Disclosure of Invention
The invention aims to provide a method for detecting the heating energy efficiency ratio of an air conditioner on line, which realizes real-time detection of the heating energy efficiency ratio under different operating conditions of the air conditioner.
In order to achieve the above purpose, the method for detecting the heating energy efficiency ratio on line provided by the invention is realized by adopting the following technical scheme:
a method for detecting the heating energy efficiency ratio of an air conditioner on line comprises the following steps:
in the running process of the air conditioner, acquiring real-time press frequency f, real-time indoor temperature tn, real-time outdoor temperature tw, real-time inner machine rotating speed nn and real-time outer machine rotating speed nw;
determining a real-time core energy efficiency ratio COPc corresponding to the real-time press frequency f and the real-time indoor temperature tn according to a known typical press frequency, a typical indoor temperature, a typical core energy efficiency ratio and a typical relation; the typical relation comprises a relation between the typical core energy efficiency ratio and the typical press frequency under the same typical indoor temperature and a relation between the typical core energy efficiency ratio and the typical indoor temperature under the same typical press frequency;
determining a real-time outdoor temperature energy efficiency ratio correction factor COPTW according to the real-time outdoor temperature Tw and the rated outdoor temperature Tw, determining a real-time indoor unit rotating speed energy efficiency ratio correction factor COPnn according to the real-time indoor unit rotating speed Nn and the rated indoor unit rotating speed Nn, and determining a real-time outdoor unit rotating speed energy efficiency ratio correction factor COPnn according to the real-time outdoor unit rotating speed Nw and the rated outdoor unit rotating speed Nw;
determining the real-time heating energy efficiency ratios COPs:
COPs=[(COPc/COPcr)*d+e]*COPsr+COPtw+COPnn+COPnw;
COPcr is a rated core energy efficiency ratio corresponding to a rated press frequency fr and a rated indoor temperature tnr, which is determined according to the typical press frequency, the typical indoor temperature, the typical core energy efficiency ratio and the typical relational expression; COPsr is the nominal heating energy efficiency ratio of the air conditioner; d and e are correction coefficients.
In the above method, the determining the real-time core energy efficiency ratio COPc corresponding to the real-time press frequency f and the real-time indoor temperature tn according to the known typical press frequency, typical indoor temperature, typical core energy efficiency ratio, and a typical relational expression specifically includes:
determining a plurality of intermediate core energy efficiency ratios corresponding to the real-time press frequency f at a plurality of typical indoor temperatures according to a relational expression between the typical core energy efficiency ratios and the typical press frequency;
determining a relational expression of the intermediate core energy efficiency ratio and the typical indoor temperature under the real-time press frequency f according to the plurality of intermediate core energy efficiency ratios and the relational expression of the typical core energy efficiency ratio and the typical indoor temperature;
and determining a real-time core energy efficiency ratio corresponding to the real-time indoor temperature tn under the real-time press frequency f according to a relational expression of the intermediate core energy efficiency ratio and the typical indoor temperature, and taking the real-time core energy efficiency ratio as a real-time core energy efficiency ratio COPc corresponding to the real-time press frequency f and the real-time indoor temperature tn.
In the above method, the determining the real-time core energy efficiency ratio COPc corresponding to the real-time press frequency f and the real-time indoor temperature tn according to the known typical press frequency, typical indoor temperature, typical core energy efficiency ratio, and a typical relational expression specifically includes:
determining a plurality of intermediate core energy efficiency ratios corresponding to the real-time indoor temperature tn under a plurality of typical press frequencies according to a relational expression of the typical core energy efficiency ratios and typical indoor temperatures;
determining a relational expression between the intermediate core energy efficiency ratio and the typical press frequency under the real-time indoor temperature tn according to the plurality of intermediate core energy efficiency ratios and the relational expression between the typical core energy efficiency ratio and the typical press frequency;
and determining a real-time core energy efficiency ratio corresponding to the real-time press frequency f at the real-time indoor temperature tn according to a relational expression between the middle core energy efficiency ratio and the typical press frequency, and taking the real-time core energy efficiency ratio as a real-time core energy efficiency ratio COPc corresponding to the real-time press frequency f and the real-time indoor temperature tn.
