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CN107122704A - A kind of gait recognition method based on motion sensor - Google Patents

A kind of gait recognition method based on motion sensor
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CN107122704A
CN107122704ACN201710155546.8ACN201710155546ACN107122704ACN 107122704 ACN107122704 ACN 107122704ACN 201710155546 ACN201710155546 ACN 201710155546ACN 107122704 ACN107122704 ACN 107122704A
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mrow
data
matching
candidate
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柳宇非
刘洁锐
晋建秀
林宏辉
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South China University of Technology SCUT
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Abstract

Translated fromChinese

本发明公开了一种基于运动传感器的步态识别方法,包括下列步骤:通过运动传感器采集获得佩戴用户在行走过程中产生的步态数据;对步态数据进行步态周期估计,对步态数据进行定位切割,实现步态数据的特征值提取;通过步态数据特征值曲线的上升沿延续长度及时间跨度的匹配比较,从匹配库筛选出匹配度高于判定阈值的候选人,将步态数据特征值在频域分别与每一个待识别的候选人的傅里叶变换之后的步态数据进行误差积分得到对每一个待识别的候选人的匹配度,将匹配度最大的候选人认定为身份匹配成功。该方法对用户身份的识别是基于人的步态特征,与指纹识别等传统技术相比更难被仿造,安全性更高,验证过程在使用者自然行走中完成,使用体验更流畅。

The invention discloses a gait recognition method based on a motion sensor, which comprises the following steps: collecting and obtaining gait data generated by a wearing user during walking through a motion sensor; estimating the gait period of the gait data; Carry out positioning and cutting to realize the feature value extraction of gait data; through the matching and comparison of the rising edge continuation length and time span of the gait data feature value curve, the candidates whose matching degree is higher than the judgment threshold are screened out from the matching library, and the gait In the frequency domain, the eigenvalues of the data are integrated with the gait data after the Fourier transform of each candidate to be identified to obtain the matching degree of each candidate to be identified, and the candidate with the highest matching degree is identified as Identity matching succeeded. This method is based on the gait characteristics of human beings to identify the user's identity. Compared with traditional technologies such as fingerprint identification, it is more difficult to be imitated and has higher security. The verification process is completed while the user is walking naturally, and the user experience is smoother.

Description

Translated fromChinese
一种基于运动传感器的步态识别方法A Gait Recognition Method Based on Motion Sensor

技术领域technical field

本发明涉及人体生物识别的技术领域,具体涉及一种基于运动传感器的步态识别方法。The invention relates to the technical field of human body biometrics, in particular to a motion sensor-based gait recognition method.

背景技术Background technique

当今世界,信息技术创新日新月异,以数字化、网络化、智能化为特征的信息化浪潮蓬勃兴起。可穿戴设备已经走进人们的生活,在人们随身的物件上,集成了智能芯片等设备,可以收集用户的生理及使用习惯相关数据,并能通过网络等手段实现习惯的记录,体验的改进,功能的延伸等。但是信息技术高速发展的同时,也给用户的个人数据安全带来了风险,这使得个人数据安全和设备使用便利性存在着一定程度上的矛盾。In today's world, information technology innovation is changing with each passing day, and the wave of informatization characterized by digitization, networking, and intelligence is booming. Wearable devices have entered people's lives. On people's belongings, smart chips and other devices are integrated, which can collect data related to users' physiology and usage habits, and can record habits and improve experience through the Internet and other means. function extension, etc. However, with the rapid development of information technology, it also brings risks to the security of users' personal data, which leads to a certain degree of contradiction between personal data security and device convenience.

当前对步态识别的研究,基本都是基于机器视觉和深度学习,需要同时有多个摄像头获取步态视频进行数据分析,这样会极大增加步态识别实现的成本。目前,亟待提出一种实现成本较低,计算量小,普通终端便可实现,应用范围更广泛的步态识别方法。The current research on gait recognition is basically based on machine vision and deep learning, which requires multiple cameras to acquire gait videos for data analysis at the same time, which will greatly increase the cost of gait recognition. At present, it is urgent to propose a gait recognition method with lower implementation cost, less calculation amount, which can be realized by ordinary terminals and has a wider application range.

