2012-04-08-fourier-wavelet-motion-3.pdf对小波变换的基础知识，

文件名称: 2012-04-08-fourier-wavelet-motion-3.pdf

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详细说明：对小波变换的基础知识，我们就讲到这里。需要注意的是，这只是小波变换最基本最基本的知识，但也是最核心的知识。掌握了这些，代表你对小波变换的物理意义有了一定的了解。但对于小波变换本身的讲解，一本书都不一定能将讲透，还有很多的基础知识我都没有讲，比如如何构建自己的scaling function，选取合适的系数集 h[k]，并由此构建自己的wavelet functions。所以，如果有深入下去研究的同学，好好买一本书来看吧。而只是希望用小波变换来服务自己的应用的同学，个人觉得这些知识已经足够让你用来起步了。functionality make it attractive for most drivers. Even drivers who do not cur- rently own a(P)HEV could use this application to predict the energy and en vironmental impacts if they switch to(P)HEVS. Moreover, the aggregated data from a large number of drivers can be invaluable for vehicle manufacturers and researchers as they keep improving the design of (P)heVs A number of sensing capabilities are available in modern smartphones, mak- ing it possible for personalized driving behavior monitoring and analysis. How ever, signals obtained from individual sensors suffer from a number of intrinsic and contextual issues: (1)noise, drift, and mis-synchronization of multi-modality driver-vehicle data; (2) substantial disorientation of vehicle movement sensing at the start of and during each driving trip; and (3)complex(p)hev operation mechanisms and driver-dependent vehicle performance To address these issues, we propose innovative techniques that "fuse"to- gether multiple types of sensor readings to enhance signal quality and driver vehicle sensing, as well as techniques that classify driver-specific operation modes and analyze the corresponding energy and environmental impacts Our work makes the following contributions: (1) Multi-modality driver-vehicle sensing. We propose fully-automated, phone-based sensing techniques that effectively correct the noise, drift, mis synchronization in multiple types of sensor data, as well as compensating ini- tial/dynamic phone-vehicle disorientation using wavelet-based analysis (2)Driver-specific(P)HEV analysis. We propose operation mode classifi cation, run-time energy use and fuel-CO2 emission modeling to map specific driving behavior to(P)hev energy and environmental impacts; and (3) Real-world deployment and user driving studies. System evaluation demonstrates high correlation for vehicle sensing (0.88-0.96), energy use and fuel use modeling(0. 918, 0.996), operation mode classification(89.9%, 87.8% accurac The rest of the paper is organized as follows. Section 2 presents the prob lem formulation and design overview. Section 3 and Section 4 describe in de tail multi-modality driver-vehicle sensing and driver-specific(P)HEV analysis Section5 describes system deployment and user studies. Section 6 evaluates the proposed system. Section 7 discusses related work Section 8 concludes 2 Problem Formulation and Design Overview HEVs and PHEVs are the emerging solutions for transportation electrification HEVs feature a gasoline internal combustion engine(Ice) and an electric mo- tor equipped with a battery system for harnessing and storing run-time braking energy PHEVs have an additional electrical plug to directly recharge the bat- tery system from the electrical grid The energy and environmental impacts of (P)HEVs are primarily determined by(P)hEV operation, which in turn is heav- ly affected by user-specific run-time driving behavior, such as speed, accelera tion, and road condition etc Figure 2 shows the fuel use, CO2 emissions, and battery system long-term capacity degradation based on eight different users 5 3 4 2 Driver Q dRiver 3 Driver 6 1 Driver 4 Driver 8 0 0 02468101214 Driver ID Year Fig. 2. Heterogeneous fuel use, CO2 emissions, and battery system long-term capacity degradation based on eight different users' daily commute driving profiles daily commute driving profiles Among the eight drivers, over 3x variation is observed in terms of fuel use and co2 emissions for battery system, and based on the system-level battery model developed by Li et al. [16], over 9x long-term capacity variation can be expected a comprehensive and quantitative sensing and analysis system is thus es sential for advancing(P)HEV technology and promoting its market adoption by individual drivers. We propose a personalized multi-modality sensing and analysis system that effectively captures and fuses the following signals: (1) user-specific driving behavior, including speed, acceleration, road and traffic conditions; and(2)(P)HEv operation profile, including fuel use, battery sys- tem charge/discharge current and voltage Accurate characterization and quantification of the relationships between user-specific driving behavior and(P)hEv energy and environmental impacts require fine-grained time-stamped, robust sensor readings during users'driv ing trips, as well as accurate modeling of (P)HEV internal operation mecha nisms. We propose a two-staged process, as illustrated in Figure 1 1. Multi-modality driver-vehicle sensing: The first stage captures and en hances the quality of multiple types of sensor data using novel de-noise, cali bration, and synchronization techniques. It then automatically identifies poten tial phone-vehicle disorientation and