Preferably, the relation between the typical core energy efficiency ratio and the typical press frequency is a linear function relation; the relation between the typical core energy efficiency ratio and the typical indoor temperature is a quadratic function relation.
In the above method, the determining the real-time outdoor temperature energy efficiency ratio correction factor COPtw according to the real-time outdoor temperature Tw and the rated outdoor temperature Tw specifically includes:
determining a real-time outdoor temperature energy efficiency ratio correction factor COPtw according to the following formula COPtw ═ a (Tw-Tw); a is a correction coefficient of not less than 0.
According to the method, the determining of the real-time internal machine rotation speed energy efficiency ratio correction factor COPnn according to the real-time internal machine rotation speed Nn and the rated internal machine rotation speed Nn specifically includes:
determining a real-time internal engine rotating speed energy efficiency ratio correction factor COPnn according to the following formula COPnn ═ b (Nn-Nn); b is a correction coefficient of not less than 0.
In the above method, determining the real-time external machine rotation speed energy efficiency ratio correction factor COPnw according to the real-time external machine rotation speed Nw and the rated external machine rotation speed Nw specifically includes:
determining a real-time rotating speed energy efficiency ratio correction factor COPnw of the external machine according to the following formula COPnw ═ c (Nw-Nw); c is a correction coefficient of not less than 0.
Preferably, the method further comprises:
and displaying the real-time heating energy efficiency ratios COPs.
The invention also aims to provide a method for detecting the heating capacity of the air conditioner on line, so as to realize real-time detection of the heating capacity of the air conditioner under different operating conditions.
In order to achieve the purpose, the heating capacity online detection method provided by the invention is realized by adopting the following technical scheme:
an on-line detection method for the heating capacity of an air conditioner comprises the following steps:
in the air conditioner operation process, acquiring the real-time heating energy efficiency ratios COPs and the real-time operation power P of the air conditioner;
determining the real-time heating quantity W: w ═ COPs × P;
and the real-time heating energy efficiency ratios COPs are determined according to the method for detecting the heating energy efficiency ratios on line.
The method as described above, further comprising: and displaying the real-time heating quantity W.
Compared with the prior art, the invention has the advantages and positive effects that: according to the air conditioner heating energy efficiency ratio online detection method provided by the invention, the real-time press frequency with large influence on the heating energy efficiency ratio and the real-time core energy efficiency ratio corresponding to the real-time indoor temperature are determined through the typical press frequency, the typical indoor temperature, the typical core energy efficiency ratio and the typical relational expression, the energy efficiency ratio correction factor with small influence on the heating energy efficiency ratio is determined based on the real-time outdoor temperature, the real-time indoor machine rotating speed and the real-time outdoor machine rotating speed, and finally the real-time heating energy efficiency ratio is determined according to the real-time core energy efficiency ratio and the plurality of energy efficiency ratio correction factors, so that the real-time detection on the heating energy efficiency ratio under different working conditions in the air conditioner operation process can be realized, the detection result has high accuracy, the actual operation working condition is met, and the intuitive and; based on the detected real-time heating energy efficiency ratio, the actual heating capacity of the air conditioner in the operation process can be obtained, the real-time detection of the heating capacity is realized, and the intuitive and accurate real-time heating capacity is further provided for a user.
Other features and advantages of the present invention will become more apparent from the following detailed description of the invention when taken in conjunction with the accompanying drawings.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail with reference to the accompanying drawings and examples.
First, the technical idea of the present invention is briefly explained:
theoretical analysis and experimental verification prove that the factors which have larger influence on the heating energy efficiency ratio during air heating operation are indoor temperature and compressor frequency, and outdoor temperature, indoor machine rotating speed and outdoor machine rotating speed have smaller influence on the heating energy efficiency ratio. Therefore, in order to simplify the on-line detection process of the heating energy efficiency ratio and ensure the detection accuracy, the application proposes that the heating energy efficiency ratio influenced by the real-time indoor temperature and the real-time press frequency is taken as the core energy efficiency ratio and is determined by adopting an experimental data calculation mode; and the energy efficiency ratio of the factor having a small influence on the heating energy efficiency ratio is determined by correcting the energy efficiency ratio according to the real-time value and the rated value. And then, determining the total real-time heating energy efficiency ratio under the influence of all factors, and realizing the online real-time detection of the heating energy efficiency ratio.
