CN105046880A - Method of intelligent mobile terminal for carrying out danger monitoring and early warning based on Doppler effect - Google Patents

Abstract

The invention provides a method of an intelligent mobile terminal for carrying out danger monitoring and early warning based on a Doppler effect. The present study rarely involves detection for a potential danger brought about by usage of intelligent equipment, and an existing method based on images and additional equipment has inherent limitations and deficiencies. The method provided by the invention comprises the steps of firstly judging whether a user stays at a walking state or not by using accelerometer data, then monitoring the ambient environment in real time by using a sound Doppler effect and sound ranging, judging whether environmental information has a potential danger or not through a classifier, carrying out early warning on the danger according to the danger level, and timely warning the user of existence of the danger. The method provided by the invention has the characteristics of convenience, timeliness, accuracy, ability of being user-friendly, low power consumption and the like. An experimental result shows that the method has high accuracy and high timeliness and can carry out early warning on dangers. It is believed that the method can play the characteristics of convenience, efficiency and accuracy and has long-term and general applications in the field of mobile danger detection and the field of blind guidance.

Description

A kind of intelligent mobile terminal carries out the method for hazards monitoring and early warning based on Doppler effect

Technical field

The invention belongs to signal transacting, sorter and sensor field, be specifically related to a kind of intelligent mobile terminal carries out hazards monitoring and early warning method based on Doppler effect.

Background technology

Along with the continuous progress of society and making rapid progress of science and technology, the life style of people is constantly changed.The high-performance intelligent mobile terminal of new generation taking smart mobile phone as representative is simple to operate with it, and the feature such as to be easy to carry gives people great facility in life, and in this case, people also improve gradually for the degree of dependence of smart machine.On the other hand, a lot of people is caused all to be absorbed in mobile phone whenever and wherever possible to the dependence of mobile phone just, even if also play in hand in trip process, thus be easy to ignore hazards potential in surrounding environment owing to diverting one's attention, produce potential safety hazard, gently then fall, heavy then get into an accident.Therefore how effectively to avoid causing diverting one's attention and meeting accident being problem demanding prompt solution owing to playing mobile phone.

Traditional Environment Obstacles detection method, mainly based on ranging technology, comprises laser ranging, infrared distance measuring, ultrasonic ranging etc.This type of Environment Obstacles detection technique precision is high, identification is accurate, belongs to precise distance measurement, is widely used in military field, industrial measurement and control field etc.But above ranging technology need specific sensor and corresponding hardware supported, cost high, be not easy to carry with, be not suitable for the use of individual and family.

Also there is detection of obstacles application in smart machine, mainly comprise two kinds of solutions.The first is directly obtained ambient image by the post-positioned pick-up head of smart machine and then utilized computer vision technique to judge whether there is barrier in environment.The method can be more accurate environmental risk factors is judged, but himself has very high requirement to equipment posture, external light source brightness and line of sight direction, usually can only detect the barrier in bright light environments on specific direction, and when detecting, resource consumption is large, real-time is low.The second increases a laser range finder or ultrasonic wave module acquisition environmental information by extra on smart machine, at the enterprising row relax of smart machine, obtains the distance of barrier.The method precision is high, but needs extra hardware device, and portability is low.

Summary of the invention

In order to solve the problems of the prior art, the present invention proposes one and utilizes accelerometer to judge to walk line state, and obtain ambient condition information based on sound Doppler effect and sound ranging, the danger classes that combining classification device obtains carries out early warning, evades people and to carry out the method for hazards monitoring and early warning based on Doppler effect owing to using mobile phone cause the diverting one's attention intelligent mobile terminal of the potential safety hazard produced.

In order to realize above object, the technical solution adopted in the present invention is: comprise the following steps:

1) state-detection: judge whether user is in walking states, and whether use intelligent mobile terminal equipment;

2) environmental monitoring: detect the mistiming t launching sound wave and reflective sound wave, calculate the distance S between sound source and barrier, when sound source and user carry out relative motion, the different generation frequency displacement of the frequency that acoustic vibration frequency and sound source that user receives send, the frequency shift (FS) of sound wave and reflective sound wave is launched in contrast, the speed of related movement in surrounding environment between mobile object and intelligent mobile terminal equipment can be detected, thus judge whether by dangerous generation;

3) danger classes classification and early warning: judge whether dangerous signal by support vector machine classifier, if dangerous signal, then judge that dangerous degree is carried out after early warning obtains threat data by KNN algorithm, utilize KNN algorithm to build vector space model and hazard level to be classified and to user's early warning.

