An approach was developed for computer statistical analysis of big, multi-dimensional arrays of technology parameters and industrial product quality indexes. It provides fully objective, mathematically comprehensive, scientifically grounded and physically interpretable description of the manufacturing factor effects on the performance of an industrial product. The approach integrates a basic Data Mining exploratory technique, multiple regression models construction and Monte-Carlo simulations. The approach was applied to industrial statistical arrays investigations for the ASTM A514 steel. The results obtained are in a good accordance with the known Material Science data and were confirmed in industry
One of the current trends of the modern stage of the Industry 4.0 development is to improve the big manufacturing technology data analysis techniques for increasing effectiveness of the Industry 4.0 platform components [1, 2]. The basic finishing goals of the components are, as it known, to increase manufacturing productivity, improve quality and reliability of a product by eliminating employed technologies lacks with minimal expenses. Cardinal role in the situation is played by the industrial computer statistical investigations because of: their high potentials in treating multifactor industrial phenomena; principal low effectiveness of laboratory researches, not enabling to simulate exactly the real industrial manufacturing environment; practical impossibility to conduct the real, in depth industrial experiments in an operating plant conditions. Nevertheless, the statistical techniques currently applied in the industry are not enough effective in meeting actual practical and theoretical challenges. Typically asrecorded, raw industrial data require the preliminary treatment. The most widely currently used relevant tool in the case is the Data Mining technology, which is the collection of several computer aided statistical techniques [3-5]. Among the techniques the most effective ones today are the artificial neural networks (ANN) [6, 7] and classification and regression trees (C&RT) [8, 9]. 2
Both ANN and C&RT techniques have been effectively applied to solving a number of industrial technology improvement and product quality problems [10-13], particularly in the fields of Material Engineering. The obtained results are in contrast [14, 16] to those ones provided by direct use of the traditional statistical analysis techniques: multiple regression models, MANOVA, ANOVA etc., under the same conditions. Nevertheless, both ANN and C&RT procedures as such have some lacks, considerably decreasing their application effectiveness. Particularly, ANN is not capable of to express a regression dependence revealed in the conventional visual, mathematic and physically interpretable forms, while C&RT does not provide the discovered visual relations in a quantitative form of a regression equation. Such features are typical for the most of the statistical techniques that restricts the ability of the modern computer modeling and simulation technologies to be effectively applied in industrial practice and fundamental multifactor phenomena researches. The features may also be considered as probable reasons of low effectiveness of the modern statistical technologies in revealing the factors which determine spreading the last decade’s epidemic deceases.
Besides, such widely used statistical analysis tool as the multiple regression modeling under the sole, direct application for treating multi-dimensional data arrays is also extremely ineffective due to typical simultaneous changes of numerous input variables that makes it impossible to reveal any regression dependence [13-15] within the arrays. In addition, a powerful tool of modern computer technologies known as Monte-Carlo simulations or computer experiments is not practically involved now in statistical investigations contrary to other areas of scientific researches [16].
Aim of the paper is to outline the main features of a developed integrated approach to industrial statistical investigations together with basic results of its application for the case of ASTM A514 steel.
The steel is one of a modern mass produced multi-alloy steels, characterized by extreme performance instabilities due to its complex alloying and heat treating technologies interactions.
The used approach is aimed to provide in the real industrial environment: ─ revealing the statistically valuable industrial technology factors effecting each performance index of a product or process considered; ─ on-line, semi-quantitative characterizing the factors separate and collective effects to solve possible actual technology problems; ─ corresponding adequate regression models specifying; ─ comprehensive on-line computer control of an industrial technology process; ─ off-line computer investigations of the collective and separate effects for the revealed industrial factors with possible novel synergetic phenomena discovering; ─ specifying the fields of possible further industrial technology improvements, deep specific laboratory applied or fundamental researches . 3
As input data arrays for the statistical investigations performed in the work the industrially obtained results of the quality inspection tests for thick sheets made of the ASTM A514 steel were used which specify the steel chemical element concentrations and the sheet standard mechanical properties indexes.
