Generalized displacement cable tension monitoring progressive identification method for damaged cable and concentrated loads

[0137] Aiming at the problem of cable structure health monitoring, this method realizes two functions that the existing methods cannot have. They are: 1. When the cable structure undergoes a generalized displacement of the support, the concentrated load and the temperature change of the structure (environment) are affected by the structure. The influence of the generalized displacement of the cable structure support, the change of the concentrated load and the change of the structure temperature on the identification result of the health state of the cable structure can be eliminated, so as to accurately identify the structural health monitoring method of the damaged cable; When the cable is damaged, the change of the concentrated load can be identified at the same time, that is, the method can eliminate the influence of the generalized displacement of the cable structure support, the change of the structure temperature and the change of the health state of the support cable, and realize the correct identification of the change degree of the concentrated load. The following description of embodiments of the present method is merely exemplary in nature and is in no way intended to limit the application or use of the present method.

[0138] The method employs an algorithm for identifying damaged cables and changes in concentrated loads. In practice, the following steps are one of various steps that can be taken.

[0139] Step 1: First, confirm the amount of concentrated load that the cable structure bears that may change. According to the characteristics of the concentrated loads borne by the cable structure, confirm "all the concentrated loads that may change", or consider all the concentrated loads as "all the concentrated loads that may change", and set a total of JZW concentrated loads that may change. load.

[0140] Concentrated load is divided into two types: concentrated force and concentrated force couple. In a coordinate system, such as in Cartesian rectangular coordinate system, a concentrated force can be decomposed into three components, and a concentrated force couple can also be decomposed into three components. A concentrated force component or a concentrated force couple component is called a concentrated load in this method.

[0141] The sum of the number of supporting cables of the cabled structure and the number of "all possible varying concentrated loads" is N. For the convenience of description, this method collectively refers to the evaluated support cable and "all the concentrated loads that may change" as "evaluated objects", and there are a total of N evaluated objects. The evaluated objects are numbered consecutively, which will be used to generate vectors and matrices in subsequent steps.

[0142] There are M total in the cable system 1 Root support cable, structural cable force data includes this M 1 The cable force of the root support cable, obviously M 1 less than the number N of evaluated objects. just by M 1 M of the root support cable 1 It is impossible to solve the state of the unknown N evaluated objects by using the cable force data. This method monitors all M 1 On the basis of the root support cable force, increase the pair not less than (N-M 1 ) other monitored quantities.

[0143] increase not less than (N-M 1 ) The other monitored quantity is still the cable force, which is described as follows:

[0144] Before the structural health inspection system starts to work, artificially increase M on the cable structure 2 (M 2 not less than N-M 1 ) root cable, called the sensor cable, the newly added M 2 The stiffness of the root sensing cable should be much smaller than the stiffness of any supporting cable in the cable structure, for example, 20 times smaller. The newly added M 2 The cable force of the root sensing cable should be small, for example, its cross-sectional normal stress should be less than its fatigue limit. These requirements can ensure that the newly increased M 2 The root sensor cable does not suffer from fatigue damage, and the newly added M 2 Both ends of the root sensing cable should be fully anchored to ensure that there will be no slack. The newly added M 2 The root sensing cable should be adequately protected against corrosion to ensure that the newly added M 2 Root sensing cords do not suffer damage and relaxation, and this newly added M will be monitored during structural health monitoring. 2 The cable force of the root sensor cable.

[0145] It is also possible to use more sensor cables to ensure the reliability of health monitoring, such as making M 2 not less than N-M 1 In the process of structural health monitoring, only the cable force data of the intact sensing cables are selected (called the actual monitored quantity that can be used, and the number is recorded as K, and K must not be less than N) and the corresponding cable structure The unit change matrix ΔC of the monitored quantity is used to evaluate the state of health, since M 2 not less than N-M 1 2 times, can guarantee the number of effective sensor cables that can actually be used plus M 1 not less than N. This newly added M will be monitored during structural health monitoring 2 The cable force of the root sensor cable. Newly added M 2 The root sensing cable should be installed on the structure and easily accessible by personnel to facilitate non-destructive testing by personnel.

[0146] The newly added M in this method 2 The root sensing cable is a part of the cable structure. When the cable structure is mentioned later, the cable structure includes increasing M 2 The cable structure in front of the root sensing cable and the newly added M 2 The root sensor cable, that is to say, when referring to the cable structure later, it refers to the newly added M 2 The cable structure of the root sensing cable. Therefore, when it is mentioned later that the "cable structure steady-state temperature data" is obtained by measurement and calculation according to the "temperature measurement and calculation method of the cable structure of this method", the cable structure includes the newly added M 2 Root sensing cable, the obtained "cable structure steady-state temperature data" includes the newly added M 2 Steady-state temperature data of the root sensing cable to obtain the newly added M 2 The method for the steady-state temperature data of the root sensing cable is the same as that of the M cable structure. 1 The method of obtaining the steady-state temperature data of the root support cable will not be explained one by one in the following text; 2 The method of the cable force of the root sensing cable is the same as the M of the cable structure. 1 The method of measuring the cable force of the root support cable will not be explained one by one in the following paragraphs; when any measurement is performed on the support cable of the cable structure, the newly added M 2 The same measurement is performed on the root sensor cable, which will not be explained in the following text; the newly added M 2 In addition to the absence of damage and relaxation of the root sensor cord, the newly increased M 2 The information amount of the root cable is the same as that of the support cable of the cable structure, and will not be explained one by one in the following text; the newly added M 2 The cable force of the root sensing cable is increased by not less than (N-M 1 ) of other monitored quantities. When establishing various mechanical models of the cable structure later, the newly added M 2 The root sensing cable is treated as the support cable of the cable structure. Except for the occasions where the damage and slack of the support cable are mentioned, the newly added M is included when the support cable is mentioned in other situations. 2 root.

[0147] Combining the above monitored quantities, the entire cable structure has a total of M (M=M 1 +M 2 ) The M monitored quantities of the cable, M shall not be less than the number N of the evaluated objects.

[0148] For convenience, "all monitored parameters of the cable structure" are simply referred to as "monitored quantities" in this method. The M monitored quantities are consecutively numbered, which will be used to generate vectors and matrices in subsequent steps. This method uses the variable j to represent this number, j=1,2,3,...,M.

