CN116663402A - A method for predicting the quality of concrete in a mixing plant based on digital twins - Google Patents

Abstract

The invention relates to a mixing station concrete quality prediction method based on digital twin, which comprises the following steps: 1) Establishing a geometric model of the mixing station digital twin body; 2) Constructing a data model of the mixing station digital twin body; 3) Establishing a mixing station digital twin body; 4) Generating an electronic account for concrete production; 5) Processing the concrete production electronic account by a digital twin body of the mixing station to obtain a production virtual image of the mixing station; 6) And excavating historical data from the concrete production electronic ledger, training a machine learning model on line, and predicting the quality of concrete produced subsequently by using the trained machine learning model. The method can improve the visibility of operators of the mixing station to each production link, thereby being beneficial to formulating a more accurate concrete proportioning scheme, realizing the fine management of the production process and solving the problems of blind production and rough management existing in the current concrete mixing station.

Description

A method for predicting the quality of concrete in a mixing plant based on digital twins

technical field

The invention belongs to the technical field of digital twins, and relates to a method for predicting the quality of concrete in a mixing plant based on digital twins.

Background technique

In the existing concrete production process, the entire production line produces concrete that meets the pouring strength of the project site according to the project design requirements. The production line includes not only the production center such as the mixing station, but also the storage and transportation of raw materials and finished concrete. Corresponding departments, each department cooperates with each other to complete the production of concrete. In order to ensure that the delivered concrete is qualified. The mixing station and various departments often communicate and cooperate with each other, and there are multiple cross-checks on the quality of the concrete to ensure the quality of the concrete.

However, the current concrete production and quality management are completed by different units in the production process, the relationship is relatively loose, and the ability to coordinate and manage quality issues is poor. For example, for the concrete mixing plants supporting major infrastructure construction projects, since large-scale projects are often built in high mountains and valleys, with little network coverage and poor communication capabilities, most of the work is done manually, and manual negligence in any link may The quality of concrete is unqualified, and traceability is extremely difficult.

The digital twin technology takes the physical entity in the real scene as the focus object. By establishing a multi-physics field and multi-scale virtual model, with the help of the mapping feedback of information between the two, the virtual model is used as a digital mirror image of the physical entity, and it is always consistent with the physical entity. The consistency of the state, through data fusion analysis, artificial intelligence and other means, to achieve the maintenance and optimization of physical entities.

Digital twin technology can realize the management covering the entire production process, effectively improve the utilization of data in the concrete production process, realize the advanced judgment of concrete quality through the introduction of artificial intelligence, and provide a basis for quality management and ratio optimization.

In view of the above-mentioned technical defects of the existing technology, it is urgent to develop a method for predicting the concrete quality of a mixing plant based on digital twins.

Contents of the invention

The purpose of the present invention is to overcome the shortcomings existing in the prior art, and provide a method for predicting the concrete quality of a mixing plant based on digital twins, so as to solve the problems existing in the quality assurance of concrete in the current production process.

In order to achieve the above object, the present invention provides the following technical solutions:

A method for predicting the quality of concrete in a mixing plant based on digital twins, characterized in that it comprises the following steps:

1) Obtain the attribute parameters of each sub-physical entity of the mixing plant, and establish the geometric model of the digital twin of the mixing plant;

2) Real-time collection of production status data of the mixing station during operation, and construction of a data model of the digital twin of the mixing station;

3), combining the data model with the geometric model to establish a digital twin of the mixing station;

4), obtain the production record data of the mixing station in real time, associate the production record data with the production state data according to the production batch, obtain the detailed process record data of each production batch of concrete, and record the detailed process The data is stored and the electronic ledger for concrete production is generated;

5), process the concrete production electronic ledger by the digital twin of the mixing station, and obtain the production virtual image of the mixing station;

6), mining historical data from the concrete production electronic ledger, online training machine learning model, predicting the concrete quality of follow-up production with the machine learning model after training.

Preferably, the processing of the concrete production electronic ledger by the digital twin of the mixing station further includes: determining whether the working status of the mixing station reflected in the concrete production electronic ledger is abnormal, and if the working status is displayed If there is an abnormality, a warning will be given to the abnormal situation.

