressure 5 is for detection of the hydraulic pressure of water system; The temperature that ambient temperature detection device 6 is current for detection of system; Outlet water control valve 3 is for opening or stopping supplying water to the user; Controller 8 is mainly realized the input of correlation parameter, the demonstration of running status and the operation of system control program; The controlled quentity controlled variable that frequency converter 7 mainly sends by receiving controller, realize the pump motor variable frequency regulating speed control.

Variable declaration is as follows: q ₁(t) be inflow; q ₂(t) be aquifer yield; The hydraulic pressure value that p (t) is pipe network; F (t) is the frequency converter output frequency; Air pressure tank air chamber volume is v ₁(t); Air pressure tank air chamber pressure p _a(t), air pressure tank hydroecium volume is v ₂(t), the air pressure tank sectional area is S, and the air pressure tank cumulative volume is V _z, air pressure tank rated pressure value P _b, air pressure tank air chamber nominal volume V _b, air pressure tank rated temperature T _b, environment temperature is T (t), and t is time variable, and ρ is fluid density, and g is acceleration of gravity.During the water system stable state: force value is P, and the frequency converter output frequency is F, and the Inlet and outlet water flow is Q, and environment temperature is T, and air pressure tank air chamber volume is V ₁, the hydroecium volume is V ₂, the unit of above-mentioned all amounts is international unit.Definition t=0 is the last moment of system with frequency F stable operation constantly, exists:

$\left\{\begin{array}{c}{q}_1\left(0\right)=Q\\ q_2\left(0\right)=Q\\ f\left(0\right)=F\\ p_a\left(0\right)=P-\mathrm{\&rho;g}\frac{V_2}{S}\\ T\left(0\right)=T\\ p\left(0\right)=P\\ v_1\left(0\right)=V_1\\ v_2\left(0\right)=V_2\end{array}\right.$

Suppose at [0, T _d] running frequency of water pump is in the time: f (t)=F+ Δ F, Δ F is the frequency disturbance increment, T _dfor being greater than 0 time value, according to varying in size of water system power, artificially determine in advance; Hydraulic pressure value is p (t)=P+ Δ p (t), the water pressure fluctuations value that Δ p (t) causes for Δ F; The inflow of water pump is q ₁(t)=Q+ Δ q ₁(t), Δ q ₁(t) the flow of inlet water undulating quantity caused for Δ F; The aquifer yield of water pump is q ₂(t)=Q+ Δ q ₂(t), Δ q ₂(t) the water flow undulating quantity caused for Δ F; From University Of Chongqing's Master's thesis " research and design based on PLC tea place constant pressure spriukler irrigation control system ", the pass between water feeding of water pump flow, hydraulic pressure and motor running frequency is:

$\frac{q_1\left(t\right)p\left(t\right)}{\mathrm{\&eta;}}=\frac{m_1{k}_u^2\frac{R_2}{s}f{\left(t\right)}^2}{{(R_1+\frac{R_2}{s})}^2+{(X_{1\mathrm{\&sigma;}}+X_{2\mathrm{\&sigma;}})}^2}---\left(1\right)$

Wherein: the efficiency that η is water pump, the i.e. ratio of motor useful power and shaft power;

S is revolutional slip;

R ₁, R ₂, X _{1 σ}, X _{2 σ}, m ₁,

intrinsic parameter for pump motor;

Because pump motor adopts variable frequency regulating speed control, so s remains unchanged substantially.Order:

$\frac{m_1{k}_u^2\frac{R_2}{s}}{{(R_1+\frac{R_2}{s})}^2+{(X_{1\mathrm{\&sigma;}}+X_{2\mathrm{\&sigma;}})}^2}=k---\left(2\right)$

K is only relevant with the structural parameters of motor own, with flow, pressure independent.So formula can be reduced to:

$\frac{q_1\left(t\right)p\left(t\right)}{\mathrm{\&eta;}}=\mathrm{kf}{\left(t\right)}^2---\left(3\right)$

Make k'=η k., when t=0, have:

QP＝k'F ² (4)

At t ∈ [0, T _d], by q ₁(t)=Q+ Δ q ₁(t), f (t)=F+ Δ F and p (t)=P+ Δ p (t) substitution formula (3):