[0149] Determine the "temperature measurement and calculation method of the cable structure of this method", and the specific steps of the method are as follows:

[0150]Step a: Query or actual measurement (can be measured by conventional temperature measurement methods, such as using thermal resistance measurement) to obtain the material of the cable structure and the temperature-dependent heat transfer parameters of the environment where the cable structure is located, using the design drawing of the cable structure, The as-built drawings and the geometrical measured data of the cable structure are used to establish a heat transfer calculation model (such as a finite element model) of the cable structure using these data and parameters. Query the meteorological data in recent years for not less than 2 years at the location of the cable structure, and count the number of cloudy days during this period as T cloudy days, and obtain statistics from 0:00 to the next day for each cloudy day in the T cloudy days The maximum and minimum temperatures between 30 minutes after the sunrise time, the sunrise time refers to the meteorological sunrise time determined according to the law of the earth's rotation and revolution. At the sunrise time of a day, the maximum temperature difference between the maximum temperature and the minimum temperature between 0:00 and 30 minutes after the sunrise time of the next day on each cloudy day is called the maximum temperature difference of the daily temperature of the cloudy day. There are T cloudy days, There is the maximum temperature difference of the daily temperature of the T cloudy days, and the maximum value of the maximum temperature difference of the daily temperature of the T cloudy days is taken as the reference daily temperature difference, and the reference daily temperature difference is recorded as ΔT r; Query the meteorological data in recent years at the location of the cable structure and its altitude interval of not less than 2 years or obtain the data and change law of the temperature of the environment where the cable structure is located with time and altitude, and calculate the location and altitude of the cable structure. The maximum change rate ΔT of the temperature of the environment where the cable structure is located in recent years with an interval of not less than 2 years h , for the convenience of description, take ΔT h The unit is °C/m; take "R cable structure surface points" on the surface of the cable structure, and the specific principle of taking "R cable structure surface points" is described in step b3, and the R points will be obtained through actual measurement records later. The temperature of the surface point of the cable structure is called the “measured data of the surface temperature of the R cable structures”. temperature, the calculated temperature data is called "the surface temperature calculation data of R cable structures". From the lowest altitude to the highest altitude where the cable structure is located, select no less than three different altitudes evenly on the cable structure. For example, if the altitude of the cable structure is between 0m and 200m, the altitude of 0m can be selected , 50m, 100m, and 200m above sea level, at each selected altitude, use an imaginary horizontal plane to intersect the surface of the cable structure to obtain the intersection line, and the intersection of the horizontal plane and the cable structure is obtained. The intersection line is the outer edge line of the intersection surface. Six points are selected at the intersection of the horizontal plane and the surface of the cable structure, and the outer normals of the surface of the cable structure are indexed from the selected points. The direction of the temperature distribution of the measured cable structure along the wall thickness intersects the "intersection of the horizontal plane with the surface of the cable structure". In the selected six directions of measuring the temperature distribution of the cable structure along the wall thickness, the cable structure is first determined according to the meteorological data of the four seasons of the year in the area where the cable structure is located, the geometric dimensions, spatial coordinates, and the surrounding environment of the cable structure. The sunny side and the shady side of the cable structure are part of the surface of the cable structure. At each selected altitude, the aforementioned intersection line has a section in the sunny side and the shady side. Each of the two segments has a midpoint, and the outer normal of the cable structure is obtained through these two midpoints. In this method, these two outer normals are called the outer normal of the cable structure's sunny side and the outer normal of the shady side of the cable structure. , this method refers to these two outer normal directions as the outer normal direction of the cable structure’s sunny side and the outer normal direction of the shady side of the cable structure. When the intersection line intersects, there are also two intersection points. These two intersection points divide the intersection line into two line segments. Two points are taken on the two line segments, for a total of four points. The points taken will be the two line segments of the intersection line. Each line segment is divided into 3 segments of equal length, and the outer normals of the surface of the cable structure are taken at these 4 points, so that a total of 6 outer normals of the surface of the cable structure are selected at each selected altitude, The direction of the 6 outer normals is "the direction of the temperature distribution of the measured cable structure along the wall thickness". Each "measure the direction of the temperature distribution of the cable structure along the wall thickness" line has two intersection points with the surface of the cable structure. If the cable structure is hollow, these two intersection points are one on the outer surface of the cable structure and the other on the inner surface. If the cable structure is solid, the two intersection points are on the outer surface of the cable structure, connect these two intersection points to get a straight line segment, and select three points on the straight line segment, these three points are all the straight line segment. Divided into four sections, measure the temperature of the cable structure at the selected three points and the two end points of the straight line section, a total of 5 points. Specifically, you can drill holes on the cable structure first, and how to bury the temperature sensor in these 5 points At the point, the measured temperature is called the "temperature distribution data of the cable structure along the thickness", and the "measurement of the temperature distribution of the cable structure along the wall thickness" intersects with the same "intersection line between the horizontal plane and the surface of the cable structure". The "temperature distribution data of the cable structure along the thickness" obtained by the measurement of the "direction" is called "the temperature distribution data of the cable structure along the thickness of the same altitude" in this method. Assuming that H different altitudes are selected, at each altitude, the direction of the temperature distribution of B measuring cable structures along the wall thickness is selected, and the direction of the temperature distribution along the wall thickness of each measuring cable structure is in the cable structure. E points are selected in , where H and E are not less than 3, and B is not less than 2. Let HBE be the product of H, B and E, corresponding to a total of HBE “points for measuring the temperature distribution data of the cable structure along the thickness” , the temperature of the HBE “points measuring the temperature distribution data of the cable structure along the thickness” will be obtained through the actual measurement, and the measured temperature data will be called “the measured temperature data of the HBE cable structure along the thickness”. If the cable structure is used In the heat transfer calculation model, the temperature at the point where the temperature distribution data of the HBE cable structures are measured along the thickness is obtained through heat transfer calculation, and the calculated temperature data is called "the HBE cable structure temperature calculation data along the thickness"; let BE is the product of B and E, there are BE “temperature distribution data along the thickness of the cable structure at the same altitude” at each selected altitude in this method. Select a position at the location of the cable structure according to the requirements of meteorological measurement of temperature, and record the temperature of the environment where the cable structure meets the requirements of meteorological measurement of temperature; Every day of the year should get the fullest sunshine that the place can get on that day (as long as there is a sunrise on that day, the location should be illuminated by sunlight), and a piece of carbon steel ( For example, a flat plate made of 45# carbon steel (such as a square flat plate with a width of 30 cm and a thickness of 3 mm) is called the reference flat plate. The reference flat plate should not be in contact with the ground. To measure the top of the wooden louver box required, the side of this reference slab is facing the sun, called the sunny side (for example, in the northern hemisphere, the sunny side is facing up and facing south and is illuminated throughout the day, and the sunny side should have a suitable slope so that the snow should not accumulate or clear the sun side after snow), the sun side of the reference slab is rough and dark (good for receiving sunlight), the sun side of the reference slab should get a slab on every day of the year The most sufficient sunshine of the day that can be obtained in this place, the non-sunny side of the reference plate is covered with thermal insulation material (such as 5mm thick calcium carbonate thermal insulation material), and the temperature of the sunny side of the reference plate will be obtained by real-time monitoring and recording.