发明内容Contents of the invention

本发明的目的是为了解决现有技术中的上述缺陷,提供一种基于运动传感器的步态识别方法,该步态识别方法利用在脚,小腿,或大腿上的运动传感器采集佩戴人的步态信息,这些传感器包括但不限于口袋中的手机,智能运动鞋,运动脚环。然后通过低功耗处理器分析后与数据库中事先采集好的数据进行比较已达到验证佩戴人身份的目的。The purpose of the present invention is to provide a kind of gait recognition method based on motion sensor in order to solve the above-mentioned defect in the prior art, and this gait recognition method utilizes in pin, calf, or the gait of wearing people's collection of motion sensor on thigh Information, these sensors include but are not limited to mobile phones in pockets, smart sports shoes, and sports anklets. Then, after analysis by a low-power processor, it is compared with the pre-collected data in the database to achieve the purpose of verifying the identity of the wearer.

本发明的目的可以通过采取如下技术方案达到:The purpose of the present invention can be achieved by taking the following technical solutions:

一种基于运动传感器的步态识别方法,所述步态识别方法包括下列步骤:A kind of gait recognition method based on motion sensor, described gait recognition method comprises the following steps:

S1、通过运动传感器采集获得佩戴用户在行走过程中产生的步态数据;S1. Obtain the gait data generated by the wearing user during walking through motion sensor collection;

S2、对步态数据进行步态周期估计,然后通过估计的步态周期对步态数据进行定位切割,实现步态数据的特征值提取;S2. Estimating the gait period of the gait data, and then positioning and cutting the gait data through the estimated gait period, so as to realize the feature value extraction of the gait data;

S3、通过步态数据特征值曲线的上升沿延续长度及时间跨度的匹配比较,从匹配库筛选出匹配度高于判定阈值的候选人,将步态数据特征值在频域分别与每一个待识别的候选人的傅里叶变换之后的步态数据进行误差积分得到对每一个待识别的候选人的匹配度,将匹配度最大的候选人认定为身份匹配成功。S3. Through the matching comparison of the rising edge continuation length and time span of the characteristic value curve of the gait data, the candidates whose matching degree is higher than the judgment threshold are screened out from the matching library, and the characteristic value of the gait data is compared with each candidate in the frequency domain. The gait data after the Fourier transform of the identified candidate is integrated to obtain the matching degree of each candidate to be identified, and the candidate with the highest matching degree is identified as a successful identity match.

进一步地,所述步骤S2包括:Further, the step S2 includes:

S201、通过不同的周期步态识别算法进行步态数据识别,对计算的周期进行评价,并且返回置信度,采用置信度最高的周期步态识别算法估计的步态周期值;S201. Perform gait data recognition through different cycle gait recognition algorithms, evaluate the calculated cycle, and return a confidence level, using the gait cycle value estimated by the cycle gait recognition algorithm with the highest confidence;

S202、根据估计的所述步态周期值对每一步的数据精确定位并切割单独提取出来作为特征值。S202. According to the estimated gait cycle value, the data of each step is accurately positioned and cut and extracted separately as feature values.

进一步地,所述步骤S3包括:Further, the step S3 includes:

S301、对步态数据特征值曲线进行上升沿延续长度及时间跨度的匹配比较,从匹配库首先初步筛选出匹配度高于判定阈值的候选人;S301. Perform a matching comparison of the continuation length of the rising edge and the time span on the characteristic value curve of the gait data, and initially screen out candidates whose matching degree is higher than the judgment threshold from the matching database;

S302、对候选人在匹配库中的步态数据进行压缩或者拉伸,实现步态周期标准化,对步态周期标准化后的步态数据特征值曲线进行傅里叶变换,将时域上特征不明显的数据映射到频域上,将步态数据特征值在频域分别与每一个待识别的候选人的傅里叶变换之后的步态数据进行误差积分得到对每一个待识别的候选人的匹配度,将匹配度最大的候选人认定为身份匹配成功。S302. Compress or stretch the gait data of the candidate in the matching library to realize the standardization of the gait cycle, perform Fourier transform on the eigenvalue curve of the gait data after the standardization of the gait cycle, and convert the different features in the time domain The obvious data is mapped to the frequency domain, and the gait data of the gait data in the frequency domain are respectively integrated with the gait data after the Fourier transform of each candidate to be identified to obtain the Matching degree, the candidate with the highest matching degree is identified as a successful identity match.