compensates the corresponding sensor readings at run-time for accurate vchicle movement sensing Driver-specific(P)HEV analysis: In the second stage, we propose to first map users' driving behaviors to the corresponding(P)hev operation modes ffective mode classifier. Then, leveraging battery system modeling and fuel-CO2 emission modeling, we quantitatively analyze the energy and envi ronmental impacts of (P)HEVs under specific user driving behavior 3 Multi-modality Driver-Vehicle Sensing Using multiple types of sensors that are readily available on mobile phones,we propose techniques to obtain high-quality sensor data for both user driving be- havior and vehicle movement. The challenge is to achieve personalized, accu- rate, and run-time data acquisition with minimum inconvenience and obstruc tion to individual drivers. Specifically, we allow the phone to be unrestricted in the vehicle (i. e, not mounted in a fixed position), yet still effectively identify and remove noises and inconsistencies in multiple types of sensor data, as well as compensating for potential phone-vehicle disorientation e05 8 Pitch 0. 3-axis ceelerouete ont Right 3-axis gyroscope filtered accA Time(s) Fig 3. Linear angular acceleration Fig 4. Acceleration noise when vehicle is sta sensing using accelerometer and gyro- tionary; de-noise via low-pass filtering 3.1 User Driving Behavior Sensing A user's specific driving behavior can be represented by his/her driving trips with regard to speed, acceleration, slope, and turning at individual time points Specifically, speed is directly reported by gPS; slope of the road can be calcu lated from altitude reported by GPS; acceleration is reported by accelerometer but requires further compensation by gyroscope; and vehicle turning informa- tion is derived from gyroscope readings and calibrated by digital compass. as illustrated in Figure 3, accelerometer and gyroscope can be used to sense lincar and angular acceleration. By combining the readings of both sensors, detailed information about the device s six - axis movement in space can be derived noise of sensor is a major technical barrier to precise sensing. There are two primary kinds of noise sources. One is intrinsic high frequency noise due to the combined effects of thermally dependent electrical and mechanical noise [21] The other is contextual noise caused by vchicle vibration during a trip whose frequency usually peaks at around 3-5Hz. For example( Figure 4), acceleration readings ranging from -0.2 to 0. 2m/s- are reported even when the vehicle is stationary(speed=O). A low-pass filter with 2Hz cutoff frequency is applied to improve the signal to noise ratio. The noise characteristics of gyroscope are more complex, which we address later in this section nother source the drift of sensor. In particul calculating the angular position using gyroscope requires integration of noisy angle change rate readings, which accumulates over time and results in large drift. Such drift can be potentially compensated by periodically resetting the yroscope to the known directional source: gravity, which is collected when ever the phone is determined to be stationary, e.g. when the vehicle is stopped for traffic light. The acceleration vector of gravity is parallel to the yaw-axis of the reference coordinate system, which requires special calibration with the dig ital compass. Figure 5 shows an experiment in which the phone was returned to the original position after 14 minutes of driving We can see that digital com- 40 000 ∠ Speed- g10 Gyro Calibrated 360 Speed Gyro Original 180 10152025303540 0152025303540 00000 90 90 45 45 Current Current 180 1806“101520253035 10152025303540 360 360 180 180 0150300450600750900 Time(s) 4202 AccA 0 Acca 10152025303540 10152025 Time (S) Fig. 5. Degree of drift: Digital compass Fig. 6. Unsynchronized (left)vs synchronized vS. gyroscope(original and calibrated).(right) signals pass has much less drift than gyroscope. In our system, the gyroscope value is calibrated whenever the compass reading is steady for a period of time Using OBd devices, information regarding the(P)hEV operations can also be collected, including speed, steering, battery system charge/discharge and fuel use. Such information is used as ground truth in our evaluations. One ma or challenge lies in appropriate synchronization of multi-modality data from three different data sources: mobile phone internal combustion engine, and battery system. As demonstrated in Figure 6, when the vehicle speeds up from stationary status both current and acceleration should change to non-zero val ues at the same time, but they did not in the raw monitored data. We propose to synchronize the multi-modality data streams by maximizing the correlation between each data stream and the reference data stream (A,B) EI(A-WA(B-uB) OAOB We select acceleration as the reference stream since its noise can be effectively removed and is more precise than others. We also exploit stops(based on speed and acceleration to segment each trip into several sub-trips and apply synchro- nization to cach sub-trip 3.2 Vehicle Movement Sensing Although it is