Preferably, in step 1), the attribute parameters of each sub-physical entity of the mixing plant are obtained, and the geometric model of the digital twin of the mixing plant is specifically included;

1.1), divide the mixing station into several sub-physical entities according to their functions, including material storage system, metering system, conveying system, liquid supply system, pneumatic system, mixing system, main building, control room and dust removal system;

1.2), obtain the attribute parameters of the mixing station, build the geometric model of the digital twin of the mixing station based on the attribute parameters, and the attribute parameters include the appearance shape, size, internal structure, spatial position, posture and assembly of each sub-physical entity relation.

Preferably, the production record data of the mixing station acquired in real time in step 4) includes raw material ratio information, raw material monitoring information, feeding error, concrete strength grade, slump and production volume.

Preferably, in step 6), mining historical data from the concrete production electronic ledger, online training machine learning model, predicting the concrete quality of follow-up production with the machine learning model after training specifically includes:

6.1), use the production record data in the concrete production electronic ledger to construct a data set, analyze the variables that can significantly affect the various strength indicators of the concrete through the principal component analysis method, and determine it as the variable of the various strength indicators of the concrete main variable;

6.2), adopt the incremental machine learning algorithm to set up the machine learning model of each strength index of concrete respectively, use the main variable of each strength index of the concrete as an independent variable to carry out the machine learning model of each strength index of the concrete respectively train;

6.3), use the machine learning model of each strength index of the trained concrete to predict the quality of the concrete in subsequent production.

Preferably, the various strength indicators of the concrete include compressive strength, tensile strength, frost resistance and impermeability.

Preferably, after each detailed process record data of a production batch of concrete is stored in the concrete production electronic ledger, the main variables of the new concrete strength indicators are extracted from the new detailed process record data, and the new concrete each The main variable of each strength index trains the machine learning model of each strength index of concrete, and completes the parameter update of the machine learning model of each strength index of concrete.

Preferably, the incremental machine learning algorithm is the Houghding tree algorithm, and the machine learning model of the various strength indicators of the concrete is based on the Houghding tree model with a sliding window added, and the Houghting tree model is set at the same time The Ding tree model uses the data in the sliding window to train the backup subtree in the background of each node. When the node splitting gain of the backup subtree is significantly greater than the current subtree, the node splitting is completed.

Preferably, the method for predicting the concrete quality of a mixing plant based on digital twins further includes displaying the production virtual image and the prediction results of the subsequent produced concrete quality through the user front end.

Compared with the prior art, the digital twin-based concrete quality prediction method of the mixing plant of the present invention has one or more of the following beneficial technical effects:

1. Based on the digital twin of the mixing station, the present invention processes the electronic ledger data of the operation of the mixing station and the collected current state data to obtain the virtual image data of the mixing station, which can be fed back to the user front end and directly displayed to the concrete The operators on the production site help the operators to grasp the production status of the mixing plant in real time, so that the abnormal status generated in the mixing plant can be reflected through the collected status data, which is convenient for the operators to find out the fault in time.

2. With the help of the detailed data stored in the electronic ledger data operated by the mixing station, the present invention uses the incremental machine learning method to train the concrete strength prediction model online, and closely combines the prediction model with the digital twin. Predict the strength index of concrete, assist operators to judge the qualification of concrete quality by comparison, and can continuously optimize the feeding ratio scheme according to the error between theoretical mixing strength and predicted strength.

Description of drawings

Fig. 1 is a flow chart of the method for predicting the concrete quality of a mixing plant based on digital twins in the present invention.

Fig. 2 is a flow chart of the Houghting tree algorithm adopted by the present invention.

Figure 3 takes the prediction of the compressive strength of concrete as an example, and the comparison chart of the prediction index results after 300 iterations of the Hofding tree algorithm before and after the improvement.

Detailed ways

The present invention will be further described below in conjunction with the accompanying drawings and examples, and the contents of the examples are not intended to limit the protection scope of the present invention.

Aiming at the problems existing in concrete quality assurance in the current production process, the present invention provides a method for predicting the concrete quality of a mixing plant based on digital twins, which can improve the visibility of mixing plant operators to each production link, thereby helping to formulate A more accurate concrete proportioning scheme realizes refined management of the production process and solves the problems of blind production and extensive management in current concrete mixing plants.

Fig. 1 shows a flow chart of the method for predicting the concrete quality of a mixing plant based on digital twins of the present invention. As shown in Figure 1, the concrete quality prediction method of mixing plant based on digital twin of the present invention comprises the following steps:

1. Obtain the attribute parameters of each sub-physical entity of the mixing plant, and establish the geometric model of the digital twin of the mixing plant.

