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This paper is based on the use of experimental data and a new evolutionary truly multi-objective optimization algorithm for simultaneously optimizing several properties of steel alloys while minimizing the number of experimental evaluations of the candidate alloys. This approach has been shown to have the potential of identifying new chemical compo...
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... The sensitivity of the alloy properties is rarely been taken into account [18] during complex optimization processes because of the lack of fast models for the property robustness, which is defined as the inverse of the sensitivity. The general concept of multi-objective robust optimization was initially developed by Deb et al [19] from single-objective robust optimization [20,21], and it is has been summarized in detail by Beyer et al [22]. ...
Alloys-by-design is a term used to describe new alloy development techniques based on numerical simulation. These approaches are extensively used for nickel-base superalloys to increase the chance of success in alloy development. During alloy production of numerically optimized compositions, unavoidable scattering of the element concentrations occurs. In the present paper, we investigate the effect of this scatter on the alloy properties. In particular, we describe routes to identify alloy compositions by numerical simulations that are more robust than other compositions.
In our previously developed alloy development program package MultOPT, we introduced a sensitivity parameter that represents the influence of alloying variations on the final alloy properties in the post-optimization process, because the established sensitivity calculations require high computational effort.
In this work, we derive a regression-based model for calculating the sensitivity that only requires one-time calculation of the regression coefficients. The model can be applied to any function with nearly linear behavior within the uncertainty range. The model is then successfully applied to the computational alloys-by-design work flow to facilitate alloy selection using the sensitivity of a composition owing to the inaccuracies in the manufacturing process as an additional minimization goal.
... The addition of alloying element should be aimed at achieving good mechanical properties of the materials. Therefore it is essential to add optimum amount of alloying element to improve the mechanical properties of the magnesium alloy [4]. The Taguchi method [5,6] is one of the best tool to design and analysis of experiments for enhancing the product quality. ...
In this investigation, the grey-based Taguchi method was used for optimizing the composition elements of magnesium alloy. The purpose of optimization is to achieve high performance in material characteristics. For the study, experiments were conducted by Taguchi (L9) orthogonal array and to optimize the process parameters, grey based Taguchi techniques has been adopted. Analysis of variance was used to determine the significant parameter and that affects the mechanical properties. Key Word : Magnesium Alloy, Taguchi Method, Grey Relation Analysis. 1.Introduction Magnesium alloys have enormous applications in the automobile, defence and aerospace industry owing to the low density and good specific strength [1-3]. The addition of alloying element should be aimed at achieving good mechanical properties of the materials. Therefore it is essential to add optimum amount of alloying element to improve the mechanical properties of the magnesium alloy [4]. The Taguchi method [5,6] is one of the best tool to design and analysis of experiments for enhancing the product quality. The grey system theory proposed by Deng [7] in 1982 has been proven to be useful for dealing with poor, incomplete, and uncertain information. The grey relational analysis based on the grey system theory can be used to solve complicated interrelationships among multiple performance characteristics effectively [8]. A grey relation analysis of the S/N ratios can convert the optimization of a multiple performance characteristics into the optimization of a single performance characteristic called the grey relation grade [9]. Narender Singh et al [10] to optimize the multi response characteristics of Electric Discharge Machining of Al–10 % SiCp composites in to a single response by using grey relational grade. The grey-based Taguchi method can be preferred to optimise the multi-response objective through the settings of process parameters [11]. In this investigation, the use of the grey-based Taguchi method to optimize the composition elements in developing magnesium alloy by powder metallurgy route with considerations of multiple characterization responses such as tensile strength, ductility and hardness was reported. 2.Taguchi based grey relation analysis Taguchi method is an effective and systematic tool to optimize designs for performance and quality. The orthogonal array is used to design the experiments and support to minimize the number of experiments. Also this method optimizes the process parameters by the analysis signal-to–noise ratio [12]. Based on the nature of the problem, the mean quality characteristic can adjust through a special control factor, called an adjustment factor. S/N can be used to predict the quality loss after correct adjustment has been made. In this study, tensile strength and hardness are the higher-the-better performance characteristic. The loss function for the higher-the-better characteristic can be expressed as
... Even with this approach, the number of alloys that need to be manufactured and experimentally evaluated becomes too large, as the number of alloying elements in an alloy is increased. The proposed methodology45678910111213 for simultaneously extremizing the multiple properties of alloys, by accurately determining proper concentrations of each of the alloying elements, is based on combining: a) experimentally obtained multiple properties of the alloys and b) an advanced, stochastic, multiobjective, evolutionary optimization algorithm using multidimensional response surface as a metamodel. During the iterative computational design procedure, a relatively small number of new alloys need to be periodically manufactured and experimentally evaluated for their properties in order to continuously verify and improve the accuracy of the entire design methodology. ...
