Abstract:
An optimum workload corresponding to a target heart rate of an user is determined by the following method, which is preferably utilized for providing a safe training or an accurate examination of physical strength to the user. After the target heart rate is set, a first steady heart rate of the user is measured during an initial exercise cycle in which a first workload is applied to the user. The first workload is derived in accordance with the target heart rate and a statistically obtained workload versus heart rate correlation corresponding to at least one factor selected from the group consisting of the user&#39;s age, gender, body weight, and body height, etc. In addition, a second steady heart rate of the user is measured during at least one subsequent exercise cycle in which a second workload is applied to the user. The second workload is derived by entering as input parameters the applied workload and the measured heart rate at the immediately previous exercise cycle into a multiple variate model equation. Consequently, the optimum workload is determined by entering the applied workload and the measure heart rate at the last exercise cycle into the multiple variate model equation. The model equation is prepared by utilizing a neural network analysis or a multiple variate analysis.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a method of determining an optimum workload corresponding to a target heart rate of an user, which is utilized for providing a safe training or an accurate examination of physical strength to the user, and an exercise device therefor. 
     2. Disclosure of the Prior Art 
     In the past, a treadmill exerciser for walking or running on a movable belt-like floor and a bicycle ergometer, etc., are used as an exercise device for a training or an examination of physical strength of an user. In the treadmill exerciser, a workload applied to the user is determined by controlling a moving speed and a slope of the belt-like floor. On the other hand, as shown in FIG. 4, the bicycle ergometer 1 comprises a pair of foot pedals 2, saddle 3, handle 4, sensor 5 for measuring a heart rate of the user during a pedaling thereof, and a workload controller 6 of the workload applied to the pedals 2. An exercise program of the bicycle ergometer 1 can be divided roughly into two categories. That is, one of the categories is that the workload applied to the pedals 2 is set by the user, and then the user pedals the ergometer for a required time period under the workload. The other one is that a target heart rate (HR Target ) is set by the user, and then the user pedals the ergometer for a required time period while the workload is controlled to reach and keep the target heart rate during the pedaling. In the earlier exercise program, the user usually pedals the ergometer for more than 10 minutes under the workload in the range of 40 to 120 W (watt) for the purpose of reducing the user&#39;s weight. On the other hand, in the later exercise program, the workload is usually set in accordance with a statistically obtained maximum heart rate (HR max ) corresponding to the user&#39;s age and gender, and body weight, etc. The maximum heart rate is represented by, for example, the following regression equations  1! and  2!, 
     
         MALE: HRmax (beats/min)=209-0.69×age                  1! 
    
     
         FEMALE: HRmax (beats/min)=205-0.75×age.               2! 
    
     To be exact, the maximum heart rate is defined as a heart rate corresponding to a maximal oxygen uptake (VO 2max ) taken in the body per 1 kg of the body weight and per 1 minute. In addition, the target heart rate (HR Target ) is usually determined in accordance with the following equation  3!, 
     
         HR.sub.Target =(HR.sub.max -HR.sub.normal)×EL/100+HR.sub.normal   3! 
    
