Sensor Array Design for Complex Sensing Tasks.

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Review in Advance first posted online on June 24, 2015. (Changes may still occur before final publication online and in print.)

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Annual Review of Analytical Chemistry 2015.8. Downloaded from www.annualreviews.org Access provided by WIB6013 - Freie Universitaet Berlin - FU Berlin on 07/02/15. For personal use only.

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Sensor Array Design for Complex Sensing Tasks∗ Kevin J. Johnson and Susan L. Rose-Pehrsson Chemistry Division, US Naval Research Laboratory, Washington, DC 20375; email: [email protected], [email protected]

Annu. Rev. Anal. Chem. 2015. 8:14.1–14.24

Keywords

The Annual Review of Analytical Chemistry is online at anchem.annualreviews.org

chemical sensors, sensor arrays, array optimization

This article’s doi: 10.1146/annurev-anchem-062011-143205

Abstract

∗

This is a work of the US Government and is not subject to copyright protection in the United States.

Chemical detection in complex environments presents numerous challenges for successful implementation. Arrays of sensors are often implemented for complex chemical sensing tasks, but systematic understanding of how individual sensor response characteristics contribute overall detection system performance remains elusive, with generalized strategies for design and optimization of these arrays rarely reported and even less commonly adopted by practitioners. This review focuses on the literature of nonspecific sensor array design and optimization strategies as well as related work that may inform future efforts in complex sensing with arrays.

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1. INTRODUCTION


A persistent problem in chemical sensing lies in developing and implementing sensor systems that are capable of reliably addressing complex sensing tasks and environments. Such conditions are regularly encountered in a highly diverse range of practical endeavors, including environmental monitoring, industrial process control, toxic chemical and fire detection, flavor and fragrance assessment, and medical diagnostics, among other applications. Often, these tasks are centered on the detection of chemical signatures rather than individual chemical compounds. However, even seemingly basic sensing tasks centered on detection of individual analytes are often complicated significantly by unavoidable environmental conditions and nuances that surround any realistic application, such as backgrounds with relatively dynamic physical conditions and multiple potentially interfering chemical species. This can lead to surprisingly poor performance in real-world environments after excellent results have been demonstrated in the laboratory (1–3). Thus, understanding the surrounding contextual details of a chemical sensing problem is critical to finding a solution, together with knowing and addressing the target analytes themselves. Further complicating matters, there is often a considerable degree of uncertainty regarding the underlying parameters of a sensing task. This includes uncertainty regarding which potential analytes and interfering species may or may not be present and what environmental conditions might be encountered, as well as more fundamental problems such as a lack of a priori knowledge as to the identity and number of potential target analytes and interferants. Perniciously, the existence of such uncertainties are often, themselves, poorly understood prior to implementation of a sensor system. Explicit recognition of this situation leads to the logic of an open-world assumption (4), implying that some limits on the extent of inference and deduction that may be derived from measured sensor responses be placed. Importantly, although development of individual sensors is generally driven by a desire to improve selectivity and sensitivity relative to current alternatives, complex environments make these metrics difficult to evaluate. Selectivity, which is defined by the International Union of Pure and Applied Chemistry in strictly qualitative terms (5), has meaning only in the context of a specific background of potential interferants. In a practical sense, selectivity subsumes the problem of sensitivity, as it reflects the challenge of maximizing sensitivity to the chemical species of interest in the sensing task while minimizing sensitivity to others. Even in the best-case scenario where an exhaustive catalog of the potential interferants and target analytes is known, design and implementation of a rigorous, exhaustive series of laboratory experiments for evaluating sensor performance becomes impractical unless there is relatively few analytes and the field environment in which the sensor is to implemented is known to be fairly static. In more typical scenarios, such evaluation is essentially impossible due to the uncertainties described above. Thus, sensing in complex environments can be seen as what amounts to, in some degree, an exercise in general-purpose chemical analysis of unknown samples rather than straightforward target analyte detection. Although it is perhaps intuitive that the design of any sensor system imparts specific constraints dictating the scope of analytical challenges it is capable of addressing, it is not necessarily obvious how such systems should be designed to meet arbitrary, complex sensing challenges, and perhaps more importantly, to assess the ability of a sensor system to generalize to new sensing tasks that might be encountered in the future. Broadly, however, the less one knows about the parameters surrounding a particular analytical task, the more analytical capability one needs to bring to bear to reliably address it. In a sense, each piece of knowledge about the parameters of the sensing task potentially removes some degree of freedom with which an analytical strategy must contend. Inversely, reserve analytical capability in a sensing system serves as a means to hedge against unanticipated conditions.

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It is for this reason that relatively complex instruments such as gas chromatographs with mass-selective detection (gas chromatography–mass spectrometry) have become ubiquitous for general-purpose chemical analyses, whereas chemical sensors continue, by and large, to occupy narrower-scope niche applications. However, there is a conceptual middle ground between individual chemical sensors and complex laboratory instrumentation that is occupied by sensor systems comprised of arrays of nonspecific sensors coupled to multivariate data analysis algorithms. The idea of employing such an array as a relatively general-purpose chemical detection system is inspired by analogy to the vertebrate olfactory system and garnered great enthusiasm starting in the mid-1980s (6). However, there have been difficulties since then in realizing widespread commercial appeal of such devices, at least as general-purpose solutions to varied chemical sensing applications (6, 7). Nevertheless, the idea of sensor arrays as a potential alternative to more costly analytical instrumentation remains popular and continues to be an active area of research in the sensing community, where, owing to a persistent desire in most applications to utilize simpler, less costly hardware whenever possible, there remains significant motivation to develop and build sensor arrays for complex sensing tasks. However, designing a sensor array configuration that addresses a complex sensing task to a desired performance level can be difficult. There is limited specific guidance and theory as to how such systems should be built, and this has doubtless slowed their adoption in the past few decades. There is massive diversity in the scope of possible configurations of nonspecific chemical sensor arrays, both an advantage and a drawback of such systems. The advantage is that, in theory, instrumental complexity can be tailored to an analytical task of arbitrary scope. However, this also means that great caution must be taken when attempting to utilize a commercially available sensor array for a complex task for which it was not explicitly designed. This work reviews the analytical potential and limitations of arrays of nonspecific chemical sensors as well as strategies for designing sensor arrays for complex environments and sensing tasks. Section 2 provides a brief review of chemical sensors and sensor arrays that have been implemented in the literature. Section 3 describes the underlying geometry of sensor arrays and reviews strategies for optimizing them for sensing tasks. Section 4 provides conclusions and discussion of future directions.

2. SENSORS AND SENSOR ARRAYS 2.1. Sensor Types There is significant diversity in the modes of chemical sensor transduction and the corresponding responses that are observed, leading to a wide assortment of candidate sensor technologies that can be brought to bear on complex sensing tasks. Numerous articles and reviews have been published over the past few decades, covering various sensor technologies as well as chemical sensing technology in general (8–33). These techniques exist at varying levels of technological maturity, from commercially available commodity devices to cutting-edge research prototypes, and offer widely divergent capabilities; however, no single technology presents a definitive solution to general-purpose chemical sensing. Although an exhaustive review of all sensor technologies is not within the scope of this article, the sensor types that are most commonly reported in chemical sensing applications can be grouped as belonging to one of three major families according to transduction mechanism: electrochemical, mechanical, or optical. Electrochemical sensors function by measuring a change induced in the electrical properties of the sensing material induced by analyte vapor. They include chemiresistors based on metal oxide semiconductors (10), conducting polymers (11), metal-organic frameworks (12), and nanostructured materials (13–15), as well as those based on other metal oxide semiconductor field effect www.annualreviews.org • Sensor Array Design


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transistors and potentiometric devices (16, 17). Mechanical sensors function by measuring change in the physical properties of the sensing material induced by analyte vapor (18). They include devices based on quartz crystal microbalance (QCM) and surface acoustic wave (SAW) sensors (19, 20), and microelectromechanical systems (MEMS) (21). In both QCM and SAW sensors, this is a change in the resonant frequency of an oscillator induced by absorption of analyte vapor into a polymer coating. In MEMS sensors, this is generally either deflection or change in oscillating frequency of a polymer-coated microcantilever. Finally, optical sensors include those based on materials in which analyte vapor induces a change in the way light is absorbed, emitted, or refracted by the sensing material (22–30). These include sensors based on vapochromic dyes (24–27), fluorescence (28, 29), chemiluminescence (30, 31), and surface plasmon resonance (32, 33).


