CN106295903A - The efficiency Forecasting Methodology of WSN data Lossy Compression Algorithm based on linear fit - Google Patents

Abstract

The present invention proposes the efficiency Forecasting Methodology of a kind of WSN data Lossy Compression Algorithm based on linear fit, first according to the hardware parameter computing hardware coefficient k of sensing node；Then fitting of a polynomial predicted method is used to determine compression ratio R of specific algorithm_CWith the relation of error margin ε of data compression, and by the value of given error margin ε, obtain R_cPredictive value；Further according to algorithmic code structure prediction software coefficient s and R_CRelation, determine the software coefficient s of algorithm；Finally by k value and s, R_cPredictive value bring efficiency calculating formula η into_E=(R_cS/k) × 100%, obtain the predictive value of the efficiency of specific algorithm.This Forecasting Methodology is only relevant with hardware coefficient, compression ratio under compression algorithm is error free and error margin, algorithm efficiency under energy on-line prediction assigned error tolerance limit and correction compression ratio predictor formula, calculating is simple for it, it is low to consume energy, and provides foundation for sensing node on-line selection high energy efficiency compression algorithm in WSN.

Description

The efficiency Forecasting Methodology of WSN data Lossy Compression Algorithm based on linear fit

Technical field

The technology of the present invention relates to a kind of efficiency on-line prediction method of data compression algorithm, and the method is applicable to wireless sensing Based on linear fit in net damage data compression algorithm, be mainly used in requiring compression algorithm is carried out online according to compression accuracy Select, more efficiently to save electric energy.

Background technology

Along with SOC(system on a chip) (SoC), micro electronic mechanical system (MEMS), embedded system low-power consumption technology and sensor The fast development of technology etc., as wireless sense network (the Wireless Sensor of the comprehensive intelligent information processing platform Networks, WSN) paid close attention to widely, have broad application prospects, be the most active in computerized information area research One of focus, be also one of important technical changing future life.

WSN, using sensing node as elementary cell, is limited by use cost, and these node volumes are little, and it processes, storage Resource is the most limited with calculating, they can perception, measure and collect the relevant information of surrounding, and carry out according to this locality instruction Processing, the mode finally by radio communication is sent to user.Owing to node volume is the least, the calculating speed of node, storage Space and energy supply are the most very limited, and use battery to power, due to the particularity in node perceived region under normal circumstances Big with the quantity of node, change battery and be difficult to or unpractical.Therefore, the most maximized energy utilizing node limited Amount resource becomes the hot issue of WSN research.

The energy of sensing node mainly consume data perception, process and transmit on.Wherein, data be wirelessly transferred ring The energy that joint is consumed is most, thus most of energy of node has been used in being wirelessly transferred of data.There are some researches show: logical Cross wireless device to send the energy needed for 1bit data and be at least needed for an addition instruction execution process 480 times of energy.Cause This, by using suitable compression algorithm, it is possible to reduce energy expenditure required during node-node transmission data, thus extend node Life-span.

Traditional compression algorithm is only with compression ratio as target, it is not necessary to consider power saving.Some compression methods can realize Compression ratio high, but its algorithm complex is the highest.Owing to the execution of algorithm will consumed energy and algorithm complex its consumption the highest Can be the most, if the required energy consumed of compression algorithm self-operating is more than the communication energy saved by compression data, Data compression is so used just not reach energy-conservation purpose.Therefore, the requirement to the compression algorithm of WSN application is different from and answers tradition It is whether evaluating data compression algorithm is suitable for and good and bad master by the requirement of algorithm, energy-saving effect or energy efficiency (abbreviation efficiency) Want factor, and this efficiency is relevant with the power of communications of sensing node.Data compression algorithm for WSN, it is desirable to it passes through The energy that compression data are saved have to be larger than and realizes the energy that compression is consumed, namely compression algorithm must have positive energy Efficiency or positive efficiency.

Data compression method is divided into lossless compress and lossy compression method two class.Lossless compress will not make the data compressed lose Very, namely can completely recover through the data of lossless compress, but the compression ratio of lossless compression algorithm is relatively low, is only applicable to Those require the compression distortionless application scenario of data.Damage data compression, as the term suggests, number will necessarily be made when compressing data According to impaired so that be there is a certain degree of error by the relatively primitive data of the data recovered after data compression, reconstructed The approximation of simply initial data that has of data rather than initial data itself.But, the compression ratio of Lossy Compression Algorithm is high.If Allow the error of data being recovered to obtain by compression data the biggest, the most compressible fall data the most, the compression ratio of algorithm is just The highest, the efficiency of algorithm also will improve accordingly.Therefore, based on damage the energy-saving efficiency of data compression method also with allow to damage The error size that compression exists is relevant, and lossless compress does not the most exist this problem.