     wherein HR normal  is a heart rate measured at rest, and EL is an exercise level (%) which is ordinarily selected from the range of 30% to 70%. 
     By the way, in the later exercise program, it is known that the workload is increased stepwise at a fixed rate, for example, 10 W per 30 sec., for reaching the target heart rate of the user, and in each step, a steady heart rate is measured by the sensor 5. However, since the workload is increased at the fixed rate in spite that each of the users has an individual physical strength, it causes a problem that the heart rate of the user having a low physical strength is reached to the target heart rate by pedaling the ergometer for a relatively short time period, and on the contrary, it takes a relatively long time period for reaching the heart rate of the user having a high physical strength to the target heart rate. Therefore, it is expected that such stepwise increasing of the workload at the fixed rate does not always provide an efficient training to the individual user. In addition, when the workload is increased stepwise at a raised rate, the efficient training would be provided to the user having the high physical strength. However, in case of the user having the low physical strength, there is a probability of causing a serious problem that since the next increased workload is applied to the user before the user&#39;s heart rate is reached to the steady heart rate corresponding to the applied workload., the user is made to pedal the ergometer under an excess workload. Generally, it is taught that it takes more than 3 minutes for measuring the steady heart rate in each step. 
     U.S. Pat. No. 4,678,182 discloses a training device using a bicycle ergometer and a method, in which the bicycle ergometer is used to obtain an optimum load value and a steady number of pulses per minute for the continuous exercise of the user. 
     SUMMARY OF THE INVENTION 
     A primary object of the present invention is to provide a method of determining an optimum workload corresponding to a target heart rate (HR Target ) of an user which is utilized for providing a safe and efficient training or an accurate examination of physical strength to the user. That is, after the target heart rate of the user is set, a first steady heart rate of the user is measured during an initial exercise cycle, in which a first workload is applied to the user. The first workload is derived in accordance with the target heart rate and a statistically obtained workload versus heart rate correlation corresponding to at least one factor selected from the group consisting of the user&#39;s age, gender, body weight, body height, and whole body fat, etc. In addition, a second steady heart rate of the user is measured during at least one subsequent exercise cycle in which a second workload is applied to the user. The second workload is derived by entering as input parameters the applied workload and the measured heart rate at the immediately previous exercise cycle into a first multiple variate model equation. The optimum workload is determined by entering the applied workload and the measured heart rate at the last exercise cycle into the first multiple variate model equation. 
     In the initial exercise cycle, it is possible that the first workload is derived by entering as input parameters at least two factors selected from the group consisting of the user&#39;s age, gender, body weight, body height, and whole body fat into an initial multiple variate model equation. 
     On the other hand, after the initial exercise cycle, it is further possible that the optimum workload is determined by entering the first workload and the first heart rate into the first multiple variate model equation. 
     It is also possible that the second workload is derived by multiplying an exercise level EL (%)/100 by a maximum aerobic capacity of the user which is predicted by entering as input parameters the applied workload and the measured heart rate at the immediately previous exercise cycle into a second multiple variate model equation, and also the optimum workload is determined by multiplying the exercise level EL (%)/100 by the maximum aerobic capacity predicted by entering the applied workload and the measured heart rate at the last exercise cycle into the second multiple variate model equation. The maximum aerobic capacity is defined as a maximum workload corresponding to a maximum heart rate (HR max ) of the individual user. The exercise level EL (%) is calculated by the equation  3&#39;!, that is, 
     
         EL (%)=100×(HR.sub.Target -HR.sub.Normal)/(HR.sub.max -HR.sub.Normal)  3&#39;! 
    
     wherein HR Normal  is a normal heart rate of the user measured at rest. It is preferred that the exercise level EL (%) is selected from the range of 30% to 80%. In this case, it is also preferred that the input parameters of the second model equation further include at least one factor selected from the group consisting of the user&#39;s age, gender, body height, body weight and whole body fat, integrated value of heart rate, integrated value of workload, workload applying time period, and the maximum aerobic capacity predicted at the immediately previous exercise cycle. 
     In addition, it is also possible that the second workload is derived by multiplying the exercise level EL (%)/100 by a maximum oxygen uptake of the user which is predicted by entering as input parameters the applied workload and the measured heart rate at the immediately previous exercise cycle into a third multiple variate model equation, and also the optimum workload is determined by multiplying the exercise level EL (%)/100 by the maximum oxygen uptake predicted by entering the applied workload and the measured heart rate at the last exercise cycle into the third multiple variate model equation. In this case, it is also preferred that the input parameters of the third model equation further include at least one factor selected from the group consisting of the user&#39;s age, gender, body height, body weight and whole body fat, integrated value of heart rate, integrated value of workload, workload applying time period, and the maximum oxygen uptake predicted at the immediately previous exercise cycle. Additionally, it is possible that the maximum aerobic capacity can be converted to the maximum oxygen uptake (VO 2max ) by, for example, the following equation  4!, 
     
         VO.sub.2max (ml/kg/min.)×Body Weight(kg) =233+13.08×Maximum Aerobic Capacity (W)                                       4! 
    