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2.2. Sensor Performance Metrics Although the specific data processing and feature extraction methods vary among the different types of sensors, the goal to derive a response value that is related to analyte concentration according to some known function is the same. These response curves are evaluated by traditional analytical figures of merit such as sensitivity, limit of detection/signal-to-noise ratio, dynamic range, and selectivity (34). The first three describe sensor performance with respect to individual analytes, whereas selectivity is related to a sensor’s ability to preferentially respond to one analyte in the presence of one or more others. Thus, any concept or calculation of selectivity is inherently bound to the parameters of a specific sensing task. Specificity is the hypothetical ultimate of selectivity: a specific sensor responds only to analytes of interest, whereas a nonspecific sensor exhibits varying responses to both target analytes and other compounds, i.e., interferants. Often, sensors are designed for particular target analytes for which sensitivity and selectivity are optimized relative to a particular sample matrix. In general, greater sensitivity places greater demands on selectivity; conversely, greater selectivity places reduced demands on sensitivity. Thus, a significant portion of sensor research and development for complex sensing environments lies in engineering progressively greater selectivity into such devices. Of course, the end goal of sensor optimization is producing a detection system that best provides the information one is seeking to measure. For instance, a device intended for toxic vapor detection might be evaluated in terms of a receiver operating characteristic curve, which summarizes the trade-off between detection and false positive rates over a range of decision thresholds applied to the sensor data (35). Alternatively, sensor data could be used to provide quantitative predictions of analyte vapor concentration, which would typically be evaluated in terms of calibration model fit and estimates of error of prediction (36, 37). In either case, it is important to understand that the success of the overall detection system rests fundamentally on the capability of the sensor responses to support the informational output that is desired and that this is related to both the sensor response characteristics and the parameters of the analytical task.

2.3. Sensor Arrays Chemical sensors are usually not truly specific, especially for arbitrary, complex detection tasks with uncertain parameters. In the absence of guaranteed specificity, a significant limitation of sensors with univariate output (i.e., those that provide one response value per measurement) for complex sensing tasks is that they are generally incapable of estimating analyte concentration in the presence of unknown amounts of other compounds, and are thus not useful in analysis of mixtures or in the presence of unknown amounts of interfering species (38). This limitation 14.4

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can be addressed by augmenting the sensor with one or more others to provide complementary information, forming an array of nonspecific sensors. From a mathematical standpoint, the data from such an array is thus analogous to a low-resolution version of the multivariate data one might acquire from conventional spectroscopic or mass spectrometric laboratory instrumentation. Identification of pure compounds in these cases is often based on spectral patterns rather than on any one channel within the spectrum, enabling identification of more compounds than the number of channels in the spectrum. Additionally, multivariate regression enables calibration of individual mixture components in the presence of unknown amounts of others (39). The vertebrate olfaction system is a common inspiration for using arrays of nonspecific sensors to solve difficult chemical detection tasks. This system incorporates an array of roughly 100 million olfactory receptor neurons, each expressing one of approximately 1,000 unique receptor types and all exhibiting varying nonspecific interactions with potential odorant molecules. Patterns of neural activity within the peripheral olfaction system are then transmitted to the olfactory cortex of the brain where they are mapped in a highly nonlinear fashion to enable perception of tens of thousands of unique odors (40). Despite the equally analogous relationship between spectral analytical instrumentation and its utility in chemical identification, olfaction is arguably the motivating ideal behind much of the chemical sensor array work performed to date and a reason why such devices have commonly been referred to as electronic noses (or electric tongues for liquid sample sensors) and machine olfaction in the technical literature. However, despite considerable overlap, electronic noses are not synonymous with chemical sensor arrays. First, the term electronic nose is a generic descriptor for odor-profiling devices, including those based on analytical instrumentation. Second, not all chemical sensing tasks are properly termed olfaction, as this refers specifically to problems involving odor perception. In an early review of machine olfaction, Pearce (41) describes how the approach was the result of the confluence of the development of chemical sensors in the 1950s and 1960s and early work describing signal processing in neural olfaction systems in the late 1960s, which culminated in 1982 in Persaud & Dodd’s (42) first description of a three-sensor electronic nose. Following this, there was a rapid expansion of reports of sensor arrays for chemical detection; see References 43–47 for examples. Since this early work, sensor arrays of nearly every type of chemical sensor technology available have been reported in the literature. For example, Grate and colleagues (18, 19, 48–51) have reported extensively on the use of SAW and other sorption-based sensor arrays in detection of chemical vapors. Zellers and colleagues (52–55) have reported microfabricated arrays of chemiresistor and hybrid arrays applied to binary and ternary chemical mixtures. Suslick and colleagues (56–60) have reported colorimetric sensor arrays applied to many complex chemical sensing problems. Promising work on surface-functionalized nanostructures has recently garnered much attention (61–64) and Marco et al. (7), have developed a very large-scale array of conducting polymer chemical sensors for biomimetic olfaction. An alternative to a physical array of sensors is so-called adaptable sensors that are capable of adjusting their operating parameters or environment to alter their response functions during use (65). In this way, adaptable sensors acquire what is effectively sensor array data with a single sensing element at some cost in data acquisition time over a comparable multisensor array. Furthermore, an array of adaptable sensors could be assembled such that it operates as a second-order analytical instrument, producing a matrix of sensor responses per measurement. Such systems could leverage the chemometric second-order advantage (38) which could allow for analysis of target compounds in the presence of uncalibrated interferant backgrounds. They also open the potential to build sensor systems that can adapt to changing environments and sensing tasks, gaining efficiency by limiting the number of measurements made to only those that are necessary (66). For example, www.annualreviews.org • Sensor Array Design


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microhotplate sensors precisely control the temperature of a metal oxide sensor surface, thus altering the sensor response characteristics in a repeatable, programmable fashion (67, 68). This approach has been demonstrated to provide enhanced information for complex sensing tasks such as detection of chemical vapors in backgrounds of common commercial cleaning products. In other examples, sensors have been coupled to reagent chemistries, catalysts, or filters to enable variable selectivity (69–73). Finally, sensors can be coupled to sampling devices that provide spatial or temporal separation of analyte mixtures prior to detection (74). Numerous books and reviews of sensor array technology have since been authored with at least one published nearly every year since 1997, demonstrating the continued interest in and vitality of the approach (6, 18, 19, 41, 67, 75, 76, 77–102). The majority of these reviews are focused on describing various sensor technologies and applications for which sensor arrays have been used, whereas a smaller fraction focus instead on data analysis strategies for sensor arrays. However, only a few provide any focus on optimization strategies for arrays (82, 83, 91, 98, 99). There have also been periodic surveys of commercially available sensor-array devices, generally uncovering several new manufacturers with each iteration (6, 75, 87, 90, 95). Applications of these arrays are frequently reported in the literature where they have been described as successfully applied to a wide variety of tasks (see, e.g., those reviewed in 103). However, it has been noted repeatedly that such devices do not seem to have made significant progress toward widespread commercial use (6, 7). The reason for this is likely an overestimation of sensor array capabilities combined with an underestimation of sensing task complexity and a lack of sound validation and design principles (1–3). As is often the case with new technologies, enthusiasm can outpace actual utility, leading to subsequent disappointment that perhaps unfairly clouds any realistic assessment of the capabilities of these devices.


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3. SENSOR ARRAY OPTIMIZATION Great caution should be taken with the assumption that an arbitrary chemical sensor array will exhibit emergent sensing properties similar to those observed in biological olfaction (or, for that matter, those associated with multivariate spectral instrumentation) as the differences between them are significant. For example, most sensor arrays reported in the literature contain at most two or three dozen different sensors—a more than tenfold reduction in repertoire size relative to biological olfaction systems, even neglecting the prospect of significant correlation among sensors. Furthermore, the sensors employed do not necessarily have similar response profiles to biological olfactory receptors (which are as yet poorly understood themselves (104), nor are their responses typically processed and interpreted in the same manner, although there are some exceptions (105). How then can one understand and optimize the utility of nonspecific arrays in various complex sensing contexts? Although the relationships between sensor response and detector performance are straightforward for simple sensing tasks and individual sensors, it can be difficult to intuit and predict the impact of individual response characteristics of component sensors to overall performance of an ensemble of sensors applied in a complex environment. Logically, the complexity required of a detection system to achieve a given performance specification should be related to the desired complexity of the underlying analytical task. If the complexity of an arbitrary sensor array is operationally defined as the information-generating capacity of that device, and similarly the complexity of a given analytical question as the information required to accurately address it, then the goal of optimization is to identify the sensor array configuration that most efficiently supports the informational requirements of a set of desired sensing tasks. There are hundreds of examples in the literature of empirical evaluations of the efficacy with which particular sensor systems address specific analytical tasks. Often these assessments are either flawed by a fundamental underestimation of the complexity of the analytical task or are focused on 14.6

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relatively narrow-scoped analytical problems (1). The net result is that much of this work is not exceptionally useful in providing general conclusions regarding sensor array design. It is relatively uncommon to find work that seeks to explicitly address the broader philosophical questions in sensor array design for complex environments. In particular, how (and to what extent) can a sensor array be engineered to effectively address a complex sensing task? Or, inversely, how is application-specific sensor array performance related to varying array configurations? In other words, how useful is a given sensor array for general-purpose chemical sensing? The ultimate question is whether it is practical or even possible to build a sensor system that approaches the utility of conventional analytical instrumentation or the capabilities of biological olfaction.