[0151] The bth step, real-time monitoring (can be measured by conventional temperature measurement methods, such as using thermal resistance measurement, for example, measuring and recording temperature data every 10 minutes) and recording to obtain the R cable structure surface temperature measured data of the above R cable structure surface points , at the same time real-time monitoring (can be measured by conventional temperature measurement methods, such as using thermal resistance measurement, such as measuring and recording temperature data every 10 minutes) to obtain the previously defined temperature distribution data of the cable structure along the thickness, while real-time monitoring (can use conventional Measurement of temperature measurement methods, such as placing a thermal resistance in a wooden louver box that meets the requirements of meteorological temperature measurement to measure the temperature, such as measuring and recording temperature data every 10 minutes) Record the environment of the cable structure that meets the requirements of meteorological measurement of temperature. Air temperature data; recorded through real-time monitoring (can be measured by conventional temperature measurement methods, such as placing a thermal resistance in a wooden louver box that meets the requirements of meteorological temperature measurement to measure air temperature, such as measuring and recording temperature data every 10 minutes) to obtain the current day The temperature measurement data sequence of the environment where the cable structure is located from the time of exit to 30 minutes after the sunrise time of the next day. The measured air temperature data of the environment where the cable structure is located are arranged in chronological order, find the highest temperature and the lowest temperature in the measured air temperature data sequence of the environment where the cable structure is located, and subtract the lowest temperature from the highest temperature in the measured air temperature data sequence of the environment where the cable structure is located. Obtain the maximum temperature difference between the sunrise time of the day when the cable structure is located and 30 minutes after the sunrise time of the next day, recorded as ΔT emax; From the temperature measured data sequence of the environment where the cable structure is located, through conventional mathematical calculations (for example, curve fitting the temperature measured data sequence of the environment where the cable structure is located, and then by calculating the derivative of the curve with respect to time or by using numerical methods to find each curve on the curve. A point-to-time rate of change corresponding to the time of measuring and recording data) to obtain the rate of change of the air temperature in the environment where the cable structure is located with respect to time, and the rate of change also changes with time; through real-time monitoring (can be measured by conventional temperature measurement methods, such as Use thermal resistance to measure the temperature of the reference plate's sunny side, for example, measure and record the temperature data every 10 minutes) to obtain the measured data sequence of the temperature of the reference plate's sunny side between the sunrise time of the day and 30 minutes after the sunrise time of the next day , the measured data sequence of the temperature of the sunny side of the reference plate is arranged in chronological order from the time of sunrise on the current day to 30 minutes after the sunrise time of the next day. The highest temperature and the lowest temperature in the measured data series of the temperature of the reference plate, subtract the lowest temperature from the highest temperature in the measured data series of the temperature of the sun-facing surface of the reference plate to obtain the temperature of the sun-facing surface of the reference plate. Sunrise time to time of the day The maximum temperature difference between 30 minutes after the sunrise time, recorded as ΔT pmax; Through real-time monitoring (can be measured by conventional temperature measurement methods, such as measuring the surface points of cable structures using thermal resistance measurement, such as measuring and recording temperature data every 10 minutes), the time of sunrise on the current day to 30 minutes after the sunrise time of the next day is recorded. The measured data sequence of the surface temperature of the cable structure between all R cable structure surface points, there are R measured data sequences of the surface temperature of the cable structure surface, and each measured data sequence of the surface temperature of the cable structure consists of a cable structure. The measured data of the surface temperature of the cable structure between the sunrise time of the current day and the sunrise time of the next day for 30 minutes are arranged in chronological order, and the highest temperature and the lowest temperature in the measured data sequence of the surface temperature of each cable structure are found. Subtract the lowest temperature from the highest temperature in the measured data sequence of the surface temperature of each cable structure to obtain the maximum temperature difference between the sunrise time of the day and 30 minutes after the sunrise time of the next day for the temperature of each cable structure surface point, there are R The surface point of the cable structure has R maximum temperature difference values ​​between the sunrise time of the day and 30 minutes after the sunrise time of the next day, and the maximum value is recorded as ΔT smax; From the measured data sequence of the surface temperature of each cable structure, through conventional mathematical calculation (for example, first perform curve fitting on the measured data sequence of the surface temperature of each cable structure, and then by calculating the derivative of the curve with respect to time or by using numerical methods to find each curve on the curve. A point-to-time rate of change corresponding to the time the data was measured and recorded) was obtained to obtain the rate of change of temperature with respect to time at each cable structure surface point, and the rate of change of temperature with respect to time at each cable structure surface point also varied with time. After obtaining the "temperature distribution data of the cable structure along the thickness" of the HBE at the same time between the sunrise time of the current day and the sunrise time of the next day and 30 minutes after the sunrise time of the next day through real-time monitoring, calculate the total BE at each selected altitude. The difference between the highest temperature and the lowest temperature in the "temperature distribution data of the cable structure at the same altitude along the thickness", the absolute value of this difference is called "the maximum temperature difference in the thickness direction of the cable structure at the same altitude", and H selected There are H "maximum temperature differences in the thickness direction of the cable structure at the same altitude" at different altitudes, and the maximum value among the H "maximum temperature differences in the thickness direction of the cable structure at the same altitude" is called "the maximum temperature difference in the thickness direction of the cable structure". , denoted as ΔT tmax.