     In case that there is a linear relationship between a target value, for example, the maximum aerobic capacity, and the input parameters, it is preferred that a multiple variate analysis selected from Multiple Regression Analysis, Multidimetional Quantification 1, and Group Method of Data Handling (GMDH), etc., is used for making each multiple variate model equation. For example, a general model equation  5! prepared by the multiple variate analysis is shown below, 
     
         W=f(v1, v2 . . . , Vn)                                      5! 
    
     wherein W is the target value, f is a multiple variate function, v1, v2, . . . vn are input parameters of the function, and n is the number of the input parameters. 
     On the other hand, in case that there is a non-linear relationship between the target value and the input parameters, it is also preferred that a neural network analysis is used for making each multiple variate model equation. For example, as shown in FIG. 1, a structure of the neural network analysis indicates that the optimum workload is determined through a plurality of hidden layers, each of which includes all kinds of the input parameters. For example, the relationship between the target value and the input parameters is represented by the following equations  6! to  10! according to the neural network analysis, 
     
         W=1/(1+e.sup.-Z)                                            6! 
    
     W :target value 
     Z :value determined by the equation  7!, ##EQU1## Bi :coefficient Θ:constant 
     k : the number of hidden layers 
     Yi :value determined by the equation  8!, 
     
         Yi=1/(1+e.sup.-Xi)                                          8! 
    
     Xi :value determined by the equation  9!, ##EQU2## Ai :coefficient θ:constant 
     Vi :value normalized by the equation  10!, 
     
         Vi=(vi-vi.sub.MIN)/(vi.sub.MAX -vi.sub.MIN)                 10! 
    
     wherein vi is one of the input parameters, vi MIN  is a minimum value of vi, and vi MAX  is a maximum value of vi. 
     By the way, since it takes a relatively long operating time period in case of using the neural network analysis, it is preferred that, for example, a linear simplified equation  11! represented below is used for improving an operating speed, that is, ##EQU3## wherein C is a constant, Di is a coefficient peculiar to each input parameter, and n is the number of the input parameters. 
     Therefore, each multiple variate model equation is prepared by using the multiple variate analysis or the neural network analysis, and also experimental data obtained by a submaximum workload applying method which is a kind of examination of physical strength. In the present invention, for example, the experimental data were drawn from 70 healthy male and female subjects aged 20 to 60 years. In the submaximum workload applying method, a variable workload applied to the subject is increased stepwise, and in each step a steady heart rate of the subject is measured. After the final workload applying step, in which the heart rate of the subject reaches to the target heart rate, the VO 2  max or maximum aerobic capacity of each subject is determined from a regression line prepared according to thus obtained workload versus heart rate relation. For reference, ages of the subjects categorized into five age ranges, and average heart rates corresponding to the exercise levels 40% to 80% of the subjects of each of the age ranges are listed in TABLE A. 
     
                       TABLE A______________________________________Exer-Average heart rate (beats/min.) in each agecise range (yr.) of subjectsLevel≦29       30 ˜ 39               40 ˜ 49                     50 ˜ 59                           60≦                                Subjective Exercise(%)  (yr.)  (yr.)   (yr.) (yr.) (yr.)                                Degree (20 yr.≦)______________________________________80%  165    160     150   145   135  17 VERY HARD                                1670%  149    145     140   135   123  15 HARD60%  137    133     129   125   115  1450%  124    122     119   115   107  13 SLIGHTLY HARD40%  112    110     108   105   99______________________________________ 
    
     It is also possible that a maximum workload applying method is utilized in place of the submaximum workload method. In the maximum workload applying method, the workload is increased stepwise, and in each step the steady heart rate of the subject is measured. After a maximum workload applying step, in which the subject could no longer continue despite verbal encouragement, the VO 2  max or maximum aerobic capacity of each subject is determined. In addition, when an expiration analysis and the maximum workload applying method or the submaximum workload method are performed together for obtaining the experimental data, it is preferred for improving the accuracy of the multiple variate model equation. 
     It is also preferred that the workload applied to the user is timely adjusted during each exercise cycle in such a manner of a control table or a fuzzy control method for preventing the occurrence of a dangerous case in which the user is made to exercise for a long time period under an excess workload corresponding to a heart rate more than the target heart rate. That is, even if the excess workload is applied to the user in one of the exercise cycles, it is timely adjusted during the exercise cycle such that the long exercise of the user under the excess workload is prevented. The control table method is useful in case of a small number of input parameters. TABLE B shows a control table using as the input parameters a workload range and a difference between the target heart rate and a measured heart rate, in which the input parameters are respectively categorized into three ranges. For example, when the applied workload is in the range of &#34;Medium&#34; and the difference between the heart rates is in the range of &#34;Small&#34;, an adjustment value E 21  is selected for adjusting the workload. 
     