进一步地,所述步态周期标准化为400个点,将从匹配库中获得的步态离散数据连续化,再将连续化的步态数据按400个点进行分离,得到各个相邻点之间相关性最好的离散数据,其中数据压缩或者拉伸变换的公式如下:Further, the gait cycle is standardized to 400 points, the gait discrete data obtained from the matching library is serialized, and then the continuous gait data is separated by 400 points, and the distance between each adjacent point is obtained. Discrete data with the best correlation, where the formula for data compression or stretching transformation is as follows:

其中XI代表变换后的数据的第I个点,YI代表原始步态数据的第I个点,PER为原始步态数据的周期,INT()为取整函数。Wherein XI represents the I point of the transformed data, YI represents the I point of the original gait data, PER is the period of the original gait data, and INT () is a rounding function.

进一步地,所述匹配度的计算公式如下:Further, the calculation formula of the matching degree is as follows:

其中,s(n)为待识别步态数据,c(n)为候选人步态数据。Among them, s(n) is the gait data to be recognized, and c(n) is the candidate gait data.

进一步地,所述运动传感器为佩戴在脚,小腿,或大腿上的可穿戴智能设备,其中,所述步态数据为佩戴用户在行走过程中产生的加速度数据。Further, the motion sensor is a wearable smart device worn on the foot, calf, or thigh, wherein the gait data is the acceleration data generated by the wearing user during walking.

进一步地,所述匹配库为事先建立的,该匹配库中存储有用户的步态数据,可自动识别出没有记录的用户的步态数据,并自动存储到匹配库中。Further, the matching library is established in advance, and the user's gait data is stored in the matching library, and the user's gait data that has not been recorded can be automatically identified and stored in the matching library.

本发明相对于现有技术具有如下的优点及效果:Compared with the prior art, the present invention has the following advantages and effects:

1、实现简单,方便普及,成本低廉,理论上可以装配到现有的所有带有加速度传感器的智能设备上。1. The implementation is simple, convenient and popular, and the cost is low. Theoretically, it can be assembled on all existing smart devices with acceleration sensors.

2、使用方便,本发明对人身份的识别是基于人的步态特征,验证的过程可以在使用者自然行走的过程中完成,所以使用体验更加流畅。2. It is easy to use. The identification of a person's identity in the present invention is based on the gait characteristics of the person, and the verification process can be completed during the natural walking of the user, so the user experience is smoother.

3、安全性更高,本发明采集的是步态数据,与指纹识别等传统技术相比更难被仿造。3. Higher security. The present invention collects gait data, which is more difficult to be counterfeited than traditional technologies such as fingerprint identification.

4、与其它基于摄像头的步态识别方案相比,本发明的实现成本更低,计算量小,应用范围更广泛。4. Compared with other camera-based gait recognition schemes, the present invention has lower implementation cost, less calculation amount and wider application range.

附图说明Description of drawings

图1是本发明公开的基于运动传感器的步态识别方法的流程步骤图。FIG. 1 is a flowchart of a motion sensor-based gait recognition method disclosed in the present invention.

具体实施方式detailed description

为使本发明实施例的目的、技术方案和优点更加清楚,下面将结合本发明实施例中的附图,对本发明实施例中的技术方案进行清楚、完整地描述,显然,所描述的实施例是本发明一部分实施例,而不是全部的实施例。基于本发明中的实施例,本领域普通技术人员在没有作出创造性劳动前提下所获得的所有其他实施例,都属于本发明保护的范围。In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments It is a part of embodiments of the present invention, but not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without creative efforts fall within the protection scope of the present invention.

实施例Example

本实施例公开了一种基于运动传感器的步态识别方法,该方法利用佩戴在脚,小腿,或大腿上的可穿戴智能设备(包括但不限于口袋中的手机,智能运动鞋,运动脚环),采集佩戴人的步态信息,然后通过低功耗处理器分析后与数据库中事先采集好的数据进行比较已达到验证佩戴人身份。This embodiment discloses a method for gait recognition based on a motion sensor. The method utilizes a wearable smart device (including but not limited to a mobile phone in a pocket, smart sports shoes, and a sports foot ring) worn on a foot, a calf, or a thigh. ), collect the gait information of the wearer, and then compare it with the pre-collected data in the database after analysis by a low-power processor to verify the identity of the wearer.

当用户佩戴智能可穿戴设备行走的时候,利用本发明公开的基于运动传感器的步态识别方法就可以自行收集用户的步态信息并确认佩戴人是否是合法持有人。整个识别过程不需要用户的参与,因此十分方便。When the user wears the smart wearable device and walks, the gait recognition method based on the motion sensor disclosed in the present invention can collect the user's gait information and confirm whether the wearer is a legal holder. The entire identification process does not require user participation, so it is very convenient.