(Q+Δq ₁(t))(P+Δp(t))=k'(F+ΔF) ² (5)

Launch (5), and arrange:

PQ+QΔp(t)+PΔq ₁(t)+Δq ₁(t)Δp(t)＝k'(F ²+2FΔF+ΔF ²) (6)

(4) substitution (6) can be obtained:

QΔp(t)+PΔq ₁(t)+Δq ₁(t)Δp(t)＝k'(2FΔF+ΔF ²) (7)

The lift that Fig. 2 is system-pipe resistance characteristic curve, wherein: horizontal ordinate is flow Q, ordinate is pressure P, n _i(i=1,2,3,4,5,6) mean the velocity of rotation of water pump; R _i(i=1,2,3,4,5,6,7,8) mean the resistance of pipe system in valve different opening situation, and aperture is less, and resistance is larger.

As aquifer yield q ₂(t) very little, during stable state Q hour, as shown in Figure 2, when valve opening is very little, the resistance of the pipe of system is very large, the rotation speed change of pressure and pump motor is very little for the impact of water flow.Thereby can think Δ q ₂(t)=0, i.e. q ₂(t)=Q.Thereby at time [0, T _d] in, the value of the Δ p (t) that Δ F causes is less, so exist:

|Δp(t)|＜＜P (8)

So arranging (7) obtains:

QΔp(t)+PΔq ₁(t)＝k'(2FΔF+ΔF ²) (9)

Formula (9) can be obtained divided by (4):

$\frac{\mathrm{\&Delta;}{q}_1\left(t\right)}{Q}+\frac{\mathrm{\&Delta;p}\left(t\right)}{P}=\frac{2F\&times;\mathrm{\&Delta;F}+\mathrm{\&Delta;}{F}^2}{F^2}---\left(10\right)$

Air pressure tank kinetics equation: at t ∈ [0, T _d], the volume change of air pressure tank hydroecium is:

$\begin{array}{c}\mathrm{\&Delta;}{v}_2\left(t\right){=\&Integral;}_0^t(q_1\left(t\right)-q_2\left(t\right))\mathrm{dt}\\ ={\&Integral;}_0^t(Q+\mathrm{\&Delta;}{q}_1\left(t\right)-Q)\mathrm{dt}\\ ={\&Integral;}_0^t\mathrm{\&Delta;}{q}_1\left(t\right)\mathrm{dt}\end{array}---\left(11\right)$

So, t ∈ [0, T _d] the hydroecium volume is:

$v_2\left(t\right)=V_2+{\&Integral;}_0^t\mathrm{\&Delta;}{q}_1\left(t\right)\mathrm{dt}---\left(12\right)$

Because V remains unchanged, thereby the air chamber volume is:

$v_1\left(t\right)=V_1-{\&Integral;}_0^t\mathrm{\&Delta;}{q}_1\left(t\right)\mathrm{dt}---\left(13\right)$

Suppose [0, the T at t ∈ _d] in the time, environment temperature remains unchanged, from equation for ideal gases:

$\frac{p_a\left(t\right)}{p_a\left(0\right)}=\frac{V_1}{v_1\left(t\right)}---\left(14\right)$

(13) substitution (14) is obtained:

$\frac{p_a\left(t\right)-p_a\left(0\right)}{p_a\left(0\right)}=\frac{{\&Integral;}_0^t\mathrm{\&Delta;}{q}_1\left(t\right)\mathrm{dt}}{V_1-{\&Integral;}_0^t\mathrm{\&Delta;}{q}_1\left(t\right)\mathrm{dt}}---\left(15\right)$

Make Δ p _a(t)=p _a(t)-p _a(0) be air pressure tank air chamber pressure variable quantity:

$\mathrm{\&Delta;}{p}_a\left(t\right)=\frac{p_a\left(0\right){\&Integral;}_0^t\mathrm{\&Delta;}{q}_1\left(t\right)\mathrm{dt}}{V_1-{\&Integral;}_0^t\mathrm{\&Delta;}{q}_1\left(t\right)\mathrm{dt}}---\left(16\right)$