The method realizing data lossy compression method is varied, and wherein compression method based on linear fitting of time series is one What class was common is simply applicable to the Lossy Compression Algorithm of WSN, has much research both at home and abroad to this and obtains corresponding achievement.? In this kind of compression algorithm based on linear fitting of time series, typical algorithm has: based on Linear Regression Model in One Unknown empty time number According to compression algorithm, calculate based on the sectional linear fitting algorithm returned and regression model adjustment algorithm combination based on confidence interval Method, DP algorithm improves the optimal curve data compression algorithm of compression accuracy and algorithm complex, utilize piecewise constant to force Nearly sampled data carries out PMC-MR algorithm and PMC-MEAN, the top-down piecewise linear approximation algorithm of linear fit, etc..This A little same or analogous compression algorithms of basic ideas, are not quite similar in specific implementation, and its performance is the most variant, be respectively arranged with side Weight.But, this kind of compression algorithm has such common trait, it may be assumed that when the linear fit expression formula of a corresponding initial data When the difference of value of calculation and this initial data is less than allowable error, this initial data can be substituted by linear fit value of calculation, Namely these data can be compressed out.Therefore, using this kind of Lossy Compression Algorithm, part initial data to be compressed, part is former Beginning data are retained.The data retained are the fewest, then compression ratio is the highest.Obviously, the error of compression algorithm or precision and compression ratio are all Relevant with the compression mechanism of specific algorithm, and compression ratio is also relevant with the compressed error allowed.

Typically, the algorithm that compression ratio is relatively high, its complexity is the most relatively high, but high compression rate does not represent high energy efficiency.? In WSN, compress the energy-conservation energy of a Bit data relevant to the hardware effort parameter of node.If the merit for radio communication Rate is relatively large, then compress the energy that a Bit data saved also the most relatively large, in the case of other conditions are identical, algorithm Efficiency will be high；Otherwise, if the power of radio communication is little, in the case of other conditions are identical, the efficiency of compression algorithm will Low.On the other hand, the wireless communication power of WSN node is determined by communication distance, environmental condition and QoS requirement. So, the efficiency towards the compression algorithm of WSN is not by the single decision of compression ratio, further relates to complexity and the application of algorithm Actual hardware parameter under the node specific works state of compression algorithm.For Lossy Compression Algorithm, then affect algorithm efficiency Factor also includes the size of the compressed error that actual application allowed.

For WSN, just because of above-mentioned many reasons or factor so that how to calculate from multiple applicable compression In method, appropriate selection is a kind of can meet the current logarithmic restriction requirement according to compressed error, can play again having of optimum energy-saving effect Damage compression algorithm highly to study, and there is practical value.Judge whether certain data compression algorithm just has at present The method of efficiency is to perform this algorithm on node and test the energy consumption of its each several part, then judges further according to power consumption values.This Method is cumbersome and time consuming, should not promote.In view of this kind of data Lossy Compression Algorithm based on linear fitting of time series has It is applicable to the feature of WSN, therefore, studies and a kind of can predict the method for Lossy Compression Algorithm efficiency in WSN, and according to this prediction These algorithms of result reasonable selection, save the energy improving WSN node and have highly important meaning.

Summary of the invention

Solved by the invention technical problem is that, for the deficiencies in the prior art, it is provided that a kind of WSN based on linear fit The efficiency Forecasting Methodology of data Lossy Compression Algorithm, can online and be accurately judged to whether used compression algorithm just has The compression algorithm of efficiency or on-line selection more high energy efficiency, so that node can save more energy.

The technical scheme is that

The efficiency Forecasting Methodology of a kind of WSN data Lossy Compression Algorithm based on linear fit, comprises the steps of

Step 1: selected sensing node and wireless sensing network data Lossy Compression Algorithm based on linear fit；

Step 2: according to the actual hardware parameter of sensing node, calculate its hardware coefficient k by formula (1)；

$k=\frac{U_{RF}{I}_{RF}}{U_{mcu}{I}_{mcu}}\×\frac{f_{mcu}}{R_{baud}}---\left(1\right)$

Wherein, U_mcuAnd I_mcuAverage current under the running voltage of the respectively MCU of sensing node and activity pattern, U_RFWith I_RFIt is respectively the average current under the running voltage of wireless communication module of sensing node and activity pattern, f_mcuWork for MCU Frequency, R_baudBaud rate for radio communication；

Step 3: according to normalized sensor samples data, to error margin ε and compression ratio R_CRelation carry out multinomial Formula matching, shown in polynomial fitting such as formula (2)；Factor alpha in digital simulation multinomial₁,α₂,…,α_n, obtain R_CPrediction Expression formula；

R_C=R_C0+α₁ε+α₂ε²+α₃ε³+…+α_nεⁿ (2)