[0152] Step c, measure and calculate the steady-state temperature data of the cable structure; first, determine the time when the steady-state temperature data of the cable structure is obtained. There are six conditions related to the time when the steady-state temperature data of the cable structure is obtained. The first condition is: The time to obtain the steady-state temperature data of the cable structure is between the sunset time of the current day and the sunrise time of the next day 30 minutes. The sunset time refers to the meteorological sunset time determined according to the law of the earth's rotation and revolution. The required sunset time of each day is obtained by conventional meteorological calculations; the a condition of the second condition is that during the period between the sunrise time of the current day and 30 minutes after the sunrise time of the next day, ΔT pmax and ΔT smaxIt is not greater than 5 degrees Celsius; the second condition that must be satisfied is that during the period between the sunrise time of the current day and 30 minutes after the sunrise time of the next day, the ΔT calculated by the previous measurement emax Not greater than the reference daily temperature difference ΔT r , and measure the calculated ΔT before pmax minus 2 degrees Celsius is not greater than ΔT emax , and measure the calculated ΔT before smax not greater than ΔT pmax; Only one of the conditions a and b of the second item is satisfied, and the second condition is satisfied; the third condition is that when the steady-state temperature data of the cable structure is obtained, the temperature of the environment where the cable structure is located is related to time The absolute value of the rate of change is not greater than 0.1 degrees Celsius per hour; the fourth condition is the rate of change of the temperature of each of the R cable structure surface points with respect to time at the moment when the steady-state temperature data of the cable structure is obtained. The absolute value of is not greater than 0.1 degrees Celsius per hour; the fifth condition is that at the moment when the steady-state temperature data of the cable structure is obtained, the measured data of the surface temperature of the cable structure for each of the R cable structure surface points is the current day The minimum value between the exit time and 30 minutes after the sunrise time of the next day; the sixth condition is that when the steady-state temperature data of the cable structure is obtained, the "maximum temperature difference in the thickness direction of the cable structure" ΔT tmax not more than 1 degree Celsius. This method uses the above six conditions, and any one of the following three times is called "the mathematical time for obtaining the steady-state temperature data of the cable structure". The first to fifth conditions in the “Conditions related to the time of the time, the third time is the time when the first to sixth conditions in the above-mentioned "conditions related to the time for determining the time to obtain the steady-state temperature data of the cable structure" are simultaneously satisfied; when the mathematical time when the steady-state temperature data of the cable structure is obtained It is one of the actual recorded data times in this method, and the moment when the steady-state temperature data of the cable structure is obtained is the mathematical moment when the steady-state temperature data of the cable structure is obtained; if the mathematical moment when the steady-state temperature data of the cable structure is obtained is not the actual time At any time in the recorded data time, the time of the actual recorded data that is closest to the mathematical time of obtaining the steady-state temperature data of the cable structure is taken as the time when the steady-state temperature data of the cable structure is obtained; The cable structure related health monitoring analysis is carried out with the measured and recorded quantities of the cable structure steady-state temperature data at the moment; this method approximately considers that the cable structure temperature field at the moment when the cable structure steady-state temperature data is obtained is in a steady state, that is, the cable structure temperature at this moment does not follow the curve. The time changes, this time is the time when the steady-state temperature data of the cable structure is obtained in this method; then, according to the heat transfer characteristics of the cable structure, the R measured data of the surface temperature of the cable structure at the time when the steady-state temperature data of the cable structure is obtained and the "HBE" are used. The measured temperature data along the thickness of the cable structure”, using the heat transfer calculation model of the cable structure (such as the finite element model), and through the conventional heat transfer calculation (such as the finite element method) to obtain the cable structure at the moment when the steady-state temperature data of the cable structure is obtained. The temperature distribution of the structure. At this time, the temperature field of the cable structure is calculated according to the steady state. The calculated temperature distribution data of the cable structure at the moment when the steady-state temperature data of the cable structure is obtained include the calculation of the R surface points of the cable structure. Temperature, the calculated temperature of the R cable structure surface points is called the R cable structure steady-state surface temperature calculation data, and also includes the calculation of the cable structure at the previously selected HBE points of "measurement of the temperature distribution data along the thickness of the cable structure". Temperature, the calculated temperature of the HBE "points for measuring the temperature distribution data of the cable structure along the thickness" is called "the HBE temperature calculation data along the thickness of the cable structure". When the calculated surface temperature data are equal, and the "measured data of HBE cable structure along the thickness temperature" and "HBE cable structure temperature calculated along the thickness data" are correspondingly equal, the calculated temperature at the moment when the steady-state temperature data of the cable structure is obtained. The temperature distribution data of the cable structure is called "the steady-state temperature data of the cable structure" in this method, and the "measured data of the surface temperature of the R cable structures" at this time is called the "measured data of the steady-state surface temperature of the R cable structures", " The measured data of the HBE cable structure along the thickness of the temperature" is called "HBE cable structure along the thickness of the steady-state temperature measured data". When taking "R cable structure surface points" on the surface of the cable structure, the number and distribution of "R cable structure surface points" must satisfy three conditions. The first condition is that when the temperature field of the cable structure is in a steady state, When the temperature of any point on the surface of the cable structure is obtained by linear interpolation of the measured temperature of the point adjacent to the arbitrary point on the surface of the cable structure in the "R cable structure surface points", the temperature of any point on the surface of the cable structure obtained by linear interpolation The error between the temperature of the point and the actual temperature of this arbitrary point on the surface of the cable structure is not more than 5%; the surface of the cable structure includes the surface of the supporting cable; The number is not less than 4, and the points at the same altitude among the "R cable structure surface points" are evenly distributed along the cable structure surface; all pairs of adjacent cable structure surface points along the altitude of the "R cable structure surface points" The maximum value of the absolute value of the difference in altitude Δh is not greater than 0.2°C divided by ΔT h The obtained value is taken as ΔT for the convenience of description h The unit is °C/m, and the unit of Δh is m for the convenience of description; the definition of "R cable structure surface points" two adjacent cable structure surface points along the altitude means that when only the altitude is considered, in the "R cable structure surface point" There is not a single cable structure surface point in "each cable structure surface point", and the altitude value of the cable structure surface point is between the altitude values ​​of two adjacent cable structure surface points; the third condition is to query or press the weather Then, according to the geometric characteristics and orientation data of the cable structure, find the positions of those surface points on the cable structure that receive the most sunshine time throughout the year. At least one cable structure surface point in "Surface Points" is one of those surface points on the cable structure that receive the most sunlight throughout the year.

[0153] Step 2: Establish an initial mechanical calculation benchmark model A o.