                       TABLE B______________________________________Workload   ΔHR *.sup.1Range      Small        Medium  Large______________________________________Small      E11          E12     E13Medium     E21          E22     E23Large      E31          E32     E33______________________________________ *.sup.1: ΔHR is a difference between the target heart rate and a measured heart rate at an exercise cycle E11 to E33: Adjustment values 
    
     In addition, the fuzzy control method is useful for adjusting the workload in case of a large number of the input parameters. The adjustment is performed by using membership functions with respect to input parameters of the fuzzy control method. It is preferred that input parameters of the fuzzy control method or the control table include the difference between the target heart rate and a measured heart rate, workload, and workload applying time period. On the other hand, it is further preferred that a control table prepared by analyzing the membership functions with &#34;Min-Max&#34; method or &#34;Mean-Load&#34; method is utilized for adjusting the workload. 
     In another preferred embodiment of the present invention, a modified workload, which is obtained by multiplying the workload derived in each exercise cycle by a safety coefficient of less than 1, is applied to the user for providing the safe training. Since the modified workload can be readily adjusted by slightly increasing the modified workload according to the fuzzy control method or the control table, the excess workload is not applied to the user in any case, so that it will provide the safe training and examination of physical strength to the user. 
     By utilizing the method of determining the optimum workload of the present invention, an examination of physical strength of the user can be proceeded, as explained below. At least two exercise levels (%) are preferably selected from the range of 30% to 80%, and a target heart rate corresponding to each exercise level is set. The optimum workload corresponding to each target heart rate is determined by the above method of the present invention to thereby obtain a workload versus heart rate regression line peculiar to the individual user. In case that the physical strength is defined as the maximum aerobic capacity of the user, it can be readily estimated by extrapolation of the regression line, as shown in FIG. 2. 
     Another object of the present invention is to provide an exercise device which applies a variable workload to an user thereof during a plurality of consecutive exercise cycles for obtaining an optimum workload corresponding to a target heart rate of the user. The exercise device comprises a sensor for monitoring the heart rate of the user, a setting unit for setting the target heart rate, a loading unit for applying to the user the variable workload comprising first and second workload, a first workload unit for deriving the first workload applied to the user in an initial exercise cycle in which a first steady heart rate is measured by the sensor, a second workload unit for deriving the second workload applied to the user in at least one subsequent exercise cycle in which a second steady heart rate is measured by the sensor, an optimum workload determination unit for determining the optimum workload. In the first workload unit, the first workload is derived in accordance with the target heart rate and a statistically obtained workload versus heart rate correlation corresponding to at least one factor selected from the group consisting of the user&#39;s age, gender, body weight, body height, and whole body fat. In the second workload unit, the second workload is determined by entering as input parameters the applied workload and the measured heart rate at the immediately previous exercise cycle into a multiple variate model equation. In addition, in the optimum workload determination unit, the optimum workload is determined by entering the applied workload and the measured heart rate at the last exercise cycle into the multiple variate model equation. 
     In a preferred embodiment of the present invention, in the first workload unit, the first workload is determined by entering as input parameters at least two factors selected from the group consisting of the target heart, age, gender, body weight, body height, and whole body fat into an initial multiple variate model equation. 
     Other features, objects and advantages of the present invention will become more apparent from the following description about the preferred embodiments taken with reference to the accompanied drawings. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 shows a conceptional structure of a neural network analysis utilized in the present invention; 
     FIG. 2 is an explanatory graph indicating a workload versus heart rate regression line; 
     FIG. 3 shows explanatory graphs of membership functions utilized for a fuzzy control method in the present invention; and 
     FIG. 4 is a perspective view of a bicycle ergometer. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     In FIRST and SECOND EMBODIMENTS, an optimum workload corresponding to a target heart rate of an user is determined in accordance with the present method by a bicycle ergometer 1 which comprises a pair of foot pedals 2, saddle 3, handle 4, sensor 5 for measuring a heart rate of the user during a pedaling thereof, and a workload controller 6 of the workload applied to the pedals 2, as illustrated in FIG. 4. In THIRD to NINTH EMBODIMENTS, a physical strength of the user is examined by using the ergometer 1. 
     FIRST EMBODIMENT 
     A method of determining an optimum workload corresponding to a target heart rate of an user is explained below. The user is a healthy female subject aged 25 yr. having 45 kg of body weight and 152 cm of body height. A maximum heart rate (HR max ) of the user is obtained by the equation  2!, and a normal heart rate (HR Normal ) thereof is measured at rest. An exercise level selected in this embodiment is 50% which is effective for the purpose of reducing the user&#39;s weight. Therefore, the target heart rate of the user is 124 beats/min, which is represented by the equation  3!. The method comprises four consecutive exercise cycles, and in each cycle, a heart rate of the user and a workload applied to the pedals 2 of the ergometer 1 are measured by the sensor 5, and also an integrated value of the heart rate and an integrated value of the workload are calculated. In the first exercise cycle, a first workload is applied to the user for 1 min. The first workload is derived by multiplying the exercise degree (%)/100, by a first maximum aerobic capacity which is predicted by entering as input parameters age, gender, body height and body weight of the user into a first multiple variate model equation. Subsequently, in the second exercise cycle, a second workload is applied to the user for 2 min. The second workload is derived by multiplying the exercise degree (%)/100 by a second maximum aerobic capacity which is predicted by entering as input parameters gender, age, body height, and body weight of the user, the integrated value, the measured heart rate and the applied workload at the immediately previous exercise cycle into a second multiple variate model equation. In the third exercise cycle, a third workload is applied to the user for 3 min. The third workload is derived by multiplying the exercise degree (%)/100 by a third maximum aerobic capacity which is predicted by entering the input parameters into the second model equation. After the third exercise cycle, a fourth workload is applied to the user for 14 min. The fourth workload is determined as the optimum workload by multiplying the exercise degree (%)/100 by a fourth maximum aerobic capacity which is predicted by entering the input parameters into the second model equation. Details of the FIRST EMBODIMENT are summarized on TABLE 1. 
     