... The total number of alloys that needs to be manufactured and experimentally evaluated as a part of this optimization strategy is expected to be approximately at least 2 * A * A * 1 + PP, where A is the number of design variables (concentrations of alloying elements) and P is the number of simultaneous objectives (properties of the alloy that need to be extremized simultaneously). The proposed computational design optimization method was recently verified by Ni-based steel superalloys using strictly experimental data678 and has already been applied to design optimization of H-class steels [4, 5], bulk metallic glasses91011, and titanium-based alloys [12]. The proposed optimization methodology is expected to perform equally well in the optimization of chemical concentrations and thermal treatment protocols of aluminum alloys. ...
The objective of this study is to develop a new family of aluminum alloys with superior stress corrosion cracking resistance (SCCR) and mechanical properties. This approach uses experimentally obtained stress corrosion resistance, tensile strength, and yield strength data from the literature and then performs hybrid multiobjective evolutionary optimization combined with multidimensional response surfaces. This software has the proven capability to deal with various alloy design applications using minimal amount of experimental data. The selected objectives in this study are superior stress corrosion resistance, tensile strength, and yield strength. The design variables are concentrations of alloying elements and the individual alloy tempers as they are important parameters that directly affect macroscopic properties and microscopic details of the alloy such as grains, phases, precipitates, etc. The computational trials yield optimal alloys' chemical compositions and standard thermal treatment protocols for the best combination of superior stress corrosion resistance and mechanical properties. Single-objective optimization results confirm the known experimental observations that dilute Al alloys yield the best corrosion resistance at the expense of tensile strength. Optimizations with two simultaneous objectives and more alloying elements create better trade-off solutions. Quality and number of initially available experimentally evaluated alloys have decisive effects on accuracy of this alloy design method.
... Specifically, we are currently concentrating on simultaneously maximizing T g , T l and T g /T l and minimizing density of Zr-based BMGs [18, 19]. The proposed optimization method is based on combining experimentally obtained multiple properties of the BMGs and a computational optimization algorithm2021222324 rather than on traditional experimentation alone, expert experience and intuition. Specifically, the proposed BMG design method combines an advanced stochastic multiobjective evolutionary optimization algorithm based on self-organizing graph theory and a self-adapting response surface methodology [22, 25]. ...
... Specifically, the proposed BMG design method combines an advanced stochastic multiobjective evolutionary optimization algorithm based on self-organizing graph theory and a self-adapting response surface methodology [22, 25]. During the iterative computational design procedure, a small set of new BMG alloys is periodically predicted, manufactured and experimentally evaluated for their properties in order to continuously verify the accuracy of the entire design methodology2021222324. The proposed BMG alloy design optimization method is thus experimentally verified. ...
... Because of its proven robustness, computing speed and versatility we have decided to use the multi-objective constrained indirect optimization based upon self-organization (IOSO) algorithm18192021222324 25]. This multi-objective optimization algorithm allows for concentrations of the alloying elements to be optimized so that several of the BMG alloy properties (maximizing T g , T l and T g /T l and minimizing density) are simultaneously extremized, while satisfying a number of equality and inequality constraints (minimum and maximum specified concentrations for each of the alloying elements). ...
Thermo-mechanical-physical properties of bulk metallic glasses (BMGs) depend strongly on the concentrations of each of the chemical elements in a given alloy. The proposed methodology for simultaneously optimizing these multiple properties by accurately determining proper concentrations of each of the alloying elements is based on the use of computational algorithms rather than on traditional experimentation, expert experience and intuition. Specifically, the proposed BMG design method combines an advanced stochastic multi-objective evolutionary optimization algorithm based on self-adapting response surface methodology and an existing database of experimentally evaluated BMG properties. During the iterative computational design procedure, a relatively small number of new BMGs need to be manufactured and experimentally evaluated for their properties in order to continuously verify the accuracy of the entire design methodology. Concentrations of the most important alloying elements can be predicted so that new BMGs have multiple properties optimized in a Pareto sense. This design concept was verified for superalloys using strictly experimental data. Thus, the key innovation here lies in arriving at the BMG compositions which will have the highest glass forming ability by utilizing an advanced multi-objective optimization algorithm while requiring a minimum number of BMGs to be manufactured and tested in order to verify the predicted performance of the predicted BMG compositions.