Wherein, n is the order of polynomial fitting, R_C0It is compression ratio time zero (i.e. without compressed error) for error margin；

Step 4: according to current given or that input (determining according to the required precision of reality application) data lossy compression method Error margin (i.e. allowable error) ε, calculates compression ratio R by polynomial fitting_CPredictive value；

Step 5: calculate the software coefficient s of selected compression algorithm by formula (3)；

S=aR_C+b (3)

Wherein, coefficient a and b meets formula (4):

$a=\frac{1}{m}(N_{cycle3}-N_{cycle4}),b=\frac{1}{m}(N_{cycle2}+N_{cycle4})---\left(4\right)$

In formula, N_cycle2For each data need the algorithm steps performed carry out the clock week needed for unit data compression Issue, N_cycle3Be the algorithm steps only data being compressed out just performed carry out needed for unit data compression clock week Issue, N_cycle4It is that the algorithm steps that the data only remained being not compressed just perform carries out unit data compression Required clock periodicity；M represents that each data determined by data type need to account for memory-aided number of bits；

Step 6: by the hardware coefficient k of sensing node calculated in above-mentioned steps, compression ratio R_CPredictive value and selected The software coefficient s of compression algorithm, brings the efficiency computing formula (5) of algorithm into, obtains the efficiency predictive value η of algorithm_E:

${\mathrm{\η}}_E=(R_C-\frac{s}{k})\×100\%---\left(5\right)$

I.e. η_E=-b/k+ (1-a/k) (R_C0+α₁ε+α₂ε²+…+α_nεⁿ) (6)

Described step 3 comprises the following steps:

1) initial value of the order n of empirically determined polynomial fitting, n is positive integer；

2) polynomial fitting is set as shown by the following formula:

R_C=R_C0+α₁ε+α₂ε²+α₃ε³+…+α_nεⁿ；

3) according to the maximum ε of n and input or given error margin_max, by formula ε₁=ε_max/ n determines as certainly The reduced scale ε of the i.e. abscissa of the error margin of variable₁；

4) according to formula ε_i=i ε₁Determine the Along ent ε of error margin_i(i=1,2 ..., n)；

To same distribution characteristics, normalized sensor samples data, by the error margin (allowable error) of corresponding Along ent Value is compressed respectively, obtains Along ent ε_i(i=1,2 ..., n) corresponding compression ratio R_Ci(i=1,2 ..., actual value n) and mistake Difference tolerance limit is compression ratio R when zero_C0Actual value；

5) according to the actual value (ε of Along ent and the compression ratio of correspondence thereof₁,R_C1)、(ε₂,R_C2) ..., (ε_n,R_Cn), use rule Generalized fitting of a polynomial computing formula (7) calculates the polynomial coefficient b that standardizes₁,b₂,…,b_n；

$\left[\begin{array}{c}{b}_1\\ b_2\\ .\\ .\\ .\\ b_n\end{array}\right]={\left[\begin{array}{cccc}1& 2& \mathrm{...}& 1\\ 2& 2^2& \mathrm{...}& 2^n\\ .& .& & .\\ .& .& \mathrm{...}& .\\ .& .& & .\\ n& n^2& \mathrm{...}& n^n\end{array}\right]}^{-1}\left[\begin{array}{c}{R}_{C1}-R_{C0}\\ R_{C2}-R_{C0}\\ .\\ .\\ .\\ R_{Cn}-R_{C0}\end{array}\right]---\left(7\right)$

6) the coefficient b obtained according to formula (7)₁,b₂,…,b_n, by relational expressionCalculate polynomial fitting Factor alpha₁,α₂,…,α_n；

7) according to polynomial fitting R_C=R_C0+α₁ε+α₂ε²+α₃ε³+…+α_nεⁿ, calculate Along ent ε_i(i=1,2 ..., n) right Compression ratio R answered_Ci(i=1,2 ..., predictive value n)；

8) by compression ratio R_Ci(i=1,2 ..., predictive value n) and actual value, calculate average fit error；If average fit Error exceedes input or given error margin, and n adds 1, returns the 2nd) step；Until average fit error is less than or equal to input Or given error margin, terminate the Fitting Calculation；By the up-to-date order n obtained and factor alpha₁,α₂,…,α_nMultinomial as matching The order of formula and coefficient, obtain R_CPrediction expression.

Described step 1) in, if to error margin ε and compression ratio R_CRelation carry out whole section of matching, then the initial value of n takes 4；If to error margin ε and compression ratio R_CRelation two sections be fitted, then the initial value of n takes 2.

Described step 8) in, average fit error calculating step is:

For arbitrary R_Ci(i=1,2 ..., n), calculate its relative error；Relative error is equal to R_CiPredictive value and actual value The absolute value of difference divided by this actual value；

Calculate all R_Ci(i=1,2 ..., average fit error n)；Average fit error is equal to all R_Ci(i=1, 2 ..., the arithmetic mean of instantaneous value of relative error n).