Specifically, the establishment of the geometric model of the digital twin of the mixing station includes the following;

1. Divide the mixing plant into several sub-physical entities according to their functions. Among them, these sub-physical entities include material storage system, metering system, conveying system, liquid supply system, pneumatic system, mixing system, main building, control room and dust removal system, etc., which are used to complete the storage, metering, conveying, Stirring, discharging, controlling and other tasks.

2. Obtain the attribute parameters of the mixing station, and build a geometric model of the digital twin of the mixing station based on the attribute parameters. The attribute parameters include the appearance shape, size, internal structure, spatial position, posture and assembly relationship of each sub-physical entity.

The attribute parameters of the mixing station can be obtained from the design document of the mixing station, or can be obtained by measurement or the like.

2. Collect the production status data of the mixing station during operation in real time, and construct the data model of the digital twin of the mixing station.

In the present invention, various sensors arranged in each sub-physical entity of the mixing plant can be used to obtain the production status data during the operation of the concrete mixing plant. With the production status data, the data model of the digital twin of the mixing plant can be constructed.

3. Combining the data model with the geometric model to establish a digital twin of the mixing station.

According to the preset mapping relationship, the collected production status data is substituted into the geometric model, and the status of the geometric model is dynamically updated to obtain the digital twin of the mixing station.

4. Obtain the production record data of the mixing station in real time, associate the production record data with the production state data according to the production batch, obtain the detailed process record data of each production batch of concrete, and record the detailed process data Store and generate electronic ledgers for concrete production.

In the present invention, the production record data of the mixing station acquired in real time includes raw material ratio information, raw material monitoring information, feeding error, concrete strength grade, slump and production volume, etc. Through the production record data, the production capacity of the mixing station can be obtained.

5. The digital twin of the mixing station processes the concrete production electronic ledger to obtain a production virtual image of the mixing station.

The concrete production electronic ledger is input into the digital twin of the mixing station in real time, and the production status and production records of the digital twin of the mixing station are updated in real time, so that the production virtual image of the mixing station can be obtained.

Of course, the processing of the concrete production electronic ledger by the digital twin of the mixing station also includes: determining whether there is any abnormality in the working status of the mixing station reflected in the concrete production electronic ledger. If it is abnormal, it will give a warning to the abnormal situation.

In the present invention, the working state of the concrete mixing plant can be judged based on preset rules. For example, detecting whether the air path pressure and the air pressure of the concrete arch are within a reasonable range can determine whether the air compressor is operating normally; detecting the liquid flow can determine whether the operating pipelines of the water supply system and the admixture system are smooth. Through the judgment, the abnormal working status of each sub-physical entity of the concrete mixing plant can be recorded and warned.

6. Mining the historical data from the concrete production electronic ledger, training the machine learning model online, and using the trained machine learning model to predict the quality of the concrete in subsequent production.

In the present invention, mining historical data from the concrete production electronic ledger, online training machine learning model, and using the trained machine learning model to predict the quality of concrete for subsequent production specifically includes:

1. Utilize the production record data in the concrete production electronic ledger to construct a data set, analyze the variables that can significantly affect the various strength indicators of the concrete through the principal component analysis method, and determine it as the main factor of the various strength indicators of the concrete. variable.

Wherein, the various strength indicators of the concrete include compressive strength, tensile strength, frost resistance and impermeability.

Through the principal component analysis method, the data set that can significantly affect the compressive strength, tensile strength, frost resistance, and impermeability of concrete can be obtained from the data set constructed by using the production record data in the concrete production electronic ledger. variable, and use it as the main variable.

That is, each strength index of the concrete, such as compressive strength, tensile strength, frost resistance or impermeability strength, is used as the prediction target respectively, and the principal component analysis method is used to analyze which data in the data set have a significant impact on the prediction target , which is used as the main variable for predicting the target.

Specifically, the existing records in the concrete production electronic ledger are used to construct a data set, the variance contribution rate of each principal component is calculated by principal component analysis, and the principal component with a high contribution rate is selected as the main variable.