... The proposed methodology [4][5][6][7][8][9][10][11][12][13] for simultaneously extremizing the multiple properties of alloys, by accurately determining proper concentrations of each of the alloying elements, is based on combining: a) experimentally obtained multiple properties of the alloys and b) an advanced, stochastic, multiobjective, evolutionary optimization algorithm using multidimensional response surface as a metamodel. During the iterative computational design procedure, a relatively small number of new alloys need to be periodically manufactured and experimentally evaluated for their properties in order to continuously verify and improve the accuracy of the entire design methodology. ...
... The proposed computational design optimization method was recently verified by Ni-based steel superalloys using strictly experimental data [6][7][8] and has already been applied to design optimization of H-class steels [4,5], bulk metallic glasses [9][10][11], and titanium-based alloys [12]. The proposed optimization methodology is expected to perform equally well in the optimization of chemical concentrations and thermal treatment protocols of aluminum alloys. ...
Summary This paper deals with the application of inverse concepts in drying. The ob- jective of the paper is estimation of the moisture diffusivity of a drying body by using only temperature measurements. Potato and apple slices have been chosen as representative drying bodies with significant shrinkage effects. A mathematical model of the drying process of shrinking bodies has been applied. The Levenberg- Marquardt method and a hybrid optimization method of minimization of the least- squares norm were used to solve the present parameter estimation problem.
... We propose here a novel methodology for predicting the concentration of each of the important alloying elements in BMGs so that the new BMGs will have improved glass forming ability and thermal stability. The proposed optimization method is based on combining experimentally obtained multiple properties of the BMGs and a computational optimization al- gorithm1617181920 rather than on traditional experimentation alone, expert experience, and intuition. Specifically, the proposed BMG design method combines an advanced stochastic multi-objective evolutionary optimization algorithm based on self-organizing graph theory and a self-adapting response surface methodology212223. ...
... Specifically, the proposed BMG design method combines an advanced stochastic multi-objective evolutionary optimization algorithm based on self-organizing graph theory and a self-adapting response surface methodology212223. During the iterative computational design procedure, a small set of new BMG alloys is periodically predicted, manufactured, and experimentally evaluated for their properties in order to continuously verify the accuracy of the entire design methodology1617181920. The proposed BMG alloy design optimization method is thus experimentally verified and minimizes the need for costly and time-consuming experimental evaluations of new BMG alloys. ...
... The algorithms and approaches that we propose have a universal nature and are applicable to any complex engineering system. An example of the recently published application of IOSO optimization to design of steel superalloys1617181920 is depicted inFigure 3. It demonstrates the ability of the proposed methodology to immediately in the first iteration create the superalloys with properties that are superior to any of the alloys in the original experimental data set. Our recent publication [30] gives a preliminary attempt to create a new generation of BMGs with improved multiple properties. ...
Metallic glass is basically an alloy whose metallic species are “frozen” in amorphous glassy state rather than forming a standard
crystalline structure. Metallic glasses have no grain boundaries and no dislocations and stacking faults. They are several
times stronger than steel and considerably harder and more elastic. Formation of metallic glasses by extremely high cooling
(~105 K/sec) of the melt was first accomplished in 1960s. The resulting metallic glass thickness was limited to extremely
thin ribbons. In the 1990s, researchers formed new classes of metallic glasses in bulk. The bulk metallic glasses (BMGs) are
composed of three or more metals in the alloy melt and a few diatomatous earth ingredients in order to lower the cooling rate.
Cooling rates of the new alloys are from 100 K/s to 1 K/s. The possible thickness of these newer metallic glasses increased
from micrometers to centimeters. One of the keys to lowering the cooling speed and creating larger specimens is that bulk
metallic glasses should have ingredients with atomic species having large size and chemical differences. Thus, multiple thermo-mechanical
properties and the cooling speed of bulk metallic glass alloys depend strongly on the concentrations of each of the chemical
elements in a given alloy. The proposed methodology for accurately determining concentration of each of the important alloying
elements is based on the use of a combination of a robust multiobjective optimization algorithm and on traditional experimentation.