The efficiency Forecasting Methodology of described WSN data Lossy Compression Algorithm based on linear fit, also includes following to compression Rate R_CPrediction expression carry out the step of on-line correction:

) the selected algorithm of observation reality given or under the error margin of input, carry out sensing data and compress the pressure obtained The actual value of shrinkage；

) according to step 8) R that obtains_CPrediction expression, be calculated under the actual given or error margin of input, The predictive value of compression ratio；

) according to the actual value of compression ratio and predictive value, calculate the relative error of compression ratio predictive value；

If) this relative error less than or equal to set threshold value, then R_CPrediction expression keep constant；Otherwise, should The actual value of sensing data, the actual error margin given or input and corresponding compression ratio that sensing node is the last is made For sample data, and sensing data therein is first done normalized, the most again to error margin ε and compression ratio R_CPass System carries out fitting of a polynomial, updates R_CPrediction expression；Described setting threshold value is less than the given or error margin of input；

) proceed to step 4.

Described step) described in set that threshold value draws the error margin of fixed or input 90%～95%.

In described step 4, according to compression algorithm program code, by IAR simulation development system platform, carry out following meter Calculate:

1) calculate the algorithm steps being required for performing to each data and carry out the clock periodicity needed for unit data compression N_cycle2；

2) calculate the algorithm steps only data being compressed out just performed and carry out the clock needed for unit data compression Periodicity N_cycle3；

3) calculate needed for the data being retained when only just need the algorithm steps performed carry out unit data compression Clock periodicity N_cycle4；

4) press the value of formula (4) design factor a and b, be calculated software coefficient s by formula (3) the most again.

The technology of the present invention is contemplated that:

Data compression calculation is damaged with being applicable to the based on linear fit of WSN data compression for concrete sensing node Method, according to three parameters contained by the computing formula (5) of algorithm efficiency and wherein the software coefficient s of algorithm and compression ratio R_cTwo Relation between person, represents s and R of concrete compression algorithm respectively with explicit expression_cRelation and R_cWith data compression error The variation relation of ε, then these expression formulas are brought into formula (5) obtains concrete compression algorithm efficiency η_ERelation table with variable ε Reach formula, thus the permissible value and hardware parameter according to compressed error realizes the on-line prediction to algorithm efficiency, based on R_cPrediction Method also can be pre-to compression ratio according to the relative error situation of the algorithm realistic compression ratio to sensing data Yu compression ratio predictive value Survey formula carries out on-line amending.

Selected sensor node and WSN data Lossy Compression Algorithm based on linear fit

According to application scenario it needs to be determined that the operating frequency of the hardware parameter of sensor node: MCU, voltage, electric current and The running voltage of Wireless Telecom Equipment, electric current and baud rate.Several concrete WSN data based on linear fit are selected to damage pressure Compression algorithm.

According to the hardware parameter of node, calculate k value by the computing formula (1) of hardware coefficient k

Hardware coefficient, as the term suggests being the coefficient the most relevant with hardware, unrelated with compression algorithm and compressed object.By public affairs Formula (1) is it can be seen that hardware coefficient relates to two platform: MCU and radio communication platform.Algorithm routine is performed by MCU, different MCU when often having different power consumption, different MCU architectural framework and instruction set that identical algorithms also can be made to perform Actual power loss the most different, and then affect compression algorithm run energy consumption.Transmitting power and phase due to different radio frequency chip The performance such as the receiving sensitivity answered is different, and in reality, the Configuration of baud rate of data transmission may be different, inter-node communication distance with And site environment is different or change, these all make the power consumption levels corresponding to unit of transfer's data different or need adjustment to change Become, thus wireless communications environment also has remote-effects as the factor of an aspect to energy-saving efficiency.

Just running voltage U of MCU and Wireless Telecom Equipment can be obtained by the data book of hardware platform_mcuAnd U_RF, and The average current I of its activity pattern_mcuAnd I_RF, MCU operating frequency f_mcu, also radio communication baud rate R_baud.According to formula (1) Just k value can be calculated.

According to R_CForecasting Methodology, calculate R_CFactor alpha in prediction expression (2)₁,α₂,…,α_n；

Compression ratio R_CMain relevant with error margin ε set by compressed object and algorithm, and it has been investigated that for clothes From the compressed object of the same regularity of distribution, R_CTo present similar non-linear relation between ε.Can for this non-linear relation To use the method for fitting of a polynomial to be determined by curve matching, thus obtain R_CPrediction expression, in evaluator system During number, select normalized polynomial match computational methods.Owing to the method is simple, it is easy to programming realization and being easy to has in resource Carry out on the sensor node of limit fitting coefficient in line computation, it is simple to according to the realistic compression ratio of selected algorithm at super setting threshold In the case of value, to R_CPrediction expression do on-line amending.