Described step 1) in judge whether user uses mobile phone according to whether lighting of intelligent mobile terminal equipment screen, light expression and use, do not light expression and do not use.

Described step 1) in utilize the regularity of the accelerometer data of intelligent mobile terminal equipment to vibrate to judge people whether in walking, under static state accelerometer data microvibration near 0, on foot time, data can to vibrate by a relatively large margin.

Described step 2) in the sound wave of intelligent mobile terminal equipment periodic transmission particular amplitude, frequency and sampling rate, detect the mistiming t launching sound wave and reflective sound wave, sound wave is velocity of propagation v=332m/s in atmosphere, thus the distance S obtained between intelligent mobile terminal equipment and barrier is:

Described step 2) in intelligent mobile terminal equipment and barrier have relative motion, the reflective sound wave received has frequency shift (FS) with transmitting sound wave, the aerial velocity of propagation of sound wave is v=332m/s, f is the original transmitted frequency of sound wave, the reflective sound wave frequency that frequency displacement occurs is f ', then the relative velocity v of user and barrier ₀drawn by following formula:

Wherein ,+represent both there is close relative motion ,-represent both have away from relative motion.

Described step 2) launch and adopt Butterworth LPF to reduce ambient noise in the detection of sound wave and reflective sound wave to obtain reflective sound wave.

Described step 3) in obtain after threat data, KNN algorithm adopts vector space model to classify, the data similarity of identical category is high, may classifying of unknown categorical data is predicted by the similarity calculated with known class data, utilize Hamming distances as distance metric, calculate the individual minimum distance of K in Hamming distances and classification by majority voting, can danger classes be obtained.

Described step 3) obtain after danger classes, according to danger classes classification different with different intelligent mobile terminal shockproofness to user's early warning.

Described step 3) in need Training Support Vector Machines sorter, Doppler shift, obstacle distance, motion state, movement velocity input sorter are carried out training to adjust classifier parameters, deconditioning after the rate of accuracy reached of sorter in certain distance to threshold value.

Described support vector machine builds higher-dimension lineoid and classifies, and optimal hyperlane found by training classifier, and finding optimal hyperlane is minimize under constraint condition | and w|, w are hyperplane method vector:

$\arg {\min }_{w,b}\frac{{||w||}^2}{2}$

Meet y _i(wx _i-b)>=1, wherein 1=1 ..., n;

Use non-negative Lagrange's multiplier α _isolve:

$\arg {\min }_{w,b}{\max }_{\mathrm{\α}\≥0}\{\frac{1}{2}{||w||}^2-\underset{i=1}{\overset{n}{\Σ}}{\mathrm{\α}}_i\[y_i({\mathrm{wx}}_i-b)-1\]\}$

Utilize Quadratic Programming Solution:

$w=\underset{i=1}{\overset{n}{\Σ}}{\mathrm{\α}}_i{y}_i{x}_i$

Corresponding x _ibe exactly support vector, these support vectors are on edge and meet y _i(wx _i-b)=1.

Compared with prior art, the present invention utilizes accelerometer to judge, and user walks line state, and based on sound Doppler effect and sound distance-finding method Real-Time Monitoring surrounding environment, sorter model is utilized to classify to environmental information, early warning is carried out according to danger classes, additionally do not increasing on the basis of specialized equipment, achieve and be easy to carry, accuracy in detection is high, real-time is good, user friendly, the feature such as low in energy consumption, in time for the people being absorbed in intelligent mobile terminal provides surrounding environment danger early warning, and can guide service further for there being the crowd of visual function disorder to provide simple and reliable.

Further, utilize whether lighting of device screen to judge whether user uses intelligent mobile terminal, light expression and use, do not light expression and do not use; People's health when walking can rise and fall along with paces, vibrates within the specific limits.The regularity vibration of accelerometer data can be used for judging that whether people is in walking.The object of state-detection is to select user to need the state of risk prediction, other time etching system be in dormant state, to reduce the consumption of electricity.

Further, environmental monitoring can be launched sound wave and be gathered reflective sound wave, and ultimate principle detects the mistiming of launching sound wave and reflective sound wave, can calculate the distance between sound source and barrier.When Doppler effect and sound source and observer carry out relative motion, the different generation frequency displacement of the frequency that acoustic vibration frequency and sound source that observer receives send, the frequency shift (FS) of sound wave and reflective sound wave is launched in contrast, the speed of related movement in surrounding environment between mobile object and smart machine can be detected, thus judge whether by dangerous generation.