                       TABLE 1______________________________________Workload         Maximum        DifferenceExer-applying Work-   aerobic                        Measured                                between targetcise time     load    capacity                        heart rate                                and measuredcycle(min.)   (W)     (W)    (beats/min.)                                heart rates (%) *1______________________________________1    1        70      137.9  115     7.32    2        50      102.8  124     0.03    3        55      111.3  125     0.84    14       60      116.7  *2      --______________________________________ *1: Difference between the target heart rate (HR.sub.Target) and a measured heart rate (HR) of the user is represented by the following equation Difference (%) = | 100 × (HR - HR.sub.Target) / HR.sub.Target *2: In the fourth exercise cycle, the heart rate of the user was not measured. 
    
     SECOND EMBODIMENT 
     An optimum workload corresponding to a target heart rate of an user is determined by the substantially same method as FIRST EMBODIMENT except for the following. In this case, the user is a healthy male subject aged 19 yr. having 60 kg of body weight. A maximum heart rate (HR max ) of the user is obtained by the equation  1!, and a normal heart rate (HR Normal ) thereof is measured at rest. An exercise level selected in this embodiment is 50%. Therefore, the target heart rate of the user is 124 beats/min, which is represented by the equation  3!. In addition, the first workload is determined from a statistically obtained data separately according to age and gender which is listed on TABLE 2, and is memorized in a memory of the workload controller 6 of the bicycle ergometer 1. Details of the SECOND EMBODIMENT are summarized on TABLE 3. 
     