3.1. Geometry of Sensor Arrays A useful way to conceptualize sensing task and sensor array complexity is to describe them as geometric spaces, with the sensor response functions providing a transformation from one space to the other. Gardner & Bartlett (106) discussed the need to standardize the manner in which the capabilities of sensor array systems are characterized. They introduced a general geometric description of signal processing in electronic noses based on a linear algebraic model of sensor arrays with linear, power law, and Langmuir isotherm-modeled sensor response curves. This enabled mathematical consideration of propagation of sample and sensor errors and their impact on array performance in classifying odors. It was also in line with contemporary chemometric treatments of data from sensor arrays and other multivariate instrumentation (39, 43–46). In this approach, the sensing task is described as an m-dimensional space where m is the number of unique analytes that are to be detected. The members of this set can be individual chemical species, a particular mixture of chemical species (e.g., an odor), or some other phenomena with varying intensity that provokes a sensor response. The distance along each axis corresponds to the concentration of the analyte associated with that axis, with each location in this space referring to a unique mixture of analytes. The desired range and gradations of concentration to be discerned thus define the spacing and extent of a grid within this sample space, which reflects the total span of desired knowledge regarding the sample to be sensed. This amounts to a geometric description of the frame of discernment for the underlying classification problem implied by the analytical task. The dimension of the sample space should be informed by not only the desired target analytes, but also by the span of all potential interferants. Next, the set of possible sensor array responses can similarly be described by a grid of discrete points, this time in an n-dimensional space where n is the number of data sources in the array. This can include raw sensor responses as well as features extracted from sensor data or other algorithmic processing of raw sensor data. Distance along each axis represents signal intensity from a single data source, with the collection of all points in the space representing the span of all possible output vectors from the sensor array. The resolution and spacing on this grid are determined by the resolution, limit of detection, and dynamic range of the individual data sources. This space is referred to as the measurement space of the sensor array. The ability of any particular multivariate or fused sensor system to address a given analytical task can be informed by examining the projection of the sample space associated with the task into the measurement space associated with the sensor array. This projection is provided by the set of response functions of each sensor to each analyte, and this is how each individual sensor contributes to the overall performance of the sensor array. In a simple example, assuming an array of sensors with linear response curves and additive response to analyte mixtures, the response, R, of a particular sensor to a mixture of m analytes will www.annualreviews.org • Sensor Array Design


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Figure 1 Geometric depiction of sensor array response to specific sensing tasks. A sample space contains every possible analyte mixture, with one dimension per analyte. The set of response functions for each sensor for each analyte provides a mapping function to a measurement space containing every possible array response, one dimension per sensor data source. The circle, triangle, and square markers indicate examples of corresponding locations between the sample space (a) and its projection into the measurement space (b).

be

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where c i is the concentration of the ith analyte and s i is the sensitivity of the sensor to the ith analyte. Extending this relationship for an array of n sensors leads to a system of linear equations: ⎡ ⎤ s 1,1 · · · s 1,n ⎢ . .. ⎥ .. ⎥ 2. [c 1 · · · c m ] × ⎢ . . ⎦ = [r1 · · · rn ], ⎣ .. s m,1 · · · s m,n where s i, j is the sensitivity of the jth sensor to the ith analyte and r j is the response from the jth sensor. The matrix of sensitivity values, S, for a sensor array specifies the geometric transform that maps locations in the sample space to corresponding locations in the measurement space of that array. Responses due to a single analyte at varying concentrations within the dynamic range of the sensors appear as a linear trajectory in the measurement space, whereas responses due to binary mixtures at varying concentrations of both analytes appear as a plane bounded by trajectories of the pure mixture components. Figure 1 depicts a simple scenario in which mixtures of two analytes are to be detected by an array with two sensors. The sample space is thus a two-dimensional grid with each coordinate pair specifying a different mixture ratio. The measurement space of the system is also a two-dimensional grid, with each axis running from zero to the upper limit of that sensor’s linear dynamic range. The projection of the sample space into the measurement space, as described by Equation 2, takes the form of a shear-mapped version of itself. From this geometric view, array analogs of single-sensor analytical figures of merit become clear. The magnitude of array response is the length of the response vector, whereas the sensitivity is the per-unit concentration response vector length. In this way, the marginal increase in sensitivity an additional sensor provides for a particular analyte can be calculated. A consequence of this is that the sensitivity benefit provided by combining two sensors is maximized when the two exhibit 14.8

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roughly similar sensitivities. Otherwise, the combined sensitivity will simply converge to that of the better-performing sensor as the disparity between them increases. As expected, fusing sensors with identical sensitivities will result in an array sensitivity that scales with the square root of the number of sensors, as observed with signal-to-noise reduction with repeated measurements. Selectivity of the sensor array between two locations in the sample space can be expressed by the angle between the two corresponding response vectors (107). A useful related concept from chemometrics is the net analyte signal (NAS) (38, 108). This is defined as the projection of a response vector onto an axis orthogonal to the subspace spanned by the responses to interferants. In this example, this corresponds to the geometric relationship shown in Equation 3 between the magnitude of the analyte response vector, r, that of the NAS and the angle, θ, between the two vectors: NAS . 3. sin θ = r Thus, the sine of the angle between an analyte vector and the subspace spanned by known interferants can be interpreted as the fractional loss in sensitivity that one would incur in calibrating against the defined interferants. Although linear response functions are often used as an acceptable approximation over limited concentration ranges in sensing applications, there are often better functional approximations for different types of sensors that are more accurate over a wider portion of the sensor’s dynamic range. As a sensor response function departs from linearity, the sample space projection becomes correspondingly distorted relative to the n-dimensional parallelotopes obtained from linear sensors. For example, as Pearce (109) notes, conducting polymer sensors exhibit Langmuir-type response curves, whereas metal oxide sensors have been shown to exhibit power law response curves. A generalization to nonlinear systems can be made by using the Jacobian matrix to define the sample space to measurement space transformation in place of the sensitivity matrix (109): ⎡ ∂r ∂rn ⎤ 1 ··· ⎢ ∂c 1 ∂c 1 ⎥ ⎢ . ⎥ .. ⎥ .. S= ⎢ . 4. . ⎢ .. . ⎥ ⎣ ∂r ⎦ ∂r 1 n ··· ∂c m ∂c m c 1 ...c m This matrix provides a localized sensitivity matrix as a function of each sensor’s response curve characteristics at a given set of analyte concentrations. Thus, related metrics become similarly locally defined and must be integrated over the volume of the sample space to provide an aggregate assessment of sensor response characteristics. This approach continues to assume that responses to mixtures of analytes are additive, necessitating more complex models to include nonadditive behavior, such as analyte competition for sites in a sensor. Due to measurement errors, responses due to repeated measurements of a sample occupy a distribution within the measurement space. Gardner & Bartlett (106) define a parameter for expressing the resolving power of a sensor array for an arbitrary binary classification problem: RP =

SAB σ A2 + σ B2

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and is equivalent to notions of chromatographic resolution, or to the classic Fisher ratio used in linear discriminate analysis (LDA) (110). In practical terms, similarity among the rows of the sensitivity matrix of a sensor array dictates the displacement between the sample space projection axes in the measurement space and thus, along with the magnitude of the sensitivity values, the amount of the measurement space utilized by a given sensing task. This is an important quantity because it provides a measure of how close together adjacent locations in the sample space are within the measurement space. As locations become closer together in the measurement space, the ability of any decision algorithm to reliably discern between them diminishes, and thus also the ability to discern between the corresponding locations in the sample space. For example, as shown in Figure 2, two linear sensors that exhibit orthogonal (i.e., completely independent) responses with respect to two analytes will span the full measurement space out to the responses corresponding to the maximum concentrations specified by the sample space. At the other extreme, two sensors with identical responses to the analytes will utilize only a linear one-dimensional portion of the measurement space. In this way, the intrinsic dimensionality of the measurement space is given by the rank of the row space of the sensitivity matrix. For example, an array of three sensors in which one is linearly dependent on the other two will inhabit a two-dimensional measurement space, and an array of any number of identical sensors will only ever allow a one-dimensional measurement space. It is possible for a sensor transduction method itself to limit the dimensionality of an array. For example, Grate et al. (51) have shown that the individual sensitivities of SAW sensors are dictated by a finite number of linear solvation parameters, limiting the maximum dimensionality of any SAW sensor array to roughly five. Another example would be sensors based on a single color change of a vapochromic dye (56). Although the data collected is three-dimensional [i.e., red, green, and blue (RGB) values extracted from an image], it occupies a one-dimensional manifold within RGB space, and thus only contributes one dimension to a sensor array measurement space. The intrinsic dimensionality of the measurement space is important, as it limits the number of independent analytes that can be quantitatively represented by the sensor array. If the dimensionality of the measurement space is greater than that of the sample space (i.e., n > m), the m-dimensional sensing task results in a projection that is an m-dimensional subspace within the measurement space of the sensor array. However, if the dimensionality of the sample space is greater than that of the measurement space (i.e., n < m) the underlying system of equations is underdetermined, which leads to ambiguities in the relationship between analyte concentration and sensor response. When considering a finite list of target analytes and interferants, this scenario is very common. Adding consideration of potential unknown interferants, it becomes almost certain. Geometrically, this can be observed as the projection of the sample space folds in as a lower-dimensional shadow of itself in the measurement space and there is no longer a one-to-one correspondence between the sample space and its projection in the measurement space, as shown in Figure 3. One can either acknowledge and accept these ambiguities as an inherent uncertainty in the output of the detection system or address this problem by either incorporating more linearly independent sensors into the array or adjusting the parameters of sensing task to reduce the