As the components of the approach the following techniques were consistently used: ─ C&RT procedure resulting in the dendrogram building for each product performance index depicting the responsible technology factors and their effects with the 98 % confidence probability; ─ based on the revealed variables construction of the multiple regression model for every control (dependent) characteristic; ─ computer experiment workability verification for each built regression model with the possible model coefficients correction to achieve the highest adequacy; ─ MC simulations of the traditional pair regression scatter plots obtained under the simultaneous change conditions for all responsible factors, which are typically built in the course of the conventional industrial quality analysis using unsorted, raw experimental data, as an additional workability verification tool for each regression model; ─ MC simulations of the separate effects for each regressor under the constant values of the rest ones in a regression model, for the research purposes of the manufacturing technologies improvements. ─ Multi-purpose optimization of the revealed technology parameters with applying a
MC extremum searching technique. 4
Some results obtained by the above approach industrial application are considered below. The final goal of the conducted research was to specify chemical composition and heat treating technology parameters values providing for ASTM A514 steel the standard mechanical properties combination which exceeds the technical requirements with 98% confidence probability. Actuality of the researches is caused by the extreme performance instabilities for the thick sheets made of the Boron containing steel due to its complex alloying and heat treating technologies interactions.
According to the methodology proposed, the first step of the investigations was C&RT analysis, resulting in the dendrograms building for each steel performance index. As it follows from the dendrogram for the steel yield stress shown on Fig. 1, the following statistically valuable technology factors effect the static steel strength:
Q t temp cooling duration at the steel quenching tcool and tempering cool , holding temperatures at austenitizing TA and tempering Ttemp together with the following chemical elements concentrations: V and B. Semi-quantitative characterization the factors separate and collective effects on the static steel strength may be also visually obtained from the dendrogram.
Further step of the approach was to elaborate the multiple regression models,
based on the corresponding dendrogram related data. The model developed for the
steel yield stress based on the dendrogram shown on Fig. 1 is as follows:
YS 400 63(В 4) 15(V 35) 0.03TA 1 25105 Ttemp tQ
cool 14 (0.12V B) (
The necessary in such a case adequacy verification for the obtained regression models was conducted by the use of MC technique to build the frequency distributions for each performance index considered in the current investigation.
Taking into account the statistical comprehensiveness of such a mathematic description of a measured quantity, the procedure employed may be considered as a regression model workability verification. The MC simulated frequency distributions built using the constructed regression models were compared with the real experimental ones. The simulation results for the considered above performance index obtained using the corresponding regression model 1 are shown on Fig. 2 as the frequency distribution line. As it seen, good correspondence of the simulated (line) and real experiment (histogram) distributions had been reached.
An important formal advanced feature of the regression models like the shown 200 150 r e b m u n ion100 t a v r e s b O 50 1 2 0 750 800 850 900 950
Yield Stress, MPa 1000 1050 1100 above one should be outlined. Namely, the obtained models provide high workability in the performance descriptions by taking into account only real values of the technology parameters and their multiplications without using the terms of two or higher power. It allows to propose a real, physically grounded interpretation of such equations in terms of the industrial factors separate effects and their interactions. In turn, such conclusions may be further used for the corresponding phenomena mechanisms investigations. Workability of the models was also verified by the MC simulations of two dimensional scatter plots corresponding to pair regression relations of a performance index vs. an industrial factor, under the conditions of all the factors simultaneous variations. Such effect of the factors should evidently be considered as collective one caused by interactions of all the factors simultaneously changed.
Some examples of the MC simulated and real experimental scatter plots for the steel currently studied are shown on Fig. 3, 4. As it seen, good agreement of the simulated and experimental data is provided that is an additional confirmation of the regression model high workability.
An important role in control of multi-factor phenomena and systems of complex physical-social-economical nature such as industrial technological processes, finished products etc. is played by specifying the sole effects of each valuable manufacturing factor on the performance indexes. As a rule, such information is unavailable under 1400 1200 aP1000 M , trsse800 S lde600 i Y 400 200 1400 real industrial environment due to simultaneous variations of numerous effecting manufacturing factors. Such research methodology restrictions can be avoided by analyzing currently available industrial data using the considered approach. An example of the revealed separate effects of the valuable manufacturing factors on the yield stress of ASTM A514 steel is shown on Fig. 5. The corresponding shown regression dependences were simulated for each valuable manufacturing factor which varies under some different constant values of the rest variables. These constant values for each accompanying variable were chosen randomly within the intervals of its possible 4 4.5 5 5.5
6 B*104, % 6.5 7 7.5
8 50
100 150 Cooling duration from TA, min 200 variation in the steel.
As it seen, varying the values of accompanying variables considerably influencing the steel yield stress levels or even the general character of its dependence from a considered factor. Particularly, the boron dependence of the steel yield stress changes from decreasing to increasing type under simultaneous transition to the parameters values: > 0.5 % V; cooling duration from austenite temperature < 45 min; cooling duration from subcritical temperatures 10 min; austenitizing temperature < 900 C or > 930 C. It should be additionally noted that the above results are in a good accordance with the known specific Material Science data concerned with the considered factors effects on structure and properties of corresponding steels and allow to explain the discrepancies often observed for boron containing steels in the literature.
Based on the results obtained using the applied integrated approach, some predictions were made aimed to improve of the industrial manufacturing technologies for the steel, particularly, its chemical composition and heat treatment technology.
The technology parameters thus predicted provide guaranteed exceeding the technical requirements to the steel performance indexes with 98% confidence probability. The adequacy of the corresponding technology recommendations was verified in real industrial conditions: the following combination of the performance indexes for thick sheets made of the researched steel was provided: YS = 950 40 МPа, = 56.5 4%, KV = 44 2 J. It should be noted the considerably low standard deviations for the just given standard mechanical properties characteristics, that is in violent contrast with the previously obtained industrial data, particularly shown in Fig. 1 and Fig. 2. So, the results of the developed integrated statistical investigation approach employment show considerable improvement of the finished industrial product reliability comparing with the same product made in traditional industrial conditions.
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Fig. 5. Computer simulated scatter plots showing separate effects of the revealed valuable
manufacturing factors on yield stress of ASTM A514 steel. Numerals on the plots
correspond consecutive numbers of randomly chosen combinations of the variables values used
in Eq(
Conclusions 1. In view of the Industry 4.0 needs, an approach to the industrial statistical investigations was developed aimed to improve effectiveness of big data, multi-dimensional array analysis and its results practical applications. 2. The developed approach integrates: C&RT technique, as a Data Mining procedure allowing the obtained results further physical interpretation and mathematical treatment; multiple regression models building to express the revealed draft regularities in a rigorous mathematical form; Monte-Carlo simulations to verify the regression models, to conduct computer investigations and outgoing product quality index predictions, to specify further research areas. 3. The approach developed was applied to solving some industrial quality and reliability problems for thick sheets made of boron-containing ASTM A514 steel concerned with its typical low and unstable yield stress and impact resistance on the levels: YS = 900 100 МPа, KV = 35 12 J. 4. The main performance indexes values obtained in industry for the steel with the confidence probability 98%, as a result of the approach application, are as follows: YS = 950 40 МPа, KV = 44 2 J. 5. As a result of the approach application the following technology advantages have been reached providing the guaranteed finished industrial product performance improvements: ─ specification of industrial technology factors having valuable effects on the product quality and reliability; ─ development of regression models providing the statistically comprehensive description of the revealed effects; ─ determination of separate effects for each of the revealed factors and conditions of the effects realization; ─ determination of the multipurposely optimized industrial technology parameters providing increase and stabilizing a combination of the finished product quality indexes. 6. In view of the demonstrated high effectiveness of the developed approach in solving the task having been considered together with generality of its background principles, successful application of the approach to solving analogous multi-factor problems in various technical and social environment should be expected. 3. Lee, J., Bagheri, B., Kao, H.: Recent Advances and Trends of Cyber-Physical Systems and Big Data Analytics in Industrial Informatics. Proceeding of Int. Conference on Industrial Informatics (INDIN) (2014) doi: 10.13140/2.1.1464.1920. 4. Lee, J., Lapira, E., Bagheri, B., Kao, H.: Recent advances and trends in predictive manufacturing systems in big data environment. Manufacturing Letters. 1: pp. 38-41 (2013) doi: 10.1016/j.mfglet.2013.09.005 5. Witten, I., Frank, E., Hall, M.: Data Mining: Practical Machine Learning Tools and Techniques. 3rd Edition, Morgan Kaufmann, Massachusetts (2011) 6. Bethge, M., Ecker, A., Gatys, L.: A Neural Algorithm of Artistic Style. (2015) arXiv: 1508.06576 7. Ojha, V., Abraham, A., Snášel, V.: Metaheuristic design of feedforward neural networks: A review of two decades of research. Engineering Applications of Artificial Intelligence 60: pp. 97–116 (2017) doi: 10.1016/j.engappai.2017.01.013 8. Wang, F., Rudin, C.: Falling Rule Lists. Artificial Intelligence and Statistics. 1013-1022 (2015) 9. Gareth, J., Witten, D., Hastie, T., Tibshirani, R.: An Introduction to Statistical Learning.
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