According to the Forecasting Methodology of software coefficient s, calculate coefficient a and b in s prediction expression (3) according to formula (4)

The computing formula of software coefficient s such as formula (7).

$s=\frac{N_{cycle}}{N_{uncmp}\×m}---\left(8\right)$

Wherein N_cycleAnd N_uncmpBeing respectively algorithm routine and run required clock periodicity and original data volume, m represents original Number of bits shared by data type.Original data volume one timing of compression, as long as calculating N_cycleJust can get the value of s.Pin Damaging data compression algorithm to based on linear fit, the Structure and Process of such algorithm is as shown in Figure 1.According to flow process shown in Fig. 2 The common trait analysis of figure and aforementioned this kind of algorithm understands, and the execution process of whole algorithm can be divided into following four parts, That is: part once, part to be performed, the part that only data being compressed out just can be performed, the most right is performed The part that retained data just can perform.The most 8. process in Fig. 1 has only carried out once, and process is the most required Clock periodicity is defined as N_cycle1；3. process is carried out once by each data, and the number of times of execution is then time series data Length N_uncmp, process performs required clock periodicity the most every time and is defined as N_cycle2, total clock periodicity is N_cycle2× N_uncmp；Process the most only set error margin in data be just performed, the most only exist compressible fall data Can perform the two process, the number of times of execution is number N of the data being compressed out_cmped, needed for process performs the most every time Clock periodicity is defined as N_cycle3, then altogether required clock periodicity is N_cycle3×N_cmped；The most 6. process only has the most not Data in error margin are just performed, and i.e. only there are the data needing to remain and just can perform these three process, hold Number N that number of times is the data remained of row_saved, these three process performs required clock periodicity every time and is defined as N_cycle4, then altogether required clock periodicity is N_cycle4×N_saved.Can be obtained by above-mentioned analysis, algorithm perform needed for time Clock periodicity N_cycleSuch as formula (9):

N_cycle=N_cycle1+N_cycle2×N_uncmp+N_cycle3×N_cmped+N_cycle4×N_saved (9)

Formula (9) is brought into formula (8) arrangement and can obtain formula (10).

$s=\frac{1}{m}(\frac{N_{cycle1}}{N_{uncmp}}+N_{cycle2}+N_{cycle4}+(N_{cycle3}-N_{cycle4})\×\frac{N_{cmped}}{N_{uncmp}})---\left(10\right)$

As m × N_uncmp>>N_cycle1Time, formula (10) becomes formula (11).

$s=\frac{1}{m}(N_{cycle3}-N_{cycle4})\×R_C+\frac{1}{m}(N_{cycle2}+N_{cycle4})---\left(11\right)$

OrderThen

S=aR_C+b (12)

For the compression algorithm determined, a, b are constant so that software coefficient s only with compression ratio R_CRelevant, and be R_C's Linear function.

Due to N_cycle2、N_cycle3And N_cycle4Represent the clock periodicity needed for the instruction execution of algorithm each several part, and work as hardware Platform and selected its value rear of compressed object immobilize, and only require to obtain N_cycle2、N_cycle3And N_cycle4And calculate the value of a, b, just Can be according to compression ratio R_CValue computation software coefficient s.

By s, R_CBring efficiency computing formula (5) with k respectively into and i.e. obtain algorithm efficiency η_EPrediction expression (6).

The k value obtained above-mentioned, R_CThe prediction expression of prediction expression and s substitutes into efficiency computing formula (5) i.e. respectively The prediction expression (6) of algorithm efficiency can be obtained.

According to current given or the hardware coefficient k value damaging data compression error margin value ε, node of input, by formula (6) the efficiency predictive value of selected compression algorithm is calculated.

By by error margin value ε determined by the precision of actual applied compression algorithm or allowable error requirement and according to Node current operation mode calculated hardware coefficient k substitutes into formula (6), can be calculated this compression algorithm of employing and carries out data The efficiency predictive value of compression.

Beneficial effect:

WSN data lossy compression method based on linear fit can be calculated by the on-line prediction method of the algorithm efficiency according to the present invention The efficiency of method has carried out on-line prediction, and the method calculating is simple, it is low to consume energy, and prediction expression coefficient can be implemented in line meter Calculate, it was predicted that result is the most accurate, it is possible to as carrying out the foundation of on-line selection high energy efficiency compression algorithm before compressing the data, from And save the energy of node to greatest extent, extend the life-span of network.

Accompanying drawing explanation

Fig. 1 is flow chart of the present invention

Fig. 2 WSN based on linear fit Lossy Compression Algorithm flow chart

The compression ratio prognostic chart of Fig. 3 PMC-MR compression algorithm Gaussian distributed data

The software coefficient prognostic chart of Fig. 4 PMC-MR algorithm

The prognostic chart of Fig. 5 PMC-MR algorithm efficiency

Detailed description of the invention

Below in conjunction with the drawings and specific embodiments, the present invention is described in more detail.

The invention discloses the efficiency Forecasting Methodology of a kind of WSN data Lossy Compression Algorithm based on linear fit, including Following steps:

Step 1) select sensing node and WSN data Lossy Compression Algorithm based on linear fit

Compression algorithm selects the PMC-MR algorithm in wireless sensing network data Lossy Compression Algorithm based on linear fit, pressure The sample data of contracting object select Gaussian distributed, the microcontroller of sensor node is MSP430F2611, operates in Under 3.0V, 512 μ A, 1MHz；Wireless transport module uses CC2420, operates under 3.0V, 17.4mA, with the baud of 150kpbs Rate carries out data transmission, and as a example by above-mentioned object and running parameter, practices the present invention and is described in further details.

PMC-MR is that a kind of typical WSN based on linear fit damages data compression algorithm, and its principle is: by monitoring The input range of input data, when the input range of data is beyond predetermined threshold value, then by the previous position of these data and Midrange (maximum and the arithmetical average of minima) exports, thus reaches to compress purpose.PMC-MR algorithm false code is as follows.

Step 2) according to the hardware parameter of node, calculate k value by the computing formula (1) of hardware coefficient k

Owing to this example node M CU uses MSP430F2611, operate in running voltage 3.0V, electric current 512 μ A and frequency 1MHz Under the conditions of；Radio transmission apparatus uses CC2420, operates in running voltage 3.0V, under the conditions of electric current 17.4mA, with 150kpbs's Baud rate carries out data transmission, and calculates k value according to formula (1).

$k=\frac{U_{RF}{I}_{RF}}{U_{mcu}{I}_{mcu}}\×\frac{f_{mcu}}{R_{baud}}=\frac{3\×17.4\×{10}^{-3}}{3\×512\×{10}^{-6}}\×\frac{{10}^6}{150}\≈227$

Step 3) according to R_CForecasting Methodology, calculate R_CFactor alpha in prediction expression (2)₁,α₂,L,α_n；

1) for whole segment data matching, take n=4, the most generally use 4 rank fitting of a polynomials, average phase can be met To the error requirement less than 2%；

2) by n=4 and ε_max=4 (for ease of calculating, these data can zoom in or out), utilize formula ε₁=ε_max/ n determines The reduced scale ε of abscissa₁=1；

3) according to formula ε_i=i ε₁Determine the Along ent ε of error margin₁=1, ε₂=2, ε₃=3, ε₄=4；

4) according to the sample data compression measurement result (ε of corresponding Along ent_i,R_ci): (0,0.0137), (1,0.7246), (2,0.9590), (3,0.9980), (4,0.9980), code requirement fitting of a polynomial computing formula (7) calculates standardization Polynomial coefficient b₁,b₂,b₃,b₄, i.e.

$\left[\begin{array}{c}{b}_1\\ b_2\\ b_3\\ b_4\end{array}\right]={\left[\begin{array}{cccc}1& 1& 1& 1\\ 2& 2^2& 2^3& 2^4\\ 3& 3^2& 3^3& 3^4\\ 4& 4^2& 4^3& 4^4\end{array}\right]}^{-1}\left[\begin{array}{c}0.7109\\ 0.9453\\ 0.9843\\ 0.9843\end{array}\right]=\left[\begin{array}{c}1.0740\\ -0.4360\\ 0.0780\\ -0.0052\end{array}\right]$

5) according to prediction expression coefficient formulasCalculate factor alpha₁=1.0740, α₂=-0.4360, α₃=0.0780, α₄=-0.0052.

Fitting result is as it is shown on figure 3, the maximum relative error of matching is 5.7%, and average relative error is 1.32%.

Step 4) according to the prediction computational methods of software coefficient s, according to the coefficient a in formula (4) calculation expression (3) and b

1) according to PMC-MR false code, algorithm steps (5) and second (11) during the execution of algorithm, time series In each data be required for performing once, the clock periodicity N that they are required_cycle2=6；

2) algorithm steps (6), (11) and (12) only exist compressible fall data just can perform these three step, these Clock periodicity needed for step performs determines N_cycle3=634；

3) algorithm steps (6), (7), (8) and (9) only existence needs the data remained just can perform these four steps Suddenly, the clock periodicity N needed for these four steps perform_cycle4=1045.

4) according to formula (4), first calculate coefficient a and b in predictor formula, then obtain the predictor formula of software coefficient s.

$a=\frac{1}{32}(634-1045)=-12.84,b=\frac{1}{32}(6+1046)=32.84$

S=-12.84 × R_C+32.84

As shown in Figure 4, can find that from figure the predictive value of s is the most close with measured value clearly, maximum relative error It is 0.7%, it was predicted that result is ideal.

Step 5) by s, R_CBring efficiency computing formula (5) with k respectively into and i.e. obtain algorithm efficiency η_EPrediction expression (6).

Obtaining k value, R_CCarry it into formula (5) after expression formula and s prediction expression respectively and obtain η_EPrediction expression For:

${\mathrm{\η}}_E=(R_C-\frac{s}{k})\×100\%=(R_C-\frac{112.84\×R_C+32.84}{227})\×100\%=(1.0566R_C-0.1447)\×100\%$

Arrange:

η_E=(-0.1302+1.1348 ε-0.4607 ε²+0.0824ε³-0.0055ε⁴) × 100%

Step 6) by previous step gained efficiency η_EConcrete prediction expression, by the concrete allowable error value generation of compression algorithm Enter to calculate, draw efficiency η_EPredictive value.

Corresponding compression algorithm allowable error scope is that the efficiency prediction curve of the PMC-MR algorithm of 0～4 is as it is shown in figure 5, institute Having predictive value the most close with measured value, maximum relative error is 5.18%, and average relative error is 0.49%, it was predicted that result Ideal.

Claims (7)

1. the efficiency Forecasting Methodology of a WSN data Lossy Compression Algorithm based on linear fit, it is characterised in that comprise following Step:

Step 1: selected sensing node and wireless sensing network data Lossy Compression Algorithm based on linear fit；

Step 2: according to the actual hardware parameter of sensing node, calculate its hardware coefficient k by formula (1)；

$k=\frac{U_{RF}{I}_{RF}}{U_{mcu}{I}_{mcu}}\×\frac{f_{mcu}}{R_{baud}}--\left(1\right)$

Wherein, U_mcuAnd I_mcuAverage current under the running voltage of the respectively MCU of sensing node and activity pattern, U_RFAnd I_RFPoint Not Wei average current under the running voltage of wireless communication module of sensing node and activity pattern, f_mcuWork frequency for MCU Rate, R_baudBaud rate for radio communication；

Step 3: according to normalized sensor samples data, to error margin ε and compression ratio R_CRelation carry out multinomial plan Close, shown in polynomial fitting such as formula (2)；Factor alpha in digital simulation multinomial₁,α₂,…,α_n, obtain R_CPrediction express Formula；

R_C=R_C0+α₁ε+α₂ε²+α₃ε³+…+α_nεⁿ (2)

Wherein, n is the order of polynomial fitting, R_C0It is compression ratio when zero for error margin；

Step 4: according to the current given or error of that input (determining according to the required precision of reality application) data lossy compression method Tolerance limit (i.e. allowable error) ε, calculates compression ratio R by polynomial fitting_CPredictive value；

Step 5: calculate the software coefficient s of selected compression algorithm by formula (3)；

S=aR_C+b (3)

Wherein, coefficient a and b meets formula (4):

$a=\frac{1}{m}(N_{cycle3}-N_{cycle4}),b=\frac{1}{m}(N_{cycle2}+N_{cycle4})---\left(4\right)$

In formula, N_cycle2For each data need the algorithm steps performed carry out the clock periodicity needed for unit data compression, N_cycle3It is that the algorithm steps only just performed the data being compressed out carries out the clock periodicity needed for unit data compression, N_cycle4It is needed for the algorithm steps that the data only remained being not compressed just perform carries out unit data compression Clock periodicity；M represents that each data determined by data type need to account for memory-aided number of bits；

Step 6: by the hardware coefficient k of sensing node calculated in above-mentioned steps, compression ratio R_CPredictive value and selected compression calculate The software coefficient s of method, brings the efficiency computing formula (5) of algorithm into, obtains the efficiency predictive value η of algorithm_E:

${\mathrm{\η}}_E=(R_C-\frac{s}{k})\×100\%---\left(5\right).$

The efficiency Forecasting Methodology of WSN data Lossy Compression Algorithm based on linear fit, its feature the most according to claim 1 Being, described step 3 comprises the following steps:

1) initial value of the order n of empirically determined polynomial fitting, n is positive integer；

2) polynomial fitting is set as shown by the following formula:

R_C=R_C0+α₁ε+α₂ε²+α₃ε³+…+α_nεⁿ；

3) according to the maximum ε of n and input or given error margin_max, by formula ε₁=ε_max/ n determines as independent variable The reduced scale ε of the i.e. abscissa of error margin₁；

4) according to formula ε_i=i ε₁Determine the Along ent ε of error margin_i(i=1,2 ..., n)；

To same distribution characteristics, normalized sensor samples data, it is compressed respectively by the error margin value of corresponding Along ent, Obtain Along ent ε_i(i=1,2 ..., n) corresponding compression ratio R_Ci(i=1,2 ..., when actual value n) and error margin are zero Compression ratio R_C0Actual value；

5) according to the actual value (ε of Along ent and the compression ratio of correspondence thereof₁,R_C1)、(ε₂,R_C2) ..., (ε_n,R_Cn), code requirement Fitting of a polynomial computing formula (7) calculates the polynomial coefficient b that standardizes₁,b₂,…,b_n；

$\left[\begin{array}{c}{b}_1\\ b_2\\ .\\ .\\ .\\ b_n\end{array}\right]={\left[\begin{array}{cccc}1& 1& \mathrm{...}& 1\\ 2& 2^2& \mathrm{...}& 2^n\\ .& .& & .\\ .& .& \mathrm{...}& .\\ .& .& & .\\ n& n^2& \mathrm{...}& n^n\end{array}\right]}^{-1}\left[\begin{array}{c}{R}_{C1}-R_{C0}\\ R_{C2}-R_{C0}\\ .\\ .\\ .\\ R_{Cn}-R_{C0}\end{array}\right]---\left(7\right)$

6) the coefficient b obtained according to formula (7)₁,b₂,…,b_n, by relational expressionCalculate the coefficient of polynomial fitting α₁,α₂,…,α_n；

7) according to polynomial fitting R_C=R_C0+α₁ε+α₂ε²+α₃ε³+…+α_nεⁿ, calculate Along ent ε_i(i=1,2 ..., n) corresponding Compression ratio R_Ci(i=1,2 ..., predictive value n)；

8) by compression ratio R_Ci(i=1,2 ..., predictive value n) and actual value, calculate average fit error；If average fit error Exceeding input or given error margin, n adds 1, returns the 2nd) step；Until average fit error less than or equal to input or Given error margin, terminates the Fitting Calculation；By the up-to-date order n obtained and factor alpha₁,α₂,…,α_nAs polynomial fitting Order and coefficient, obtain R_CPrediction expression.

The efficiency Forecasting Methodology of WSN data Lossy Compression Algorithm based on linear fit, its feature the most according to claim 2 It is, described step 1) in, if to error margin ε and compression ratio R_CRelation carry out whole section of matching, then the initial value of n takes 4；If It is to error margin ε and compression ratio R_CRelation two sections be fitted, then the initial value of n takes 2.

The efficiency Forecasting Methodology of WSN data Lossy Compression Algorithm based on linear fit, its feature the most according to claim 2 It is, described step 8) in, average fit error calculating step is:

For arbitrary R_Ci(i=1,2 ..., n), calculate its relative error；Relative error is equal to R_CiThe difference of predictive value and actual value Absolute value divided by this actual value；

Calculate all R_Ci(i=1,2 ..., average fit error n)；Average fit error is equal to all R_Ci(i=1,2 ..., n) The arithmetic mean of instantaneous value of relative error.

The efficiency Forecasting Methodology of WSN data Lossy Compression Algorithm based on linear fit, its feature the most according to claim 2 It is, also includes following to compression ratio R_CPrediction expression carry out the step of on-line correction:

) the selected algorithm of observation reality given or under the error margin of input, carry out sensing data and compress the compression ratio obtained Actual value；

) according to step 8) R that obtains_CPrediction expression, be calculated under the actual given or error margin of input, compression The predictive value of rate；

) according to the actual value of compression ratio and predictive value, calculate the relative error of compression ratio predictive value；

If) this relative error less than or equal to set threshold value, then R_CPrediction expression keep constant；Otherwise, by this node The actual value of nearly sensing data, the actual error margin given or input and corresponding compression ratio once is as sample number According to, and sensing data therein is first done normalized, the most again to error margin ε and compression ratio R_CRelation carry out many Item formula matching, updates R_CPrediction expression；Described setting threshold value is less than the given or error margin of input；

) proceed to step 4.

The efficiency Forecasting Methodology of WSN data Lossy Compression Algorithm based on linear fit, its feature the most according to claim 5 Being, described setting threshold value draws the 90%～95% of error margin that is fixed or that input.

The efficiency Forecasting Methodology of WSN data Lossy Compression Algorithm based on linear fit the most according to claims 1 to 6, its It is characterised by, in described step 4, according to compression algorithm program code, by IAR simulation development system platform, carries out following meter Calculate:

1) calculate the algorithm steps being required for performing to each data and carry out the clock periodicity needed for unit data compression N_cycle2；

2) calculate the algorithm steps only data being compressed out just performed and carry out the clock cycle needed for unit data compression Number N_cycle3；

3) calculate only the data being retained when just are needed the algorithm steps of execution carry out needed for unit data compression time Clock periodicity N_cycle4；

4) press the value of formula (4) design factor a and b, be calculated software coefficient s by formula (3) the most again.