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S1 A1 Figure 3 Projections of one- (a), two- (b), and three-dimensional (c) sample spaces onto two-dimensional measurement spaces. The projection of a three-dimensional sample space into a two-dimensional measurement space leads to superposition of unique regions of that sample space as it is flattened in the projection. This figure was created by the authors, as inspired by table 14.1 of Reference 111.

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dimensionality or extent of the sample space. For example, if a separation step prior to detection could be employed to ensure that only pure compounds would be sensed, only the outer axes of sample space would be projected into the measurement space, and ambiguities would only occur if two analytes exhibited the same response on every sensor. Perhaps more realistically, a separation stage could be used also to divide the sensing task into a series of separate lower-rank tasks, as one might expect with a microfabricated GC system with a chemical sensor array detector (74).


3.2. Sensor Array Performance Measures To describe the analytical capacity of a sensor array, Gardner & Bartlett (106) define a metric expressing the maximum number of resolvable response vectors as the ratio of the total hypervolume of the sensor array measurement space to the hypervolume associated with the standard error of a sensor array response: Vs . 6. Nn = Vn Here, Vn is the volume of a hyperellipsoid comprising a set of n sensors with semiaxes defined by the standard error, and Vs is the volume of the sensor array measurement space as a product of the full-scale deflection (FSD) values of each sensor as given by Equations 7 and 8: i=n 2π n/2 i=1 σ Si 7. Vn = n (n/2) Vs =

i=n

FSD(Si ).

8.

i=1

They note that concentration-dependent errors will render this volume nonuniform over the measurement space and define a sensor number density related to the inverse of the concentrationdependent error volume. This expresses the number of resolvable response vectors per unit sensor output as a local measure of resolving power. Integrating this value over the measurement space thus provides a maximum number of distinct vectors the array is capable of resolving. The impact of hypothetical changes in sensor array configuration or performance can be estimated by changing the appropriate model parameters and calculating the impact on resolving power of the array, enabling theoretical optimization of the array. In the Handbook of Machine Olfaction, however, Pearce and colleagues (75) note that the resolving power measure proposed by Gardner & Bartlett (106) does not account for the fact that a given sensing task may not access the entire measurement space of the sensor array due to correlations in response among the sensors. To acknowledge this they define the accessible measurement space as the projection of the sample space associated with the sensing task into the measurement space (111). After providing expressions for this volume based on the determinant of the sensitivity matrix, they generalize this volume as the determinant of the Jacobian matrix of Equation 4, integrated over the sample space: Vs =

c m

c 2 c 1 |S| dc1 dc2 . . . dcm ,

... 0

0

9.

0

where c i is the maximum concentration of the ith analyte. By substituting this volume for the total volume of the measurement space in Equation 6, a more realistic estimate of resolving capability for specific sensing tasks is achieved that is dependent on both measurement error and the underlying geometry of the array response. www.annualreviews.org • Sensor Array Design


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Pearce and colleagues (75) also demonstrated that the geometric transform implied by a sensor array can be used to calculate signal-to-noise values associated with specific displacements in the sample space (i.e., specific classifications within the sample space.) The inverse of this transform enables the propagation of sensor measurement error into sample space, allowing calculation of the estimated total squared error of concentration, as well as error contributions from each sensor, and error associated with each analyte. Following this, they discuss an alternate strategy using the Fisher information as a means of estimating the minimum variance of concentration. The Fisher information has been used in many applications involving statistical estimation, including quantum chemistry, experimental design, and neural programming (112–116). Equation 10 defines the Fisher information matrix for a single sensor i and concentration vector c:

∂ ∂ Jij j (c) = dri p(ri |c) ln p(ri |c) ln p(ri |c) , 10. ∂c j ∂c j


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where p(ri |c) is the conditional probability of a response of the ith sensor, given c. Assuming uncorrelated noise, the Fisher information matrix of the array is the sum of the matrices from each sensor. According to the Cramer-Rao bound, the total expected squared reconstruction error for an unbiased estimator across the entire array is related to the Fisher information matrix by the following equation: var(ˆc |c) =

m j =1

var(cˆ j |c) ≥

m

(J−1 (c )) j j ≡ εc2j opt .

11.

j =1

The equivalence of the Fisher information and geometric approaches for calculation of local signal to noise, or discriminability, is demonstrated with the conclusion that either the geometric or Fisher information approaches are appropriate for optimization of sensor arrays for maximal signal to noise for a given sensing task. It was suggested that the geometric approach should be used to optimize an array that maximizes the total number of separate analytes that can be detected, noting that Shannon information approaches might be more appropriate than Fisher information approaches in this situation. Finally, a hypothetical example is provided in which a three-dimensional sample space is to be addressed by some configuration of a three-sensor array, chosen from among the 125 possible sensors, each exhibiting one of five different sensitivity levels to each of the three analytes. The Fisher information is calculated and then used to derive the corresponding expected squared error for each of the 317,750 possible sensor configurations in this scenario. This not only provided an optimal configuration; it also demonstrated the need for quantitative optimization, as randomly choosing a far-from-optimal array configuration was shown to be very likely. In particular, it was shown that there was a 22.46% probability that a randomly chosen array would lead to an expected error more than 100 times greater than optimum. Hierlemann & Guiterrez-Osuna (91) provide a thorough review of higher-order chemical sensing, including general considerations of the implications of the sensor arrays’ dimensionality and optimization. After reviewing the work of Gardner & Bartlett as well as that of Pearce and colleagues, they suggest that sensor array optimization is more commonly approached empirically as a feature subset selection problem. This type of problem is often encountered in pattern recognition and machine learning contexts, as well as in chemometric applications (117–120). A specific variant of this problem lies in the optimization of excitation profiles of adaptable sensors such as those described in Reference 68, which was reviewed by Hierlemann & Gutierrez-Osuna as well as Vergara & Llobet (98). There are two approaches to feature selection: filter approaches, which characterize the information content of selected feature subsets according to some figure of merit, and wrapper 14.14