And the pressure variety caused by the hydroecium volume change is:

$\mathrm{\&Delta;}{p}_s\left(t\right)=\frac{\mathrm{\&rho;g}{\&Integral;}_0^t\mathrm{\&Delta;}{q}_1\left(t\right)\mathrm{dt}}{S}---\left(17\right)$

So, the variation in water pressure amount

$\begin{array}{c}\mathrm{\&Delta;p}\left(t\right)=\mathrm{\&Delta;}{p}_a\left(t\right)+\mathrm{\&Delta;}{p}_s\left(t\right)\\ =\frac{p_a\left(0\right){\&Integral;}_0^t\mathrm{\&Delta;}{q}_1\left(t\right)\mathrm{dt}}{V_1-{\&Integral;}_0^t\mathrm{\&Delta;}{q}_1\left(t\right)\mathrm{dt}}+\frac{\mathrm{\&rho;g}{\&Integral;}_0^t\mathrm{\&Delta;}{q}_1\left(t\right)\mathrm{dt}}{S}\end{array}---\left(18\right)$

If parameter T _dchoose rationally, meet

:

$\mathrm{\&Delta;p}\left(t\right)=\frac{p_a\left(0\right)+\mathrm{\&rho;g}\frac{V_1}{S}}{V_1}{\&Integral;}_0^t\mathrm{\&Delta;}{q}_1\left(t\right)\mathrm{dt}---\left(19\right)$

Will

substitution formula (19), and arrange:

$\mathrm{\&Delta;p}\left(t\right)=\frac{P-\mathrm{\&rho;g}\frac{V_2}{S}+\mathrm{\&rho;g}\frac{V_1}{S}}{V_1}{\&Integral;}_0^t\mathrm{\&Delta;}{q}_1\left(t\right)\mathrm{dt}---\left(20\right)$

By formula (20), can be obtained:

$\frac{P-\mathrm{\&rho;g}\frac{V}{S}}{V_1}{\&Integral;}_0^t\mathrm{\&Delta;}{q}_1\left(t\right)\mathrm{dt}<\mathrm{\&Delta;p}\left(t\right)<\frac{P+\mathrm{\&rho;g}\frac{V}{S}}{V_1}{\&Integral;}_0^t\mathrm{\&Delta;}{q}_1\left(t\right)\mathrm{dt}---\left(21\right)$

Wherein: V=V ₁+ V ₂.Due to

the hydraulic pressure produced corresponding to the air pressure tank vertical height, normally much smaller than actual lift (the constant pressure water supply lift is generally more than 14m), so

So have:

$\mathrm{\&Delta;p}\left(t\right)\&ap;\frac{P}{V_1}{\&Integral;}_0^t\mathrm{\&Delta;}{q}_1\left(t\right)\mathrm{dt}---\left(22\right)$

(22) substitution (10) arrangement can be obtained:

$\frac{\mathrm{\&Delta;}{q}_1\left(t\right)}{Q}+\frac{{\&Integral;}_0^t\mathrm{\&Delta;}{q}_1\left(t\right)\mathrm{dt}}{V_1}=\frac{2F\&times;\mathrm{\&Delta;F}+\mathrm{\&Delta;}{F}^2}{F^2}---\left(23\right)$

So equation (23) is about Δ q ₁(t) a Differential Equation with Constant Coefficients, can separate:

$\mathrm{\&Delta;}{q}_1\left(t\right)=\frac{Q(2F\&times;\mathrm{\&Delta;F}+\mathrm{\&Delta;}{F}^2)}{F^2}{e}^{-\frac{Q}{V_1}t}---\left(24\right)$

Simultaneous formula (24) and (10) can obtain:

$\mathrm{\&Delta;p}\left(t\right)=\frac{P(2F\&times;\mathrm{\&Delta;F}+\mathrm{\&Delta;}{F}^2)}{F^2}(1-e^{-\frac{Q}{V_1}t})---\left(25\right)$

Suppose that air pressure tank is without Leakage Gas, from equation for ideal gases:

$\frac{P_b\&times;V_b}{T_b}=\frac{P\&times;V_1}{T}---\left(26\right)$

Simultaneous formula (25) and (26), and arrange:

$\mathrm{\&Delta;p}\left(t\right)=\frac{P(2F\&times;\mathrm{\&Delta;F}+\mathrm{\&Delta;}{F}^2)}{F^2}(1-e^{-\frac{\mathrm{QP}{T}_b}{P_b{V}_{b}T}t})---\left(27\right)$

Due to parameter P, F, Δ F, P _b, V _b, T _b, T and t be observable quantity and known quantity, thereby by test pressure disturbance quantity Δ p (t) at t ∈ [0, T _d] value just can calculate the size of the flow Q value of system when stable state.Formula (27) carried out to Taylor series expansion at the t=0 place and arrange:

$\mathrm{\&Delta;p}\left(t\right)=\frac{P(2F\&times;\mathrm{\&Delta;F}+\mathrm{\&Delta;}{F}^2)}{F^2}\underset{n=0}{\overset{\&infin;}{\mathrm{\&Sigma;}}}{(-1)}^{n-1}{\left(\frac{\mathrm{QP}{T}_b}{P_b{V}_{b}T}t\right)}^n---\left(28\right)$

Because Q is very little, so formula (28) is approximately:

$\frac{\mathrm{\&Delta;p}\left(t\right)}{P}=\frac{2F\&times;\mathrm{\&Delta;F}+\mathrm{\&Delta;}{F}^2}{F^2}\frac{\mathrm{QP}{T}_b}{P_b{V}_{b}T}t---\left(29\right)$

At t ∈ [0, T _d], formula (29) is set up must meet following constraint condition:

$\left|\frac{(2F\&times;\mathrm{\&Delta;F}+\mathrm{\&Delta;}{F}^2)}{F^2}\right|\frac{\mathrm{QP}{T}_b}{P_b{V}_{b}T}t<<1---\left(30\right)$

The invention provides a kind of low discharge online test method based on Grey Incidence, comprise the steps:

(1) with sampling period T _sfor being sampled in interval by hydraulic pressure value and the frequency converter output frequency of water system pipe network, sampled value is labeled as p (1) and f (1) for the first time; Current sampling number is k, makes k=1;

(2) set up the hydraulic pressure value array { p (i) } formed by M element, and frequency converter output frequency array { f (i) }, i={k-M+1 wherein, k-M+2 ... k}, M is the predefined positive integer that is greater than 1, k is current sampling number; P (i) | _i<=0=0, f (i) | _i<=0=0;

(3) judge that whether water system is in steady state (SS).Steady state (SS) is defined as: the standard deviation of calculating M sampled pressure value p (t)

and the standard deviation of frequency converter output frequency f (t)

judge whether to meet: σ simultaneously _p<ε _pand σ _f<ε _f(wherein: ε _p, ε _ffor set on the occasion of, can be set according to real system, such as getting 0.1 or 0.2).If meet, think that water system is in steady state (SS), enter step (4); Otherwise water system plays pendulum, proceed to step (13).

(4) solve the mean value of hydraulic pressure value

mean value with the frequency converter output frequency $\stackrel{\&OverBar;}{F}=\frac{1}{M}\underset{i=k-M+1}{\overset{k}{\mathrm{\&Sigma;}}}f\left(i\right).$

(5) be designated as t=0 constantly with blaze now, give fixing Arbitrary Perturbation Δ F of output frequency, $f\left(m{T}_s\right)=\stackrel{\&OverBar;}{F}+\mathrm{\&Delta;F},$

(6) definition Q ^g[m] is t=mT _sflow estimated value constantly, definition Δ p ^g(m) be corresponding hydraulic pressure disturbance quantity estimated value; M=1 wherein, 2 ..., N,

t _dfor predefined observation interval; Order

wherein

initial value for any flow estimated value of setting; For without loss of generality,

value is larger.

Make m=1, second level lowest difference Δ (min)=0, the maximum poor Δ (max)=1 in the second level, resolution ratio γ=0.5;

(7) judgement mT _s>T _dwhether set up, if set up, proceed to step (13); Otherwise, calculate $\mathrm{\&Delta;p}\left(m\right)=p\left(m\right)-\stackrel{\&OverBar;}{P}.$

(8) judgement whether set up.Be false, proceed to step (13); Otherwise, by estimated value Q ^g[m] and t=mT _s,

Δ F, P _b, V _b, T _bwith T substitution formula $\frac{\mathrm{\&Delta;}{p}^g\left(m\right)}{\stackrel{\&OverBar;}{P}}=\frac{2\stackrel{\&OverBar;}{F}\&times;\mathrm{\&Delta;F}+\mathrm{\&Delta;}{F}^2}{{\stackrel{\&OverBar;}{F}}^2}\frac{Q^g\left[m\right]\stackrel{\&OverBar;}{P}{T}_b}{P_b{V}_{b}T}m{T}_s,$ Solve and draw Δ p ^g(m).

(9) using Δ p (m) as with reference to sequence, Δ p ^g(m) sequence as a comparison, and to Δ p (m), Δ p ^g(m) carry out normalized and obtain corresponding normalization sequence Δ p ₁(m) and

(10) error of calculation sequence ${\mathrm{\&Delta;}}_0\left(m\right)=\left|\right|\mathrm{\&Delta;}{p}_1\left(m\right)-\mathrm{\&Delta;}{p}_1^g\left(m\right)\left|\right|.$ Solve Δ p ₁(m),

correlation coefficient ξ ₀(m): ${\mathrm{\&xi;}}_0\left(m\right)=\frac{\mathrm{\&Delta;}\left(\min \right)+\mathrm{\&gamma;\&Delta;}\left(\max \right)}{{\mathrm{\&Delta;}}_0\left(m\right)+\mathrm{\&gamma;\&Delta;}\left(\max \right)}.$

(11) solve degree of association r:

wherein: ξ ₀(ψ) | _ψ<=0=0.

Judge whether r>=0.95 sets up.Set up, enter step (12); Otherwise,

New variables: m=m+1 more;

$Q^g\left[m\right]=Q^g[m-1]+\frac{1}{r}\mathrm{sgn}\left(\mathrm{\&Delta;p}\right[m-1]-\mathrm{\&Delta;}{p}^g[m-1\left]\right)$

Return to step (7).

(12) judgement

whether set up, wherein:

for peak flow values corresponding to low discharge running status, by the user, according to the size of minimum water consumption, set.If set up, Q ^g[m] is exactly the system flow value, exits; Otherwise, illustrate that water system, not in the low discharge state, proceeds to step (13).

(13) make k=k+1; After this sampling period finishes, sample, and the sampled value of mark hydraulic pressure value and frequency converter output frequency is p (k) and f (k) next time; Return to step (2).

Claims (2)

1. the low discharge online test method based on Grey Incidence, is characterized in that, comprises the steps:

(1) with sampling period T _sfor being sampled in interval by hydraulic pressure value and the frequency converter output frequency of water system pipe network, sampled value is labeled as p (1) and f (1) for the first time; Current sampling number is k, makes k=1;

(2) set up the hydraulic pressure value array { p (i) } formed by M element, and frequency converter output frequency array { f (i) }, i={k-M+1 wherein, k-M+2 ... k}, M is the predefined positive integer that is greater than 1, k is current sampling number; P (i) | _i<=0=0, f (i) | _i<=0=0;

(3) judge that whether water system is in steady state (SS); If so, enter step (4); Otherwise water system plays pendulum, proceed to step (13);

(4) solve the mean value of hydraulic pressure value

and the mean value of frequency converter output frequency $\stackrel{\&OverBar;}{F}=\frac{1}{M}\underset{i=k-M+1}{\overset{k}{\mathrm{\&Sigma;}}}f\left(i\right);$

(5) the mark current time is the t=0 moment, gives fixing Arbitrary Perturbation Δ F of frequency converter output frequency;

(6) definition Q ^g[m] is t=mT _sflow estimated value constantly, definition Δ p ^g(m) be corresponding hydraulic pressure disturbance quantity estimated value; M=1 wherein, 2 ..., N,

t _dfor predefined observation interval; Order wherein

initial value for any flow estimated value of setting;