Extract the existing records in the concrete production electronic ledger at the current moment, use the variables in it to construct a sample array, the constructed sample array is a set of n p-dimensional vectors, and standardize the changes of the sample array elements as shown in formula (1) :

Among them, x _ij represents the i-th value in the j-th feature, Indicates the average value of the jth feature, Get the normalized matrix Z.

For the standardized matrix Z, its correlation coefficient matrix is obtained as shown in formula (2):

in

Solve the characteristic equation |R-λI _p |=0 of the sample correlation matrix R, get p characteristic roots, and determine the m principal components whose information utilization rate of the principal components reaches the set index.

2. Adopt the incremental machine learning algorithm to set up the machine learning models of the various strength indexes of the concrete respectively, and use the main variables of the various strength indexes of the concrete as the independent variables to calculate the strength indexes of the concrete respectively as the predictive models of the various strength indexes. The machine learning model of the item intensity index (that is, the prediction model of each intensity index) is trained.

In the present invention, the incremental machine learning algorithm-Hovding tree algorithm is used to respectively establish the machine learning models of the various strength indexes of concrete, that is, the compressive strength machine learning model, the tensile strength machine learning model, the frost resistance strength Machine learning model, anti-seepage strength machine learning model, etc., as prediction models for compressive strength, tensile strength, frost resistance and impermeability strength, etc. Based on the existing data, that is, the main variables of the various strength indexes of the concrete, the training of the prediction model corresponding to the strength indexes is carried out.

The Hofting tree model utilizes the Hofting bound, which enables the determination of optimal splitting properties on nodes in a relatively small-scale training data. The expression of the Höffding bound is shown in formula (3):

Consider a real-valued random variable r with range R, assume that n independent observations have been made of the variable, and calculate their mean According to Hofferding's inequality, under the premise that the probability is set to 1-δ, the calculation result of the mean value of the variable is at least

The Höffding bound has the property of being independent of the probability distribution from which the observations are generated, at the cost of its bounds being more conservative than distribution-dependent bounds, requiring more observations to achieve the same δ and ε. Let G(X _i ) be the calculation method of information gain, where X _a and X _b are the two attributes with the largest information gain, and the information gain difference between the two attributes is expressed as As shown in formula (4):

If the information gain difference of the two attributes is larger than the Hoeffding bound, that is Then it can be proved that the confidence degree of X _a as the attribute with the largest information gain is 1-δ. At this time, X _a can be selected as the split point to turn the leaf node into a branch node.

In the Hofting tree model, information gain is used to select the best split attribute on the root node and internal nodes. The information gain IG is the difference between the information entropy H(D) and the corresponding conditional entropy H(D|X). The calculation of information entropy and conditional entropy is shown in formulas (5), (6) and (7):

IG＝H(D)-H(D|X) (7)

When constructing the Hofferding tree model, after observing m independent objects on a leaf node, let X _a be the attribute IG(X _a ) with the highest IG value, and X _b be the attribute IG(X _b ), and then subtract IG(X _b ) from IG(X _a ) to get a new variable ΔIG. If ΔIG is larger than ε, X _a is selected as the splitting attribute, and if ΔIG is not obvious, it will take a long time to determine the best splitting attribute. When the present invention uses the Hofferding tree model to deal with the regression problem, the variance reduction is selected to replace the information gain function in the classification tree, as shown in formulas (8) and (9), let S be the data in the node, and the total amount of data is N, select the attribute A of the data and use h _A as the boundary to divide the current node into two parts, where S _R and S _L are the data in the two parts, and the data volumes are N _R and N _L respectively, that is, S=S _L + S _R , N=N _L +N _R .

The Hofding tree algorithm is built on a premise that the data stream analyzed and processed by the algorithm is distributed smoothly. The Hofding tree model itself does not complete the design of updating the model itself for outdated samples, resulting in the Hoffding tree The model cannot handle sample data feature shifts in the data stream. The present invention adds a sliding window structure on the basis of the Hofding tree model, so that the Hofding tree model can continuously update the range of data concerned, and at the same time, the Hofding tree model is set to use the data in the sliding window in the background of each node for training. subtree, when the node splitting gain of the standby subtree is significantly greater than that of the current subtree (for example, three times that of the current subtree), the splitting of the node is completed. Fig. 2 shows the Hoffding tree algorithm flow chart of the present invention.