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approaches, which characterize the predicative accuracy of calibration models trained on selected feature subsets. The former approach is less computationally intensive, whereas the latter provides better accuracy, as the feature subset is tuned to the bias of the calibration model used. Although filters can find feature sets that are more generally applicable to a wide range of calibration models, Hierlemann and Gutierrez-Osuna (91) note that it is difficult to design filters that correlate well with final predicative accuracy of the calibration model that is eventually used. Thus, if a specific calibration model is to be used and there are adequate computational resources available, it would be advantageous to use a wrapper approach and evaluate feature selection in terms of predicative performance. Otherwise, a filter approach might be a better choice. The combinatorial nature of the problem of optimal feature selection means that an exhaustive search over all possible array configurations is not feasible for all but the simplest problems [see, e.g., Pearce’s three-sensor example problem, which exhibited more than 300,000 possible configurations (111)]. Thus, for complex sensing applications one must generally turn to the use of more efficient search strategies, which is an entire field of study unto itself. In sensor array applications, there are published examples of genetic algorithms (121–123) as well as step-wise algorithms (124–126) for nonexhaustive searching for optimal subsets. Various measures and heuristics have been proposed as filters to evaluate selection of sensors for an array. For example, Marth et al. (127) describe an array optimization approach based on the chemometric NAS figure of merit. Muezzinoglu et al. (128) demonstrate an approach using the Mahalanobis distance between response distributions in the measurement space to evaluate sensor configurations. In Computational Methods for Sensor Selection, Raman et al. (129) propose an LDAbased approach for array optimization in which a ratio expressing class separability is calculated for each candidate configuration and then discounted with a penalty term for the number of sensors used. Raman also utilized a correlation metric between sensor response vectors to evaluate sensor selection. Homer et al. (130) implement several other selectivity measures: a normalized cityblock distance as a measure of cross-analyte distance, a sum of all pair-wise normalized response differences, and a difference between maximal and minimal response over an analyte set for each sensor. The standard deviation of a sensor’s response strength distribution across an analyte set is discussed as a measure of diversity in sensor response. The general idea behind this approach is to favor diversity among sensors as a means of ensuring that the array offers the greatest degree of complementary information possible. In a geometric interpretation, this corresponds to the desire to ensure that the sensor responses offer the largest possible projection of the sample space into the array measurement space (130). Finally, an interesting approach lies in the characterization of sensor systems as communication processes, for example, considering sensor outputs as coding strategies and considering information bandwidth. Arguably, Pearce and colleagues (112) fall within this category with their use of the Fisher information, as previously discussed, and having published similar work in a neural programming context. Yang et al. (131) recently described a ratio-metric chemical communication system in which information is encoded as timed emissions of binary vapor mixtures, which are then sensed by an array of four SAW sensors. The bandwidth of the system is evaluated to be approximately 0.015 bits per second, and it is shown how a change in the feature extraction strategy can double this rate. Although not discussed in that work, this raises the possibility that sensor array components could be evaluated and optimized according to their ability to transmit information. Again from the perspective of the field of neurocomputing, Alkasab et al. (132) discuss the use of mutual information as a metric of the informational match between a sensor array and analyte set in complex chemosensors and olfactory systems. The mutual information expresses the amount of variability within the measurement space that can be accounted for by the variation within the sample space and is calculated in bits as shown in Equation 12, where xi represents a particular www.annualreviews.org • Sensor Array Design


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location among Nx possible locations in the measurement space, yi represents a particular location among Ny possible locations in the sample space, and p (xi |yi ) is the conditional probability of observing response xi given the analyte mixture yi is present: IT =

Ny Nx i=1 j =1

p(yi ) p (xi |yi ) log2

p(xi |yi ) . p(xi )

12.


This approach has been used in other sensor applications as well. For example, Fonollosa et al. (133), used mutual information to optimize temperature profiles in metal oxide sensors and Wang et al. (134) used it in sensor selection. Although the mutual information expresses nearly exactly the conceptual relationship between informational complexity of a sensing task and informational complexity of a sensor array, it is also notoriously difficult to calculate, as it requires specification and integration of potentially high-dimensional joint probability distributions over the entire measurement and sample spaces (135). Other information-theoretic measures such as the Kullbeck-Leibler and Jensen-Shannon information divergences may also be used to provide measures of discriminability in sensor array performance and thus aid in sensor selection, although they will suffer similar computational problems as mutual information (136, 137).

3.3. General-Purpose Array Design Considerations Significantly, the optimization approaches discussed thus far focus on quantitatively describing the efficacy of a sensor array with respect to a specific, well-defined analytical task. This is a natural consequence of the fact that traditional analytical figures of merit are intrinsically based on specific sensing contexts (e.g., sensitivity for a given analyte, or selectivity against a particular interferant) and this influences the way in which researchers and practitioners in chemical sensing think about the challenge of sensor design. However, a hallmark of complex environment sensing is that the underlying analytical tasks are difficult to define and usually partially unknown. This means that in such scenarios, there is not a clearly defined set of parameters against which to optimize, and one must instead consider optimizing against a set of probable parameters, thus adding an extra dimension of complexity to the optimization problem. In their review Hierlemann & Guiterrez-Osuna (91) ask the basic question, “Are more sensors better?” (p. 583), and then quickly state that a general answer to this question is difficult, if not impossible to provide. This is because the optimal number of sensors is a balance between providing sufficient information and redundancy while minimizing the increased complexity, noise, and risk of overfitting associated with high-dimensional spaces. Thus, including more sensors can potentially decrease performance, as has been experimentally observed (138). Such issues are well-known in the areas of machine learning, data mining, and pattern recognition, where so-called curse of dimensionality refers to phenomena that arise out of exponential scaling of measurement space volume with the dimensionality of a sensor array. Hierlemann & Guiterrez-Osuna discuss the geometric aspects of high-dimensional spaces, including that the volume of such spaces becomes disproportionally concentrated in the outer regions of the space, and thus populated regions tend to become progressively more sparse. This is problematic for multiple reasons. First, finding an optimal projection from a high-dimensional measurement space onto a more tractable lower-dimensional subspace is complicated by the tendency of such projections to become more normally distributed according to the central limit theorem, regardless of initial distribution shape, thus potentially obscuring useful information. Second, due to the increase in volume of the measurement space, substantially more data can be required to adequately train models of sensor response distributions for use in optimization, classification, or 14.16

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calibration algorithms and reference work that demonstrates that a fixed training set size implies an optimum number of dimensions (i.e., sensors) beyond which performance degrades (139). Owing to the uncertain nature of complex environment sensing tasks, an important measure of sensor array quality is the ability to resolve sets of random unknown analytes. The ability to design an array for truly general-purpose detection is limited by the lack of a well-defined relationship between perceivable analytes with which to exhaustively define the global sample space. This is in sharp contrast to other sensory problems such as perception of color and sound (140). Nonetheless, there is some potential to address this question. The metric shown in Equation 6 provides a measure of the maximum number of analyte mixtures that a sensor array can describe for a known sample space, but does not offer predictions of the expected overlap in the measurement space one might expect to incur with random subsets of analytes. Davis and colleagues (141, 142) have performed extensive work modeling the statistics of peak overlap in multidimensional separations, which could be leveraged to provide useful predictions of analyte capacity in sensor arrays for sensing tasks involving unknown complex mixtures. Such an approach would be limited in part by the need to make assumptions regarding the distributions of sensor array response over the span of all possible analytes. The feasibility of such an assumption is based on the degree to which the sensor transduction mechanism is understood and can be related to molecular structure. For example, the dependence of SAW sensor response on linear solvation parameters should enable reasonable estimates of SAW sensor array response distribution across numerous chemical species (50, 51, 143). In a similar vein, Lancet et al. (144) used statistical models to predict olfactory response, and Harel and colleagues (145) used an information space modeling approach to estimate a lower bound on the size of the olfactory repertoire purely from constraints imposed by the binding characteristics of olfactory receptors. This estimate was in line with current biological estimates, providing evidence for the commonly held notion that the olfactory system has been optimized for efficiency through evolution. More interesting, though, is the ability of this approach to relate the basic transduction principles of a sensor system to complex, general-purpose chemical tasks; note, however, that this work was focused mainly on estimating repertoire size for a given capability rather than maximizing capability for a give repertoire size. Other aspects of study into biological olfaction could also be informative for design and implementation of sensor arrays for complex environments (146). For example, the impact of heterogeneity in olfactory receptor tuning width has been discussed in studies of olfactory function (147). Alkasab et al. (132) discuss the impact on chemical sensor tuning parameters on overall performance from an olfactory perspective, suggesting that certain mixtures of broadly and narrowly tuned (i.e., of varying selectivity) sensors more efficiently convey sample space information in their responses. This could have useful implications in the design and selection of sensors for inclusion into arrays for chemical detection.

4. CONCLUSIONS AND FUTURE DIRECTIONS Chemical sensing in complex environments is challenged by the need for selectivity for multiple target analytes against a dynamic and often unpredictable background, the parameters of which may only be partially understood. However, individual chemical sensors are inherently limited to addressing only simple sensing tasks due to the fundamental geometric relationship between the sample space associated with a sensing task and the measurement space of the sensor system. This limitation can be overcome by either leveraging the output of an array of multiple sensors, by implementing some type of variable sample pretreatment prior to sensing (e.g., a chromatographic separation,) or by using adaptive sensors with tunable selectivities, providing a virtual sensor array. In any case, the dimensionality of the measurement space is increased with the idea that doing www.annualreviews.org • Sensor Array Design