possible to obtain vehicle movement information by mounting a phone in a fixed position before each trip, it is cumbersome and inconvenier for users. Our solution allows the phone to be unrestricted in the vehicle. This leads to potential phone-vehicle disorientation. Let(X,Y, z) be the vehicle's Cartesian frame of reference, and(a, 3, 2)be the phonc's frame of reference. As illustrated in Figure 7, these two frames of reference should be well-oriented in the ideal case. However the phone may be placed anywhere in the vehicle (e.g. driver's pocket)at trip start(initial disorientation), and may shift around during a driving trip(dynamic disorientation). Such disorientation can be sub- stantial and highly dynamic, as shown in Figure 8 Fig. 7. Frame of ref orientation of (red). Left ented: Middle: initial disorientation: Right dynamic disorientation Initial Disorientation Compensation. The phone's(a, 3, a)axes are disoriented with respect to the vehicles(x, Y, Z) axes. Leveraging the automatic attitude initialization method originally proposed by Mohan et al. [20], the rotation ma trix needs to be calculated and applied to y, and z in sequence in order to transform arbitrary orientation of (C, y, 2) to(X,Y, 2). According to the defini- tion of Euler Angle [1], any orientation of the accelerometer can be represented a p o of y followed by a tilt 0 of z, and then a post-rotation a of Y. Thus, the rotation matrices associated with these three rotation angles are cos o0-sin g cos o sin00 cos ao-sin a 6=010,R in 0 cos00,R 010 noO cOS o sin a o cos a reading ar, ag, az] when the vehicle is stationary, i.e. gravity [0, 10/ ometer nd e can lated by applying the rotation matrix to the accele cos 0 sing 0 0-sinφ 木木C in 6 cos 0 0 010 a(3) n 0 coS Thus, 0 Next, we need to estimate the post-rotation a of y. whe rip starts, the vehicle goes from stationary to acceleration, producing a force in a known direc- tion. Suppose that after rotation of o and 0, the acceleration vector [ax, ay, azI hanges to az, reflecting the force produced. While in the vchicle's co ordinate system, only az has a significant value and ax should be 0 he summation vector of ax and a is exactly az, and we get a an In the end, we get a rotation matrix R =Ra*Re Ro, which can transform accelerometer readings of the mobile phone to the vehicle's true accelerations Note that this approach also works when car starts on a non-flat surface Dynamic disorientation Compensation Dynamic disorientation is highly un- predictable and may occur at anytime during a trip. If not detected and cor- rected in real time, it introduces significant crror to the sensing valuc, as illus trated in Figure 8. Thus, it needs to be compensated before the measured accel- eration values can be used We propose a wavelet-based technique, which ana lyzes the rotation information received from the gyroscope in order to separate true vehicle movement from contextual noise. This technique is based on multi resolution analysis [26l, by which a given time-series signal can be decomposed into multiple wavelet levels, each corresponding to a specific frequency range 5 Oriented Disoriented Before filtering After filtering 己30 83 0100200300400500600700 80090010001100120013001400 Time(s) Time(s) Fig 8. Error of dynamic disorientation. Fig 9 Gyroscope de-noise using wavelets One important observation is that vehicle movements and phone movements have different characteristics and tend to occur in different time-frequency domains, e.g,vehicle changing lane vs phone moving in driver's pocket Wavelets are particularly suitable for such joint time-frequency analysis Wavelet-based gyroscope noise filtering. The gyroscope signal has unique noise characteristics. True rotation can appear in both high frequency and low frequency, and signal noise cannot be removed via simple low /high-pass filter ing. We leverage a wavelet-based de-noise method [23] to improve the signal quality from gyroscope. Let s(n)=f(n)+ oe(n) be the raw gyroscope signal, where n is the index of equally-spaced time points, f(n) is the true signal and e(n)models the noise. We assume e(n) is a Gaussian white noise and the noise level o equals to 1. We make the following observations: (i) Signal from gyro- scope should be mostly smooth, with a few abrupt changes caused by vehicle turning or phones sudden movement. Therefore, it should have only a few non-zero wavelet coefficients. (ii)A white noise signal is reflected by the coef ficients at all levels. Also, a Gaussian noise after orthogonal wavelet transform still preserves the gaussian property. Thus, noise can be estimated by removing e correla ted signal at each level. Thus, for each level of decomposed signal,we select a threshold(0. 