In the improved Hofting tree model of the present invention, each internal node in the tree has a list of replacement subtrees, and the subtrees start training when the concept drift occurs in the data flow, that is, information about some other attribute on the node is found When the gain is better than the current attribute gain, start the generation of an alternative subtree, and the new attribute gain difference satisfies and /> When the replacement of subtrees is completed, the improved Hofding tree model protects the model from the impact of earlier outdated data, while maintaining the lightness of the prediction model. Taking the concrete compressive strength prediction model as an example, the comparison of the prediction index results after 300 iterations of the model before and after the improvement is shown in Figure 3.

In summary, the Hofding tree model is a classic incremental online learning algorithm. Because online learning is different from offline learning, which uses batch data to adjust model parameters, the model is more likely to be unstable. The Hofding tree algorithm uses the Hofding boundary to ensure that the node samples can approximate the overall distribution with arbitrary precision. The Hofding tree The method itself is applied to the classification problem. By changing the information gain function of the original algorithm, the modified Hofferding tree model can be used to predict such regression problems of the concrete strength index.

At the same time, the Hofding tree model itself does not have a pruning design, which means that the algorithm can only handle smoothly distributed data flow. When the data flow changes dynamically, the Hofding tree model cannot adjust the outdated part of the tree structure. The improvement of this algorithm in the present invention mainly includes two aspects. First, a concept drift detector (sliding window structure) is added to the data stream, so that the model can only consider the recent data contained in the sliding window, while the previous model needs to consider The entire historical data, the improvement makes the model immune to the influence of obsolete data. Secondly, when the gain of the current attribute in the node decreases, the model starts to train a backup subtree for the corresponding node in the background. When the gain of the selected attribute of the backup subtree is significantly higher than the gain of the current attribute, the replacement of the subtree is completed. This is very similar to the process of new node splitting, but the requirements are stricter, so as to effectively prevent the generation of too many replacement subtrees. The split growth method of the replacement subtree is the same as that of the decision tree. Each replacement subtree will obtain the data stream obtained by its corresponding node for subtree training. Through the above improvements, the adaptability of the prediction model is substantially enhanced, maintaining This improved the lightness of the model and achieved better predictive results in tests using existing data on concrete compressive strength as an example.

In addition, in the present invention, preferably, after the detailed process record data of a production batch of concrete is stored in the concrete production electronic ledger, the main variables of the new concrete strength indexes are extracted from the new detailed process record data , and use the main variables of the new concrete strength indexes to train the machine learning models of the concrete strength indexes, and complete the parameter update of the machine learning models of the concrete strength indexes.

Therefore, after the concrete production electronic ledger completes a complete record of concrete production, it extracts the principal component eigenvector from the new record as a new sample, uses the new sample to train the prediction model, and completes the parameter update of the model , so that the model is more in line with the actual situation.

3. Use the machine learning model of each strength index of the trained concrete to predict the quality of the subsequent produced concrete.

After establishing and training the machine learning model of each strength index of concrete, the main variables of each strength index of concrete can be extracted from the concrete production electronic ledger generated in real time during the production process, and input into the corresponding In the machine learning model of the machine learning model, the prediction results of the concrete quality of the mixing plant can be obtained.

In order to realize the method for predicting the concrete quality of a mixing plant based on a digital twin of the present invention, it is necessary to cooperate with a corresponding concrete quality prediction system for a mixing plant based on a digital twin. Wherein, the prediction system includes a data collection terminal, a server terminal, a user front end and a background feedback terminal.

The data acquisition terminal includes sensors and related intelligent terminal equipment distributed in each sub-physical entity of the concrete mixing plant. The data acquired by the data acquisition terminal is transmitted to the server in real time, and the server completes the real-time mapping of the data in the digital twin according to the pre-established mapping relationship of the digital twin, and the abnormal production status of the mixing station A warning is issued, and the background feedback terminal sends an abnormal signal to the main console of the mixing station. The server also associates the production status data with the production record data and saves them in the concrete production electronic ledger, and extracts the data in the electronic ledger to train the prediction model. Operators can view the current production status of the mixing plant and the prediction results of concrete strength indicators in the user front end, thereby solving the problems of blind production and extensive management in traditional concrete production to a certain extent.

The above-mentioned embodiments of the present invention are only examples for clearly illustrating the present invention, rather than limiting the implementation of the present invention. For those of ordinary skill in the art, other changes or changes in different forms can be made on the basis of the above description. All the implementation manners cannot be exhaustively listed here. All obvious changes or variations derived from the technical solutions of the present invention are still within the protection scope of the present invention.