如附图1所示,本实施例公开的基于运动传感器的步态识别方法包括下列步骤:As shown in accompanying drawing 1, the gait recognition method based on motion sensor disclosed in this embodiment comprises the following steps:

S1、通过运动传感器采集获得佩戴用户在行走过程中产生的步态数据,其中,步态数据为佩戴用户在行走过程中产生的加速度数据,其中,运动传感器为佩戴在脚,小腿,或大腿上的可穿戴智能设备,包括但不限于口袋中的手机,智能运动鞋,运动脚环。S1. Obtain the gait data generated by the wearing user during walking through motion sensor collection, wherein the gait data is the acceleration data generated by the wearing user during walking, wherein the motion sensor is worn on the foot, calf, or thigh Wearable smart devices, including but not limited to mobile phones in pockets, smart sports shoes, sports anklets.

S2、对步态数据进行步态周期估计,然后通过估计的步态周期对步态数据进行定位切割,实现步态数据的特征值提取;S2. Estimating the gait period of the gait data, and then positioning and cutting the gait data through the estimated gait period, so as to realize the feature value extraction of the gait data;

具体实施方式中,该步骤具体包括:In a specific implementation manner, this step specifically includes:

S201、通过不同的周期步态识别算法进行步态数据识别,对计算的周期进行评价,并且返回置信度,采用置信度最高的周期步态识别算法估计的步态周期值。S201. Perform gait data recognition through different cycle gait recognition algorithms, evaluate the calculated cycle, and return a confidence level, using the gait cycle value estimated by the cycle gait recognition algorithm with the highest confidence level.

S202、根据估计的步态周期值对每一步的数据精确定位并切割单独提取出来作为特征值。S202. According to the estimated gait cycle value, the data of each step is accurately positioned and cut and extracted separately as feature values.

该步骤根据之前估计出来的周期大小,将每一步的数据精确定位并分段切割后单独提取出来,为以后更深层次的数据处理打好基础。In this step, according to the previously estimated cycle size, the data of each step is accurately positioned and segmented, and then extracted separately, laying a solid foundation for further in-depth data processing.

同时,在分段的过程中,将对数据的周期性强弱进行分析,如果周期性不明显,那么将这段数据将被认为成是错误数据并丢弃,以节约宝贵的计算资源。At the same time, in the process of segmentation, the periodicity of the data will be analyzed. If the periodicity is not obvious, then this piece of data will be considered as wrong data and discarded to save valuable computing resources.

S3、通过步态数据特征值曲线的上升沿延续长度及时间跨度的匹配比较,从匹配库筛选出匹配度高于判定阈值的候选人,将步态数据特征值在频域分别与每一个待识别的候选人的傅里叶变换之后的步态数据进行误差积分得到对每一个待识别的候选人的匹配度,将匹配度最大的候选人认定为身份匹配成功。S3. Through the matching comparison of the rising edge continuation length and time span of the characteristic value curve of the gait data, the candidates whose matching degree is higher than the judgment threshold are screened out from the matching library, and the characteristic value of the gait data is compared with each candidate in the frequency domain. The gait data after the Fourier transform of the identified candidate is integrated to obtain the matching degree of each candidate to be identified, and the candidate with the highest matching degree is identified as a successful identity match.

其中,匹配库为事先建立的,该匹配库中存储有用户步态数据,可自动识别出没有记录的用户的步态数据,并自动存储到匹配库中。Wherein, the matching library is established in advance, and the user's gait data is stored in the matching library, and the gait data of the users who have not been recorded can be automatically identified and stored in the matching library.

因此,匹配库在录入新的陌生人的步态数据时不用单独进行,可以在识别的过程中发现数据库中没有录入的用户并自动记录,这大大方便了数据的采集。Therefore, the matching database does not need to be entered separately when entering the gait data of new strangers. During the identification process, users who are not entered in the database can be found and automatically recorded, which greatly facilitates data collection.

该匹配步骤中评价体系采用双层评价结构。第一层匹配的时候主要进行粗略的比较,将可能正确的人挑出来,并传入下一次匹配。由于第一次匹配的计算量较小,因此可以有效的节约计算资源。第二次匹配采用精确匹配,精确判断待评价的候选人与每一个经过了第一轮筛选的人的匹配度。比较后选取匹配度最高的那个人作为识别结果。The evaluation system in this matching step adopts a two-layer evaluation structure. During the first level of matching, a rough comparison is mainly performed to pick out the person who may be correct and pass it into the next match. Since the calculation amount of the first matching is small, the calculation resources can be effectively saved. The second matching uses exact matching to accurately judge the degree of matching between the candidates to be evaluated and each person who has passed the first round of screening. After the comparison, the person with the highest matching degree is selected as the recognition result.