Further, use the noise in Butterworth LPF removal environment, thus obtain reflective sound wave and improve accuracy.

Further, in daily life, the security threat that the motor vehicle of fast running causes far above the threat of fixed obstacle, on the other hand, in-plant barrier is also more dangerous than slightly remote barrier, so the present invention arranges three kinds of danger classess: high, medium and low.The potential danger of the motor vehicle in traveling is high-grade, and the fixed obstacle within 3 meters is middle grade, and the fixed obstacle within 5 meters is inferior grade.Danger is in various degree with different shockproofness reminding users, and higher grade, shakes stronger.The classification of danger classes is realized by two steps.

Accompanying drawing explanation

Fig. 1 is entire system process flow diagram;

Fig. 2 is walking states overhaul flow chart;

Fig. 3 is the vibrorecord of walking states;

Fig. 4 is that Doppler and sound ranging carry out environment measuring process flow diagram.

Embodiment

Below in conjunction with accompanying drawing and specific embodiment, the present invention is further illustrated.

See Fig. 1, the present invention includes following steps:

1) state-detection: judge whether user is in walking states, and whether use intelligent mobile terminal equipment;

2) environmental monitoring: detect the mistiming t launching sound wave and reflective sound wave, calculate the distance S between sound source and barrier, when sound source and user carry out relative motion, the different generation frequency displacement of the frequency that acoustic vibration frequency and sound source that user receives send, the frequency shift (FS) of sound wave and reflective sound wave is launched in contrast, the speed of related movement in surrounding environment between mobile object and intelligent mobile terminal equipment can be detected, thus judge whether by dangerous generation;

3) danger classes classification and early warning: judge whether dangerous signal by support vector machine classifier, if dangerous signal, then judge that dangerous degree is carried out after early warning obtains threat data by KNN algorithm, utilize KNN algorithm to build vector space model and hazard level to be classified and to user's early warning.

See Fig. 2 and Fig. 3, state-detection judges whether user is in walking states and whether uses equipment, walks while need to carry out danger early warning when using mobile phone as user.Utilize whether lighting of device screen to judge whether user uses mobile phone, light expression and use, do not light expression and do not use.People's health when walking can rise and fall along with paces, vibrates within the specific limits.The regularity vibration of accelerometer data can be used for judging that whether people is in walking.The object of state-detection is to select user to need the state of risk prediction, other time etching system be in dormant state, to reduce the consumption of electricity.

See Fig. 4, environmental monitoring can be launched sound wave and be gathered reflective sound wave, and ultimate principle detects the mistiming of launching sound wave and reflective sound wave, can calculate the distance between sound source and barrier.When Doppler effect and sound source and observer carry out relative motion, the different generation frequency displacement of the frequency that acoustic vibration frequency and sound source that observer receives send, the frequency shift (FS) of sound wave and reflective sound wave is launched in contrast, the speed of related movement in surrounding environment between mobile object and smart machine can be detected, thus judge whether by dangerous generation.After acquisition voice data, need to use the noise in bandpass filter removal environment, thus obtain reflective sound wave and improve accuracy.The present invention detect two kinds dangerous close: the active of the motor vehicle in traveling near and fixing barrier passive close.Motor vehicle speed in traveling is very fast, if reflected sound wave frequency raises represent that motor vehicle is just near people, if reflected sound wave frequency reduces represent that motor vehicle is from people.The frequency produced due to the engine in motor-driven vehicle going process and tire and pavement friction is lower, and the present invention utilizes smart machine to launch the sound of 1500Hz, receives its reflective sound wave.If motor vehicle speed is 15m/s, the Doppler shift of generation is about Δ f=67Hz, easily detects.Because direction any around user occurs that the potential danger of the motor vehicle in traveling is all very high, as long as so detect by motor vehicle close to just carrying out early warning to user.For fixed obstacle, the average velocity of people's walking is generally 1.5m/s, the Doppler shift Δ f=1.5Hz now occurred, and this frequency change is less, is not easy to detect, so adopt distance measuring method to obtain the distance of barrier.People is when outdoor walking, and range finding mainly can detect the barrier of four direction all around, and whether be in user front to distinguish barrier, the present invention retains the historical information of the obstacle distance detected, the distance of up-to-date detection is compared with historical information.If there is one group of range information substantially to remain unchanged, illustrate that it represents user and the distance of barrier being similar to wall, because user is in advance, so wall is in the left side or the right of user, this both direction all can not cause danger.If one group of range information becomes large gradually, user is described away from this barrier, this barrier has been in after one's death, can not cause danger.If one group of range information diminishes gradually, user is described just gradually near this barrier, now needs to user's early warning.The present invention rejects the barrier at about user and rear by the method, only pays close attention to the barrier in front and early warning.