                       TABLE 2______________________________________Range of         First workload (W)age (yr.)        Male   Female______________________________________&lt;30              100    6030 ˜ 39    90     5040 ˜ 49    80     4550 ˜ 59    70     4060&lt;              60     35______________________________________ 
    
     
                       TABLE 3______________________________________Workload          Maximum        DifferenceExer-applying Work-    aerobic                         Measured                                 between targetcise time     load     capacity                         heart rate                                 and measuredcycle(min.)   (W)      (W)    (beats/min.)                                 heart rates (%)______________________________________1    1        100      --     110     11.32    2        110      219.6  117     5.63    3        115      227.5  122     3.24    14       140      280.8  *1      --______________________________________ *1: In the fourth exercise cycle, the heart rate of the user was not measured. 
    
     THIRD EMBODIMENT 
     A physical strength of an user is estimated as a maximum aerobic capacity thereof which is a maximum workload corresponding to a maximum heart rate of the user. The maximum heart rate is presented by the equation  1! or  2!. The maximum workload is determined by extrapolation of a workload versus heart rate regression line of the user. The regression line is prepared by the following method. That is, a variable workload is increased in five consecutive exercise steps, and in each exercise step, a heart rate of the user and a workload are measured. In the first exercise step, a first workload is applied to the user for 1 min. The first workload is determined by multiplying a first exercise level (%)/100 by a first maximum aerobic capacity which is predicted by entering as input parameters age, gender, and body weight of the user into a first multiple variate model equation. In each of the exercise steps 2 to 5, the workload applied to the user is determined by multiplying an exercise level (%)/100 of the exercise step by a maximum aerobic capacity which is predicted by entering as input parameters, age, gender, body weight, the measured heart rate, the applied workload and the predicted maximum aerobic capacity at the previous exercise step, integrated value of heart rate, integrated value of workload into a second multiple variate model equation. The exercise level (%) and a workload applying time in each exercise step are listed on TABLE 4. The total of the workload applying times is 16 min. From thus obtained data, the physical strength of the user is estimated by preparing the workload versus heart rate regression line, and determining the maximum workload corresponding to the maximum heart rate of the user by extrapolation of the regression line. 
     By the way, the second model equation used in the THIRD EMBODIMENT is prepared according to a neural network analysis and is made to learn 40,000 times with respect to statistically obtained data for improving accuracy of the predicted maximum aerobic capacity. In addition, the model equation is modified to a simplified model equation for improving an operating speed. Details of the THIRD EMBODIMENT are summarized on TABLE 4. 
     
                       TABLE 4______________________________________Work-load                         Exer-Exer-apply-                       cise Meancise ing     Input parameters of a multiple variate                             level                                  errorstep time    model equation.      (%)  (*1)______________________________________1    1 min.  gender, age, and body weight                             30   26.72    3 min.  age, gender, body weight, the measured                             40   24.93    4 min.  heart rate, the applied workload and the                             50   24.14    4 min.  predicted maximum aerobic capacity at                             60   20.65    4 min.  the previous exercise step, integrated                             70   16.8        value of heart rate, integrated value of        workload______________________________________ *1: A mean error (W (Watt)) of maximum aerobic capacity predicted in each exercise step against a maximum aerobic capacity determined by extrapolation of a workload versus heart rate regression line. 
    
     FOURTH EMBODIMENT 
     A physical strength of an user is estimated by the substantially same method as THIRD EMBODIMENT except that the first workload is selected from the range of 20 to 40 W in response to age and gender of the user, and the input parameters of the second multiple variate model equation are the applied workload and the measured heart rate at the immediately previous exercise step. Details of the FOURTH EMBODIMENT are summarized in TABLE 5. 
     
                       TABLE 5______________________________________Work-load                         Exer-Exer-apply-                       cise Meancise ing     Input parameters of a multiple variate                             level                                  errorstep time    model equation       (%)  (*1)______________________________________1    1 min.  --                   --   --2    3 min.  the measured heart rate and the applied                             40   48.4 W3    4 min.  workload at the immediately previous                             50   38.4 W4    4 min.  exercise step        60   30.3 W5    4 min.                       70   19.6 W______________________________________ *1: A mean error (W (Watt)) of a maximum aerobic capacity predicted in each of the exercise steps 2 to 5 against a maximum aerobic capacity determined by extrapolation of a workload versus heart rate regression line 
    