步骤S3具体过程如下:The specific process of step S3 is as follows:

S301、对步态数据特征值曲线进行上升沿延续长度及时间跨度的匹配比较,从匹配库首先初步筛选出匹配度高于判定阈值的候选人;S301. Perform a matching comparison of the continuation length of the rising edge and the time span on the characteristic value curve of the gait data, and initially screen out candidates whose matching degree is higher than the judgment threshold from the matching database;

第一层识别算法:曲线上升沿延续长度及时间跨度的比较。The first layer recognition algorithm: the comparison of the length of the rising edge of the curve and the time span.

通过实验获得大量的不同人的数据曲线,经过分析后发现,不同人的曲线在特定的位置都有较为明显的上升趋势,并在一定时间内保持这种趋势。而进一步对比后发现,不同人的曲线上升沿的延续长度及时间跨度也是具有较明显差别,因此可利用此特定进行较粗略的身份验证。A large number of data curves of different people are obtained through experiments. After analysis, it is found that the curves of different people have a relatively obvious upward trend in a specific position, and maintain this trend for a certain period of time. After further comparison, it is found that the continuation length and time span of the rising edge of the curves of different people are also significantly different, so this specificity can be used for rough identity verification.

S302、对候选人在匹配库中的步态数据进行压缩或者拉伸,实现步态周期标准化,对步态周期标准化后的步态数据特征值曲线进行傅里叶变换,将时域上特征不明显的数据映射到频域上,将步态数据特征值在频域分别与每一个待识别的候选人的傅里叶变换之后的步态数据进行误差积分得到对每一个待识别的候选人的匹配度,将匹配度最大的候选人认定为身份匹配成功。S302. Compress or stretch the gait data of the candidate in the matching library to realize the standardization of the gait cycle, perform Fourier transform on the eigenvalue curve of the gait data after the standardization of the gait cycle, and convert the different features in the time domain The obvious data is mapped to the frequency domain, and the gait data of the gait data in the frequency domain are respectively integrated with the gait data after the Fourier transform of each candidate to be identified to obtain the Matching degree, the candidate with the highest matching degree is identified as a successful identity match.

第二层识别算法:特征曲线的提取和比较。The second layer recognition algorithm: the extraction and comparison of characteristic curves.

考虑到就算是同一个人,不同时间录入的数据周期可能会稍微有点差别。这时就采用了数据压缩或拉伸,使一个周期达到准确的400个点。将所获得离散数据连续化,再将连续化的数据按400进行分离,得到各个相邻点之间相关性最好的离散数据。数据压缩变换的核心算法部分如下Considering that even if it is the same person, the data period entered at different times may be slightly different. At this time, data compression or stretching is used to make a cycle reach exactly 400 points. Continuousize the obtained discrete data, and then separate the continuous data by 400 to obtain discrete data with the best correlation between adjacent points. The core algorithm part of data compression transformation is as follows

其中XI代表变换后的步态数据的第I个点,YI代表原始步态数据的第I个点,PER为原始数据的周期,INT()为取整函数。通过这个公式可以把周期为PER的原始数据变换为周期固定为400的标准数据,这样可以方便比较。Wherein XI represents the I point of the transformed gait data, YI represents the I point of the original gait data, PER is the cycle of the original data, and INT () is a rounding function. Through this formula, the original data with a period of PER can be converted into standard data with a fixed period of 400, which is convenient for comparison.

对步态周期标准化后的特征值曲线进行采样频率为256个点的傅里叶变换,将时域上特征不明显的数据映射到频域上,使其特征值更加明显便于比较。The Fourier transform with a sampling frequency of 256 points is performed on the eigenvalue curve after normalization of the gait cycle, and the data with inconspicuous characteristics in the time domain are mapped to the frequency domain, making the eigenvalues more obvious and easy to compare.