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so will make the system more commensurate with the sensing task. Unfortunately, there are few established design principles for such systems, and those that have been reported do not enjoy widespread adoption, leading to a widely acknowledged performance gap between proofof-concept laboratory experiments and less controlled, more realistic applications in complex real-world scenarios. The most critical aspect in designing or optimizing a chemical sensor array is in understanding as completely as possible the parameters of the analytical question to be answered. Underestimating the complexity of a sensing task can lead to insufficient optimization during development and poor robustness to dynamic backgrounds during implementation. Several potential sensor array optimization metrics have been reported and although each express different subtleties of quality, each are centered on quantitating some aspect of the informational match between sensing task requirements and sensor array information as a function of array configuration. These methods differ in applicability according to the nature of the task, the available information, and the tolerance of intensive computational requirements. Regardless of the optimization metric chosen, the combinatorial nature of the number of potential sensor array configurations in realistic sensing tasks renders exhaustive, brute-force optimization approaches intractable and necessitates more sophisticated search strategies. Care should be taken as simple random selection carries a high risk of selecting a suboptimal array configuration. The criteria for choice (or design) of chemical sensors to be used in an array should be substantially different from that used when designing stand-alone sensors. Although high selectivity is an advantage for detection of an individual target analyte by a single sensor, studies in neural programming and olfaction have shown that it is a heterogeneous distribution of sensing elements with both broadly and narrowly tuned partial selectivities that gives arrays of nonspecific sensors the ability to sense a wide range of target analytes. For this reason, caution should be taken in assembling arrays from commercial off-the-shelf sensors that were originally intended and optimized for stand-alone use, as the narrow tuning of these devices may present a risk of not adequately covering the desired sample space. Conversely, the diversity of sensor responses should also be carefully considered. Correlation among sensors leads to an intrinsic dimensionality that is smaller than the dimensionality implied by the number of sensors/data sources, and may lead to unexpected reductions in efficiency and analytical capabilities. Although this review does not cover data processing strategies for sensor array data, such as multivariate pattern recognition and regression techniques, statistical estimators, and other decision theoretic algorithms, such techniques are intended to leverage the information that is already there. If the information required by a sensing task is not present in the acquired data, it cannot be created later via postprocessing. If the information is minimally supported, this will likely result in reduced performance. Similarly, noise or drift exhibited by the sensors will potentially compromise the inherent informational capacity of the sensor array (see, e.g., 80, 82, 84, 88, 91, 99 for reviews of sensor data processing strategies). The ability to design sensor arrays for truly general-purpose chemical sensing is limited by the lack of a simple systematic metric for chemical similarity that would allow an exhaustive description of a global chemical sample space. However, there are some general guidelines that can be gleaned from studies in related fields. Estimates of array sizes required for general olfaction have been derived from characteristics of the underlying sensor transduction mechanisms. Other studies have estimated the optimum dimensionality of a sensor system for a given amount of available training set data. Finally, statistical studies of overlap in multidimensional chromatographic systems suggest the potential for measures of effective analyte capacity of arrays of nonspecific sensors. Future trends in sensor array design will involve continued elucidation of the role of individual response functions in contributing to overall array performance. Of particular interest is the


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continued development of theoretics for the ground-up design of sensors explicitly for use in sensor arrays and the potential of arrays of adaptable sensors to serve as higher-order analytical devices that can leverage the power of multiway chemometric data analysis techniques. It is also highly likely that advances in the study of biological olfaction will continue to offer insights toward understanding how to design complex multisensory chemical detection systems. Such systems will likely never replicate biological olfaction exactly, but this is not the point, as it is far from clear that doing so would even be useful in many chemical sensing scenarios, especially those requiring quantitative, objective assessment of vapor concentration. Rather, biological olfaction systems represent an opportunity to learn from a specific evolution-optimized solution for complex chemical sensing, rather than as a de facto model for general-purpose chemical analysis.

DISCLOSURE STATEMENT The authors are not aware of any affiliations, memberships, funding or financial holdings that might be perceived as affecting the objectivity of this review. LITERATURE CITED 1. Marco S. 2014. The need for external validation in machine olfaction: emphasis on health-related applications. Anal. Bioanal. Chem. 406:3941–56 2. Boeker P. 2014. On “electronic nose” methodology. Sens. Actuators B 204:2–17 3. Goodner KL, Dreher JG, Rouseff RL. 2001. The dangers of creating false classifications due to noise in electronic nose and similar multivariate analyses. Sens. Actuators B 80:261–66 4. Smets P. 1988. Belief function. In Non-Standard Logics for Automated Reasoning, ed. P Smets, A Mamdani, D Dubois, H Prade, pp. 253–86. London: Academic 5. Vessman J, Stefan RI, van Staden JF, Danzer K, Lindner W, et al. 2001. Selectivity in analytical chemistry. Pure Appl. Chem. 73(8):1381–86 6. Zubritsky E. 2000. E-noses keep an eye on the future. Anal. Chem. 72(11):421A–26A 7. Marco S, Gutiérrez-Gálvez A, Lansner A, Martinez D, Rospars JP, et al. 2014. A biomimetic approach to machine olfaction, featuring a very large-scale chemical sensor array and embedded neuro-bio-inspired computation. Microsyst. Technol. 20:729–42 8. Janata J. 2009. Principles of Chemical Sensors. New York: Springer. 2nd ed. 9. Wilson DM, Hoyt S, Janata J, Booksh K, Obando L. 2001. Chemical sensors for portable, handheld field instruments. IEEE Sens. J. 1(4):256–74 10. Wang C, Yin L, Zhang L, Xiang D, Gao R. 2010. Metal oxide gas sensors: sensitivity and influencing factors. Sensors 10(3):2088–106 11. Janata J, Josowicz M. 2003. Conducting polymers in electronic chemical sensors. Nat. Mater. 2:19–24 12. Kreno LE, Leong K, Farha OK, Allendorf M, Van Duyne RP, Hupp JT. 2011. Metal-organic framework materials as chemical sensors. Chem. Rev. 112(2):1105–25 13. Penner RM. 2012. Chemical sensing with nanowires. Annu. Rev. Anal. Chem. 5:461–85 14. Haick H. 2007. Chemical sensors based on molecularly modified metallic nanoparticles. J. Phys. D 40(23):7173–86 15. Kemling JW, Qavi AJ, Bailey RC, Suslick KS. 2011. Nanostructured substrates for optical sensing. J. Phys. Chem. Lett. 2(22):2934–44 16. Sibbald A. 1985. A chemical-sensitive integrated-circuit: the operational transducer. Sens. Actuators 7(1):23–38 17. Janata J. 1990. Potentiometric microsensors. Chem. Rev. 90:691–703 18. Grate JW. 2008. Hydrogen-bond acidic polymers for chemical vapor sensing. Chem. Rev. 108:726–45 19. Grate JW. 2000. Acoustic wave microsensor arrays for vapor sensing. Chem. Rev. 100:2627–48 20. Raja VB, Singh H, Nimal AT, Sharma MU, Gupta V. 2013. Oxide thin films (ZnO, TeO2 , SnO2 , and TiO2 ) based surface acoustic wave (SAW) E-nose for the detection of chemical warfare agents. Sens. Actuators B 178:636–47 www.annualreviews.org • Sensor Array Design