Make m=1, second level lowest difference Δ (min)=0, the maximum poor Δ (max)=1 in the second level, resolution ratio γ=0.5;

(7) judgement mT _s>T _dwhether set up, if set up, proceed to step (13); Otherwise, calculate $\mathrm{\&Delta;p}\left(m\right)=p\left(m\right)-\stackrel{\&OverBar;}{P};$

(8) judgement

whether set up, if be false, proceed to step (13); Otherwise, by flow estimated value Q ^g[m] and t=mT _s,

Δ F, P _b, V _b, T _bwith T substitution formula $\frac{\mathrm{\&Delta;}{p}^g\left(m\right)}{\stackrel{\&OverBar;}{P}}=\frac{2\stackrel{\&OverBar;}{F}\&times;\mathrm{\&Delta;F}+\mathrm{\&Delta;}{F}^2}{{\stackrel{\&OverBar;}{F}}^2}\frac{Q^g\left[m\right]\stackrel{\&OverBar;}{P}{T}_b}{P_b{V}_{b}T}m{T}_s,$ Solve and draw Δ p ^g(m);

Wherein, P _bfor water system air pressure tank rated pressure value, V _bfor water system air pressure tank air chamber nominal volume, T _bfor water system air pressure tank rated temperature; T is environment temperature;

(9) using Δ p (m) as with reference to sequence, Δ p ^g(m) sequence as a comparison, and to Δ p (m), Δ p ^g(m) carry out normalized and obtain corresponding normalization sequence Δ p ₁(m) and

(10) error of calculation sequence ${\mathrm{\&Delta;}}_0\left(m\right)=\left|\right|\mathrm{\&Delta;}{p}_1\left(m\right)-\mathrm{\&Delta;}{p}_1^g\left(m\right)\left|\right|;$

Solve Δ p ₁(m),

correlation coefficient ξ ₀(m), ${\mathrm{\&xi;}}_0\left(m\right)=\frac{\mathrm{\&Delta;}\left(\min \right)+\mathrm{\&gamma;\&Delta;}\left(\max \right)}{{\mathrm{\&Delta;}}_0\left(m\right)+\mathrm{\&gamma;\&Delta;}\left(\max \right)};$

(11) solve degree of association r, ξ wherein ₀(ψ) | _ψ<=0=0;

Judge whether r>=0.95 sets up; If set up, enter step (12); Otherwise more new variables, make m=m+1, $Q^g\left[m\right]=Q^g[m-1]+\frac{1}{r}\mathrm{sgn}\left(\mathrm{\&Delta;p}\right[m-1]-\mathrm{\&Delta;}{p}^g[m-1\left]\right),$ Return to step (7);

(12) judgement whether set up; Wherein,

for peak flow values corresponding to predefined low discharge running status; If set up, Q ^g[m] is exactly the system flow value, exits; Otherwise, enter step (13).

(13) make k=k+1; After this sampling period finishes, sample, and the sampled value of mark hydraulic pressure value and frequency converter output frequency is p (k) and f (k) next time; Return to step (2).

2. the low discharge online test method based on Grey Incidence according to claim 1, is characterized in that, described steady state (SS) is defined as:

Calculate the standard deviation of array { p (i) } ${\mathrm{\&sigma;}}_p=\sqrt{\frac{M\underset{i=k-M+1}{\overset{k}{\mathrm{\&Sigma;}}}p{\left(i\right)}^2-{\left(\underset{i=k-M+1}{\overset{k}{\mathrm{\&Sigma;}}}p\left(i\right)\right)}^2}{M^2}},$ And the standard deviation of array { f (i) } ${\mathrm{\&sigma;}}_f=\sqrt{\frac{M\underset{i=k-M+1}{\overset{k}{\mathrm{\&Sigma;}}}f{\left(i\right)}^2-{\left(\underset{i=k-M+1}{\overset{k}{\mathrm{\&Sigma;}}}f\left(i\right)\right)}^2}{M^2}},$

Judge whether to meet: σ simultaneously _p<ε _pand σ _f<ε _f, wherein: ε _pand ε _ffor predefined on the occasion of; If meet, think that water system is in steady state (SS), otherwise, think that water system plays pendulum.

Images