分别与每一个待识别的候选人的傅里叶变换之后的步态数据进行误差积分。从而得到对每一个待识别的候选人的匹配程度。理想状态下当采样率间隔dx无限小得时候匹配度公式如下:Error integration is performed with the Fourier transformed gait data of each candidate to be identified respectively. Thus, the matching degree of each candidate to be identified is obtained. Ideally, when the sampling rate interval dx is infinitely small, the matching degree formula is as follows:

但是在实际计算过程中,没法达到如此精度。因此可以采用近似公式:However, in the actual calculation process, such accuracy cannot be achieved. Therefore an approximate formula can be used:

其中,s(n)为待识别步态数据,c(n)为候选人步态数据,将匹配度最大的候选人认定为身份匹配成功,即将匹配度的值最大的候选人认定为身份匹配成功。Among them, s(n) is the gait data to be identified, c(n) is the gait data of the candidate, the candidate with the highest matching degree is identified as a successful identity match, and the candidate with the highest matching degree is identified as an identity match success.

综上所述,本实施例公开的一种基于运动传感器的步态识别方法,该方法利用佩戴在脚,小腿,或大腿上的可穿戴智能设备采集佩戴人的步态信息,然后通过低功耗处理器分析后与数据库中事先采集好的数据进行比较已达到验证佩戴人身份。该方法实现简单,方便普及,成本低廉,理论上可以装配到现有的所有带有加速度传感器的智能设备上。同时,本发明对人身份的识别是基于人的步态特征,验证的过程可以在使用者自然行走的过程中完成,所以使用体验更加流畅。而且,本发明安全性更高,采集的是步态数据,与指纹识别等传统技术相比更难被仿造。In summary, this embodiment discloses a gait recognition method based on a motion sensor, which uses a wearable smart device worn on the foot, calf, or thigh to collect the gait information of the wearer, and then uses low-power After the analysis by the processor, it is compared with the pre-collected data in the database to verify the identity of the wearer. The method is simple to implement, convenient to popularize, and low in cost, and theoretically can be assembled on all existing smart devices with acceleration sensors. At the same time, the identification of a person's identity in the present invention is based on the gait characteristics of the person, and the verification process can be completed during the natural walking process of the user, so the user experience is smoother. Moreover, the present invention has higher security and collects gait data, which is more difficult to be counterfeited than traditional technologies such as fingerprint identification.

上述实施例为本发明较佳的实施方式,但本发明的实施方式并不受上述实施例的限制,其他的任何未背离本发明的精神实质与原理下所作的改变、修饰、替代、组合、简化,均应为等效的置换方式,都包含在本发明的保护范围之内。The above-mentioned embodiment is a preferred embodiment of the present invention, but the embodiment of the present invention is not limited by the above-mentioned embodiment, and any other changes, modifications, substitutions, combinations, Simplifications should be equivalent replacement methods, and all are included in the protection scope of the present invention.

Claims (7)

<mrow> <msub> <mi>X</mi> <mi>I</mi> </msub> <mo>=</mo> <msub> <mi>Y</mi> <mrow> <mi>I</mi> <mi>N</mi> <mi>T</mi> <mrow> <mo>(</mo> <mrow> <mi>P</mi> <mi>E</mi> <mi>R</mi> <mo>/</mo> <mn>400</mn> <mo>*</mo> <mi>I</mi> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> </msub> <mo>*</mo> <mrow> <mo>(</mo> <mrow> <mfrac> <mrow> <mi>P</mi> <mi>E</mi> <mi>R</mi> </mrow> <mn>400</mn> </mfrac> <mo>*</mo> <mi>I</mi> <mo>-</mo> <mi>I</mi> <mi>N</mi> <mi>T</mi> <mrow> <mo>(</mo> <mrow> <mfrac> <mrow> <mi>P</mi> <mi>E</mi> <mi>R</mi> </mrow> <mn>400</mn> </mfrac> <mo>*</mo> <mi>I</mi> </mrow> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>Y</mi> <mrow> <mfrac> <mrow> <mi>P</mi> <mi>E</mi> <mi>R</mi> </mrow> <mn>400</mn> </mfrac> <mo>*</mo> <mi>I</mi> </mrow> </msub> <mo>*</mo> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mfrac> <mrow> <mi>P</mi> <mi>E</mi> <mi>R</mi> </mrow> <mn>400</mn> </mfrac> <mo>*</mo> <mi>I</mi> <mo>+</mo> <mi>I</mi> <mi>N</mi> <mi>T</mi> <mrow> <mo>(</mo> <mrow> <mfrac> <mrow> <mi>P</mi> <mi>E</mi> <mi>R</mi> </mrow> <mn>400</mn> </mfrac> <mo>*</mo> <mi>I</mi> </mrow> <mo>)</mo> </mrow> <mo>,</mo> </mrow>
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