[0154] When the cable structure is completed, or before the establishment of the health monitoring system, the "cable structure steady-state temperature data" can be obtained by measuring and calculating according to the "temperature measurement and calculation method of the cable structure of this method" (which can be measured by conventional temperature measurement methods, such as using Thermal resistance measurement), the "cable structure steady-state temperature data" at this time uses the vector T o represented, called the initial cable structure steady-state temperature data vector T o. T is obtained in the actual measurement o At the same time, that is, at the same moment when the steady-state temperature data vector of the initial cable structure is obtained, the initial values ​​of all monitored quantities of the cable structure are directly measured and calculated using conventional methods, and the initial value vector C of the monitored quantities is formed. o.

[0155] In this method, at the same moment when the steady-state temperature data vector of a certain (such as initial or current) cable structure is obtained, a certain method can be used to measure and calculate the monitored quantity (such as cable) according to the following methods. Data of all monitored quantities of the structure): While measuring and recording the temperature (including the air temperature of the environment where the cable structure is located, the temperature of the sunny side of the reference plate and the surface temperature of the cable structure), for example, the temperature is measured and recorded every 10 minutes, then At the same time, the data of the monitored quantity of the measured quantity (such as all the monitored quantities of the cable structure) are also measured and recorded every 10 minutes. Once the moment when the steady-state temperature data of the cable structure is obtained is determined, the data of the monitored quantity of a certain measured quantity (such as all monitored quantities of the cable structure) at the same moment as the moment when the steady-state temperature data of the cable structure is obtained is called At the same moment when the steady-state temperature data of the cable structure is obtained, the data of the monitored quantity of the measured quantity obtained by the calculation method is measured by the method of a certain method.

[0156] The physical parameters (such as thermal expansion coefficient) and mechanical performance parameters (such as elastic modulus, Poisson's ratio) of various materials used in the cable structure are obtained by conventional methods (data checking or actual measurement).

[0157] The steady-state temperature data vector T of the initial cable structure is obtained from the measured calculation o At the same time, the measured and calculated data of the cable structure are obtained by using the conventional method. The measured and calculated data of the cable structure include the non-destructive testing data of the supporting cable and other data that can express the health state of the cable, the initial geometric data of the cable structure, the cable force data, the tension data of the tie rod, and the generalized coordinate data of the initial cable structure support (including the support about the support. The spatial coordinates and angular coordinates of the X, Y, and Z axes of the Cartesian Cartesian coordinate system (that is, the spatial coordinate data of the initial cable structure support and the angular coordinate data of the initial cable structure support), the measurement data of the concentrated load of the cable structure, and the measurement data of the distributed load of the cable structure , Cable structure body load measurement data, cable structure modal data, structure strain data, structure angle measurement data, structure space coordinate measurement data and other measured data. The generalized coordinate data of the initial cable structure support is composed of the generalized coordinate vector U of the initial cable structure support o. The initial geometric data of the cable structure may be the spatial coordinate data of all cable end points plus the spatial coordinate data of a series of points on the structure, in order to determine the geometrical features of the cable structure according to these coordinate data. For cable-stayed bridges, the initial geometric data can be the spatial coordinate data of the end points of all cables plus the spatial coordinate data of several points on both ends of the bridge, which is the so-called bridge type data. The initial damage vector d of the object to be evaluated is established by using the nondestructive testing data of the support cable and other data that can express the health state of the support cable and the measurement data of the concentrated load of the cable structure o , with d o Represents the cable structure (base model A with initial mechanics calculation o Represents the initial state of health of the subject being assessed. If there is no non-destructive testing data of the support cable and other data that can express the healthy state of the support cable, or when the initial state of the structure can be considered as a state of no damage and no relaxation, the vector d o The value of each element related to the support cable in the value is 0, if d o The evaluated object corresponding to a certain element of is a certain concentrated load, in this method, take d o The value of this element is 0, and the initial value representing the change of this concentrated load is 0. Using the design drawings, as-built drawings and the measured data of the initial cable structure, the non-destructive testing data of the supporting cable, the physical and mechanical properties parameters of various materials used in the cable structure that change with temperature, the generalized coordinates of the initial cable structure support vector Uo and initial cable structure steady-state temperature data vector T o , using mechanical methods (such as finite element method) to include the "cable structure steady-state temperature data" to establish the initial mechanical calculation benchmark model A o.

[0158] Regardless of the method used to obtain the initial mechanical calculation benchmark model A o , including the "cable structure steady-state temperature data" (that is, the initial cable structure steady-state temperature data vector T o ), based on A o The calculated cable structure data must be very close to the actual measured data, and the error should generally not be greater than 5%. This ensures that the use of A o The calculated cable force calculation data, strain calculation data, cable structure shape calculation data and displacement calculation data, cable structure angle data, cable structure space coordinate data, etc. under the simulated situation are reliably close to the measured data when the simulated situation actually occurs. . Model A o The state of health of the middle support cable is the initial damage vector d of the evaluated object o Represents that the steady-state temperature data of the cable structure uses the initial cable structure steady-state temperature data vector T o express. Because based on A o The calculated values ​​of all monitored quantities are very close to the initial values ​​of all monitored quantities (measured), so they can also be used in A o On the basis of , obtained by mechanical calculation, A o The calculated value of each monitored quantity constitutes the initial value vector C of the monitored quantity o. corresponds to A o The "cable structure steady-state temperature data" is the "initial cable structure steady-state temperature data vector T o "; corresponds to A o The state of health of the evaluated object is the initial damage vector d of the evaluated object o means; corresponds to A o The initial values ​​of all monitored quantities use the initial value vector C of the monitored quantities o express. corresponds to A oThe generalized coordinate data of the cable structure support is the generalized coordinate vector U of the initial cable structure support o means; T o , U o and d o is A o parameter, C o by A o The mechanical calculation results of the composition.

[0159] The third step: in this method, the letter i only indicates the number of cycles, that is, the i-th cycle, except where the letter i clearly indicates the step number; The current initial mechanical calculation benchmark model is recorded as the current initial mechanical calculation benchmark model A i o , A o and A i o Taking into account the temperature parameters, the influence of temperature changes on the mechanical properties of the cable structure can be calculated; at the beginning of the i-th cycle, corresponding to A i o The "cable structure steady-state temperature data" uses the current initial cable structure steady-state temperature data vector T i o represents, the vector T i o is defined in the same way as the vector T o is defined in the same way, T i o elements with T o One-to-one correspondence between the elements; the current initial mechanical calculation benchmark model A corresponding to the cable structure required at the beginning of the i-th cycle i o The generalized coordinate data of the cable structure support constitutes the generalized coordinate vector U of the current initial cable structure support i o , the current initial mechanical calculation benchmark model A of the cable structure is established for the first time i o when, U i o is equal to U o. The current initial damage vector of the evaluated object required at the beginning of the i-th cycle is denoted as d i o , d i o Represents the cable structure A at the beginning of the cycle i o The health status of the subject being assessed, d i o is defined in the same way as d o is defined in the same way, d i o elements with d o One-to-one correspondence between the elements of i o represents, the vector C i o is defined in the same way as the vector C o is defined in the same way, C i o Elements with C o The elements of the one-to-one correspondence, the current initial value vector C of the monitored quantity i o means corresponding to A i o The specific values ​​of all monitored quantities of ; T i o and d i o is A i o characteristic parameters of ; C i o by A i o is composed of the mechanical calculation results of ; at the beginning of the first cycle, A i o denoted as A 1 o , build A 1 o The method is to make A 1 o equal to A o; at the beginning of the first cycle, T i o denoted as T 1 o , build T 1 o method for making T 1 o equal to T o; at the beginning of the first cycle, U i o denoted as U 1 o , build U 1 o The method for making U 1 o equal to U o; at the beginning of the first cycle, d i o denoted as d 1 o , build d 1 o method for making d 1 o equal to d o; at the beginning of the first loop, C i o denoted as C 1 o , build C 1 o The way to make C 1 o equal to C o.

[0160] Step 4: Install the hardware part of the cable structure health monitoring system. The hardware part includes at least: monitoring system for monitored quantity (such as cable force measurement system, signal conditioner, etc.), generalized coordinate monitoring system for cable structure support (including total station, angle measurement sensor, signal conditioner, etc.), cable structure Temperature monitoring system (including temperature sensor, signal conditioner, etc.) and cable structure environmental temperature measurement system (including temperature sensor, signal conditioner, etc.), signal (data) collector, computer and communication alarm equipment. Each monitored quantity, the generalized coordinates of the support of each cable structure, and each temperature must be monitored by the monitoring system. The monitoring system transmits the monitored signal to the signal (data) collector; the signal is transmitted to the signal collector through the signal collector. Computer; the computer is responsible for running the health monitoring software of the assessed object of the cable structure, including recording the signals transmitted by the signal collector; when the monitored object's health status changes, the computer controls the communication alarm equipment to the monitoring personnel, the owner and the (or) Designated personnel call the police.

[0161] The fifth step: compile and install the system software for running the method on the computer. work that can be done with a computer).

[0162] Step 6: The cycle operation starts from this step. During the service process of the structure, the current data of the steady-state temperature data of the cable structure are obtained by continuous measurement and calculation according to the "temperature measurement and calculation method of the cable structure of this method". The current data of "temperature data" constitutes the steady-state temperature data vector T of the current cable structure i , the vector T i is defined in the same way as the vector T o is defined in the same way, T i elements with T o The elements of the one-to-one correspondence; in the measured vector T i At the same time, that is, when the current cable structure steady-state temperature data vector T is obtained i At the same moment of time, the current values ​​of all monitored quantities in the cable structure are actually measured, and all these values ​​form the current value vector C of the monitored quantities. i , the vector C i is defined in the same way as the vector C o is defined in the same way, C i Elements with C o The elements of is one-to-one correspondence, representing the value of the same monitored quantity at different times.

[0163] The current cable structure steady-state temperature data vector T is obtained from the actual measurement i At the same time, the current data of the generalized coordinates of the cable structure support are obtained from the actual measurement, and all the data form the generalized coordinate vector U of the current cable structure measured support. i.

[0164] The current cable structure steady-state temperature data vector T is obtained from the actual measurement i At the same time, for the newly added M 2 Perform non-destructive testing on the root sensor cable, such as ultrasonic flaw detection, visual inspection, and infrared imaging inspection, to identify damaged or loose sensor cables. The elements corresponding to the identified damaged or slack sensor cables are removed from each vector of the rule number, and the identified damaged or slack sensor cables no longer appear in the vectors and matrices that appear after this method. Corresponding elements, when referring to a sensor cord after this method, do not include a sensor cable identified here as damaged or loosened, and when referring to a monitored quantity after this method, no longer include a sensor cable identified here as damaged or slack. The cable force of the slack sensing cable; if several damaged or slack sensing cables are identified from the cable structure, the M 2 Decrease M by the same amount.

[0165] Step 7: After obtaining the generalized coordinate vector U of the measured support of the current cable structure i and the current cable structure steady-state temperature data vector T i Then, compare U respectively i and U i o , T i and T i o , if U i equal to U i o and T i equal to T i o , then there is no need for A i o , U i o and T i o Update, otherwise, the current initial mechanical calculation benchmark model A needs to be i o , the generalized coordinate vector U of the current initial cable structure support i o , the current initial cable structure steady-state temperature data vector T i o and the current initial value vector C of the monitored quantity i o is updated, while the current initial damage vector d of the object being evaluated i o Remaining unchanged, the update method proceeds as follows from steps a to c:

[0166] a. Calculate U i with U o difference, U i with U o The difference is the generalized displacement of the support of the cable structure support about the initial position, the generalized displacement of the support is represented by the generalized displacement vector V of the support, and V is equal to U i minus U o , there is a one-to-one correspondence between the elements in the generalized displacement vector V of the support and the generalized displacement component of the support. The value of an element in the generalized displacement vector V of the support corresponds to the generalized displacement of a designated support in a designated direction.

[0167] b. Calculate T i with T o difference, T i with T oThe difference is the change of the steady-state temperature data of the current cable structure with respect to the steady-state temperature data of the initial cable structure, T i with T o The difference is represented by the steady-state temperature change vector S, which is equal to T i minus T o , S represents the change in the steady-state temperature data of the cable structure.