     FIFTH EMBODIMENT 
     A physical strength of an user is estimated by the substantially same method as THIRD EMBODIMENT except that the first workload is derived from a maximum oxygen uptake predicted by entering as input parameters age, gender, and body weight of the user into a third multiple variate model equation, and also in each of the exercise steps 2 to 5, the workload applied to the user is derived from a maximum oxygen uptake predicted by entering as input parameters, age, gender, body weight, the measured heart rate, the applied workload and the predicted maximum oxygen uptake at the previous exercise step, integrated value of heart rate, integrated value of workload into a fourth multiple variate model equation. The maximum oxygen uptake (VO 2max ) predicted in each step is converted to the maximum aerobic capacity by the equation  4!, as described before. 
     Details of the FIFTH EMBODIMENT are summarized in TABLE 6. 
     
                       TABLE 6______________________________________Work-load                         Exer-                                  Mean-Exer-apply-                       cise square-cise ing     Input parameters of a multiple variate                             level                                  errorstep time    model equation.      (%)  (*1)______________________________________1    1 min.  gender, age, and body weight                             30   15.02    3 min.  the measured heart rate, the applied                             40   13.13    4 min.  workload and the predicted maximum                             50   12.94    4 min.  oxygen uptake at the previous exercise                             60   12.05    4 min.  step, integrated value of heart rate,                             70   12.0        integrated value of workload______________________________________ *1: A meansquare-error of a maximum aerobic capacity converted from a maximum oxygen uptake predicted in each exercise step against a maximum aerobic capacity determined by extrapolation of a workload versus heart rate regression line 
    
     SIXTH EMBODIMENT 
     A physical strength of an user is estimated by the substantially same method as THIRD EMBODIMENT except that the first workload is derived from a maximum oxygen uptake predicted by entering as input parameters age, gender, and body weight of the user into a third multiple variate model equation, and in each of the exercise steps 2 to 5, the workload applied to the user is derived from a maximum oxygen uptake predicted by entering as input parameters, a classified age, gender, a classified body weight, the measured heart rate, the applied workload and the predicted maximum oxygen uptake at the previous exercise step, integrated value of heart rate, integrated value of workload into a fourth multiple variate model equation. In this embodiment, the age is divided into two categories consisting of an old group of 45 yr. or more and a young group of less than 45 yr. On the other hand, the body weight of the male user is divided into two categories consisting of a heavy group of 60 kg or more and a light group of less than 60 kg. In addition, the body weight of the female user is divided into two categories consisting of a heavy group of 50 kg or more and a light group of less than 50 kg. Details of the SIXTH EMBODIMENT are summarized in TABLE 7. 
     
                       TABLE 7______________________________________Work-load                         Exer-                                  Mean-Exer-apply-                       cise square-cise ing     Input parameters of a multiple variate                             level                                  errorstep time    model equation.      (%)  (*1)______________________________________1    1 min.  gender, age, and body weight                             30   15.02    3 min.  a classified age, a classified body                             40   12.83    4 min.  weight, gender, the measured heart rate,                             50   12.64    4 min.  the applied workload and the predicted                             60   9.45    4 min.  maximum oxygen uptake at the prev-                             70   8.7        ious exercise step, integrated value of        heart rate, integrated value of workload______________________________________ *1: A meansquare-error of a maximum aerobic capacity converted from a maximum oxygen uptake predicted in each exercise step against a maximum aerobic capacity determined by extrapolation of a workload versus heart rate regression line 
    
     SEVENTH EMBODIMENT 
     A physical strength of an user is estimated by the substantially same method as THIRD EMBODIMENT except for the followings. The workload is timely and finely adjusted during each exercise step of THIRD EMBODIMENT by using, as a fuzzy control method, a control table prepared by analyzing membership functions with &#34;Mean-Load&#34; method. The adjustment is performed twice, that is, at 1 min. and 2 min. from the beginning of each exercise step. 
     For example, an analysis of the membership functions is briefly explained according to FIG. 3. When the workload applied to the user is, e.g., 90 W and a difference (beats) between the target heart rate and a measured heart rate of the user is, e.g., -8 beats at an exercise step, coefficient α1 and β1 corresponding to the workload and the difference between the heart rates, respectively, are obtained from graphs (a)-I and II. A smaller one of the coefficients is multiplied by +10 (W) which is an average adjustment value (Δ Average ) , and is obtained by the following equation, 
     