Dangerous degree is determined in danger classes classification.In daily life, the security threat that the motor vehicle of fast running causes far above the threat of fixed obstacle, on the other hand, in-plant barrier also than barrier is more dangerous slightly at a distance, so the present invention arranges three kinds of danger classess: high, medium and low.The potential danger of the motor vehicle in traveling is high-grade, and the fixed obstacle within 3 meters is middle grade, and the fixed obstacle within 5 meters is inferior grade.Danger is in various degree with different shockproofness reminding users, and higher grade, shakes stronger.The classification of danger classes is realized by two steps.First judge whether dangerous signal by support vector machine classifier, because support vector machine is typically used as two-value classification, filter out the efficiency that adventurous signal can improve system.If dangerous signal, then judge that dangerous degree carries out early warning by KNN algorithm.

Concrete implementation step is as follows:

Step one, state-detection:

1. user installation hazards monitoring system;

2. system hibernates;

If 3. screen is lighted, jump to 4, otherwise jump to 2;

4. background thread is waken up, and collects accelerometer data;

5. degree of will speed up counts by low-pass filter except denoising;

6. judge whether in walking by moving window;

If 7. judge that user jumps to 8 in walking, otherwise jump to 2;

If 8. screen is closed, jump to 2, otherwise jump to step 2.

Step 2, environmental monitoring:

1. original sound data is launched and is gathered: utilize smart machine audio amplifier to launch the sound wave of fixed frequency, amplitude and sampling rate, utilizes sound receiver to collect sound wave simultaneously;

2. bandpass filtering: the sonic data of collection is carried out noise reduction by Butterworth filter, obtains the reflective sound wave launching sound wave;

3. extract doppler information and range information, jump to step 3.

Step 3, danger classes are classified:

1. before system is issued, carry out Experiment Training sorter;

2., by Doppler shift, obstacle distance, motion state, movement velocity input sorter carries out training to adjust classifier parameters;

3. deconditioning after the rate of accuracy reached of sorter in certain distance to threshold value;

4. being judged as dangerous situation for being classified device, utilizing KNN algorithm to be divided into high, medium and low three danger classess;

5. according to different danger classes, vibrations early warning is carried out to user.

The present invention specifically comprises:

1. state-detection

Device screen lights waken system, collects accelerometer data.When walking, health can rise and fall along with paces, shows the vibration for numerical value on accelerometer data.See Fig. 3, under static state accelerometer numerical value microvibration near 0, when walking, numerical value can to vibrate by a relatively large margin;

Utilize this feature, arranging moving window size is 20, first numerical value is added that the absolute value of minimum value is to remove negative sign, the mean value M afterwards in calculation window and variance S.If M < is 3S, be then judged as away line state.

2. bandpass filtering noise reduction

The sound-track engraving apparatus of existing smart mobile phone all has decrease of noise functions, and because model is different, noise reduction is also not quite similar.Sonic detection need for environment reduces neighbourhood noise around, and the present invention selects Butterworth filter, and be characterized in that the frequency response curve in passband is the most level and smooth, do not rise and fall, suppressed frequency band drops to zero gradually.

Butterworth LPF can square to represent the formula of frequency with following amplitude:

${\left|H\left(\mathrm{\&omega;}\right)\right|}^2=\frac{1}{1+{\left(\frac{\mathrm{\&omega;}}{{\mathrm{\&omega;}}_c}\right)}^{2n}}=\frac{1}{1+{\mathrm{\&epsiv;}}^2{\left(\frac{\mathrm{\&omega;}}{{\mathrm{\&omega;}}_p}\right)}^{2n}}$