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21. Dufour I, Josse F, Heinrich SM, Lucat C, Ayela C, et al. 2012. Unconventional uses of microcantilevers as chemical sensors in gas and liquid media. Sens. Actuators B 170:115–21 22. Baldini F, Giannetti G, Trono C. 2012. Fundamentals of optical chemical sensors. In Optochemical Nanosensors, ed. A Cusano, FJ Arregui, M Giordano, A Cutolo, pp. 35–50. Boca Raton: CRC Press 23. Qazi HH, bin Mohammad AB, Akram M. 2012. Recent progress in optical chemical sensors. Sensors 12(12):16522–56 24. Rakow NA, Suslick KS. 2000. A colorimetric sensor array for odour visualization. Nature 406:710–71 25. LaGasse MK, Rankin JM, Askim JR, Suslick KS. 2014. Colorimetric sensor arrays: interplay of geometry, substrate and immobilization. Sens. Actuators B 197:116–22 26. Khan MRR, Kang BH, Lee SW, Kim SH, Yeom SH, et al. 2013. Fiber-optic multi-sensor array for detection of low concentration volatile organic compounds. Optics Express 21(17):20119–30 27. Dickinson TA, Michael KL, Kauer JS, Walt DR. 1999. Convergent, self-encoded bead sensor arrays in the design of an artificial nose. Anal. Chem. 71:2192–98 28. Sohn H, Sailor MJ, Magde D, Trogler WC. 2002. Detection of nitroaromatic explosives based on photoluminescent polymers containing metalloles. J. Am. Chem. Soc. 125:3821–30 29. Sutter JM, Jurs PC. 1997. Neural network classification and quantification of organic vapors based on fluorescence data from a fiber-optic sensor array. Anal. Chem. 69:856–62 30. Collins GE, Rose-Pehrsson SL. 1996. Chemiluminescent chemical sensors for inorganic and organic vapors. Sens. Actuators B 34(1–2):317–22 31. Zhang Z, Zhang S, Zhang X. 2005. Recent developments and applications of chemiluminescence sensors. Anal. Chim. Acta 541(1–2):37–46 32. Shalabney A, Abdulhalm I. 2011. Sensitivity-enhancement methods for surface plasmon sensors. Laser Photonics Rev. 5(4):571–606 33. Homola J, Yee SS, Gauglitz G. 1999. Surface plasmon resonance sensors: review. Sens. Actuators B 54(1–2):3–15 34. Riley CM. 1996. Statistical parameters and analytical figures of merit. In Development and Validation of Analytical Methods, ed. CM Riley, TW Rosanske, pp. 15–71. New York: Elsevier 35. Brown CD, Davis HT. 2006. Receiver operating characteristics curves and related decision measures: a tutorial. Chemom. Intel. Lab. Sys. 80:24–38 36. Faber K, Kowalski BR. 1997. Propagation of measurement errors for the validation of predictions obtained by principal component regression and partial least squares. J. Chemom. 11:181–238 37. Pierna JAF, Jin L, Wahl F, Faber NM, Massart DL. 2003. Estimation of partial least squares regression prediction uncertainty when the reference values carry a sizeable measurement error. J. Chemom. Intel. Lab. Sys. 65:281–91 38. Booksh KS, Kowalski BR. 1994. Theory of analytical chemistry. Anal. Chem. 66:782A–91A 39. Carey PW, Beebe KR, Kowalski BR. 1986. Selection of adsorbates for chemical sensor arrays by pattern recognition. Anal. Chem. 58:149–53 40. Buck LB. 2005. Unraveling the sense of smell. Angew. Chem. Int. Ed. 44:6128–40 41. Pearce TC. 1997. Computational parallels between the biological olfactory pathway and its analogue “the electronic nose”: Part II. Sensor-based machine olfaction. Biosystems 41:69–90 42. Persaud K, Dodd G. 1982. Analysis of discrimination mechanisms in the mammalian olfactory system using a model nose. Nature 299:352–55 43. Zaromb S, Stetter JR. 1984. Theoretical basis for identification and measurement of air contaminants using an array of sensors having partly overlapping sensitivities. Sens. Actuators 6(4):225–43 44. Rose-Pehrsson SL, Grate JW, Ballantine DS, Jurs PC. 1988. Detection of hazardous vapors including mixtures using pattern recognition analysis of responses from surface acoustic wave devices. Anal. Chem. 60:2801–11 45. Carey WP, Beebe KR, Kowalski BR. 1987. Multicomponent analysis using an array of piezoelectric crystal sensors. Anal. Chem. 59:1529–34 46. Hierold C, Mueller R. 1989. Quantitative analysis of gas mixtures with non-selective gas sensors. Sens. Actuators 17(3–4):587–92 47. Ema K, Yokoyama M, Nakamoto T, Moriizumi T. 1989. Odor-sensing system using a quartz-resonator sensor array and neural-network pattern recognition. Sens. Actuators 18(3–4):291–96


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72. Lin H, Jang M, Suslick KS. 2011. Preoxidation for colorimetric sensor array detection of VOCs. J. Am. Chem. Soc. 133(42):16786–89 73. Viricelle JP, Pauly A, Mazet L, Brunet J, Bouvet M, et al. 2006. Selectivity improvement of semiconducting gas sensors by selective filter for atmospheric pollutants detection. Mater. Sci. Eng. C 26:186– 95 74. Collin WR, Serrano G, Wright LK, Chang H, Nunovero N, Zellers ET. 2014. Microfabricated gas ˜ chromatograph forrapid, trace-level determinations of gas-phase explosive marker compounds. Anal. Chem. 86:655–63 75. Pearce TC, Schiffman SS, Nagle HT, Gardner JW, eds. 2003. Handbook of Machine Olfaction: Electronic Nose Technology. New York: Wiley 76. Ryan MA, Shevade AV, Taylor CJ, Homer ML, Blanco M, Stetter JR, eds. 2009. Computational Methods for Sensor Material Selection. New York: Springer 77. Ziegler C, Gopel W, Hämmerle H, Hatt H, Jung G, et al. 1998. Bioelectronic noses: a status report. ¨ Part II. Biosens. Bioelectron. 13:539–71 78. Nagel HT, Schiffman SS, Gutierrez-Osuna R. 1998. The how and why of electronic noses. IEEE Spectr. 35(9):22–34 79. Stefan RL, Van Staden JF, Aboul-Enein HY. 1999. Electrochemical sensor arrays. Crit. Rev. Anal. Chem. 29(2):133–53 80. Jurs PC, Bakken GA, McClelland HE. 2000. Computational methods for the analysis of chemical sensor array data from volatile analytes. Chem. Rev. 100:2649–78 81. Albert KJ, Lewis NS, Schauer CL, Sotzing GA, Stitzel SE, et al. 2000. Cross-reactive chemical sensor arrays. Chem. Rev. 100:2595–626 82. Wilson DM, Garrod S, Hoyt S, McKennoch S, Booksh KS. 2002. Array optimization and preprocessing techniques for chemical sensing microsystems. Sens. Update 10(1):77–106 83. Snopok BA, Kruglenko IV. 2002. Multisensor systems for chemical analysis: state-of-the-art in electronic nose technology and new trends in machine olfaction. Thin Solid Films 418:21–41 84. Gutierrez-Osuna R. 2002. Pattern analysis for machine olfaction: a review. IEEE Sens. J. 2(3):189–202 85. Stetter JR, Penrose WR. 2002. Understanding chemical sensors and chemical sensor arrays (electronic noses): past, present, and future. Sens. Update 10(1):189–229 86. Ampuero S, Bosset JO. 2003. The electronic nose applied to dairy products a review. Sens. Actuators B 94:1–12 87. Arshak K, Moore E, Lyons GM, Harris J, Clifford S. 2004. A review of gas sensors employed in electronic nose applications. Sens. Rev. 24(2):181–98 88. Scott SM, James D, Ali Z. 2007. Data analysis for electronic nose systems. Microchim. Acta 156:183–207 89. Ciosek P, Wroblewski W. 2007. Sensor arrays for liquid sensing - electronic tongue systems. Analyst 132(10):963–78 90. Rock F, Barsan N, Weimar U. 2008. Electronic nose: current status and future trends. Chem. Rev. 108:705–25 91. Hierlemann A, Gutierrez-Osuna R. 2008. Higher-order chemical sensing. Chem. Rev. 108:563–613 92. Perisa M, Escuder-Gilabert L. 2009. A 21st century technique for food control: electronic noses. Anal. Chim. Acta 638:1–15 93. Berna A. 2010. Metal oxide sensors for electronic noses and their application to food analysis. Sensors 10:3882–910 94. Miranda OR, Creran B, Rotello VM. 2010. Array-based sensing with nanoparticles: “chemical noses” for sensing biomolecules and cell surfaces. Curr. Opin. Chem. Bio. 14:728–36 95. Wilson AD, Baietto M. 2011. Advances in electronic-nose technologies developed for biomedical applications. Sensors 11:1105–76 96. del Valle M. 2012. Sensor arrays and electronic tongue systems. Int. J. Electrochem. 2012:986025 97. Smyth H, Cozzolino D. 2013. Instrumental methods (spectroscopy, electronic nose, and tongue) as tools to predict taste and aroma in beverages: advantages and limitations. Chem. Rev. 113:1429–40 98. Vergara A, Llobet E. 2012. Sensor selection and chemo-sensory optimization: toward an adaptable chemo-sensory system. Front. Neuroeng. 4:19