[0168] c. first to A o The generalized displacement constraint of the support is imposed on the cable structure support in o A temperature change is applied to the cable structure in , and the value of the applied temperature change is taken from the steady-state temperature change vector S. o The current initial mechanical calculation benchmark model A is updated after the temperature change is applied to the cable structure in i o , update A i o At the same time, T i o All element values ​​also use T i The values ​​of all elements of the corresponding replacement, that is, updated T i o , which correctly corresponds to A i o T i o; at this time d i o remains the same; when updating A i o After, A i o The health of the cable is the current initial damage vector d of the cable system i o means that A i o The steady-state temperature of the cable structure uses the current data vector T of the steady-state temperature of the cable structure i means that A i o The generalized coordinates of the supports are the generalized coordinates vector U of the supports with the current initial cable structure i o express. update C i o The method is: when updating A i o After, A i o The health status of the evaluated object is the current initial damage vector d of the evaluated object i o means that A i o The steady-state temperature of the cable structure uses the current data vector T of the steady-state temperature of the cable structure i means that A i o The generalized coordinates of the supports are the generalized coordinates vector U of the supports with the current initial cable structure i o means, update C i o The method is: when updating A i o After that, A is obtained by mechanical calculation i o The current specific values ​​of all monitored quantities in the i o;

[0169] Step 8: Calculate the benchmark model A in the current initial mechanics i o On the basis of , carry out several mechanical calculations according to steps a to d, and establish the numerical change matrix ΔC of the monitored quantity of unit damage through calculation. i and the unit change vector D of the evaluated object i u.

[0170] a. At the beginning of the i-th cycle, directly follow the methods listed in steps b to d to obtain ΔC i and D i u; at other times, when in step 7 for A i o After the update, ΔC must be regained as listed in steps b to d i and D i u , if there is no pair A in step 7 i o To update, go directly to the ninth step for follow-up work here.

[0171] b. In the current initial mechanical calculation benchmark model A i o On the basis of several mechanical calculations, the vector d i o means A i o The number of calculations is equal to the number N of all evaluated objects, and there are N evaluation objects, there are N times of calculation; each calculation assumes that there is only one evaluated object in the vector d i o The unit damage or concentrated load unit change occurs on the basis of the health state of the evaluated object. Specifically, if the evaluated object is a support cable in the cable system, then it is assumed that the support cable is in the vector d. i o Indicates that there is a unit damage on the basis of the existing damage of the support cable (for example, take 5%, 10%, 20% or 30% damage as the unit damage), if the evaluated object is a concentrated load, it is assumed that the concentrated load loads in vector d i o On the basis of the existing change of the concentrated load, the unit change of the concentrated load is added (if the concentrated load is a couple, the unit change of the concentrated load can be changed in units of 1kNm, 2kNm, 3kNm, etc.; if the concentrated load is a concentrated force, The unit change of the concentrated load can take 1kN, 2kN, 3kN, etc. as the unit change), use D i uk Record this unit damage or concentrated load unit change, where k is the number of the assessed object where the unit damage or concentrated load unit change occurs, D i uk is the unit change vector D of the evaluated object i u An element of the evaluated object unit change vector D i u The numbering scheme of the elements with the vector d o The numbering rules of the elements are the same; the evaluated object with unit damage or concentrated load unit change in each calculation is different from the evaluated object with unit damage or concentrated load unit change in other calculations, and each calculation uses the mechanical method to calculate The current calculated values ​​of all monitored quantities of the cable structure, and the current calculated values ​​of all monitored quantities obtained from each calculation form a current vector of monitored quantities to calculate; when it is assumed that the k-th evaluated object has unit damage or a unit change of concentrated load , available C i tk Indicates the corresponding "current vector calculated by the monitored quantity"; when numbering the elements of each vector in this step, the same numbering rule as other vectors in this method should be used to ensure that any element in each vector in this step is the same as The elements with the same number in other vectors express the related information of the same monitored quantity or the same object; C i tk is defined in the same way as the vector C o is defined in the same way, C i tk Elements with C o The elements of the one-to-one correspondence.

[0172] c. The vector C obtained by each calculation i tk minus the vector C i o A vector is obtained, and each element of the vector is divided by the value D of the unit change in unit damage or concentrated load assumed in this calculation i uk After that, a "value change vector δC of the monitored quantity is obtained. i k "; if there are N evaluated objects, there are N "value change vectors of monitored quantities".

[0173] d. According to the numbering rules of N evaluated objects, the N "value change vectors of the monitored quantities" are sequentially formed into a "value change matrix ΔC of the monitored quantities of unit damage" with N columns. i ”; the value change matrix ΔC of the monitored quantity of unit damage i Each column of , corresponds to a unit change vector of the monitored quantity; the value change matrix of the monitored quantity of unit damage ΔC i Each row corresponds to the different unit change amplitudes of the same monitored quantity when different evaluated objects increase the unit damage or the unit change of the concentrated load; the numerical change matrix ΔC of the monitored quantity for unit damage i The numbering sequence of the columns with the vector d o The numbering rules of the elements are the same, and the unit damage is monitored by the value change matrix ΔC i The numbering scheme of the lines is the same as the numbering scheme of the M monitored quantities.

[0174] Step 9: Establish a linear relationship error vector e i and the vector g i. Using the previous data ("the current initial value vector C of the monitored quantity i o ", "Unit damage monitored value change matrix ΔC i ”), while each calculation is performed in the eighth step, that is, when each calculation assumes that only one of the assessed objects has an increased unit damage or a change in the concentrated load unit, when it is assumed that the kth (k=1, 2,3,...,N) When the unit damage of the evaluated objects increases or the unit of the concentrated load changes, each calculation constitutes a damage vector, using d i tk Represents the damage vector, and the current vector calculated for the corresponding monitored quantity is C i tk (see step 8), the damage vector d i tk The number of elements of is equal to the number of evaluated objects, the vector d i tk The value of only one element among all elements of d is taken as the value of the unit damage or unit change of concentrated load of the assessed object assuming that an increase in unit damage or a unit change of concentrated load is assumed in each calculation, d i tk The value of other elements of the vector is 0, and the number of the element that is not 0 corresponds to the evaluated object assuming the increase in unit damage or the unit change of concentrated load, and the corresponding relationship between the elements with the same number in other vectors and the evaluated object are the same ;d i tk and the initial damage vector d of the evaluated object o The element numbering rules are the same, d i tk elements with d o The elements are in a one-to-one correspondence. will C i tk , C i o , ΔC i , d i tk Bring into equation (23), get a linear relationship error vector e i k , each calculation obtains a linear relationship error vector e i k;e i k The subscript k of , indicates that the kth (k=1, 2, 3, ..., N) evaluated object has increased unit damage or concentrated load unit change. If there are N evaluated objects, there will be N calculations, and there will be N linear relationship error vectors e. i k, the N linear relationship error vector e i k After addition, a vector is obtained, and the new vector obtained by dividing each element of this vector by N is the final linear relationship error vector e i. vector g i is equal to the final error vector e i. put the vector g i It is saved on the hard disk of the computer running the health monitoring system software for use by the health monitoring system software.