Claims (9)

1. A mixing station concrete quality prediction method based on digital twinning is characterized by comprising the following steps:

1) Acquiring attribute parameters of each sub-physical entity of the mixing station, and establishing a geometric model of a digital twin body of the mixing station;

2) Acquiring production state data of the mixing station in the running period in real time, and constructing a data model of a digital twin body of the mixing station;

3) Combining the data model with the geometric model to establish a mixing station digital twin body;

4) Acquiring production record data of a mixing station in real time, establishing a relation between the production record data and the production state data according to production batches to obtain detailed process record data of concrete in each production batch, and storing the detailed process record data to generate a concrete production electronic ledger;

5) Processing the concrete production electronic ledger by the digital twin body of the mixing station to obtain a production virtual image of the mixing station;

6) And excavating historical data from the concrete production electronic ledger, training a machine learning model on line, and predicting the quality of concrete produced subsequently by using the trained machine learning model.

2. The method for predicting concrete quality in a mixing station based on digital twinning of claim 1, wherein processing the concrete production electronic ledger by the digital twinning of the mixing station further comprises: judging whether the working state of the mixing station reflected in the concrete production electronic ledger is abnormal, and if the working state is abnormal, warning the abnormal state.

3. The mixing station concrete quality prediction method based on digital twin according to claim 1, wherein the obtaining attribute parameters of each sub-physical entity of the mixing station in step 1) specifically comprises the steps of;

1.1 Dividing the mixing station into a plurality of sub-physical entities according to functions, wherein the sub-physical entities comprise a storage system, a metering system, a conveying system, a liquid supply system, a pneumatic system, a stirring system, a main building, a control room and a dust removal system;

1.2 Acquiring attribute parameters of the mixing station, and constructing a geometric model of a digital twin body of the mixing station based on the attribute parameters, wherein the attribute parameters comprise appearance shapes, dimension sizes, internal structures, spatial positions, postures and assembly relations of all sub-physical entities.

4. The method for predicting concrete quality of mixing station based on digital twin according to claim 1, wherein the production record data of the mixing station obtained in real time in step 4) includes raw material proportioning information, raw material monitoring information, feeding errors, concrete strength grade, slump and production quantity.

5. The method for predicting concrete quality of a mixing station based on digital twinning according to claim 1, wherein in step 6), historical data is mined from the concrete production electronic ledger, a machine learning model is trained online, and the prediction of concrete quality of subsequent production by using the trained machine learning model specifically comprises:

6.1 Constructing a data set by using the production record data in the concrete production electronic ledger, respectively analyzing variables which can obviously influence each strength index of the concrete by a principal component analysis method, and determining the variables as main variables of each strength index of the concrete;

6.2 Respectively establishing machine learning models of all the strength indexes of the concrete by adopting an incremental machine learning algorithm, and respectively training the machine learning models of all the strength indexes of the concrete by taking main variables of all the strength indexes of the concrete as independent variables;

6.3 And predicting the quality of the concrete produced later by using a machine learning model of each strength index of the trained concrete.

6. The method for predicting the quality of concrete in a mixing station based on digital twinning according to claim 5, wherein the various strength indexes of the concrete comprise compressive strength, tensile strength, freezing resistance and impermeability.

7. The method for predicting the quality of concrete in a mixing station based on digital twinning of claim 6, wherein after each concrete production electronic ledger stores detailed process record data of each production batch of concrete, extracting main variables of each strength index of new concrete from the new detailed process record data, and training a machine learning model of each strength index of the concrete by using the main variables of each strength index of the new concrete to complete parameter updating of the machine learning model of each strength index of the concrete.

8. The method for predicting the quality of concrete at a mixing station based on digital twin according to claim 7, wherein the incremental machine learning algorithm is a Huo Fuding tree algorithm, and the machine learning model of each strength index of the concrete is based on a Huo Fuding tree model, wherein a sliding window is added, and a Huo Fuding tree model is set to train a spare subtree in the background of each node by utilizing data in the sliding window, and when the node splitting gain of the spare subtree is significantly larger than that of the current subtree, the node splitting is completed.

9. The method of claim 1-8, further comprising presenting the prediction of the quality of the produced virtual image and subsequently produced concrete via a user front end.