Specifically, the proposed alloy design method combines an advanced stochastic multi-objective evolutionary optimization algorithm
based on self-adapting response surface methodology and a relatively very small data set of thermo-mechanical properties and
the corresponding concentrations of alloying elements. During the iterative computational design procedure, new metallic glass
alloys need to be manufactured and experimentally evaluated for their properties in order to continuously verify the accuracy
of the entire design methodology. This metallic glass alloy design optimization method thus minimizes the need for costly
and time-consuming experimental evaluations of new metallic glass alloys to fewer than 200 new alloys.
... Our approach is based on the use and a special adaptation of a stochastic, multi-objective constrained Indirect Optimization based upon Self-Organization (IOSO) algorithm [5, 6] . IOSO stochastic multi-objective optimization algorithm allows for concentrations of a number of alloying elements to be optimized so that a finite number of properties (maximum tensile strength, maximum operating temperature, maximum time-until-rupture, minimum weight, minimum cost, etc.) of the alloy are simultaneously extremized7891011. The main benefits of this optimizer are its outstanding reliability in avoiding local minimums, its computational speed, and a remarkably small number of required experimental evaluations of alloy samples as compared to more traditional semi-stochastic optimizers such as genetic algorithms. ...
... One of the advantages of the proposed alloy optimization approach is the possibility of ensuring good approximating capabilities using a minimum amount of available information. In a recent example demonstrating the potential of this alloy design methodology91011, an initial data base, containing 120 steel alloys was generated using Sobol's algorithm [12]. The chemical compositions of these alloys were determined so that they are as uniformly distributed in the function space as possible, thus, creating conditions for very accurate response surface fit. ...
... Each symbol in these figures represents an optimized alloy with its own chemical composition. Notice that by a similar use of the constraints this approach has the potential for designing alloys with specified multiple properties, thereby maximizing their utilization at reduced cost [8, 10, 11].Fig. 2 We are hereby publishing experimental data and chemical compositions of all 120 original alloys (Table II) and the 20 optimized alloys (Table III) created in the 4th optimization cycle.Fig. 5 Table III. ...
A novel method has been developed and experimentally verified that can enable a significant part of the steel alloy development procedure to be performed computationally by using the power of a true mathematical evolutionary multi-objective optimization algorithm. During the alloy optimization process, maximized operating temperature, tensile stress, time-to-rupture, and minimized cost and weight were treated as simultaneous often conflicting objectives. Concentrations of most important alloying elements were predicted so that new alloys have the best multiple properties. This alloy design concept was verified using strictly experimental data. The number of required experimental evaluations of the candidate alloys with this optimization approach is very low. This approach has the potential of identifying the new chemical compositions of significantly superior steel alloys with only a few hundred alloy samples.
... Neural networks have been used 6 to relate the alloys' properties with their chemical concentrations, but a faster method is required to perform such correlations while utilizing as small experimental data sets as possible in order to minimize the time and cost involved in the alloy design optimization process. Use of response surfaces can be one such methodology and it has been implemented by the authors in the design optimization of high temperature superalloys [7][8][9] . This is why we are here demonstrating the possibility to use large existing experimental data sets in conjunction with a reliable software for data mining such as JMatPro to predict the multiple alloy properties purely computationally to arrive purely computationally at the superior performance alloy compositions. ...
Chemical concentrations of new generations of Ti-base alloys containing Al, Cr and V were predicted computationally that simultaneously maximize Young's modulus of elasticity while minimizing alloy density and cost of its raw materials. A software JMatPro was used to calculate the desired properties and software IOSO was used to perform multi-objective evolutionary optimization by creating several Pareto optimal generations of new alloys. The method was applied over a wide range of temperature varying from 30 ° C to 1500 ° C.
The paper is devoted to an optimization approach to a problem of statistical modeling of mechanical properties of heavy steel plates during a real industrial manufacturing process. The approach enables the manufacturer to attain a specific set of the final product properties by optimizing the alloying composition within the grade specifications. Because this composition has to stay in the agreement with earlier indicated specifications, it leads to the large system of linear constraints, and the problem itself can be expressed in the form of linear programming (LP) task. It turns out however, that certain of the constraints contain the coefficients which have to be estimated on the base of the data gathered in the production process and as such they are uncertain. Consequently, the initial optimization task should be modeled as so-called Chance Constrained Programming problem (CCP), which is a special class within the stochastic programming problems. The paper presents mathematical models of the optimization problem that result from both approaches and indicates differences which are important for the decision makers in the production practice. Some examples illustrating the differences in solutions resulting from LP and CCP models are presented as well. Although the statistical analysis presented in this paper is based on the data gathered in the ISD Czestochowa Steelworks, the proposed approach can be adopted in any other process of steel production.