Wherein n represents the exponent number of wave filter.The present invention selects 3 as the exponent number of wave filter, and now suppressed frequency band fall off rate is fast, meets filtering requirements.Neighbourhood noise mostly is high frequency noise, people around's noise of speaking is 500-700Hz, detect frequency of sound wave at about 1500Hz, therefore the present invention designs Butterworth digital band-pass filter, band connection frequency 1200-1600Hz, stopband upper limiting frequency 1700Hz, stopband lower frequency limit 1100Hz, pass band damping is less than 1dB, and stopband maximum attenuation is greater than 20dB, sampling rate 2000Hz.By bandpass filter, can filtering major part noise, to obtain target sound waves.Sound wave intensity (amplitude) in atmosphere propagation can decay, and unifrequency sound is in comparatively long-distance communications, and sound pressure level L decay (acoustic pressure gets log) is linear substantially, namely

L＝as

Wherein s is distance, and a is attenuation coefficient, can table look-up obtain according to temperature humidity frequency.By detecting acoustic pressure and frequency, reflective sound wave can be obtained.

3. sound ranging

The sound wave of smart machine periodic transmission particular amplitude, frequency and sampling rate, detect the mistiming t launching sound wave and reflective sound wave, sound wave is velocity of propagation v=332m/s in atmosphere, can the distance S between computational intelligence equipment and barrier be:

$S=\frac{1}{2}\&times;v\&times;t$

4. Doppler effect

When Doppler effect refers to that smart machine and barrier have a relative motion, the reflective sound wave received with launch sound wave and have certain frequency shift (FS) phenomenon.Ultimate principle is if user and barrier have relative velocity v ₀, the original transmitted frequency of the aerial velocity of propagation of sound wave to be v=332m/s, f be this sound wave, then occur frequency displacement reflective sound wave frequency f ' be:

$f^{\&prime;}=\left(\frac{v\&PlusMinus;v_0}{v}\right)f$

Wherein ,+represent both there is close relative motion ,-represent both have away from relative motion.

Relative velocity v between smart machine and barrier ₀for:

Wherein ,-represent both there is close relative motion ,+represent both have away from relative motion.

5. Training Support Vector Machines sorter

Support vector machine builds one or more higher-dimension lineoid and classifies, and lineoid is classification boundaries.Sorter training is exactly find optimal hyperlane.Finding optimal hyperlane is minimize under constraint condition | w|, w are hyperplane method vector:

$\arg {\min }_{w,b}\frac{{||w||}^2}{2}$

Meet y _i(wx _i-b)>=1, wherein i=1 ..., n.

Use non-negative Lagrange's multiplier α _isolve:

$\arg {\min }_{w,b}{\max }_{\mathrm{\&alpha;}\&GreaterEqual;0}\{\frac{1}{2}{||w||}^2-\underset{i=1}{\overset{n}{\&Sigma;}}{\mathrm{\&alpha;}}_i\&lsqb;y_i({\mathrm{wx}}_i-b)-1\&rsqb;\}$

Utilize Quadratic Programming Solution:

$w=\underset{i=1}{\overset{n}{\&Sigma;}}{\mathrm{\&alpha;}}_i{y}_i{x}_i$

Corresponding x _ibe exactly support vector, these support vectors on edge and meet

y _i(wx _i-b)＝1

6. utilize KNN to carry out danger classes classification

After obtaining threat data, KNN is utilized to classify to its hazard level.KNN adopts vector space model to classify, and the data similarity of identical category is high.May classifying of unknown categorical data can be predicted by the similarity calculated with known class data.Utilize Hamming distances as distance metric.Calculate K (obtaining K by evolution algorithm is 3) individual minimum distance in Hamming distances and classification by majority voting, can obtain danger classes belong to high, medium and low which kind of, and according to classification difference with different shockproofness to user's early warning.

Claims (10)

1. intelligent mobile terminal carries out a method for hazards monitoring and early warning based on Doppler effect, it is characterized in that, comprises the following steps:

1) state-detection: judge whether user is in walking states, and whether use intelligent mobile terminal equipment;

2) environmental monitoring: detect the mistiming t launching sound wave and reflective sound wave, calculate the distance S between sound source and barrier, when sound source and user carry out relative motion, the different generation frequency displacement of the frequency that acoustic vibration frequency and sound source that user receives send, the frequency shift (FS) of sound wave and reflective sound wave is launched in contrast, the speed of related movement in surrounding environment between mobile object and intelligent mobile terminal equipment can be detected, thus judge whether by dangerous generation;

3) danger classes classification and early warning: judge whether dangerous signal by support vector machine classifier, if dangerous signal, then judge that dangerous degree is carried out after early warning obtains threat data by KNN algorithm, utilize KNN algorithm to build vector space model and hazard level to be classified and to user's early warning.