Referring to fig. 1, a flowchart of an embodiment of a method for detecting an air conditioner heating energy efficiency ratio on line according to the present invention is shown.
As shown in fig. 1, the method for detecting the heating energy efficiency ratio of the air conditioner online in the embodiment includes the following steps:
step 11: in the running process of the air conditioner, the real-time press frequency f, the real-time indoor temperature tn, the real-time outdoor temperature tw, the real-time internal machine rotating speed nn and the real-time external machine rotating speed nw are obtained.
Because the compressor, the indoor fan and the outdoor fan are all controlled by the frequency and the wind speed by the instruction sent by the main controller of the air conditioner, the real-time frequency f of the compressor, the real-time rotating speed nn of the indoor unit and the real-time rotating speed nw of the outdoor unit can be conveniently obtained by the main controller of the air conditioner. The real-time indoor temperature and the real-time outdoor temperature can be detected and acquired by temperature detection devices arranged indoors and outdoors, respectively.
Step 12: determining a real-time core energy efficiency ratio COPc corresponding to the real-time press frequency f and the real-time indoor temperature tn, and determining a real-time outdoor temperature energy efficiency ratio correction factor COPTw, a real-time indoor machine rotating speed energy efficiency ratio correction factor COPnn and a real-time outdoor machine rotating speed energy efficiency ratio correction factor COPNw.
Specifically, the real-time core energy efficiency ratio COPc corresponding to the real-time press frequency f and the real-time indoor temperature tn is determined according to the known typical press frequency, the typical indoor temperature, the typical core energy efficiency ratio and the typical relation. The system comprises a compressor, a compressor. Typical compressor frequencies, typical indoor temperatures, and corresponding typical core energy efficiency ratios are typically determined by the air conditioner pre-factory laboratory and written into the air conditioner memory. The typical relation is obtained based on the typical press frequency, the typical indoor temperature and the typical core energy efficiency ratio, and specifically, the typical relation comprises a relation between the typical core energy efficiency ratio and the typical press frequency and a relation between the typical core energy efficiency ratio and the typical indoor temperature. Moreover, analysis and test verification prove that the relation between the typical core energy efficiency ratio and the typical press frequency is a linear function relation; the relation between the typical core energy efficiency ratio and the typical indoor temperature is a quadratic function relation.
One specific example of a typical press frequency, a typical indoor temperature, a typical core energy efficiency ratio, and a typical relationship is as follows:
table 1 shows a typical core energy efficiency ratio table consisting of typical press frequencies, typical room temperatures, and typical core energy efficiency ratios.
TABLE 1 typical core energy efficiency ratio Table
In the exemplary core energy efficiency ratio table shown in table 1 above, three exemplary indoor temperatures, 25 c, 30 c, 35 c, and three exemplary press frequencies, 43hz, 77hz, and 84hz, respectively, are included. Each typical press frequency and each typical indoor temperature respectively correspond to a typical core energy efficiency ratio, and nine typical core energy efficiency ratios are provided. Taking a typical core energy efficiency ratio of 4.49 corresponding to a typical indoor temperature of 25 ℃ and a typical press frequency of 43hz as an example, a method for acquiring the typical core energy efficiency ratio is briefly described as follows:
in a certain experimental environment, the indoor temperature is controlled to be 25 ℃, the running frequency of the press is controlled to be 43hz, and the outdoor temperature, the rotating speed of the indoor machine and the rotating speed of the outdoor machine are rated values (the rated values are determined and known correspondingly to the air conditioner of a determined machine type); then, the heating capacity and the power of the air conditioner are tested, and the energy efficiency ratio is determined to be 4.49 according to the ratio of the heating capacity to the power and serves as a typical core energy efficiency ratio corresponding to the indoor temperature of 25 ℃ and the press frequency of 43 hz. The laboratory test heats the apparatus and method of the power, adopt the prior art to realize.
By adopting the method, the typical core energy efficiency ratios corresponding to other typical indoor temperatures and other typical compressor frequencies are sequentially obtained, all the typical indoor temperatures, the typical compressor frequencies and the typical core energy efficiency ratios form a table 1 and are written into the memory of the air conditioner.