2506 based on our experiments) and ignore high-frequency coefficients whose absolute values are lower than the threshold. we then recon struct the signal using all remaining coefficients. As we can see in Figure 9, the gyroscope signal becomes much smoother after wavelet-based de-noise Wavelet-based movement analysis. Figure 10 schematically depicts the wavelet-based procedure that is applied to the rotation rate signal acquired from gyroscope, which is the combination of three-dimensional signals stotal ich +sroll+ yau. After dwt decomposition using the db6 wavelet func tion, the energy content of each level is calculated and plotted against the ob served movements. As shown in Figure 10, attitude change of the phone caused by vchicle movement and phone movement are well-separated after the de composition-the former by higher-level wavelet coefficients (low frequency domain)and the latter by lower-level wavelet coefficients(high frequency do main). In the left figure, level 4 and 5 coefficients are selected as they correlated well with true phone movements relative to vehicle(blue vertical lines). In the right figure, level 1 and 2 coefficients are selected as they correlated well with rue vehicle turning events 凡▲⊥、▲ a050100150200250300350400a0100200300400500600700 Time(s) Level 4 Level I 50+州+一+++5280 -30 a80 0100200300400500600700 s 10 Level 2 静一+一卡增 123 45 0100200300400500600700 10 Extracted一 Groundtruth Reconstructed 10 0100200300400500600700 Fig 10. Wavelet-based detection of phone movement(Left) and vehicle turning(Right) 4 Driver-specific (P)HEV Analysis Given the multi-modality driver-vehicle data that our sensing system collects our goal is to analyze, quantitatively, how user-specific driving behavior affects (P)HEV operation, which in turn results in different energy use and env mental impacts. This has been a challenging problem due to the high complex ity of (P)HEVS. Leveraging the multi-modality sensing data, we propose an analysis approach that consists of three key components: (1)Operation mode classification characterizes the key(P)HEV operation modes and maps user- specific driving behavior to corresponding operation mode; (2) Energy profile analysis identifies and quantifies the underlying relationship between(p)heV electricity and fuel use and different operation modes; and(3)Fuel-CO2 emis- sion analysis characterizes the relationship between fuel use and greenhouse gas emIssions 4.1 (P)HEV Operation Mode Classification First, we investigate the relationship between user driving behavior and (phev operation. Modeling(P)HEV energy use is a difficult task. On one hand, users driving behaviors are diverse and vary by road and traffic conditions. On the other hand, under different conditions, a(P)HEV may be powered by either battery or fuel, or both, each of which is a complex process. To address these ssucs,we have identified five operation modes for the Toyota Prius control system based on the operation animation displayed on dashboard. The modes are illustrated in Figure 11. Mode 1: Only the battery system is used to drive the vehicle. It occurs primarily during city driving with low speed Mode 2 Extra energy (e. g breaking) is harnessed by the vehicle to charge the batter system. It happens when the vehicle is decelerating. Mode 3: Both the ICE and battery system are providing energy to drive the vehicle. It happens when the Battery Battery Motor Vehicle Motor MotorVehicle Motor VehicteMotor Mode 1 Mode 2 Mode 4 Mode 5 Fig. 11. Categorization of (P)HEV operation modes under different driving scenarios Gear Set Battery General Fig. 12(PHEV en Motor ergy pre ofile ana sis. Engine and bat- Vehicle k TM WM the power demand Traction of the vehicle vehicle is driving at high speed and needs massive amount of energy to sustain the movement Mode 4: ICE is charging the battery system. It occurs when the energy generated by ICE exceeds the need to maintain the vehicle movement Mode 5: ICE is both charging the battery system and powering the vehicle.It typically occurs when the battery's SOC (state of charge) is very low while the vehicle has high energy demand Based on our analysis of real-world user driving data, we choose to use speed, acceleration, acceleration change, and altitude as the input for(p)hev operation mode classification. We then construct a decision tree using the cart method [5]. The output of the model is the working status of the engine(on or off)and the battery system(charging or discharging 4.2(P)HEV Energy Profile Analysis Based on the different operation modes, we develop an analytical (P)HEV model specifically for Toyota Prius in MAtLAB. Prius adopts series-parallel structure in its drive-train, where the engine, generator/motor and traction motor are coupled together through the planetary gear set to provide the demanded trac tion power. The driving power requirement is distributed between the motor and ice depending on the different modes and user-specific driving behavior co us procedure is illustrated in Figure 12. Mathematically, battery energy use can be expressed as [13] △SOC 7Cuc△t Arn△t nM(M,Wm where AsoC is the change of SOC, which is the integration of the exchanged energy between motors and battery system. nG and nM are the efficiency of gen erator /motor and traction motor respectively. They are functions of(TG, wG) and(fm, wM) respectively, where T represents output torque and w represents angular speed And fuel consumption can be calculated b 7E×UE×△t mE(TE, WE

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