2. a kind of intelligent mobile terminal according to claim 1 carries out the method for hazards monitoring and early warning based on Doppler effect, it is characterized in that: described step 1) in judge whether user uses mobile phone according to whether lighting of intelligent mobile terminal equipment screen, light expression to use, do not light expression and do not use.

3. a kind of intelligent mobile terminal according to claim 2 carries out the method for hazards monitoring and early warning based on Doppler effect, it is characterized in that: described step 1) in utilize the regularity of the accelerometer data of intelligent mobile terminal equipment to vibrate to judge that whether people is walking.

4. a kind of intelligent mobile terminal according to claim 1 carries out the method for hazards monitoring and early warning based on Doppler effect, it is characterized in that: described step 2) in the sound wave of intelligent mobile terminal equipment periodic transmission particular amplitude, frequency and sampling rate, detect the mistiming t launching sound wave and reflective sound wave, sound wave is velocity of propagation v=332m/s in atmosphere, thus the distance S obtained between intelligent mobile terminal equipment and barrier is:

5. a kind of intelligent mobile terminal according to claim 4 carries out the method for hazards monitoring and early warning based on Doppler effect, it is characterized in that: described step 2) in intelligent mobile terminal equipment and barrier have relative motion, the reflective sound wave received has frequency shift (FS) with transmitting sound wave, the aerial velocity of propagation of sound wave is v=332m/s, f is the original transmitted frequency of sound wave, the reflective sound wave frequency that frequency displacement occurs is f ', then the relative velocity v of user and barrier ₀drawn by following formula:

Wherein ,+represent both there is close relative motion ,-represent both have away from relative motion.

6. a kind of intelligent mobile terminal according to claim 5 carries out the method for hazards monitoring and early warning based on Doppler effect, it is characterized in that: described step 2) launch and adopt Butterworth LPF to reduce ambient noise in the detection of sound wave and reflective sound wave to obtain reflective sound wave.

7. a kind of intelligent mobile terminal according to claim 1 carries out the method for hazards monitoring and early warning based on Doppler effect, it is characterized in that: described step 3) in obtain after threat data, KNN algorithm adopts vector space model to classify, the data similarity of identical category is high, may classifying of unknown categorical data is predicted by the similarity calculated with known class data, utilize Hamming distances as distance metric, calculate the individual minimum distance of K in Hamming distances and classification by majority voting, can danger classes be obtained.

8. a kind of intelligent mobile terminal according to claim 7 carries out the method for hazards monitoring and early warning based on Doppler effect, it is characterized in that: described step 3) obtain after danger classes, according to danger classes classification different with different intelligent mobile terminal shockproofness to user's early warning.

9. a kind of intelligent mobile terminal according to claim 8 carries out the method for hazards monitoring and early warning based on Doppler effect, it is characterized in that: described step 3) in need Training Support Vector Machines sorter, Doppler shift, obstacle distance, motion state, movement velocity input sorter are carried out training to adjust classifier parameters, deconditioning after the rate of accuracy reached of sorter in certain distance to threshold value.

10. a kind of intelligent mobile terminal according to claim 9 carries out the method for hazards monitoring and early warning based on Doppler effect, it is characterized in that: described support vector machine builds higher-dimension lineoid and classifies, optimal hyperlane found by training classifier, finding optimal hyperlane is minimize under constraint condition | w|, w are hyperplane method vector:

$\arg {\min }_{w,b}\frac{{||w||}^2}{2}$

Meet y _i(wx _i-b)>=1, wherein i=1 ..., n;

Use non-negative Lagrange's multiplier α _isolve:

$\arg {\min }_{w,b}{\max }_{\mathrm{\&alpha;}\&GreaterEqual;0}\{\frac{1}{2}{||w||}^2-\underset{i=1}{\overset{n}{\&Sigma;}}{\mathrm{\&alpha;}}_i\&lsqb;y_i({\mathrm{wx}}_i-b)-1\&rsqb;\}$

Utilize Quadratic Programming Solution:

$w=\underset{i=1}{\overset{n}{\&Sigma;}}{\mathrm{\&alpha;}}_i{y}_i{x}_i$

Corresponding x _ibe exactly support vector, these support vectors are on edge and meet y _i(wx _i-b)=1.