In addition, a linear function relation between the typical core energy efficiency ratio and the typical press frequency at the same typical indoor temperature and a quadratic function relation between the typical core energy efficiency ratio and the typical indoor temperature at the same typical press frequency are obtained according to the typical indoor temperature, the typical press frequency and the typical core energy efficiency ratio. Specifically, the above-mentioned first order functional relation and second order functional relation are obtained by numerical fitting, and the specific relation is as follows:
the linear function of the typical core energy efficiency ratio Ycop versus the typical press frequency f at typical indoor temperatures includes:
ycop ═ 0.035f +5.999 at 25 ℃.
At 30 ℃, Ycop ═ 0.02f + 4.5.
At 35 ℃, Ycop ═ 0.013f + 3.6.
The quadratic function relation between the typical core energy efficiency ratio Ycop and the typical indoor temperature tn at the typical compressor frequency comprises:
43hz,Ycop=0.005tn2-0.451tn+12.58。
77hz,Ycop=-0.0001tn2-0.050tn+4.769。
84hz,Ycop=-0.001tn2+0.032tn+3.159。
the above relational expressions are also written into the air conditioner memory and stored.
The typical room temperature and typical press frequency in a typical core energy efficiency ratio table are limited in number, e.g., only three, and far from covering all of the actual room temperature and actual press operating frequency. Therefore, during the use of the air conditioner, the real-time core energy efficiency ratio COPc corresponding to the real-time compressor frequency f and the real-time indoor temperature tn is determined according to the data in the typical core energy efficiency ratio table and the corresponding relational expression. Moreover, the real-time core energy efficiency ratio COPc may be determined in two ways:
the method I is characterized in that the real-time core energy efficiency ratio COPc is determined according to a quadratic function relation of the core energy efficiency ratio and the indoor temperature.
Firstly, a plurality of intermediate core energy efficiency ratios corresponding to real-time press frequency f at a plurality of typical indoor temperatures are determined according to a primary relational expression of the typical core energy efficiency ratios and the typical press frequency.
For example, the typical core energy efficiency ratio table and the relation of the air conditioner are as described above, and in actual operation of the air conditioner, the real-time compressor frequency f is 52hz, and the real-time indoor temperature tn is 32 ℃. Then it is determined that,
and calculating the intermediate core energy efficiency ratio corresponding to the temperature of 30 ℃ and the frequency of 52hz by substituting f into the relational expression according to a linear function relational expression Ycop of the typical core energy efficiency ratio Ycop and the typical press frequency f at the temperature of 25 ℃, wherein the linear function relational expression Ycop is-0.035 f +5.999, and the f is 52hz, and is marked as A.
And (3) substituting f into 52hz according to a linear function relation of the typical core energy efficiency ratio Ycop and the typical press frequency f at 30 ℃ to obtain an intermediate core energy efficiency ratio corresponding to 35 ℃ and 52hz, wherein the intermediate core energy efficiency ratio is marked as B.
And calculating the intermediate core energy efficiency ratio corresponding to 40 ℃ and 52hz by substituting f into the relation according to a linear function relation of the typical core energy efficiency ratio Ycop and the typical press frequency f at 35 ℃ of-0.013 f +3.6 and f into the relation, and marking as C.
And then, determining a relational expression of the intermediate core energy efficiency ratio and the typical indoor temperature under the same real-time press frequency f according to the plurality of intermediate core energy efficiency ratios and the relational expression (namely a quadratic function relational expression) of the typical core energy efficiency ratio and the typical indoor temperature. That is, a quadratic relation between the intermediate core energy efficiency ratio and the typical indoor temperature at 52hz is determined by fitting A, B and C to the quadratic relation. The specific implementation process of fitting the quadratic function relation is referred to the prior art and will not be described in detail herein.
And finally, determining a real-time core energy efficiency ratio corresponding to the real-time indoor temperature tn under the real-time press frequency f according to a relational expression of the intermediate core energy efficiency ratio and the typical indoor temperature, and taking the real-time core energy efficiency ratio as a real-time core energy efficiency ratio COPc corresponding to the real-time press frequency f and the real-time indoor temperature tn. That is, the indoor temperature in the determined quadratic function relation between the intermediate core energy efficiency ratio and the typical indoor temperature is replaced by 32 ℃, and a core energy efficiency ratio is calculated, wherein the core energy efficiency ratio is a real-time core energy efficiency ratio COPc corresponding to a real-time compressor frequency of 52hz and a real-time indoor temperature of 32 ℃.