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99. Marco S, Gutiérrez-Gálvez A. 2012. Signal and data processing for machine olfaction and chemical sensing: a review. IEEE Sens. J. 12(11):3189–214 100. Ramgir NS. 2013. Electronic nose based on nanomaterials: issues, challenges, and prospects. ISRN Nanomater. 2013:941581 101. Wilson AD. 2013. Diverse applications of electronic-nose technologies in agriculture and forestry. Sensors 13:2295–348 102. Askim JR, Mahmoudi M, Suslick KS. 2013. Optical sensor arrays for chemical sensing: the optoelectronic nose. Chem. Soc. Rev. 42:8649–82 ´ 103. Sliwi nska M, Wi´sniewska P, Dymerski T, Namie´snik J, Wardencki W. 2014. Food analysis using artificial ´ senses. J. Agr. Food Chem. 62(7):1423–48 104. Auffarth B. 2013. Understanding smell—the olfactory stimulus problem. Neurosci. Biobehav. Rev. 37:1667–79 105. Raman B, Sun PA, Guitierrez-Galvez A, Guitierrez-Osuna R. 2006. Processing of chemical sensor arrays with a biologically inspired model of olfactory coding. IEEE Trans. Neur. Netw. 17(4):1015–24 106. Gardner JW, Bartlett PN. 1996. Performance definition and standardization of electronic noses. Sens. Actuators B 33:60–67 107. Messick NJ, Kalivas JH. 1996. Selectivity and related measures for nth-order data. Anal. Chem. 68:1572– 79 108. Olivieri AC. 2014. Analytical figures of merit: from univariate to multiway calibration. Chem. Rev. 114:5358–78 109. Pearce TC. 2000. Odor to sensor space transformations in biological and artificial noses. Neurocomp 32–33:941–52 110. Duda RO, Hart PE, Stork DG. 2001. Pattern Classification. New York: Wiley 111. Pearce TC, Sanchez-Montanes MA. 2003. Chemical sensor array optimization: geometric and information theoretic approaches. See Ref. 75, pp. 347–75 112. Sánchez-Montan´ ˜ es MA, Pearce TC. 2001. Fisher information and optimal odor sensors. Neurocomputing 38–40:35–41 113. Wilke SD, Eurich CW. 2001. Representational accuracy of stochastic neural populations. Neur. Comp. 14:155–89 114. Brown WM, Bäcker A. 2006. Optimal neuronal tuning for finite stimulus spaces. Neur. Comp. 18:1511–26 115. Nalewajski RF. 2008. Use of Fisher information in quantum chemistry. Int. J. Quantum Chem. 108(12):2230–52 116. Emery AF, Nenarokomov AV. 1998. Optimal experiment design. Meas. Sci. Tech. 9(6):864–76 117. Saeys Y, Inza I, Larranaga P. 2007. A review of feature selection techniques in bioinformatics. Bioinformatics 23(19):2507–17 118. Hoskuldsson A. 2001. Variable and subset selection in PLS regression. Chemom. Intel. Lab. Sys. 55(1– 2):23–38 119. Peng H, Long F, Ding C. 2005. Feature selection based on mutual information: criteria of maxdependency, max-relevance, and min-redundancy. IEEE Trans. Pattern Anal. Machine Intel. 27(8):1226– 38 120. Leardi R, Boggia R, Terrile M. 1992. Genetic algorithms as a strategy for feature selection. J. Chemom. 6(5):267–81 121. Xu Z, Lu S. 2011. Multi-objective optimization of sensor array using genetic algorithm. Sens. Actuators B 160:278–86 122. Phaisangittisagul E, Nagle HT, Areekul V. 2010. Intelligent method for sensor subset selection for machine olfaction. Sens. Actuators B 145:507–15 123. Gardner JW, Boilot P, Hines EL. 2005. Enhancing electronic nose performance by sensor selection using a new integer-based genetic algorithm approach. Sens. Actuators B 106:114–21 124. Petersson H, Klingvall R, Holmberg M. 2009. Sensor array optimization using variable selection and a scanning light pulse technique. Sens. Actuators B 142:435–45 125. Polikar R, Shinar R, Udpa L, Porter MD. 2001. Artificial intelligence methods for selection of an optimized sensor array for identification of volatile organic compounds. Sens. Actuators B 80:243–54 www.annualreviews.org • Sensor Array Design


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126. Yin Y, Yu H, Chu B, Xiao Y. 2014. A sensor array optimization method of electronic nose based on elimination transform of Wilks statistic for discrimination of three kinds of vinegars. J. Food Eng. 127:43– 48 127. Marth M, Maier D, Stahl U, Rapp M, Wessa T, Honerkamp J. 1999. Optimization of surface acoustic wave sensor arrays and application to high performance liquid chromatography. Sens. Actuators B 61:191– 98 128. Muezzinoglu MK, Vergara A, Huerta R, Rabinovich MI. 2010. A sensor conditioning principle for odor identification. Sens. Actuators B 146:472–76 129. Raman B, Meier DC, Semancik S. 2009. A statistical approach to materials evaluation and selection for chemical sensor arrays. See Ref. 76, pp. 221–44 130. Homer ML, Zhou H, Jewell AD, Ryan MA. 2009. Statistical methods for selecting the components of a sensing array. See Ref. 76, pp. 245–64 131. Yang J, Ráczb Z, Gardner JW, Cole M, Chen H. 2012. Ratiometric info-chemical communication system based on polymer-coated surface acoustic wave microsensors. Sens. Actuators B 173:547–54 132. Alkasab TK, Bozza TC, Cleland TA, Dorries KM, Pearce TC, et al. 1999. Characterizing complex chemosensors: information-theoretic analysis of olfactory systems. Trends Neurosci. 22(3):102:108 133. Fonollosa J, Fernández L, Huerta R, Gutiérrez-Gálvez A, Marco S. 2013. Temperature optimization of metal oxide sensor arrays using mutual information. Sens. Actuators B 187:331–39 134. Wang XR, Lizier JT, Nowotny T, Berna AZ, Prokopenko M, Trowell SC. 2014. Feature selection for chemical sensor arrays using mutual information. PLoS ONE 9(3):e89840 135. Ganguli D, Simoncelli EP. 2014. Efficient sensory encoding and Bayesian inference with heterogeneous neural populations. Neur. Comp. 26(10):2103–34 136. Chang C. 2000. An information-theoretic approach to spectral variability, similarity, and discrimination for hyperspectral image analysis. IEEE Trans. Info. Theory 46(5):1927–32 137. Vergara A, Muezzinoglu MK, Rulkov N, Huerta R. 2010. Information-theoretic optimization of chemical sensors. Sens. Actuators B 148:298–306 138. Nowotnya T, Bernab AZ, Binions R, Trowell S. 2013. Optimal feature selection for classifying a large set of chemicals using metal oxide sensors. Sens. Actuators B 187:471–80 139. Hughes G. 1968. On the mean accuracy of statistical pattern recognizers. IEEE Trans. Inf. Theory 14:55– 63 140. Martinelli E, Polese D, Dini F, Paolesse R, Filippini D, et al. 2011. An investigation on the role of spike latency in an artificial olfactory system. Front. Neuroeng. 4:16 141. Davis JM. 1993. Statistical theory of spot overlap for n-dimensional separations. Anal. Chem. 65:2014–23 142. Davis JM. 1997. Extension of statistical overlap theory to poorly resolved separations. Anal. Chem. 69:3796–805 143. Alizadeh T. 2010. Chemiresistor sensors array optimization by using the method of coupled statistical techniques and its application as an electronic nose for some organic vapors recognition. Sens. Actuators B 143:740–49 144. Lancet D, Sadovsky E, Seidemann E. 1993. Probability model for molecular recognition in biological receptor repertoires: significance to the olfactory system. Proc. Natl. Acad. Sci. 90:3715–19 145. Carmel L, Harel D, Lancet D. 2001. Estimating the size of the olfactory repertoire. Bull. Math. Bio. 63:1063–78 146. Fonollosa J, Gutierrez-Galvez A, Marco S. 2012. Quality coding by neural populations in the early olfactory pathway: analysis using information theory and lessons for artificial olfactory systems. PLoS ONE 7(6):e37809 147. Wilson RI, Mainen ZF. 2006. Early events in olfactory processing. Annu. Rev. Neurosci. 29:163–201


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Design and validation of the transparent oxygen sensor array.

Cross-Reactive Sensor Array for Metal Ion Sensing Based on Fluorescent SAMs.

Design and fabrication of a flexible MEMS-based electromechanical sensor array for breast cancer diagnosis.

Design a New Strategy Based on Nanoparticle-Enhanced Chemiluminescence Sensor Array for Biothiols Discrimination.

Design low crosstalk ring-slot array structure for label-free multiplexed sensing.

Colorimetric Sensor Array for White Wine Tasting.

Potentiometric sensing array for monitoring aquatic systems.

Polymer - Nanoparticle Assemblies for Array Based Sensing.

Design and Validation of a 150 MHz HFFQCM Sensor for Bio-Sensing Applications.

A bio-hybrid tactile sensor incorporating living artificial skin and an impedance sensing array.

Silica microspheres array strain sensor.

A Compressed Sensing Based Method for Reducing the Sampling Time of A High Resolution Pressure Sensor Array System.

G3 assisted rational design of chemical sensor array using carbonitrile neutral receptors.

MEMS Microphone Array Sensor for Air-Coupled Impact-Echo.

A Paper-Based Electrochromic Array for Visualized Electrochemical Sensing.

Virtual colorimetric sensor array: single ionic liquid for solvent discrimination.

Silver nanoparticle-based chemiluminescent sensor array for pesticide discrimination.

Polymer-waveguide-based flexible tactile sensor array for dynamic response.

Iontronic microdroplet array for flexible ultrasensitive tactile sensing.

Effective low-power wearable wireless surface EMG sensor design based on analog-compressed sensing.

A titanium nitride nanotube array for potentiometric sensing of pH.

Performance Analysis of ICA in Sensor Array.

Energy-efficient sensing in wireless sensor networks using compressed sensing.

NreB sensor complex of Staphylococcus carnosus.