[0175] e k i = abs ( Δ C i · d tk i - C tk i + C o i ) ( 23 )

[0176] Step 10: Define the current nominal damage vector d i c and the current actual damage vector d i , d i c and d i The number of elements is equal to the number of evaluated objects, d i c and d i There is a one-to-one correspondence between the elements of and the evaluated object, d i c and d i The value of the element represents the damage degree or concentrated load change degree corresponding to the evaluated object, d i c and d i and the initial damage vector d of the evaluated object o The element numbering rules are the same, d i c element, d i elements with d o The elements are in a one-to-one correspondence.

[0177] Step 11: According to the current value vector C of the monitored quantity i Same as "the current initial value vector C of the monitored quantity i o ", "Unit damage monitored value change matrix ΔC i ” and “Current nominal damage vector d i c ”, which can be expressed as formula (11), and the current nominal damage vector d is calculated according to the multi-objective optimization algorithm i c The non-inferior solution of , that is, a solution with reasonable error, but which can determine the position of the damaged cable and its nominal damage degree from all cables relatively accurately.

[0178] There are many kinds of multi-objective optimization algorithms that can be used, such as: multi-objective optimization based on genetic algorithm, multi-objective optimization based on artificial neural network, multi-objective optimization algorithm based on particle swarm, multi-objective optimization based on ant colony algorithm, constraint method (Constrain Method), Weighted Method (Weighted SUm Method), Goal Attainment Method (Goal Attainment Method) and so on. Since various multi-objective optimization algorithms are conventional algorithms, they can be easily implemented. In this implementation step, only the objective programming method is used as an example to solve the current nominal damage vector d. i c The specific implementation process of other algorithms can be implemented in a similar manner according to the requirements of their specific algorithms.

[0179] According to the objective programming method, Equation (11) can be transformed into the multi-objective optimization problem shown in Equation (24) and Equation (25). d i c The value range of each element of (this embodiment requires the vector d i c Each element of is not less than 0 and not greater than 1). Equation (24) means to find a minimum real number γ such that Equation (25) is satisfied. In formula (25), G(d i c ) is defined by Equation (25), the product of the weighting vector W and γ in Equation (25) expresses G(d in Equation (25) i c ) and the vector g i Allowable deviation between, g i See equation (17) for the definition of , and its value has been calculated in the ninth step. In the actual calculation, the vector W can be compared with the vector g i same. The specific programming implementation of the goal programming method already has a general program that can be used directly. Using the objective programming method, the current nominal damage vector d can be obtained i c.

[0180] min imize γ γ ∈ R , d c i ∈ Ω ( 24 )

[0181] G ( d c i ) - Wγ ≤ g i ( 25 )

[0182] G ( d c i ) = abs ( Δ C i · d c i - C i + C o i ) ( 26 )

[0183] Step 12: According to the current actual damage vector d of the cable system i The definition of (see formula (18)) and the definition of its elements (see formula (19)) are calculated to obtain the current actual damage vector d i Each element of , which can be determined by d i Determine the health status of the subject being assessed. The current actual damage vector d i the kth element d of i k Represents the current actual health state of the k-th evaluated object in the i-th cycle.

[0184] d i k Represents the current actual health state of the k-th evaluated object in the i-th cycle. If the evaluated object is a support cable in the cable system, then d i k Indicates its current actual damage, d i k When it is 0, it means no damage, when it is 100%, it means that the supporting cable completely loses its bearing capacity, and when it is between 0 and 100%, it means that it loses a corresponding proportion of its bearing capacity.

[0185] d i k Represents the current actual health state of the k-th evaluated object in the i-th cycle. If the evaluated object is a concentrated load, then d i k Represents its current actual concentrated load change value, so according to the current actual damage vector d of the evaluated object i It is possible to determine which support cables are damaged and how much they are damaged, and which concentrated loads have changed and their values.

[0186] So far, it can be said that this method has achieved two functions that the existing methods cannot have, namely, first, when the support has a generalized displacement, when the concentrated load and the structure (environment) temperature change at the same time, it can be eliminated. The influence of the generalized displacement of the bearing, the change of the concentrated load and the change of the structure temperature on the identification result of the structural health state of the cable, so as to accurately identify the structural health monitoring method of the damaged cable; 2. This method not only identifies the damaged cable, but also The change of the concentrated load can be identified at the same time, that is, the method can eliminate the influence of the generalized displacement of the bearing, the change of the structure temperature and the change of the health state of the support cable, and realize the correct identification of the change degree of the concentrated load.

[0187] The thirteenth step: the computer in the health monitoring system generates a report on the health status of the cable system automatically or by personnel operating the health monitoring system on a regular basis.

[0188] The fourteenth step: under the specified conditions, the computer in the health monitoring system automatically operates the communication alarm device to alarm the monitoring personnel, the owner and/or the designated personnel.

[0189] The fifteenth step: according to formula (20) to establish the identification vector B i , Equation (21) gives the identity vector B i The definition of the kth element of ; if the elements of the identification vector Bi are all 0, go back to the sixth step to continue the health monitoring and calculation of the cable system; if the identification vector B i If the elements are not all 0, the next cycle is entered after the subsequent steps are completed.

[0190] Step 16: Calculate the initial damage vector d required for the next (i+1th, i=1,2,3,4,...) cycle according to formula (22). i+1 o every element of d i+1 ok (k=1,2,3,...,N); second, in the initial mechanical calculation benchmark model A o On the basis of , first to A o The generalized displacement constraint of the support is imposed on the cable structure support in o A temperature change is applied to the cable structure in i+1 o What is obtained is the mechanical calculation benchmark model A required for the next cycle, that is, the i+1th (i=1, 2, 3, 4, ...) cycle i+1; The current initial cable structure steady-state temperature data vector T required for the next (i+1th, i=1,2,3,4,...) cycle i+1 o equal to T i o , the generalized coordinate vector U of the current initial cable structure support required for the next (i+1th, i=1,2,3,4,...) cycle i+1 o equal to U i o. get an A i+1 , d i+1 o , U i+1 o and T i+1 o After that, A is obtained by mechanical calculation i+1 The current specific values ​​of all monitored quantities in i+1 o.

[0191] Step 17: Go back to Step 6 and start the cycle from Step 6 to Step 17.