And secondly, determining the real-time core energy efficiency ratio COPc according to a linear function relation of the core energy efficiency ratio and the frequency of the press.
Firstly, a plurality of intermediate core energy efficiency ratios corresponding to real-time indoor temperatures tn under a plurality of typical press frequencies are determined according to a quadratic relation between the typical core energy efficiency ratios and the typical indoor temperatures.
For example, the typical core energy efficiency ratio table and the relation of the air conditioner are as described above, and in actual operation of the air conditioner, the real-time compressor frequency f is 52hz, and the real-time indoor temperature tn is 32 ℃. Then it is determined that,
according to a quadratic function formula Ycop of a typical core energy efficiency ratio Ycop and a typical indoor temperature tn under 43hz, the Ycop is 0.005tn2-0.451tn +12.58, and substituting tn at 32 ℃ into the equationThe middle core energy efficiency ratio corresponding to 43hz and 32 ℃ is recorded as D.
A quadratic function based on a typical core energy efficiency ratio Ycop at 77hz and a typical room temperature tn, Ycop ═ 0.0001tn2-0.050tn +4.769, where tn is 32 ℃ and the relation is substituted, and the intermediate core energy efficiency ratio corresponding to 77hz and 32 ℃ is calculated and denoted as E.
According to a quadratic function of a typical core energy efficiency ratio Ycop and a typical indoor temperature tn at 84hz, the Ycop is-0.001 tn2+0.032tn +3.159, where tn is 32 ℃ and is substituted into the relational expression, the intermediate core energy efficiency ratio corresponding to 84hz and 32 ℃ is calculated and denoted as F.
And then, determining a relational expression of the intermediate core energy efficiency ratio and the typical press frequency under the same real-time indoor temperature tn according to the plurality of intermediate core energy efficiency ratios and the relational expression (namely a linear function relational expression) of the typical core energy efficiency ratio and the typical press frequency. Namely, a linear function relation between the intermediate core energy efficiency ratio and the typical press frequency at 32 ℃ is determined by fitting the linear function relation according to D, E and F. The specific implementation process of fitting the linear function relation is referred to the prior art and will not be described in detail herein.
And finally, determining a real-time core energy efficiency ratio corresponding to the real-time indoor temperature tn under the real-time press frequency f according to a relational expression of the middle core energy efficiency ratio and the typical press frequency, and taking the real-time core energy efficiency ratio as a real-time core energy efficiency ratio COPc corresponding to the real-time press frequency f and the real-time indoor temperature tn. Namely, replacing the press frequency in the determined linear function relation between the intermediate core energy efficiency ratio and the typical press frequency with 52hz, and calculating to obtain a core energy efficiency ratio, wherein the core energy efficiency ratio is the real-time core energy efficiency ratio COPc corresponding to the real-time press frequency of 52hz and the real-time indoor temperature of 32 ℃.
The real-time core energy efficiency ratio COPc corresponding to the real-time press frequency f and the real-time indoor temperature tn is determined by adopting the relational expression, only a small amount of typical press frequency, typical indoor temperature and typical core energy efficiency ratio are needed, and the method is particularly suitable for being used under the condition that the experiment time is limited or the experiment conditions are limited and more typical core energy efficiency ratios cannot be obtained.
In addition, a real-time outdoor temperature energy efficiency ratio correction factor COPtw, a real-time indoor unit rotating speed energy efficiency ratio correction factor COPnn and a real-time outdoor unit rotating speed energy efficiency ratio correction factor COPnw are determined. Specifically, the method comprises the following steps:
and determining a real-time outdoor temperature energy efficiency ratio correction factor COPTw according to the real-time outdoor temperature Tw and the rated outdoor temperature Tw. As a preferred embodiment, a real-time outdoor temperature energy efficiency ratio correction factor COPtw is determined according to a formula COPtw ═ a (Tw-Tw); a is a correction coefficient of not less than 0. Preferably, a is in the range of [0,6], for example, a is 4.
And determining a real-time internal machine rotating speed energy efficiency ratio correction factor COPnn according to the real-time internal machine rotating speed Nn and the rated internal machine rotating speed Nn. As a preferred embodiment, a real-time internal engine speed energy efficiency ratio correction factor COPnn is determined according to a formula COPnn ═ b (Nn-Nn); b is a correction coefficient of not less than 0. Preferably, b is in the range of [0,0.4] and 0.15.