         Δ.sub.Average =(W.sub.max +W.sub.min)/2, 
    
     wherein W max  and W min  are maximum and minimum adjustment values of the graphs (a)-III. In this case, since these coefficients α1 and β1 are respectively about 0.8 and 0.5, 0.5 is multiplied by +10. Similar procedure is repeated with respect to graphs (b) to (d), so that an optimum adjustment value (Δ Optimum ) in this case is represented by the following equation, ##EQU4## wherein α1 to α4 and β1 to β4 are coefficients obtained from the graphs (a)-I, II, (B)-I,II, (c)-I,II and (d)-I,II, and in the following relation, β1&lt;α1, α2&lt;β2, β3&lt;α3, α4&lt;β4. Therefore, the workload applied to the user, 90 (W), is adjusted to 90+Δ Optimum  (W) by the analysis of the membership functions. 
     As a result, even if an excess workload is applied to the user, it is adjusted adequately during the exercise step such that a long exercise of the user under the excess workload is prevented. 
     EIGHTH EMBODIMENT 
     A physical strength of an user is estimated by the substantially same method as SEVENTH EMBODIMENT except for the followings. That is, a modified workload, which is obtained by multiplying the workload derived in each exercise step of SEVENTH EMBODIMENT by a safety coefficient of less than 1, is applied to the user in each exercise step of EIGHTH EMBODIMENT, as listed on TABLE 8. In this case, since it can be readily adjusted only by increasing the modified workload according to the fuzzy control method, an excess workload is not applied to the user in any case, so that it will provide safe training and examination of physical strength to the user. 
     
                       TABLE 8______________________________________   WorkloadExercise   applyingstep    time      Workload (W)______________________________________1       1 min.    (first workload) × 0.7(safety coefficient)2       3 min.    (second workload) × 0.7(safety coefficient)3       4 min.    (third workload) × 0.7(safe coefficient)4       4 min.    (fourth workload) × 0.8(safe coefficient)5       4 min.    (fifth workload) × 0.9(safe coefficient)______________________________________ 
    
     NINTH EMBODIMENT 
     A physical strength of an user is examined from a maximum oxygen uptake thereof. That is, a first workload is applied to the user for 1 min., and a first heart rate of the user is measured under the first workload. The first workload is determined by multiplying an exercise level (%)/100 by a first maximum oxygen uptake which is predicted by entering as input parameters age, gender, and body weight of the user into a first multiple variate model equation. In this embodiment, the exercise level is 30%. Subsequently, a second maximum oxygen uptake is predicted by entering as input parameters, age, gender, body weight, the first workload, the first heart rate, and the first maximum oxygen uptake into a second multiple variate model equation. The second maximum oxygen uptake is converted to a maximum aerobic capacity by the equation  4!. Thus obtained maximum aerobic capacity is determined as the physical strength of the user. By the way, the second multiple variate model equation is prepared according to a neural network analysis and is made to learn 40,000 times with respect to statistically obtained data for improving accuracy of the predicted maximum oxygen uptake. Details of the NINTH EMBODIMENT are summarized on TABLE 9. 
     
                       TABLE 9______________________________________Work-load                         Exer-                                  MeanExer-apply-                       cise square-cise ing     Input parameters of a multiple variate                             level                                  errorstep time    model equation.      (%)  (*1)______________________________________1    1 min.  gender, age, and body weight                             30   15.02    0 min.  age, gender, body weight, the measured                             *2   12.7        heart rate, the applied workload and the        predicted maximum oxygen uptake at        the previous exercise step______________________________________ *1: A meansquare-error of a maximum oxygen uptake predicted in each exercise step against a maximum oxygen uptake of the user examined by an expiration analysis. *2: In the exercise step 2, second maximum oxygen uptake is predicted by the second multiple variate model equation. However, a workload derived from the second maximum oxygen uptake was not applied to the user.