And determining a real-time outer machine rotating speed energy efficiency ratio correction factor COPNw according to the real-time outer machine rotating speed Nw and the rated outer machine rotating speed Nw. As a preferred embodiment, a real-time rotating speed energy efficiency ratio correction factor COPnw of the external machine is determined according to a formula COPnw ═ c (Nw-Nw); c is a correction coefficient of not less than 0. Preferably, c is in the range of [0,0.06] and 0.03.
Step 13: and determining the real-time heating energy efficiency ratios COPs.
Specifically, the real-time heating energy efficiency ratios COPs are determined according to the following formula:
COPs=[(COPc/COPcr)*d+e]*COPsr+COPtw+COPnn+COPnw。
wherein, COPc, COPTw, COPnn and COPnW are determined in step 12; the COPcr is a rated core energy efficiency ratio corresponding to a rated press frequency fr and a rated indoor temperature tnr, which is determined according to a typical press frequency, a typical indoor temperature, a typical core energy efficiency ratio and a typical relational expression, and the determination method refers to the process of determining the COPc in the step 12; COPsr is the nominal heating energy efficiency ratio of the air conditioner and is determined by adopting the prior art; d and e are correction coefficients. Preferably, d is in the range of [0,2] and e is in the range of [ -1,1 ]. For example, d is 1 and e is 0.
By adopting the method of the embodiment, the real-time press frequency with large influence on the heating energy efficiency ratio and the real-time core energy efficiency ratio corresponding to the real-time indoor temperature are determined through the typical press frequency, the typical indoor temperature, the typical core energy efficiency ratio and the typical relational expression, the energy efficiency ratio correction factor with small influence on the heating energy efficiency ratio is determined based on the real-time outdoor temperature, the real-time indoor machine rotating speed and the real-time outdoor machine rotating speed, and finally the real-time heating energy efficiency ratio is determined according to the real-time core energy efficiency ratio and the plurality of energy efficiency ratio correction factors.
In other preferred embodiments, the determined real-time heating energy efficiency ratios COPs are displayed, for example, by a display screen of a panel of the air conditioner, so that the real-time heating energy efficiency ratios in the operation process of the air conditioner can be timely and intuitively known.
Referring to fig. 2, a flowchart of an embodiment of a method for detecting the heating capacity of an air conditioner on line according to the present invention is shown.
As shown in fig. 2, the method for detecting the heating capacity of the air conditioner on line according to the embodiment includes the following steps:
step 21: in the running process of the air conditioner, the real-time press frequency f, the real-time indoor temperature tn, the real-time outdoor temperature tw, the real-time internal machine rotating speed nn and the real-time external machine rotating speed nw are obtained.
Step 22: determining a real-time core energy efficiency ratio COPc corresponding to the real-time press frequency f and the real-time indoor temperature tn, and determining a real-time outdoor temperature energy efficiency ratio correction factor COPTw, a real-time indoor machine rotating speed energy efficiency ratio correction factor COPnn and a real-time outdoor machine rotating speed energy efficiency ratio correction factor COPNw.
Step 23: and determining the real-time heating energy efficiency ratios COPs.
The specific implementation process of steps 21 to 23 is described with reference to the corresponding steps in the embodiment of fig. 1.
Step 24: and determining the real-time heating quantity W according to the real-time heating energy efficiency ratios COPs and the real-time operation power P.
The real-time operating power P can be obtained by using the prior art, and is not specifically described herein. After the real-time heating energy efficiency ratios COPs are determined in step 23, the real-time heating amount is determined according to a formula W ═ COPs × P.
Based on the detected real-time heating energy efficiency ratio, the actual heating capacity of the air conditioner in the operation process can be obtained, the real-time detection of the heating capacity is realized, and the intuitive and accurate real-time heating capacity is further provided for a user.
In other preferred embodiments, the determined real-time heating amount W is displayed, for example, by a display screen of a panel of the air conditioner, so that the real-time heating amount in the operation process of the air conditioner can be timely and intuitively known.
The above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be apparent to those skilled in the art that various changes may be made and equivalents may be substituted for elements thereof; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions.